Chiral dynamics in form factors, sepctral sum rules, meson-meson scattering and semi-local duality 

 by Zhi-Hui Guo, J.A. Oller and J. Ruiz de Elvira 
 Phys. Lett. B712 (2012) 407  and Phys.Rev.D86 (2012) 054006

Analytical Results for the meson-meson scattering within U(3) χPT from the pseudoscalar resonances, the (Subscript[δL, 8]) operator, tensor resonances (including the short-distance constraint terms).

In this sector, we provide the  meson-meson scattering amplitudes contributed by the Pseudoscalar Resonances, δL8 operator, Tensor Resonances and the terms required by the short-distance constraints in the appearance of the Tensor Resonances, which are represented by fXPsR, fXδL8, fXTensorResonan and fXTensorSD, respectively in the code, being X=1,2,3...16 . About the second multiplet of scalar resonances, their contributions share the same forms as these from the lowest multiplet. Of course, one has to correspondingly replace the resonance parameters. The explicit results for the lowest multiplet can be found in  Phys.Rev.D84 (2011) 034005 by Z.H.Guo and J.A.Oller and  we do not repeat the formulae here. 

We refer to  the mini-manual proivided in the link from  Phys.Rev.D84 (2011) 034005 by Z.H.Guo and J.A.Oller for further details. 

 The defintions of the resonance couplings and LECs are explained in the article.

Notice one should combine the formulae presented here and those in  Phys.Rev.D84 (2011) 034005 to get the final results.

(SuperPlus[π]) (SuperMinus[π]) -> (π^0)(π^0)

f1PsR[s_,t_]:= -((8 (dm^2) (mpi^4))/((Fpi^4) (MpR8^2)));

f1δL8[s_,t_]:=((16 (mpi^4) δL8)/(Fpi^4));

f1TensorResonance[s_,t_]:=(1/(3 (Fpi^4) (MsT^4) ((MsT^2)-s)))4 ((gT^2) (16 (mpi^4) (MsT^4)-(MsT^2) (s^3)+(s^4)+(MsT^4) ((s^2)+6 s t+6 (t^2))-4 (mpi^2) (MsT^2) ((s^2)+(MsT^2) (s+6 t)))-2 gT (2 (mpi^2)-s) ((MsT^2)-s) (2 (mpi^2) (MsT^2)-s ((MsT^2)+s)) βT+(((-2 (mpi^2)+s))^2) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2));


f1TensorSD[s_,t_]:=((8 (((-2 (mpi^2)+s))^2) β1SD)/(Fpi^4))+((4 (8 (mpi^4)+(s^2)+2 s t+2 (t^2)-4 (mpi^2) (s+2 t)) β2SD)/(Fpi^4))+((4 (((-2 (mpi^2)+s))^2) β3SD)/(Fpi^4));

(SuperPlus[K]) (SuperPlus[π]) -> (SuperPlus[K]) (SuperPlus[π])

f2PsR[s_,t_]:= -((8 (dm^2) (mk^2) (mpi^2))/((Fpi^4) (MpR8^2)));

 f2δL8[s_,t_]:=((16 (mk^2) (mpi^2) δL8)/(Fpi^4)) ;

 f2TensorResonance[s_,t_]:= (1/(3 (Fpi^4) (MsT^4)))2 ((1/((MsT^2)-t))((gT^2) (6 (mk^4) (MsT^4)+6 (mpi^4) (MsT^4)+6 (MsT^4) (s^2)+6 (MsT^4) s t+(MsT^4) (t^2)-(MsT^2) (t^3)+(t^4)-2 (mpi^2) (MsT^2) ((t^2)+(MsT^2) (6 s+t))+2 (mk^2) (2 (mpi^2) (MsT^4)-(MsT^2) ((t^2)+(MsT^2) (6 s+t))))-2 gT ((MsT^2)-t) (t (t ((MsT^2)+t)-(mpi^2) (2 (MsT^2)+t))+(mk^2) (4 (mpi^2) (MsT^2)-t (2 (MsT^2)+t))) βT-(2 (mk^2)-t) (-2 (mpi^2)+t) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2))+(1/(-2 (mk^2)-2 (mpi^2)+(MsT^2)+s+t))((gT^2) (9 (mk^8)+9 (mpi^8)+(MsT^4) (s^2)+(MsT^2) (s^3)+(s^4)-4 (MsT^4) s t+3 (MsT^2) (s^2) t+4 (s^3) t+(MsT^4) (t^2)+3 (MsT^2) s (t^2)+6 (s^2) (t^2)+(MsT^2) (t^3)+4 s (t^3)+(t^4)+6 (mk^6) (10 (mpi^2)-(MsT^2)-4 (s+t))-2 (mpi^2) (s+t) ((((MsT^2)+2 (s+t)))^2)-6 (mpi^6) ((MsT^2)+4 (s+t))+(mpi^4) ((MsT^4)+22 (((s+t))^2)+(MsT^2) (13 s+19 t))+(mk^4) (118 (mpi^4)+(MsT^4)+22 (((s+t))^2)+(MsT^2) (13 s+19 t)-2 (mpi^2) (29 (MsT^2)+52 (s+t)))+2 (mk^2) (30 (mpi^6)-(s+t) ((((MsT^2)+2 (s+t)))^2)-(mpi^4) (29 (MsT^2)+52 (s+t))+(mpi^2) (7 (MsT^4)+26 (((s+t))^2)+3 (MsT^2) (9 s+7 t))))-2 gT (-(mk^2)-(mpi^2)+s+t) (-(mpi^2) (MsT^2) (2 (mk^2)+(mpi^2)-s-t)-(mpi^4) (2 (mk^2)+2 (mpi^2)-s-t)-(((-2 (mk^2)-2 (mpi^2)+s+t))^3)+(MsT^4) (-2 (mk^2)-(mpi^2)+s+t)+(mk^4) (-2 (mk^2)-2 (mpi^2)+(MsT^2)+s+t)+(mk^2) (-2 (mpi^2)+(MsT^2)) (-2 (mk^2)-2 (mpi^2)+(MsT^2)+s+t)) βT+((((mk^2)+(mpi^2)-s-t))^2) (-2 (MsT^4)+(MsT^2) (2 (mk^2)+2 (mpi^2)-s-t)+(((-2 (mk^2)-2 (mpi^2)+s+t))^2)) ((βT)^2)));


 f2TensorSD[s_,t_]:=-((8 (2 (mk^2)-t) (-2 (mpi^2)+t) β1SD)/(Fpi^4))+((4 (2 (mk^4)+2 (mpi^4)+2 (s^2)+2 s t+(t^2)-2 (mpi^2) (2 s+t)+(mk^2) (4 (mpi^2)-2 (2 s+t))) β2SD)/(Fpi^4))+((2 ((mk^4)+(mpi^4)+(s^2)+2 s t+2 (t^2)-2 (mpi^2) (s+2 t)+(mk^2) (6 (mpi^2)-2 (s+2 t))) β3SD)/(Fpi^4)) ;

(SuperPlus[K]) (SuperMinus[K]) -> (K^0) (OverBar[(K^0)])

f3PsR[s_,t_]:= -((8 (dm^2) (mk^4))/((Fpi^4) (MpR8^2)));

  f3δL8[s_,t_]:= ((16 (mk^4) δL8)/(Fpi^4)) ;

  f3TensorResonance[s_,t_]:=(1/(3 (Fpi^4) (MsT^4)))((1/((MsT^2)-s))3 ((gT^2) (16 (mk^4) (MsT^4)-(MsT^2) (s^3)+(s^4)+(MsT^4) ((s^2)+6 s t+6 (t^2))-4 (mk^2) (MsT^2) ((s^2)+(MsT^2) (s+6 t)))-2 gT (2 (mk^2)-s) ((MsT^2)-s) (2 (mk^2) (MsT^2)-s ((MsT^2)+s)) βT+(((-2 (mk^2)+s))^2) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))-(1/((MsT^2)-s))((gT^2) ((s^4)-(MsT^2) (s^2) (4 (mk^2)+s)+(MsT^4) (16 (mk^4)+(s^2)+6 s t+6 (t^2)-4 (mk^2) (s+6 t)))-2 gT (2 (mk^2)-s) (-(MsT^4) s+(s^3)+2 (mk^2) ((MsT^4)-(MsT^2) s)) βT+(((-2 (mk^2)+s))^2) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))+(1/((MsT^2)-t))2 ((gT^2) ((t^4)-(MsT^2) (t^2) (4 (mk^2)+t)+(MsT^4) (16 (mk^4)+6 (s^2)+6 s t+(t^2)-4 (mk^2) (6 s+t)))-2 gT (2 (mk^2)-t) (-(MsT^4) t+(t^3)+2 (mk^2) ((MsT^4)-(MsT^2) t)) βT+(((-2 (mk^2)+t))^2) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2)));


  f3TensorSD[s_,t_]:= ((8 (((-2 (mk^2)+s))^2) β1SD)/(Fpi^4))+((4 (8 (mk^4)+(s^2)+2 s t+2 (t^2)-4 (mk^2) (s+2 t)) β2SD)/(Fpi^4))+((2 (8 (mk^4)+(s^2)+(t^2)-4 (mk^2) (s+t)) β3SD)/(Fpi^4));

(π^0)(π^0)-> η η

f4PsR[s_,t_]:= -((16 (dmt^2) (mpi^2) (-4 ((Cθ)^2) ((mk^2)-(mpi^2))+(Sqrt[2]) Cθ (2 (mk^2)-5 (mpi^2)) Sθ+2 (2 (mk^2)+(mpi^2)) ((Sθ)^2)))/(3 (Fpi^4) (MpR1^2)))-((8 (dm^2) (mpi^2) (((Cθ)^2) (8 (mk^2)+(mpi^2))-4 (Sqrt[2]) Cθ ((mk^2)+2 (mpi^2)) Sθ+2 (-4 (mk^2)+7 (mpi^2)) ((Sθ)^2)))/(9 (Fpi^4) (MpR8^2)));

  f4δL8[s_,t_]:= ((16 (mpi^4) (((Cθ)^2)-2 (Sqrt[2]) Cθ Sθ+2 ((Sθ)^2)) δL8)/(Fpi^4)) ;

  f4TensorResonance[s_,t_]:= (1/(9 (Fpi^4) (MsT^4)))4 (((Cθ)^2)-2 (Sqrt[2]) Cθ Sθ+2 ((Sθ)^2)) ((1/((MsT^2)-s))((gT^2) (6 (meta^4) (MsT^4)+6 (mpi^4) (MsT^4)+(MsT^4) (s^2)-(MsT^2) (s^3)+(s^4)+6 (MsT^4) s t+6 (MsT^4) (t^2)-2 (mpi^2) (MsT^2) ((s^2)+(MsT^2) (s+6 t))+2 (meta^2) (2 (mpi^2) (MsT^4)-(MsT^2) ((s^2)+(MsT^2) (s+6 t))))-2 gT ((MsT^2)-s) (s (s ((MsT^2)+s)-(mpi^2) (2 (MsT^2)+s))+(meta^2) (4 (mpi^2) (MsT^2)-s (2 (MsT^2)+s))) βT-(2 (meta^2)-s) (-2 (mpi^2)+s) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))+(1/((MsT^2)-t))((gT^2) (((((meta^4)-2 (meta^2) (mpi^2)+(mpi^4)-(t^2)))^2)+(MsT^4) ((meta^4)+(mpi^4)+6 (s^2)+2 (meta^2) (7 (mpi^2)-6 s-t)+6 s t+(t^2)-2 (mpi^2) (6 s+t))-(MsT^2) (4 (meta^6)+4 (mpi^6)+2 (mpi^2) (t^2)+(t^3)-(mpi^4) (6 s+7 t)-(meta^4) (4 (mpi^2)+6 s+7 t)+2 (meta^2) (-2 (mpi^4)+(t^2)+(mpi^2) (6 s+7 t))))-2 gT ((meta^2)+(mpi^2)-t) ((MsT^4) ((meta^2)+(mpi^2)-t)+t (-(meta^4)+2 (meta^2) (mpi^2)-(mpi^4)+(t^2))+(MsT^2) ((meta^4)+(mpi^4)-(mpi^2) t-(meta^2) (2 (mpi^2)+t))) βT+((((meta^2)+(mpi^2)-t))^2) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2))+(1/(-2 (meta^2)-2 (mpi^2)+(MsT^2)+s+t))((gT^2) ((MsT^4) ((meta^4)+(mpi^4)+(s^2)+2 (meta^2) (7 (mpi^2)-s-t)-4 s t+(t^2)-2 (mpi^2) (s+t))+((((meta^4)-2 (meta^2) (mpi^2)+(mpi^4)-(((-2 (meta^2)-2 (mpi^2)+s+t))^2)))^2)-(MsT^2) (6 (meta^6)+6 (mpi^6)+(meta^4) (58 (mpi^2)-19 s-13 t)+8 (mpi^2) (((s+t))^2)-(((s+t))^3)-(mpi^4) (19 s+13 t)+2 (meta^2) (29 (mpi^4)+4 (((s+t))^2)-3 (mpi^2) (7 s+9 t))))-2 gT (-(meta^2)-(mpi^2)+s+t) (-(MsT^2) ((meta^4)+(mpi^2) ((mpi^2)-s-t)+(meta^2) (6 (mpi^2)-s-t))+(MsT^4) (-(meta^2)-(mpi^2)+s+t)+(2 (meta^2)+2 (mpi^2)-s-t) (-(meta^4)+2 (meta^2) (mpi^2)-(mpi^4)+(((-2 (meta^2)-2 (mpi^2)+s+t))^2))) βT+((((meta^2)+(mpi^2)-s-t))^2) (-2 (MsT^4)+(MsT^2) (2 (meta^2)+2 (mpi^2)-s-t)+(((-2 (meta^2)-2 (mpi^2)+s+t))^2)) ((βT)^2))) ;


  f4TensorSD[s_,t_]:= -((8 (2 (meta^2)-s) (-2 (mpi^2)+s) (((Cθ)^2)+((Sθ)^2)) β1SD)/(Fpi^4))+((4 ((Sqrt[2]) Cθ-2 Sθ) Sθ ((meta^4)+(mpi^4)+(s^2)+s t+(t^2)-2 (mpi^2) (s+t)+(meta^2) (4 (mpi^2)-2 (s+t))) β13SD)/(Fpi^4))+((12 (2 (meta^2)-s) (-2 (mpi^2)+s) ((Sθ)^2) β14SD)/(Fpi^4))-((6 ((Sθ)^2) (2 (meta^4)+2 (mpi^4)+(s^2)+2 s t+2 (t^2)-2 (mpi^2) (s+2 t)+(meta^2) (4 (mpi^2)-2 (s+2 t))) β15SD)/(Fpi^4))+((4 (((Cθ)^2)+((Sθ)^2)) (2 (meta^4)+2 (mpi^4)+(s^2)+2 s t+2 (t^2)-2 (mpi^2) (s+2 t)+(meta^2) (4 (mpi^2)-2 (s+2 t))) β2SD)/(Fpi^4))+((8 (((Cθ)^2)-2 (Sqrt[2]) Cθ Sθ+2 ((Sθ)^2)) ((meta^4)+(mpi^4)+(s^2)+s t+(t^2)-2 (mpi^2) (s+t)+(meta^2) (4 (mpi^2)-2 (s+t))) β3SD)/(3 (Fpi^4))) ;

(π^0)(π^0)-> η η'

f5PsR[s_,t_]:=-((8 (dmt^2) (mpi^2) ((Sqrt[2]) ((Cθ)^2) (-2 (mk^2)+5 (mpi^2))+4 Cθ (-4 (mk^2)+(mpi^2)) Sθ+(Sqrt[2]) (2 (mk^2)-5 (mpi^2)) ((Sθ)^2)))/(3 (Fpi^4) (MpR1^2)))-((8 (dm^2) (mpi^2) (2 (Sqrt[2]) ((Cθ)^2) ((mk^2)+2 (mpi^2))+Cθ (16 (mk^2)-13 (mpi^2)) Sθ-2 (Sqrt[2]) ((mk^2)+2 (mpi^2)) ((Sθ)^2)))/(9 (Fpi^4) (MpR8^2))) ;

  f5δL8[s_,t_]:= ((16 (mpi^4) ((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2)) δL8)/(Fpi^4)) ;

  f5TensorResonance[s_,t_]:=  (1/(9 (Fpi^4) (MsT^4)))4 ((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2)) ((1/((MsT^2)-s))((gT^2) (6 (mpi^4) (MsT^4)-2 (mpi^2) (MsT^4) s-2 (mpi^2) (MsT^2) (s^2)+(MsT^4) (s^2)-(MsT^2) (s^3)+(s^4)+(meta^4) (2 (mpi^2) (MsT^2)+(2 (MsT^2)-s) s)+(metaP^4) (2 (mpi^2) (MsT^2)+(2 (MsT^2)-s) s)-12 (mpi^2) (MsT^4) t+6 (MsT^4) s t+6 (MsT^4) (t^2)-(meta^2) (-2 (mpi^2) (MsT^4)+(MsT^4) s+(MsT^2) (s^2)+(metaP^2) (4 (mpi^2) (MsT^2)-6 (MsT^4)+4 (MsT^2) s-2 (s^2))+6 (MsT^4) t)+(metaP^2) (2 (mpi^2) (MsT^4)-(MsT^2) ((s^2)+(MsT^2) (s+6 t))))-gT ((MsT^2)-s) ((meta^4) (2 (mpi^2)-s)+((metaP^2)-s) ((metaP^2) (2 (mpi^2)-s)-2 s ((MsT^2)+s)+2 (mpi^2) (2 (MsT^2)+s))-(meta^2) (-4 (mpi^2) (MsT^2)+(metaP^2) (4 (mpi^2)-2 s)+s (2 (MsT^2)+s))) βT-((meta^2)+(metaP^2)-s) (-2 (mpi^2)+s) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))+(1/(-(meta^2)-(metaP^2)-2 (mpi^2)+(MsT^2)+s+t))((gT^2) ((2 (meta^2)+(metaP^2)+(mpi^2)-s-t) ((meta^2)+2 (metaP^2)+(mpi^2)-s-t) ((meta^2)+3 (mpi^2)-s-t) ((metaP^2)+3 (mpi^2)-s-t)+(MsT^4) ((mpi^4)-2 (mpi^2) s+(s^2)+(metaP^2) (7 (mpi^2)-s-t)+(meta^2) ((metaP^2)+7 (mpi^2)-s-t)-2 (mpi^2) t-4 s t+(t^2))-(MsT^2) (6 (mpi^6)-19 (mpi^4) s+8 (mpi^2) (s^2)-(s^3)-13 (mpi^4) t+16 (mpi^2) s t-3 (s^2) t+8 (mpi^2) (t^2)-3 s (t^2)-(t^3)+(metaP^4) (11 (mpi^2)-3 (s+t))+(meta^4) (3 (metaP^2)+11 (mpi^2)-3 (s+t))+(metaP^2) (29 (mpi^4)+4 (((s+t))^2)-3 (mpi^2) (7 s+9 t))+(meta^2) (3 (metaP^4)+29 (mpi^4)+(metaP^2) (36 (mpi^2)-13 s-7 t)+4 (((s+t))^2)-3 (mpi^2) (7 s+9 t))))-gT (2 (MsT^4) ((meta^2)+(mpi^2)-s-t) ((metaP^2)+(mpi^2)-s-t)+((meta^2) (-(metaP^4)+4 (metaP^2) (mpi^2)+((((meta^2)+(metaP^2)+(mpi^2)-s-t))^2))+(meta^4) ((meta^2)+(mpi^2)-s-t)+(metaP^4) ((meta^2)+(metaP^2)+(mpi^2)-s-t)+(metaP^2) ((((meta^2)+(metaP^2)+(mpi^2)-s-t))^2)-2 ((((meta^2)+(metaP^2)+(mpi^2)-s-t))^2) ((meta^2)+(metaP^2)+3 (mpi^2)-s-t)) ((meta^2)+(metaP^2)+2 (mpi^2)-s-t)+(MsT^2) ((metaP^4) (5 (mpi^2)-s-t)+(meta^4) ((metaP^2)+5 (mpi^2)-s-t)+2 (mpi^2) (((-(mpi^2)+s+t))^2)+(metaP^2) (7 (mpi^4)-8 (mpi^2) (s+t)+(((s+t))^2))+(meta^2) ((metaP^4)+7 (mpi^4)-8 (mpi^2) (s+t)+(((s+t))^2)+(metaP^2) (4 (mpi^2)-2 (s+t))))) βT+(-2 (MsT^4)+(MsT^2) ((meta^2)+(metaP^2)+2 (mpi^2)-s-t)+((((meta^2)+(metaP^2)+2 (mpi^2)-s-t))^2)) (-(meta^2)-(mpi^2)+s+t) (-(metaP^2)-(mpi^2)+s+t) ((βT)^2))+(1/((MsT^2)-t))((gT^2) (((meta^4)-2 (meta^2) (mpi^2)+(mpi^4)-(t^2)) ((metaP^4)-2 (metaP^2) (mpi^2)+(mpi^4)-(t^2))+(MsT^4) ((mpi^4)-12 (mpi^2) s+6 (s^2)+(metaP^2) (7 (mpi^2)-6 s-t)+(meta^2) ((metaP^2)+7 (mpi^2)-6 s-t)-2 (mpi^2) t+6 s t+(t^2))-(MsT^2) (4 (mpi^6)-6 (mpi^4) s+2 (meta^4) ((metaP^2)-2 (mpi^2)-t)-7 (mpi^4) t+2 (mpi^2) (t^2)+(t^3)-2 (metaP^4) (2 (mpi^2)+t)+(metaP^2) (-2 (mpi^4)+(t^2)+(mpi^2) (6 s+7 t))+(meta^2) (2 (metaP^4)-2 (mpi^4)+(t^2)+(mpi^2) (6 s+7 t)+(metaP^2) (4 (mpi^2)-3 (2 s+t)))))-gT ((meta^4) ((metaP^2)+(mpi^2)-t) ((MsT^2)-t)+((mpi^2)-t) ((MsT^2)-t) ((metaP^4)+2 ((mpi^2)-t) ((mpi^2)+(MsT^2)+t)+(metaP^2) (-(mpi^2)+2 (MsT^2)+t))+(meta^2) ((metaP^4) ((MsT^2)-t)-2 (metaP^2) (2 (mpi^2)-(MsT^2)) ((MsT^2)-t)+(mpi^4) (-(MsT^2)+t)+2 (mpi^2) ((MsT^4)-(t^2))+t (-2 (MsT^4)+(MsT^2) t+(t^2)))) βT+((meta^2)+(mpi^2)-t) ((metaP^2)+(mpi^2)-t) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2)));


  f5TensorSD[s_,t_]:= -((2 ((Sqrt[2]) ((Cθ)^2)-4 Cθ Sθ-(Sqrt[2]) ((Sθ)^2)) ((mpi^4)-2 (mpi^2) s+(s^2)+(metaP^2) (2 (mpi^2)-s-t)+(meta^2) ((metaP^2)+2 (mpi^2)-s-t)-2 (mpi^2) t+s t+(t^2)) β13SD)/(Fpi^4))-((12 Cθ ((meta^2)+(metaP^2)-s) (-2 (mpi^2)+s) Sθ β14SD)/(Fpi^4))+((6 Cθ Sθ (2 (mpi^4)-2 (mpi^2) s+(s^2)+(metaP^2) (2 (mpi^2)-s-2 t)+(meta^2) (2 (metaP^2)+2 (mpi^2)-s-2 t)-4 (mpi^2) t+2 s t+2 (t^2)) β15SD)/(Fpi^4))+((8 ((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2)) ((mpi^4)-2 (mpi^2) s+(s^2)+(metaP^2) (2 (mpi^2)-s-t)+(meta^2) ((metaP^2)+2 (mpi^2)-s-t)-2 (mpi^2) t+s t+(t^2)) β3SD)/(3 (Fpi^4))) ;

(π^0)(π^0)-> η' η'

f6PsR[s_,t_]:= -((16 (dmt^2) (mpi^2) (2 ((Cθ)^2) (2 (mk^2)+(mpi^2))+(Sqrt[2]) Cθ (-2 (mk^2)+5 (mpi^2)) Sθ+4 (-(mk^2)+(mpi^2)) ((Sθ)^2)))/(3 (Fpi^4) (MpR1^2)))-((8 (dm^2) (mpi^2) (((Cθ)^2) (-8 (mk^2)+14 (mpi^2))+4 (Sqrt[2]) Cθ ((mk^2)+2 (mpi^2)) Sθ+(8 (mk^2)+(mpi^2)) ((Sθ)^2)))/(9 (Fpi^4) (MpR8^2)));

  f6δL8[s_,t_]:=  ((16 (mpi^4) (2 ((Cθ)^2)+2 (Sqrt[2]) Cθ Sθ+((Sθ)^2)) δL8)/(Fpi^4));

  f6TensorResonance[s_,t_]:= (1/(9 (Fpi^4) (MsT^4)))4 (2 ((Cθ)^2)+2 (Sqrt[2]) Cθ Sθ+((Sθ)^2)) ((1/((MsT^2)-s))((gT^2) (6 (metaP^4) (MsT^4)+6 (mpi^4) (MsT^4)+(MsT^4) (s^2)-(MsT^2) (s^3)+(s^4)+6 (MsT^4) s t+6 (MsT^4) (t^2)-2 (mpi^2) (MsT^2) ((s^2)+(MsT^2) (s+6 t))+2 (metaP^2) (2 (mpi^2) (MsT^4)-(MsT^2) ((s^2)+(MsT^2) (s+6 t))))-2 gT ((MsT^2)-s) (s (s ((MsT^2)+s)-(mpi^2) (2 (MsT^2)+s))+(metaP^2) (4 (mpi^2) (MsT^2)-s (2 (MsT^2)+s))) βT-(2 (metaP^2)-s) (-2 (mpi^2)+s) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))+(1/((MsT^2)-t))((gT^2) (((((metaP^4)-2 (metaP^2) (mpi^2)+(mpi^4)-(t^2)))^2)+(MsT^4) ((metaP^4)+(mpi^4)+6 (s^2)+2 (metaP^2) (7 (mpi^2)-6 s-t)+6 s t+(t^2)-2 (mpi^2) (6 s+t))-(MsT^2) (4 (metaP^6)+4 (mpi^6)+2 (mpi^2) (t^2)+(t^3)-(mpi^4) (6 s+7 t)-(metaP^4) (4 (mpi^2)+6 s+7 t)+2 (metaP^2) (-2 (mpi^4)+(t^2)+(mpi^2) (6 s+7 t))))-2 gT ((metaP^2)+(mpi^2)-t) ((MsT^4) ((metaP^2)+(mpi^2)-t)+t (-(metaP^4)+2 (metaP^2) (mpi^2)-(mpi^4)+(t^2))+(MsT^2) ((metaP^4)+(mpi^4)-(mpi^2) t-(metaP^2) (2 (mpi^2)+t))) βT+((((metaP^2)+(mpi^2)-t))^2) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2))+(1/(-2 (metaP^2)-2 (mpi^2)+(MsT^2)+s+t))((gT^2) ((MsT^4) ((metaP^4)+(mpi^4)+(s^2)+2 (metaP^2) (7 (mpi^2)-s-t)-4 s t+(t^2)-2 (mpi^2) (s+t))+((((metaP^4)-2 (metaP^2) (mpi^2)+(mpi^4)-(((-2 (metaP^2)-2 (mpi^2)+s+t))^2)))^2)-(MsT^2) (6 (metaP^6)+6 (mpi^6)+(metaP^4) (58 (mpi^2)-19 s-13 t)+8 (mpi^2) (((s+t))^2)-(((s+t))^3)-(mpi^4) (19 s+13 t)+2 (metaP^2) (29 (mpi^4)+4 (((s+t))^2)-3 (mpi^2) (7 s+9 t))))-2 gT (-(metaP^2)-(mpi^2)+s+t) (-(MsT^2) ((metaP^4)+(mpi^2) ((mpi^2)-s-t)+(metaP^2) (6 (mpi^2)-s-t))+(MsT^4) (-(metaP^2)-(mpi^2)+s+t)+(2 (metaP^2)+2 (mpi^2)-s-t) (-(metaP^4)+2 (metaP^2) (mpi^2)-(mpi^4)+(((-2 (metaP^2)-2 (mpi^2)+s+t))^2))) βT+((((metaP^2)+(mpi^2)-s-t))^2) (-2 (MsT^4)+(MsT^2) (2 (metaP^2)+2 (mpi^2)-s-t)+(((-2 (metaP^2)-2 (mpi^2)+s+t))^2)) ((βT)^2))) ;


  f6TensorSD[s_,t_]:= -((8 (2 (metaP^2)-s) (-2 (mpi^2)+s) β1SD)/(Fpi^4))-((4 Cθ (2 Cθ+(Sqrt[2]) Sθ) ((metaP^4)+(mpi^4)+(s^2)+s t+(t^2)-2 (mpi^2) (s+t)+(metaP^2) (4 (mpi^2)-2 (s+t))) β13SD)/(Fpi^4))+((12 ((Cθ)^2) (2 (metaP^2)-s) (-2 (mpi^2)+s) β14SD)/(Fpi^4))-((6 ((Cθ)^2) (2 (metaP^4)+2 (mpi^4)+(s^2)+2 s t+2 (t^2)-2 (mpi^2) (s+2 t)+(metaP^2) (4 (mpi^2)-2 (s+2 t))) β15SD)/(Fpi^4))+((4 (2 (metaP^4)+2 (mpi^4)+(s^2)+2 s t+2 (t^2)-2 (mpi^2) (s+2 t)+(metaP^2) (4 (mpi^2)-2 (s+2 t))) β2SD)/(Fpi^4))+((8 (2 ((Cθ)^2)+2 (Sqrt[2]) Cθ Sθ+((Sθ)^2)) ((metaP^4)+(mpi^4)+(s^2)+s t+(t^2)-2 (mpi^2) (s+t)+(metaP^2) (4 (mpi^2)-2 (s+t))) β3SD)/(3 (Fpi^4))) ;

(K^0)(OverBar[(K^0)])-> η η

f7PsR[s_,t_]:=  -((8 (dm^2) (((Cθ)^2) (16 (mk^4)-9 (mk^2) (mpi^2)+2 (mpi^4))+2 (Sqrt[2]) Cθ (9 (mk^4)-8 (mk^2) (mpi^2)+2 (mpi^4)) Sθ+2 (mk^2) (5 (mk^2)-2 (mpi^2)) ((Sθ)^2)))/(9 (Fpi^4) (MpR8^2)))-((8 (dmt^2) (4 ((Cθ)^2) (2 (mk^4)-3 (mk^2) (mpi^2)+(mpi^4))+(Sqrt[2]) Cθ (12 (mk^4)-8 (mk^2) (mpi^2)-(mpi^4)) Sθ+4 (mk^2) (2 (mk^2)+(mpi^2)) ((Sθ)^2)))/(3 (Fpi^4) (MpR1^2)));

  f7δL8[s_,t_]:=  ((16 (((Cθ)^2) (8 (mk^4)-7 (mk^2) (mpi^2)+2 (mpi^4))+(Sqrt[2]) Cθ (10 (mk^4)-8 (mk^2) (mpi^2)+(mpi^4)) Sθ+6 (mk^4) ((Sθ)^2)) δL8)/(3 (Fpi^4)));

  f7TensorResonance[s_,t_]:=  (1/(9 (Fpi^4) (MsT^4)))((1/((MsT^2)-s))4 (2 ((Cθ)^2)+2 (Sqrt[2]) Cθ Sθ+((Sθ)^2)) ((gT^2) (6 (meta^4) (MsT^4)+6 (mk^4) (MsT^4)+(MsT^4) (s^2)-(MsT^2) (s^3)+(s^4)+6 (MsT^4) s t+6 (MsT^4) (t^2)-2 (mk^2) (MsT^2) ((s^2)+(MsT^2) (s+6 t))+2 (meta^2) (2 (mk^2) (MsT^4)-(MsT^2) ((s^2)+(MsT^2) (s+6 t))))-2 gT ((MsT^2)-s) (s (s ((MsT^2)+s)-(mk^2) (2 (MsT^2)+s))+(meta^2) (4 (mk^2) (MsT^2)-s (2 (MsT^2)+s))) βT-(2 (meta^2)-s) (-2 (mk^2)+s) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))+(1/((MsT^2)-s))2 (((Cθ)^2)-2 (Sqrt[2]) Cθ Sθ+2 ((Sθ)^2)) ((gT^2) (6 (meta^4) (MsT^4)+6 (mk^4) (MsT^4)+(MsT^4) (s^2)-(MsT^2) (s^3)+(s^4)+6 (MsT^4) s t+6 (MsT^4) (t^2)-2 (mk^2) (MsT^2) ((s^2)+(MsT^2) (s+6 t))+2 (meta^2) (2 (mk^2) (MsT^4)-(MsT^2) ((s^2)+(MsT^2) (s+6 t))))-2 gT ((MsT^2)-s) (s (s ((MsT^2)+s)-(mk^2) (2 (MsT^2)+s))+(meta^2) (4 (mk^2) (MsT^2)-s (2 (MsT^2)+s))) βT-(2 (meta^2)-s) (-2 (mk^2)+s) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))+(1/((MsT^2)-t))(((Cθ)^2)+4 (Sqrt[2]) Cθ Sθ+8 ((Sθ)^2)) ((gT^2) ((meta^8)+(mk^8)-4 (mk^6) (MsT^2)-4 (meta^6) ((mk^2)+(MsT^2))+6 (MsT^4) (s^2)+6 (MsT^4) s t+(MsT^4) (t^2)-(MsT^2) (t^3)+(t^4)-2 (mk^2) (MsT^2) ((t^2)+(MsT^2) (6 s+t))+(mk^4) ((MsT^4)-2 (t^2)+(MsT^2) (6 s+7 t))+(meta^4) (6 (mk^4)+4 (mk^2) (MsT^2)+(MsT^4)-2 (t^2)+(MsT^2) (6 s+7 t))-2 (meta^2) (2 (mk^6)-2 (mk^4) (MsT^2)+(MsT^2) ((t^2)+(MsT^2) (6 s+t))+(mk^2) (-7 (MsT^4)-2 (t^2)+(MsT^2) (6 s+7 t))))-2 gT ((meta^2)+(mk^2)-t) ((meta^4) ((MsT^2)-t)+(mk^4) ((MsT^2)-t)-(meta^2) (2 (mk^2)-(MsT^2)) ((MsT^2)-t)-(MsT^4) t+(t^3)+(mk^2) ((MsT^4)-(MsT^2) t)) βT+((((meta^2)+(mk^2)-t))^2) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2))+(1/(-2 (meta^2)-2 (mk^2)+(MsT^2)+s+t))(((Cθ)^2)+4 (Sqrt[2]) Cθ Sθ+8 ((Sθ)^2)) ((gT^2) (9 (meta^8)+9 (mk^8)+(MsT^4) (s^2)+(MsT^2) (s^3)+(s^4)-4 (MsT^4) s t+3 (MsT^2) (s^2) t+4 (s^3) t+(MsT^4) (t^2)+3 (MsT^2) s (t^2)+6 (s^2) (t^2)+(MsT^2) (t^3)+4 s (t^3)+(t^4)+6 (meta^6) (10 (mk^2)-(MsT^2)-4 (s+t))-2 (mk^2) (s+t) ((((MsT^2)+2 (s+t)))^2)-6 (mk^6) ((MsT^2)+4 (s+t))+(mk^4) ((MsT^4)+22 (((s+t))^2)+(MsT^2) (19 s+13 t))+(meta^4) (118 (mk^4)+(MsT^4)+22 (((s+t))^2)+(MsT^2) (19 s+13 t)-2 (mk^2) (29 (MsT^2)+52 (s+t)))+2 (meta^2) (30 (mk^6)-(s+t) ((((MsT^2)+2 (s+t)))^2)-(mk^4) (29 (MsT^2)+52 (s+t))+(mk^2) (7 (MsT^4)+26 (((s+t))^2)+3 (MsT^2) (7 s+9 t))))-2 gT (-(meta^2)-(mk^2)+s+t) (-(MsT^4) (2 (meta^2)+2 (mk^2)-s-t)-(((-2 (meta^2)-2 (mk^2)+s+t))^3)+(meta^4) (-2 (meta^2)-2 (mk^2)+(MsT^2)+s+t)+(mk^4) (-2 (meta^2)-2 (mk^2)+(MsT^2)+s+t)+(mk^2) (MsT^2) (-2 (meta^2)-2 (mk^2)+(MsT^2)+s+t)-(meta^2) (2 (mk^2)-(MsT^2)) (-2 (meta^2)-2 (mk^2)+(MsT^2)+s+t)) βT+((((meta^2)+(mk^2)-s-t))^2) (-2 (MsT^4)+(MsT^2) (2 (meta^2)+2 (mk^2)-s-t)+(((-2 (meta^2)-2 (mk^2)+s+t))^2)) ((βT)^2)));


  f7TensorSD[s_,t_]:=-((8 (2 (meta^2)-s) (-2 (mk^2)+s) β1SD)/(Fpi^4))-((2 Sθ ((Sqrt[2]) Cθ+4 Sθ) ((meta^4)+(mk^4)+(s^2)+s t+(t^2)-2 (mk^2) (s+t)+(meta^2) (4 (mk^2)-2 (s+t))) β13SD)/(Fpi^4))+((12 (2 (meta^2)-s) (-2 (mk^2)+s) ((Sθ)^2) β14SD)/(Fpi^4))-((6 ((Sθ)^2) (2 (meta^4)+2 (mk^4)+(s^2)+2 s t+2 (t^2)-2 (mk^2) (s+2 t)+(meta^2) (4 (mk^2)-2 (s+2 t))) β15SD)/(Fpi^4))+((4 (2 (meta^4)+2 (mk^4)+(s^2)+2 s t+2 (t^2)-2 (mk^2) (s+2 t)+(meta^2) (4 (mk^2)-2 (s+2 t))) β2SD)/(Fpi^4))+(1/(3 (Fpi^4)))(((Cθ)^2) (2 (meta^4)+2 (mk^4)+11 (s^2)+(meta^2) (44 (mk^2)-22 s-4 t)+2 s t+2 (t^2)-2 (mk^2) (11 s+2 t))+8 (Sqrt[2]) Cθ Sθ ((meta^4)+(mk^4)+(s^2)+s t+(t^2)-2 (mk^2) (s+t)+(meta^2) (4 (mk^2)-2 (s+t)))+16 ((Sθ)^2) ((meta^4)+(mk^4)+(s^2)+s t+(t^2)-2 (mk^2) (s+t)+(meta^2) (4 (mk^2)-2 (s+t)))) β3SD  ;

(K^0)(OverBar[(K^0)])-> η η'

f8PsR[s_,t_]:=((8 (dm^2) ((Sqrt[2]) ((Cθ)^2) (9 (mk^4)-8 (mk^2) (mpi^2)+2 (mpi^4))+Cθ (-6 (mk^4)+5 (mk^2) (mpi^2)-2 (mpi^4)) Sθ+(Sqrt[2]) (-9 (mk^4)+8 (mk^2) (mpi^2)-2 (mpi^4)) ((Sθ)^2)))/(9 (Fpi^4) (MpR8^2)))+((4 (dmt^2) ((Sqrt[2]) ((Cθ)^2) (12 (mk^4)-8 (mk^2) (mpi^2)-(mpi^4))-8 Cθ (mpi^2) (-4 (mk^2)+(mpi^2)) Sθ+(Sqrt[2]) (-12 (mk^4)+8 (mk^2) (mpi^2)+(mpi^4)) ((Sθ)^2)))/(3 (Fpi^4) (MpR1^2))) ;

  f8δL8[s_,t_]:=  -((8 ((Sqrt[2]) ((Cθ)^2) (10 (mk^4)-8 (mk^2) (mpi^2)+(mpi^4))-2 Cθ (2 (mk^4)-7 (mk^2) (mpi^2)+2 (mpi^4)) Sθ-(Sqrt[2]) (10 (mk^4)-8 (mk^2) (mpi^2)+(mpi^4)) ((Sθ)^2)) δL8)/(3 (Fpi^4)));

  f8TensorResonance[s_,t_]:= -(1/(9 (Fpi^4) (MsT^4)))((1/((MsT^2)-s))2 ((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2)) ((gT^2) (6 (mk^4) (MsT^4)-2 (mk^2) (MsT^4) s-2 (mk^2) (MsT^2) (s^2)+(MsT^4) (s^2)-(MsT^2) (s^3)+(s^4)+(meta^4) (2 (mk^2) (MsT^2)+(2 (MsT^2)-s) s)+(metaP^4) (2 (mk^2) (MsT^2)+(2 (MsT^2)-s) s)-12 (mk^2) (MsT^4) t+6 (MsT^4) s t+6 (MsT^4) (t^2)-(meta^2) (-2 (mk^2) (MsT^4)+(MsT^4) s+(MsT^2) (s^2)+(metaP^2) (4 (mk^2) (MsT^2)-6 (MsT^4)+4 (MsT^2) s-2 (s^2))+6 (MsT^4) t)+(metaP^2) (2 (mk^2) (MsT^4)-(MsT^2) ((s^2)+(MsT^2) (s+6 t))))-gT ((MsT^2)-s) ((meta^4) (2 (mk^2)-s)+((metaP^2)-s) ((metaP^2) (2 (mk^2)-s)-2 s ((MsT^2)+s)+2 (mk^2) (2 (MsT^2)+s))-(meta^2) (-4 (mk^2) (MsT^2)+(metaP^2) (4 (mk^2)-2 s)+s (2 (MsT^2)+s))) βT-((meta^2)+(metaP^2)-s) (-2 (mk^2)+s) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))+(1/(-(meta^2)-(metaP^2)-2 (mk^2)+(MsT^2)+s+t))(2 (Sqrt[2]) ((Cθ)^2)+7 Cθ Sθ-2 (Sqrt[2]) ((Sθ)^2)) ((gT^2) ((mk^8)-4 (mk^6) (MsT^2)+(mk^4) (MsT^4)+6 (mk^4) (MsT^2) s-12 (mk^2) (MsT^4) s+6 (MsT^4) (s^2)-(metaP^2) (2 (mk^6)-2 (mk^4) (MsT^2)+(mk^2) (-7 (MsT^4)+(MsT^2) (7 (meta^2)+7 (metaP^2)+14 (mk^2)-s-7 t)-2 ((((meta^2)+(metaP^2)+2 (mk^2)-s-t))^2))+(MsT^2) (((((meta^2)+(metaP^2)+2 (mk^2)-s-t))^2)+(MsT^2) ((meta^2)+(metaP^2)+2 (mk^2)+5 s-t)))-(meta^2) (2 (mk^6)-2 (mk^4) (MsT^2)+2 (metaP^4) ((mk^2)+(MsT^2))-(metaP^2) (4 (mk^4)+2 (mk^2) (MsT^2)+(MsT^2) (3 (meta^2)+3 (metaP^2)+(MsT^2)+3 s-3 t))+(mk^2) (-7 (MsT^4)+(MsT^2) (7 (meta^2)+7 (metaP^2)+14 (mk^2)-s-7 t)-2 ((((meta^2)+(metaP^2)+2 (mk^2)-s-t))^2))+(MsT^2) (((((meta^2)+(metaP^2)+2 (mk^2)-s-t))^2)+(MsT^2) ((meta^2)+(metaP^2)+2 (mk^2)+5 s-t)))+7 (mk^4) (MsT^2) ((meta^2)+(metaP^2)+2 (mk^2)-s-t)-2 (mk^2) (MsT^4) ((meta^2)+(metaP^2)+2 (mk^2)-s-t)+6 (MsT^4) s ((meta^2)+(metaP^2)+2 (mk^2)-s-t)-2 (mk^4) ((((meta^2)+(metaP^2)+2 (mk^2)-s-t))^2)-2 (mk^2) (MsT^2) ((((meta^2)+(metaP^2)+2 (mk^2)-s-t))^2)+(MsT^4) ((((meta^2)+(metaP^2)+2 (mk^2)-s-t))^2)-(MsT^2) ((((meta^2)+(metaP^2)+2 (mk^2)-s-t))^3)+((((meta^2)+(metaP^2)+2 (mk^2)-s-t))^4)+(metaP^4) ((mk^4)+4 (mk^2) (MsT^2)+((meta^2)+(metaP^2)+2 (mk^2)-s-t) (-(meta^2)-(metaP^2)-2 (mk^2)+2 (MsT^2)+s+t))+(meta^4) ((metaP^4)+(mk^4)+4 (mk^2) (MsT^2)-2 (metaP^2) ((mk^2)+(MsT^2))+((meta^2)+(metaP^2)+2 (mk^2)-s-t) (-(meta^2)-(metaP^2)-2 (mk^2)+2 (MsT^2)+s+t)))-gT (-(meta^2)-(metaP^2)-2 (mk^2)+(MsT^2)+s+t) ((meta^2) ((metaP^4)+(metaP^2) (-4 (mk^2)+2 (MsT^2))-((meta^2)+(metaP^2)+(mk^2)-s-t) ((meta^2)+(metaP^2)+(mk^2)+2 (MsT^2)-s-t))+(meta^4) (-(meta^2)-(mk^2)+s+t)+((metaP^4)-2 ((meta^2)+(metaP^2)+(mk^2)-s-t) ((meta^2)+(metaP^2)+3 (mk^2)+(MsT^2)-s-t)+(metaP^2) ((meta^2)+(metaP^2)+(mk^2)+2 (MsT^2)-s-t)) (-(meta^2)-(metaP^2)-(mk^2)+s+t)) βT+(-2 (MsT^4)+(MsT^2) ((meta^2)+(metaP^2)+2 (mk^2)-s-t)+((((meta^2)+(metaP^2)+2 (mk^2)-s-t))^2)) (-(meta^2)-(mk^2)+s+t) (-(metaP^2)-(mk^2)+s+t) ((βT)^2))+(1/((MsT^2)-t))(2 (Sqrt[2]) ((Cθ)^2)+7 Cθ Sθ-2 (Sqrt[2]) ((Sθ)^2)) ((gT^2) ((mk^8)-4 (mk^6) (MsT^2)+(mk^4) (MsT^4)+6 (mk^4) (MsT^2) s-12 (mk^2) (MsT^4) s+6 (MsT^4) (s^2)+7 (mk^4) (MsT^2) t-2 (mk^2) (MsT^4) t+6 (MsT^4) s t-2 (mk^4) (t^2)-2 (mk^2) (MsT^2) (t^2)+(MsT^4) (t^2)-(MsT^2) (t^3)+(t^4)+(metaP^4) ((mk^4)+4 (mk^2) (MsT^2)+(2 (MsT^2)-t) t)+(meta^4) ((metaP^4)+(mk^4)+4 (mk^2) (MsT^2)-2 (metaP^2) ((mk^2)+(MsT^2))+(2 (MsT^2)-t) t)-(metaP^2) (2 (mk^6)-2 (mk^4) (MsT^2)+(MsT^2) ((t^2)+(MsT^2) (6 s+t))+(mk^2) (-7 (MsT^4)-2 (t^2)+(MsT^2) (6 s+7 t)))-(meta^2) (2 (mk^6)-2 (mk^4) (MsT^2)+2 (metaP^4) ((mk^2)+(MsT^2))+(MsT^2) ((t^2)+(MsT^2) (6 s+t))-(metaP^2) (4 (mk^4)-4 (mk^2) (MsT^2)+(MsT^2) ((MsT^2)+6 s+3 t))+(mk^2) (-7 (MsT^4)-2 (t^2)+(MsT^2) (6 s+7 t))))-gT ((MsT^2)-t) ((meta^2) ((metaP^4)+(metaP^2) (-4 (mk^2)+2 (MsT^2))-((mk^2)-t) ((mk^2)-2 (MsT^2)-t))+(meta^4) ((metaP^2)+(mk^2)-t)+((mk^2)-t) ((metaP^4)+2 ((mk^2)-t) ((mk^2)+(MsT^2)+t)+(metaP^2) (-(mk^2)+2 (MsT^2)+t))) βT+((meta^2)+(mk^2)-t) ((metaP^2)+(mk^2)-t) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2))) ;

 f8TensorSD[s_,t_]:= ((((Sqrt[2]) ((Cθ)^2)+8 Cθ Sθ-(Sqrt[2]) ((Sθ)^2)) ((mk^4)-2 (mk^2) s+(s^2)+(metaP^2) (2 (mk^2)-s-t)+(meta^2) ((metaP^2)+2 (mk^2)-s-t)-2 (mk^2) t+s t+(t^2)) β13SD)/(Fpi^4))-((12 Cθ ((meta^2)+(metaP^2)-s) (-2 (mk^2)+s) Sθ β14SD)/(Fpi^4))+((6 Cθ Sθ (2 (mk^4)-2 (mk^2) s+(s^2)+(metaP^2) (2 (mk^2)-s-2 t)+(meta^2) (2 (metaP^2)+2 (mk^2)-s-2 t)-4 (mk^2) t+2 s t+2 (t^2)) β15SD)/(Fpi^4))+(1/(3 (Fpi^4)))(-4 (Sqrt[2]) ((Cθ)^2) ((mk^4)-2 (mk^2) s+(s^2)+(metaP^2) (2 (mk^2)-s-t)+(meta^2) ((metaP^2)+2 (mk^2)-s-t)-2 (mk^2) t+s t+(t^2))+4 (Sqrt[2]) ((Sθ)^2) ((mk^4)-2 (mk^2) s+(s^2)+(metaP^2) (2 (mk^2)-s-t)+(meta^2) ((metaP^2)+2 (mk^2)-s-t)-2 (mk^2) t+s t+(t^2))+Cθ Sθ (-14 (mk^4)+10 (mk^2) s-5 (s^2)+28 (mk^2) t-14 s t-14 (t^2)+(metaP^2) (-10 (mk^2)+5 s+14 t)+(meta^2) (-14 (metaP^2)-10 (mk^2)+5 s+14 t))) β3SD ;

(K^0)(OverBar[(K^0)])-> η' η'

f9PsR[s_,t_]:=  -((8 (dmt^2) (4 ((Cθ)^2) (mk^2) (2 (mk^2)+(mpi^2))+(Sqrt[2]) Cθ (-12 (mk^4)+8 (mk^2) (mpi^2)+(mpi^4)) Sθ+4 (2 (mk^4)-3 (mk^2) (mpi^2)+(mpi^4)) ((Sθ)^2)))/(3 (Fpi^4) (MpR1^2)))-((8 (dm^2) (2 ((Cθ)^2) (5 (mk^4)-2 (mk^2) (mpi^2))-2 (Sqrt[2]) Cθ (9 (mk^4)-8 (mk^2) (mpi^2)+2 (mpi^4)) Sθ+(16 (mk^4)-9 (mk^2) (mpi^2)+2 (mpi^4)) ((Sθ)^2)))/(9 (Fpi^4) (MpR8^2)));

  f9δL8[s_,t_]:=  ((16 (6 ((Cθ)^2) (mk^4)-(Sqrt[2]) Cθ (10 (mk^4)-8 (mk^2) (mpi^2)+(mpi^4)) Sθ+(8 (mk^4)-7 (mk^2) (mpi^2)+2 (mpi^4)) ((Sθ)^2)) δL8)/(3 (Fpi^4)));

  f9TensorResonance[s_,t_]:=(1/(9 (Fpi^4) (MsT^4)))((1/((MsT^2)-s))2 (2 ((Cθ)^2)+2 (Sqrt[2]) Cθ Sθ+((Sθ)^2)) ((gT^2) (6 (metaP^4) (MsT^4)+6 (mk^4) (MsT^4)+(MsT^4) (s^2)-(MsT^2) (s^3)+(s^4)+6 (MsT^4) s t+6 (MsT^4) (t^2)-2 (mk^2) (MsT^2) ((s^2)+(MsT^2) (s+6 t))+2 (metaP^2) (2 (mk^2) (MsT^4)-(MsT^2) ((s^2)+(MsT^2) (s+6 t))))-2 gT ((MsT^2)-s) (s (s ((MsT^2)+s)-(mk^2) (2 (MsT^2)+s))+(metaP^2) (4 (mk^2) (MsT^2)-s (2 (MsT^2)+s))) βT-(2 (metaP^2)-s) (-2 (mk^2)+s) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))+(1/((MsT^2)-s))4 (((Cθ)^2)-2 (Sqrt[2]) Cθ Sθ+2 ((Sθ)^2)) ((gT^2) (6 (metaP^4) (MsT^4)+6 (mk^4) (MsT^4)+(MsT^4) (s^2)-(MsT^2) (s^3)+(s^4)+6 (MsT^4) s t+6 (MsT^4) (t^2)-2 (mk^2) (MsT^2) ((s^2)+(MsT^2) (s+6 t))+2 (metaP^2) (2 (mk^2) (MsT^4)-(MsT^2) ((s^2)+(MsT^2) (s+6 t))))-2 gT ((MsT^2)-s) (s (s ((MsT^2)+s)-(mk^2) (2 (MsT^2)+s))+(metaP^2) (4 (mk^2) (MsT^2)-s (2 (MsT^2)+s))) βT-(2 (metaP^2)-s) (-2 (mk^2)+s) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))+(1/((MsT^2)-t))(8 ((Cθ)^2)-4 (Sqrt[2]) Cθ Sθ+((Sθ)^2)) ((gT^2) ((metaP^8)+(mk^8)-4 (mk^6) (MsT^2)-4 (metaP^6) ((mk^2)+(MsT^2))+6 (MsT^4) (s^2)+6 (MsT^4) s t+(MsT^4) (t^2)-(MsT^2) (t^3)+(t^4)-2 (mk^2) (MsT^2) ((t^2)+(MsT^2) (6 s+t))+(mk^4) ((MsT^4)-2 (t^2)+(MsT^2) (6 s+7 t))+(metaP^4) (6 (mk^4)+4 (mk^2) (MsT^2)+(MsT^4)-2 (t^2)+(MsT^2) (6 s+7 t))-2 (metaP^2) (2 (mk^6)-2 (mk^4) (MsT^2)+(MsT^2) ((t^2)+(MsT^2) (6 s+t))+(mk^2) (-7 (MsT^4)-2 (t^2)+(MsT^2) (6 s+7 t))))-2 gT ((metaP^2)+(mk^2)-t) ((metaP^4) ((MsT^2)-t)+(mk^4) ((MsT^2)-t)-(metaP^2) (2 (mk^2)-(MsT^2)) ((MsT^2)-t)-(MsT^4) t+(t^3)+(mk^2) ((MsT^4)-(MsT^2) t)) βT+((((metaP^2)+(mk^2)-t))^2) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2))+(1/(-2 (metaP^2)-2 (mk^2)+(MsT^2)+s+t))(8 ((Cθ)^2)-4 (Sqrt[2]) Cθ Sθ+((Sθ)^2)) ((gT^2) (9 (metaP^8)+9 (mk^8)+(MsT^4) (s^2)+(MsT^2) (s^3)+(s^4)-4 (MsT^4) s t+3 (MsT^2) (s^2) t+4 (s^3) t+(MsT^4) (t^2)+3 (MsT^2) s (t^2)+6 (s^2) (t^2)+(MsT^2) (t^3)+4 s (t^3)+(t^4)+6 (metaP^6) (10 (mk^2)-(MsT^2)-4 (s+t))-2 (mk^2) (s+t) ((((MsT^2)+2 (s+t)))^2)-6 (mk^6) ((MsT^2)+4 (s+t))+(mk^4) ((MsT^4)+22 (((s+t))^2)+(MsT^2) (19 s+13 t))+(metaP^4) (118 (mk^4)+(MsT^4)+22 (((s+t))^2)+(MsT^2) (19 s+13 t)-2 (mk^2) (29 (MsT^2)+52 (s+t)))+2 (metaP^2) (30 (mk^6)-(s+t) ((((MsT^2)+2 (s+t)))^2)-(mk^4) (29 (MsT^2)+52 (s+t))+(mk^2) (7 (MsT^4)+26 (((s+t))^2)+3 (MsT^2) (7 s+9 t))))-2 gT (-(metaP^2)-(mk^2)+s+t) (-(MsT^4) (2 (metaP^2)+2 (mk^2)-s-t)-(((-2 (metaP^2)-2 (mk^2)+s+t))^3)+(metaP^4) (-2 (metaP^2)-2 (mk^2)+(MsT^2)+s+t)+(mk^4) (-2 (metaP^2)-2 (mk^2)+(MsT^2)+s+t)+(mk^2) (MsT^2) (-2 (metaP^2)-2 (mk^2)+(MsT^2)+s+t)-(metaP^2) (2 (mk^2)-(MsT^2)) (-2 (metaP^2)-2 (mk^2)+(MsT^2)+s+t)) βT+((((metaP^2)+(mk^2)-s-t))^2) (-2 (MsT^4)+(MsT^2) (2 (metaP^2)+2 (mk^2)-s-t)+(((-2 (metaP^2)-2 (mk^2)+s+t))^2)) ((βT)^2)));


  f9TensorSD[s_,t_]:=  -((8 (2 (metaP^2)-s) (-2 (mk^2)+s) β1SD)/(Fpi^4))-((2 Cθ (4 Cθ-(Sqrt[2]) Sθ) ((metaP^4)+(mk^4)+(s^2)+s t+(t^2)-2 (mk^2) (s+t)+(metaP^2) (4 (mk^2)-2 (s+t))) β13SD)/(Fpi^4))+((12 ((Cθ)^2) (2 (metaP^2)-s) (-2 (mk^2)+s) β14SD)/(Fpi^4))-((6 ((Cθ)^2) (2 (metaP^4)+2 (mk^4)+(s^2)+2 s t+2 (t^2)-2 (mk^2) (s+2 t)+(metaP^2) (4 (mk^2)-2 (s+2 t))) β15SD)/(Fpi^4))+((4 (2 (metaP^4)+2 (mk^4)+(s^2)+2 s t+2 (t^2)-2 (mk^2) (s+2 t)+(metaP^2) (4 (mk^2)-2 (s+2 t))) β2SD)/(Fpi^4))+(1/(3 (Fpi^4)))(((Sθ)^2) (2 (metaP^4)+2 (mk^4)+11 (s^2)+(metaP^2) (44 (mk^2)-22 s-4 t)+2 s t+2 (t^2)-2 (mk^2) (11 s+2 t))+16 ((Cθ)^2) ((metaP^4)+(mk^4)+(s^2)+s t+(t^2)-2 (mk^2) (s+t)+(metaP^2) (4 (mk^2)-2 (s+t)))-8 (Sqrt[2]) Cθ Sθ ((metaP^4)+(mk^4)+(s^2)+s t+(t^2)-2 (mk^2) (s+t)+(metaP^2) (4 (mk^2)-2 (s+t)))) β3SD;

η η -> η η

f10PsR[s_,t_]:= -(1/(9 (Fpi^4) (MpR1^2)))32 (dmt^2) (4 ((Cθ)^4) (8 (mk^4)-13 (mk^2) (mpi^2)+5 (mpi^4))+(Sqrt[2]) ((Cθ)^3) (64 (mk^4)-62 (mk^2) (mpi^2)+7 (mpi^4)) Sθ+6 ((Cθ)^2) (16 (mk^4)-14 (mk^2) (mpi^2)+7 (mpi^4)) ((Sθ)^2)+16 (Sqrt[2]) Cθ (2 (mk^4)-(mk^2) (mpi^2)-(mpi^4)) ((Sθ)^3)+2 (((2 (mk^2)+(mpi^2)))^2) ((Sθ)^4))-(1/(27 (Fpi^4) (MpR8^2)))8 (dm^2) (((Cθ)^4) (208 (mk^4)-176 (mk^2) (mpi^2)+49 (mpi^4))+8 (Sqrt[2]) ((Cθ)^3) (52 (mk^4)-65 (mk^2) (mpi^2)+22 (mpi^4)) Sθ+12 ((Cθ)^2) (52 (mk^4)-68 (mk^2) (mpi^2)+25 (mpi^4)) ((Sθ)^2)+16 (Sqrt[2]) Cθ (13 (mk^4)-20 (mk^2) (mpi^2)+7 (mpi^4)) ((Sθ)^3)+2 (26 (mk^4)-64 (mk^2) (mpi^2)+29 (mpi^4)) ((Sθ)^4)) ;

  f10δL8[s_,t_]:= (1/(9 (Fpi^4)))16 (((Cθ)^4) (112 (mk^4)-128 (mk^2) (mpi^2)+43 (mpi^4))+4 (Sqrt[2]) ((Cθ)^3) (56 (mk^4)-64 (mk^2) (mpi^2)+17 (mpi^4)) Sθ+12 ((Cθ)^2) (28 (mk^4)-32 (mk^2) (mpi^2)+13 (mpi^4)) ((Sθ)^2)+16 (Sqrt[2]) Cθ (7 (mk^4)-8 (mk^2) (mpi^2)+(mpi^4)) ((Sθ)^3)+2 (14 (mk^4)-16 (mk^2) (mpi^2)+11 (mpi^4)) ((Sθ)^4)) δL8 ;

  f10TensorResonance[s_,t_]:=  (1/(27 (Fpi^4) (MsT^4)))4 ((1/((MsT^2)-s))2 (4 ((Cθ)^4)+8 (Sqrt[2]) ((Cθ)^3) Sθ+12 ((Cθ)^2) ((Sθ)^2)+4 (Sqrt[2]) Cθ ((Sθ)^3)+((Sθ)^4)) ((gT^2) (16 (meta^4) (MsT^4)-(MsT^2) (s^3)+(s^4)+(MsT^4) ((s^2)+6 s t+6 (t^2))-4 (meta^2) (MsT^2) ((s^2)+(MsT^2) (s+6 t)))-2 gT (2 (meta^2)-s) ((MsT^2)-s) (2 (meta^2) (MsT^2)-s ((MsT^2)+s)) βT+(((-2 (meta^2)+s))^2) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))+(1/((MsT^2)-s))(((Cθ)^4)-4 (Sqrt[2]) ((Cθ)^3) Sθ+12 ((Cθ)^2) ((Sθ)^2)-8 (Sqrt[2]) Cθ ((Sθ)^3)+4 ((Sθ)^4)) ((gT^2) (16 (meta^4) (MsT^4)-(MsT^2) (s^3)+(s^4)+(MsT^4) ((s^2)+6 s t+6 (t^2))-4 (meta^2) (MsT^2) ((s^2)+(MsT^2) (s+6 t)))-2 gT (2 (meta^2)-s) ((MsT^2)-s) (2 (meta^2) (MsT^2)-s ((MsT^2)+s)) βT+(((-2 (meta^2)+s))^2) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))+(1/((MsT^2)-t))2 (4 ((Cθ)^4)+8 (Sqrt[2]) ((Cθ)^3) Sθ+12 ((Cθ)^2) ((Sθ)^2)+4 (Sqrt[2]) Cθ ((Sθ)^3)+((Sθ)^4)) ((gT^2) (16 (meta^4) (MsT^4)-(MsT^2) (t^3)+(t^4)+(MsT^4) (6 (s^2)+6 s t+(t^2))-4 (meta^2) (MsT^2) ((t^2)+(MsT^2) (6 s+t)))-2 gT (2 (meta^2)-t) ((MsT^2)-t) (2 (meta^2) (MsT^2)-t ((MsT^2)+t)) βT+(((-2 (meta^2)+t))^2) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2))+(1/((MsT^2)-t))(((Cθ)^4)-4 (Sqrt[2]) ((Cθ)^3) Sθ+12 ((Cθ)^2) ((Sθ)^2)-8 (Sqrt[2]) Cθ ((Sθ)^3)+4 ((Sθ)^4)) ((gT^2) (16 (meta^4) (MsT^4)-(MsT^2) (t^3)+(t^4)+(MsT^4) (6 (s^2)+6 s t+(t^2))-4 (meta^2) (MsT^2) ((t^2)+(MsT^2) (6 s+t)))-2 gT (2 (meta^2)-t) ((MsT^2)-t) (2 (meta^2) (MsT^2)-t ((MsT^2)+t)) βT+(((-2 (meta^2)+t))^2) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2))+(1/(-4 (meta^2)+(MsT^2)+s+t))2 (4 ((Cθ)^4)+8 (Sqrt[2]) ((Cθ)^3) Sθ+12 ((Cθ)^2) ((Sθ)^2)+4 (Sqrt[2]) Cθ ((Sθ)^3)+((Sθ)^4)) ((gT^2) (16 (meta^4) (MsT^4)+(MsT^2) (((-4 (meta^2)+s+t))^3)+(((-4 (meta^2)+s+t))^4)+(MsT^4) (16 (meta^4)+(s^2)+8 (meta^2) (2 s-t)-4 s t+(t^2))-4 (meta^2) (MsT^2) ((MsT^2) (4 (meta^2)+5 s-t)+(((-4 (meta^2)+s+t))^2)))-2 gT (-2 (meta^2)+s+t) (-4 (meta^2)+(MsT^2)+s+t) (-16 (meta^4)+((MsT^2)-s-t) (s+t)+(meta^2) (-2 (MsT^2)+8 (s+t))) βT+(((-2 (meta^2)+s+t))^2) (-2 (MsT^4)+(MsT^2) (4 (meta^2)-s-t)+(((-4 (meta^2)+s+t))^2)) ((βT)^2))+(1/(-4 (meta^2)+(MsT^2)+s+t))(((Cθ)^4)-4 (Sqrt[2]) ((Cθ)^3) Sθ+12 ((Cθ)^2) ((Sθ)^2)-8 (Sqrt[2]) Cθ ((Sθ)^3)+4 ((Sθ)^4)) ((gT^2) (16 (meta^4) (MsT^4)+(MsT^2) (((-4 (meta^2)+s+t))^3)+(((-4 (meta^2)+s+t))^4)+(MsT^4) (16 (meta^4)+(s^2)+8 (meta^2) (2 s-t)-4 s t+(t^2))-4 (meta^2) (MsT^2) ((MsT^2) (4 (meta^2)+5 s-t)+(((-4 (meta^2)+s+t))^2)))-2 gT (-2 (meta^2)+s+t) (-4 (meta^2)+(MsT^2)+s+t) (-16 (meta^4)+((MsT^2)-s-t) (s+t)+(meta^2) (-2 (MsT^2)+8 (s+t))) βT+(((-2 (meta^2)+s+t))^2) (-2 (MsT^4)+(MsT^2) (4 (meta^2)-s-t)+(((-4 (meta^2)+s+t))^2)) ((βT)^2)));


f10TensorSD[s_,t_]:= ((16 (6 (meta^4)+(s^2)+s t+(t^2)-4 (meta^2) (s+t)) β1SD)/(Fpi^4))-((8 Sθ ((Sqrt[2]) ((Cθ)^3)+6 ((Cθ)^2) Sθ+2 ((Sθ)^3)) (6 (meta^4)+(s^2)+s t+(t^2)-4 (meta^2) (s+t)) β13SD)/(Fpi^4))-((48 ((Sθ)^2) (6 (meta^4)+(s^2)+s t+(t^2)-4 (meta^2) (s+t)) β14SD)/(Fpi^4))-((48 ((Sθ)^2) (6 (meta^4)+(s^2)+s t+(t^2)-4 (meta^2) (s+t)) β15SD)/(Fpi^4))+((144 ((Sθ)^4) (6 (meta^4)+(s^2)+s t+(t^2)-4 (meta^2) (s+t)) β16SD)/(Fpi^4))+((16 (6 (meta^4)+(s^2)+s t+(t^2)-4 (meta^2) (s+t)) β2SD)/(Fpi^4))+((8 (3 ((Cθ)^4)+4 (Sqrt[2]) ((Cθ)^3) Sθ+12 ((Cθ)^2) ((Sθ)^2)+2 ((Sθ)^4)) (6 (meta^4)+(s^2)+s t+(t^2)-4 (meta^2) (s+t)) β3SD)/(3 (Fpi^4)));

η η -> η η'

f11PsR[s_,t_]:=(1/(9 (Fpi^4) (MpR1^2)))8 (dmt^2) ((Sqrt[2]) ((Cθ)^4) (64 (mk^4)-62 (mk^2) (mpi^2)+7 (mpi^4))+4 ((Cθ)^3) (16 (mk^4)+10 (mk^2) (mpi^2)+(mpi^4)) Sθ-3 (Sqrt[2]) ((Cθ)^2) (32 (mk^4)-46 (mk^2) (mpi^2)+23 (mpi^4)) ((Sθ)^2)-4 Cθ (40 (mk^4)-50 (mk^2) (mpi^2)+19 (mpi^4)) ((Sθ)^3)+16 (Sqrt[2]) (-2 (mk^4)+(mk^2) (mpi^2)+(mpi^4)) ((Sθ)^4))+(1/(27 (Fpi^4) (MpR8^2)))8 (dm^2) (2 (Sqrt[2]) ((Cθ)^4) (52 (mk^4)-65 (mk^2) (mpi^2)+22 (mpi^4))+((Cθ)^3) (104 (mk^4)-232 (mk^2) (mpi^2)+101 (mpi^4)) Sθ-6 (Sqrt[2]) ((Cθ)^2) (26 (mk^4)-25 (mk^2) (mpi^2)+8 (mpi^4)) ((Sθ)^2)-4 Cθ (65 (mk^4)-70 (mk^2) (mpi^2)+23 (mpi^4)) ((Sθ)^3)-4 (Sqrt[2]) (13 (mk^4)-20 (mk^2) (mpi^2)+7 (mpi^4)) ((Sθ)^4)) ;

  f11δL8[s_,t_]:=-(1/(9 (Fpi^4)))16 ((Sqrt[2]) ((Cθ)^4) (56 (mk^4)-64 (mk^2) (mpi^2)+17 (mpi^4))+((Cθ)^3) (56 (mk^4)-64 (mk^2) (mpi^2)+35 (mpi^4)) Sθ-3 (Sqrt[2]) ((Cθ)^2) (28 (mk^4)-32 (mk^2) (mpi^2)+13 (mpi^4)) ((Sθ)^2)-4 Cθ (35 (mk^4)-40 (mk^2) (mpi^2)+14 (mpi^4)) ((Sθ)^3)-4 (Sqrt[2]) (7 (mk^4)-8 (mk^2) (mpi^2)+(mpi^4)) ((Sθ)^4)) δL8 ;

  f11TensorResonance[s_,t_]:= (1/(27 (Fpi^4) (MsT^4)))4 ((1/((MsT^2)-s))((Sqrt[2]) ((Cθ)^4)-5 ((Cθ)^3) Sθ+3 (Sqrt[2]) ((Cθ)^2) ((Sθ)^2)+2 Cθ ((Sθ)^3)-2 (Sqrt[2]) ((Sθ)^4)) ((gT^2) (2 (meta^6) (MsT^2)+(metaP^4) (2 (MsT^2)-s) s+(MsT^4) (s^2)-(MsT^2) (s^3)+(s^4)-(meta^4) (4 (metaP^2) (MsT^2)-8 (MsT^4)-2 (MsT^2) s+(s^2))+6 (MsT^4) s t+6 (MsT^4) (t^2)-(metaP^2) (MsT^2) ((s^2)+(MsT^2) (s+6 t))+(meta^2) (2 (metaP^4) (MsT^2)+2 (metaP^2) (4 (MsT^4)-2 (MsT^2) s+(s^2))-3 (MsT^2) ((s^2)+(MsT^2) (s+6 t))))-gT (2 (meta^6) ((MsT^2)-s)-(meta^4) ((MsT^2)-s) (4 (metaP^2)-4 (MsT^2)+s)+s ((metaP^4) (-(MsT^2)+s)+2 s ((MsT^4)-(s^2))+(metaP^2) (-2 (MsT^4)+(MsT^2) s+(s^2)))+(meta^2) (2 (metaP^4) ((MsT^2)-s)+(metaP^2) (4 (MsT^4)-2 (MsT^2) s-2 (s^2))+3 s (-2 (MsT^4)+(MsT^2) s+(s^2)))) βT+(2 (meta^2)-s) ((meta^2)+(metaP^2)-s) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))-(1/((MsT^2)-s))2 (2 (Sqrt[2]) ((Cθ)^4)+2 ((Cθ)^3) Sθ-3 (Sqrt[2]) ((Cθ)^2) ((Sθ)^2)-5 Cθ ((Sθ)^3)-(Sqrt[2]) ((Sθ)^4)) ((gT^2) (2 (meta^6) (MsT^2)+(metaP^4) (2 (MsT^2)-s) s+(MsT^4) (s^2)-(MsT^2) (s^3)+(s^4)-(meta^4) (4 (metaP^2) (MsT^2)-8 (MsT^4)-2 (MsT^2) s+(s^2))+6 (MsT^4) s t+6 (MsT^4) (t^2)-(metaP^2) (MsT^2) ((s^2)+(MsT^2) (s+6 t))+(meta^2) (2 (metaP^4) (MsT^2)+2 (metaP^2) (4 (MsT^4)-2 (MsT^2) s+(s^2))-3 (MsT^2) ((s^2)+(MsT^2) (s+6 t))))-gT (2 (meta^6) ((MsT^2)-s)-(meta^4) ((MsT^2)-s) (4 (metaP^2)-4 (MsT^2)+s)+s ((metaP^4) (-(MsT^2)+s)+2 s ((MsT^4)-(s^2))+(metaP^2) (-2 (MsT^4)+(MsT^2) s+(s^2)))+(meta^2) (2 (metaP^4) ((MsT^2)-s)+(metaP^2) (4 (MsT^4)-2 (MsT^2) s-2 (s^2))+3 s (-2 (MsT^4)+(MsT^2) s+(s^2)))) βT+(2 (meta^2)-s) ((meta^2)+(metaP^2)-s) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))+(1/((MsT^2)-t))((Sqrt[2]) ((Cθ)^4)-5 ((Cθ)^3) Sθ+3 (Sqrt[2]) ((Cθ)^2) ((Sθ)^2)+2 Cθ ((Sθ)^3)-2 (Sqrt[2]) ((Sθ)^4)) ((gT^2) (2 (meta^6) (MsT^2)+6 (MsT^4) (s^2)+6 (MsT^4) s t+(metaP^4) (2 (MsT^2)-t) t+(MsT^4) (t^2)-(MsT^2) (t^3)+(t^4)-(meta^4) (4 (metaP^2) (MsT^2)-8 (MsT^4)-2 (MsT^2) t+(t^2))-(metaP^2) (MsT^2) ((t^2)+(MsT^2) (6 s+t))+(meta^2) (2 (metaP^4) (MsT^2)+2 (metaP^2) (4 (MsT^4)-2 (MsT^2) t+(t^2))-3 (MsT^2) ((t^2)+(MsT^2) (6 s+t))))-gT (2 (meta^6) ((MsT^2)-t)-(meta^4) ((MsT^2)-t) (4 (metaP^2)-4 (MsT^2)+t)+t ((metaP^4) (-(MsT^2)+t)+2 t ((MsT^4)-(t^2))+(metaP^2) (-2 (MsT^4)+(MsT^2) t+(t^2)))+(meta^2) (2 (metaP^4) ((MsT^2)-t)+(metaP^2) (4 (MsT^4)-2 (MsT^2) t-2 (t^2))+3 t (-2 (MsT^4)+(MsT^2) t+(t^2)))) βT+(2 (meta^2)-t) ((meta^2)+(metaP^2)-t) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2))-(1/((MsT^2)-t))2 (2 (Sqrt[2]) ((Cθ)^4)+2 ((Cθ)^3) Sθ-3 (Sqrt[2]) ((Cθ)^2) ((Sθ)^2)-5 Cθ ((Sθ)^3)-(Sqrt[2]) ((Sθ)^4)) ((gT^2) (2 (meta^6) (MsT^2)+6 (MsT^4) (s^2)+6 (MsT^4) s t+(metaP^4) (2 (MsT^2)-t) t+(MsT^4) (t^2)-(MsT^2) (t^3)+(t^4)-(meta^4) (4 (metaP^2) (MsT^2)-8 (MsT^4)-2 (MsT^2) t+(t^2))-(metaP^2) (MsT^2) ((t^2)+(MsT^2) (6 s+t))+(meta^2) (2 (metaP^4) (MsT^2)+2 (metaP^2) (4 (MsT^4)-2 (MsT^2) t+(t^2))-3 (MsT^2) ((t^2)+(MsT^2) (6 s+t))))-gT (2 (meta^6) ((MsT^2)-t)-(meta^4) ((MsT^2)-t) (4 (metaP^2)-4 (MsT^2)+t)+t ((metaP^4) (-(MsT^2)+t)+2 t ((MsT^4)-(t^2))+(metaP^2) (-2 (MsT^4)+(MsT^2) t+(t^2)))+(meta^2) (2 (metaP^4) ((MsT^2)-t)+(metaP^2) (4 (MsT^4)-2 (MsT^2) t-2 (t^2))+3 t (-2 (MsT^4)+(MsT^2) t+(t^2)))) βT+(2 (meta^2)-t) ((meta^2)+(metaP^2)-t) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2))+(1/(-3 (meta^2)-(metaP^2)+(MsT^2)+s+t))((Sqrt[2]) ((Cθ)^4)-5 ((Cθ)^3) Sθ+3 (Sqrt[2]) ((Cθ)^2) ((Sθ)^2)+2 Cθ ((Sθ)^3)-2 (Sqrt[2]) ((Sθ)^4)) ((gT^2) (72 (meta^8)+(MsT^4) (s^2)+(MsT^2) (s^3)+(s^4)-4 (MsT^4) s t+3 (MsT^2) (s^2) t+4 (s^3) t+(MsT^4) (t^2)+3 (MsT^2) s (t^2)+6 (s^2) (t^2)+(MsT^2) (t^3)+4 s (t^3)+(t^4)-2 (metaP^6) (s+t)+2 (meta^6) (60 (metaP^2)-23 (MsT^2)-51 (s+t))-(metaP^2) (s+t) ((((MsT^2)+2 (s+t)))^2)+(metaP^4) (s+t) (3 (MsT^2)+5 (s+t))+(meta^4) (56 (metaP^4)+8 (MsT^4)+43 (MsT^2) (s+t)+53 (((s+t))^2)-2 (metaP^2) (34 (MsT^2)+59 (s+t)))+(meta^2) (8 (metaP^6)-3 (s+t) ((((MsT^2)+2 (s+t)))^2)-2 (metaP^4) (7 (MsT^2)+17 (s+t))+(metaP^2) (8 (MsT^4)+34 (MsT^2) (s+t)+38 (((s+t))^2))))-gT (-78 (meta^8)+(meta^6) (-110 (metaP^2)+14 (MsT^2)+131 (s+t))-(meta^4) (58 (metaP^4)-4 (MsT^4)+13 (MsT^2) (s+t)+80 (((s+t))^2)-3 (metaP^2) (4 (MsT^2)+47 (s+t)))+(meta^2) (-10 (metaP^6)+(metaP^4) (6 (MsT^2)+45 (s+t))+2 (metaP^2) (2 (MsT^4)-5 (MsT^2) (s+t)-28 (((s+t))^2))+3 (s+t) (-2 (MsT^4)+(MsT^2) (s+t)+7 (((s+t))^2)))+(s+t) (3 (metaP^6)-(metaP^4) ((MsT^2)+8 (s+t))+(metaP^2) (-2 (MsT^4)+(MsT^2) (s+t)+7 (((s+t))^2))+2 ((MsT^4) (s+t)-(((s+t))^3)))) βT+(-2 (meta^2)+s+t) (-(meta^2)-(metaP^2)+s+t) (-2 (MsT^4)+(MsT^2) (3 (meta^2)+(metaP^2)-s-t)+(((-3 (meta^2)-(metaP^2)+s+t))^2)) ((βT)^2))-(1/(-3 (meta^2)-(metaP^2)+(MsT^2)+s+t))2 (2 (Sqrt[2]) ((Cθ)^4)+2 ((Cθ)^3) Sθ-3 (Sqrt[2]) ((Cθ)^2) ((Sθ)^2)-5 Cθ ((Sθ)^3)-(Sqrt[2]) ((Sθ)^4)) ((gT^2) (72 (meta^8)+(MsT^4) (s^2)+(MsT^2) (s^3)+(s^4)-4 (MsT^4) s t+3 (MsT^2) (s^2) t+4 (s^3) t+(MsT^4) (t^2)+3 (MsT^2) s (t^2)+6 (s^2) (t^2)+(MsT^2) (t^3)+4 s (t^3)+(t^4)-2 (metaP^6) (s+t)+2 (meta^6) (60 (metaP^2)-23 (MsT^2)-51 (s+t))-(metaP^2) (s+t) ((((MsT^2)+2 (s+t)))^2)+(metaP^4) (s+t) (3 (MsT^2)+5 (s+t))+(meta^4) (56 (metaP^4)+8 (MsT^4)+43 (MsT^2) (s+t)+53 (((s+t))^2)-2 (metaP^2) (34 (MsT^2)+59 (s+t)))+(meta^2) (8 (metaP^6)-3 (s+t) ((((MsT^2)+2 (s+t)))^2)-2 (metaP^4) (7 (MsT^2)+17 (s+t))+(metaP^2) (8 (MsT^4)+34 (MsT^2) (s+t)+38 (((s+t))^2))))-gT (-78 (meta^8)+(meta^6) (-110 (metaP^2)+14 (MsT^2)+131 (s+t))-(meta^4) (58 (metaP^4)-4 (MsT^4)+13 (MsT^2) (s+t)+80 (((s+t))^2)-3 (metaP^2) (4 (MsT^2)+47 (s+t)))+(meta^2) (-10 (metaP^6)+(metaP^4) (6 (MsT^2)+45 (s+t))+2 (metaP^2) (2 (MsT^4)-5 (MsT^2) (s+t)-28 (((s+t))^2))+3 (s+t) (-2 (MsT^4)+(MsT^2) (s+t)+7 (((s+t))^2)))+(s+t) (3 (metaP^6)-(metaP^4) ((MsT^2)+8 (s+t))+(metaP^2) (-2 (MsT^4)+(MsT^2) (s+t)+7 (((s+t))^2))+2 ((MsT^4) (s+t)-(((s+t))^3)))) βT+(-2 (meta^2)+s+t) (-(meta^2)-(metaP^2)+s+t) (-2 (MsT^4)+(MsT^2) (3 (meta^2)+(metaP^2)-s-t)+(((-3 (meta^2)-(metaP^2)+s+t))^2)) ((βT)^2))) ;


  f11TensorSD[s_,t_]:= ((2 Cθ ((Sqrt[2]) ((Cθ)^3)+12 ((Cθ)^2) Sθ-3 (Sqrt[2]) Cθ ((Sθ)^2)-4 ((Sθ)^3)) (3 (meta^4)+(s^2)+3 (meta^2) ((metaP^2)-s-t)+s t+(t^2)-(metaP^2) (s+t)) β13SD)/(Fpi^4))+((24 Cθ Sθ (((Cθ)^2)+((Sθ)^2)) (3 (meta^4)+(s^2)+3 (meta^2) ((metaP^2)-s-t)+s t+(t^2)-(metaP^2) (s+t)) β14SD)/(Fpi^4))+((24 Cθ Sθ (((Cθ)^2)+((Sθ)^2)) (3 (meta^4)+(s^2)+3 (meta^2) ((metaP^2)-s-t)+s t+(t^2)-(metaP^2) (s+t)) β15SD)/(Fpi^4))-((144 Cθ ((Sθ)^3) (3 (meta^4)+(s^2)+3 (meta^2) ((metaP^2)-s-t)+s t+(t^2)-(metaP^2) (s+t)) β16SD)/(Fpi^4))-((8 Cθ ((Sqrt[2]) ((Cθ)^3)+3 ((Cθ)^2) Sθ-3 (Sqrt[2]) Cθ ((Sθ)^2)-4 ((Sθ)^3)) (3 (meta^4)+(s^2)+3 (meta^2) ((metaP^2)-s-t)+s t+(t^2)-(metaP^2) (s+t)) β3SD)/(3 (Fpi^4))) ;

η η -> η' η'

f12PsR[s_,t_]:=-(1/(9 (Fpi^4) (MpR1^2)))16 (dmt^2) (2 ((Cθ)^4) (16 (mk^4)-14 (mk^2) (mpi^2)+7 (mpi^4))+(Sqrt[2]) ((Cθ)^3) (-32 (mk^4)+46 (mk^2) (mpi^2)-23 (mpi^4)) Sθ-12 ((Cθ)^2) (4 (mk^4)-2 (mk^2) (mpi^2)+(mpi^4)) ((Sθ)^2)+(Sqrt[2]) Cθ (32 (mk^4)-46 (mk^2) (mpi^2)+23 (mpi^4)) ((Sθ)^3)+2 (16 (mk^4)-14 (mk^2) (mpi^2)+7 (mpi^4)) ((Sθ)^4))-(1/(27 (Fpi^4) (MpR8^2)))8 (dm^2) (2 ((Cθ)^4) (52 (mk^4)-68 (mk^2) (mpi^2)+25 (mpi^4))-4 (Sqrt[2]) ((Cθ)^3) (26 (mk^4)-25 (mk^2) (mpi^2)+8 (mpi^4)) Sθ-3 ((Cθ)^2) (52 (mk^4)-80 (mk^2) (mpi^2)+31 (mpi^4)) ((Sθ)^2)+4 (Sqrt[2]) Cθ (26 (mk^4)-25 (mk^2) (mpi^2)+8 (mpi^4)) ((Sθ)^3)+2 (52 (mk^4)-68 (mk^2) (mpi^2)+25 (mpi^4)) ((Sθ)^4)) ;

  f12δL8[s_,t_]:=  ((16 (28 (mk^4)-32 (mk^2) (mpi^2)+13 (mpi^4)) (2 ((Cθ)^4)-2 (Sqrt[2]) ((Cθ)^3) Sθ-3 ((Cθ)^2) ((Sθ)^2)+2 (Sqrt[2]) Cθ ((Sθ)^3)+2 ((Sθ)^4)) δL8)/(9 (Fpi^4)));

  f12TensorResonance[s_,t_]:=  (1/(9 (Fpi^4) (MsT^4)))4 (2 ((Cθ)^4)-2 (Sqrt[2]) ((Cθ)^3) Sθ-3 ((Cθ)^2) ((Sθ)^2)+2 (Sqrt[2]) Cθ ((Sθ)^3)+2 ((Sθ)^4)) ((1/((MsT^2)-s))((gT^2) (6 (meta^4) (MsT^4)+6 (metaP^4) (MsT^4)+(MsT^4) (s^2)-(MsT^2) (s^3)+(s^4)+6 (MsT^4) s t+6 (MsT^4) (t^2)-2 (metaP^2) (MsT^2) ((s^2)+(MsT^2) (s+6 t))+2 (meta^2) (2 (metaP^2) (MsT^4)-(MsT^2) ((s^2)+(MsT^2) (s+6 t))))-2 gT ((MsT^2)-s) (s (s ((MsT^2)+s)-(metaP^2) (2 (MsT^2)+s))+(meta^2) (4 (metaP^2) (MsT^2)-s (2 (MsT^2)+s))) βT-(2 (meta^2)-s) (-2 (metaP^2)+s) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))+(1/((MsT^2)-t))((gT^2) ((meta^8)+(metaP^8)-4 (metaP^6) (MsT^2)-4 (meta^6) ((metaP^2)+(MsT^2))+6 (MsT^4) (s^2)+6 (MsT^4) s t+(MsT^4) (t^2)-(MsT^2) (t^3)+(t^4)-2 (metaP^2) (MsT^2) ((t^2)+(MsT^2) (6 s+t))+(metaP^4) ((MsT^4)-2 (t^2)+(MsT^2) (6 s+7 t))+(meta^4) (6 (metaP^4)+4 (metaP^2) (MsT^2)+(MsT^4)-2 (t^2)+(MsT^2) (6 s+7 t))-2 (meta^2) (2 (metaP^6)-2 (metaP^4) (MsT^2)+(MsT^2) ((t^2)+(MsT^2) (6 s+t))+(metaP^2) (-7 (MsT^4)-2 (t^2)+(MsT^2) (6 s+7 t))))-2 gT ((meta^2)+(metaP^2)-t) ((meta^4) ((MsT^2)-t)+(metaP^4) ((MsT^2)-t)-(meta^2) (2 (metaP^2)-(MsT^2)) ((MsT^2)-t)-(MsT^4) t+(t^3)+(metaP^2) ((MsT^4)-(MsT^2) t)) βT+((((meta^2)+(metaP^2)-t))^2) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2))+(1/(-2 (meta^2)-2 (metaP^2)+(MsT^2)+s+t))((gT^2) (9 (meta^8)+9 (metaP^8)+(MsT^4) (s^2)+(MsT^2) (s^3)+(s^4)-4 (MsT^4) s t+3 (MsT^2) (s^2) t+4 (s^3) t+(MsT^4) (t^2)+3 (MsT^2) s (t^2)+6 (s^2) (t^2)+(MsT^2) (t^3)+4 s (t^3)+(t^4)+6 (meta^6) (10 (metaP^2)-(MsT^2)-4 (s+t))-2 (metaP^2) (s+t) ((((MsT^2)+2 (s+t)))^2)-6 (metaP^6) ((MsT^2)+4 (s+t))+(metaP^4) ((MsT^4)+22 (((s+t))^2)+(MsT^2) (19 s+13 t))+(meta^4) (118 (metaP^4)+(MsT^4)+22 (((s+t))^2)+(MsT^2) (19 s+13 t)-2 (metaP^2) (29 (MsT^2)+52 (s+t)))+2 (meta^2) (30 (metaP^6)-(s+t) ((((MsT^2)+2 (s+t)))^2)-(metaP^4) (29 (MsT^2)+52 (s+t))+(metaP^2) (7 (MsT^4)+26 (((s+t))^2)+3 (MsT^2) (7 s+9 t))))-2 gT (-(meta^2)-(metaP^2)+s+t) (-(MsT^4) (2 (meta^2)+2 (metaP^2)-s-t)-(((-2 (meta^2)-2 (metaP^2)+s+t))^3)+(meta^4) (-2 (meta^2)-2 (metaP^2)+(MsT^2)+s+t)+(metaP^4) (-2 (meta^2)-2 (metaP^2)+(MsT^2)+s+t)+(metaP^2) (MsT^2) (-2 (meta^2)-2 (metaP^2)+(MsT^2)+s+t)-(meta^2) (2 (metaP^2)-(MsT^2)) (-2 (meta^2)-2 (metaP^2)+(MsT^2)+s+t)) βT+((((meta^2)+(metaP^2)-s-t))^2) (-2 (MsT^4)+(MsT^2) (2 (meta^2)+2 (metaP^2)-s-t)+(((-2 (meta^2)-2 (metaP^2)+s+t))^2)) ((βT)^2)));


  f12TensorSD[s_,t_]:=  -((8 (2 (meta^2)-s) (-2 (metaP^2)+s) (((((Cθ)^2)+((Sθ)^2)))^2) β1SD)/(Fpi^4))-((4 (2 ((Cθ)^2)-(Sqrt[2]) Cθ Sθ-2 ((Sθ)^2)) (((Cθ)^2)-((Sθ)^2)) ((meta^4)+(metaP^4)+(s^2)+s t+(t^2)-2 (metaP^2) (s+t)+(meta^2) (4 (metaP^2)-2 (s+t))) β13SD)/(Fpi^4))+((12 (2 (meta^2)-s) (-2 (metaP^2)+s) (((((Cθ)^2)+((Sθ)^2)))^2) β14SD)/(Fpi^4))-((6 (((((Cθ)^2)+((Sθ)^2)))^2) (2 (meta^4)+2 (metaP^4)+(s^2)+2 s t+2 (t^2)-2 (metaP^2) (s+2 t)+(meta^2) (4 (metaP^2)-2 (s+2 t))) β15SD)/(Fpi^4))+((144 ((Cθ)^2) ((Sθ)^2) ((meta^4)+(metaP^4)+(s^2)+s t+(t^2)-2 (metaP^2) (s+t)+(meta^2) (4 (metaP^2)-2 (s+t))) β16SD)/(Fpi^4))+((4 (((((Cθ)^2)+((Sθ)^2)))^2) (2 (meta^4)+2 (metaP^4)+(s^2)+2 s t+2 (t^2)-2 (metaP^2) (s+2 t)+(meta^2) (4 (metaP^2)-2 (s+2 t))) β2SD)/(Fpi^4))+((8 (2 ((Cθ)^4)-2 (Sqrt[2]) ((Cθ)^3) Sθ-3 ((Cθ)^2) ((Sθ)^2)+2 (Sqrt[2]) Cθ ((Sθ)^3)+2 ((Sθ)^4)) ((meta^4)+(metaP^4)+(s^2)+s t+(t^2)-2 (metaP^2) (s+t)+(meta^2) (4 (metaP^2)-2 (s+t))) β3SD)/(3 (Fpi^4)));

η η' -> η' η'

f13PsR[s_,t_]:= (1/(9 (Fpi^4) (MpR1^2)))8 (dmt^2) (16 (Sqrt[2]) ((Cθ)^4) (2 (mk^4)-(mk^2) (mpi^2)-(mpi^4))-4 ((Cθ)^3) (40 (mk^4)-50 (mk^2) (mpi^2)+19 (mpi^4)) Sθ+3 (Sqrt[2]) ((Cθ)^2) (32 (mk^4)-46 (mk^2) (mpi^2)+23 (mpi^4)) ((Sθ)^2)+4 Cθ (16 (mk^4)+10 (mk^2) (mpi^2)+(mpi^4)) ((Sθ)^3)+(Sqrt[2]) (-64 (mk^4)+62 (mk^2) (mpi^2)-7 (mpi^4)) ((Sθ)^4))+(1/(27 (Fpi^4) (MpR8^2)))8 (dm^2) (4 (Sqrt[2]) ((Cθ)^4) (13 (mk^4)-20 (mk^2) (mpi^2)+7 (mpi^4))-4 ((Cθ)^3) (65 (mk^4)-70 (mk^2) (mpi^2)+23 (mpi^4)) Sθ+6 (Sqrt[2]) ((Cθ)^2) (26 (mk^4)-25 (mk^2) (mpi^2)+8 (mpi^4)) ((Sθ)^2)+Cθ (104 (mk^4)-232 (mk^2) (mpi^2)+101 (mpi^4)) ((Sθ)^3)-2 (Sqrt[2]) (52 (mk^4)-65 (mk^2) (mpi^2)+22 (mpi^4)) ((Sθ)^4)) ;

  f13δL8[s_,t_]:=  -(1/(9 (Fpi^4)))16 (4 (Sqrt[2]) ((Cθ)^4) (7 (mk^4)-8 (mk^2) (mpi^2)+(mpi^4))-4 ((Cθ)^3) (35 (mk^4)-40 (mk^2) (mpi^2)+14 (mpi^4)) Sθ+3 (Sqrt[2]) ((Cθ)^2) (28 (mk^4)-32 (mk^2) (mpi^2)+13 (mpi^4)) ((Sθ)^2)+Cθ (56 (mk^4)-64 (mk^2) (mpi^2)+35 (mpi^4)) ((Sθ)^3)+(Sqrt[2]) (-56 (mk^4)+64 (mk^2) (mpi^2)-17 (mpi^4)) ((Sθ)^4)) δL8;

  f13TensorResonance[s_,t_]:=  (1/(27 (Fpi^4) (MsT^4)))4 (-(1/((MsT^2)-s))2 ((Sqrt[2]) ((Cθ)^4)-5 ((Cθ)^3) Sθ+3 (Sqrt[2]) ((Cθ)^2) ((Sθ)^2)+2 Cθ ((Sθ)^3)-2 (Sqrt[2]) ((Sθ)^4)) ((gT^2) (2 (metaP^6) (MsT^2)+(MsT^4) (s^2)-(MsT^2) (s^3)+(s^4)+(meta^4) (2 (metaP^2) (MsT^2)+(2 (MsT^2)-s) s)+(metaP^4) (8 (MsT^4)+2 (MsT^2) s-(s^2))+6 (MsT^4) s t+6 (MsT^4) (t^2)-3 (metaP^2) (MsT^2) ((s^2)+(MsT^2) (s+6 t))-(meta^2) (4 (metaP^4) (MsT^2)-2 (metaP^2) (4 (MsT^4)-2 (MsT^2) s+(s^2))+(MsT^2) ((s^2)+(MsT^2) (s+6 t))))-gT ((MsT^2)-s) ((meta^4) (2 (metaP^2)-s)-(meta^2) (4 (metaP^4)-2 (metaP^2) (2 (MsT^2)+s)+s (2 (MsT^2)+s))+((metaP^2)-s) (2 (metaP^4)-2 s ((MsT^2)+s)+(metaP^2) (4 (MsT^2)+s))) βT+((meta^2)+(metaP^2)-s) (2 (metaP^2)-s) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))+(1/((MsT^2)-s))(2 (Sqrt[2]) ((Cθ)^4)+2 ((Cθ)^3) Sθ-3 (Sqrt[2]) ((Cθ)^2) ((Sθ)^2)-5 Cθ ((Sθ)^3)-(Sqrt[2]) ((Sθ)^4)) ((gT^2) (2 (metaP^6) (MsT^2)+(MsT^4) (s^2)-(MsT^2) (s^3)+(s^4)+(meta^4) (2 (metaP^2) (MsT^2)+(2 (MsT^2)-s) s)+(metaP^4) (8 (MsT^4)+2 (MsT^2) s-(s^2))+6 (MsT^4) s t+6 (MsT^4) (t^2)-3 (metaP^2) (MsT^2) ((s^2)+(MsT^2) (s+6 t))-(meta^2) (4 (metaP^4) (MsT^2)-2 (metaP^2) (4 (MsT^4)-2 (MsT^2) s+(s^2))+(MsT^2) ((s^2)+(MsT^2) (s+6 t))))-gT ((MsT^2)-s) ((meta^4) (2 (metaP^2)-s)-(meta^2) (4 (metaP^4)-2 (metaP^2) (2 (MsT^2)+s)+s (2 (MsT^2)+s))+((metaP^2)-s) (2 (metaP^4)-2 s ((MsT^2)+s)+(metaP^2) (4 (MsT^2)+s))) βT+((meta^2)+(metaP^2)-s) (2 (metaP^2)-s) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))-(1/((MsT^2)-t))2 ((Sqrt[2]) ((Cθ)^4)-5 ((Cθ)^3) Sθ+3 (Sqrt[2]) ((Cθ)^2) ((Sθ)^2)+2 Cθ ((Sθ)^3)-2 (Sqrt[2]) ((Sθ)^4)) ((gT^2) (2 (metaP^6) (MsT^2)+6 (MsT^4) (s^2)+6 (MsT^4) s t+(MsT^4) (t^2)-(MsT^2) (t^3)+(t^4)+(meta^4) (2 (metaP^2) (MsT^2)+(2 (MsT^2)-t) t)+(metaP^4) (8 (MsT^4)+2 (MsT^2) t-(t^2))-3 (metaP^2) (MsT^2) ((t^2)+(MsT^2) (6 s+t))-(meta^2) (4 (metaP^4) (MsT^2)-2 (metaP^2) (4 (MsT^4)-2 (MsT^2) t+(t^2))+(MsT^2) ((t^2)+(MsT^2) (6 s+t))))-gT ((MsT^2)-t) ((meta^4) (2 (metaP^2)-t)-(meta^2) (4 (metaP^4)-2 (metaP^2) (2 (MsT^2)+t)+t (2 (MsT^2)+t))+((metaP^2)-t) (2 (metaP^4)-2 t ((MsT^2)+t)+(metaP^2) (4 (MsT^2)+t))) βT+((meta^2)+(metaP^2)-t) (2 (metaP^2)-t) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2))+(1/((MsT^2)-t))(2 (Sqrt[2]) ((Cθ)^4)+2 ((Cθ)^3) Sθ-3 (Sqrt[2]) ((Cθ)^2) ((Sθ)^2)-5 Cθ ((Sθ)^3)-(Sqrt[2]) ((Sθ)^4)) ((gT^2) (2 (metaP^6) (MsT^2)+6 (MsT^4) (s^2)+6 (MsT^4) s t+(MsT^4) (t^2)-(MsT^2) (t^3)+(t^4)+(meta^4) (2 (metaP^2) (MsT^2)+(2 (MsT^2)-t) t)+(metaP^4) (8 (MsT^4)+2 (MsT^2) t-(t^2))-3 (metaP^2) (MsT^2) ((t^2)+(MsT^2) (6 s+t))-(meta^2) (4 (metaP^4) (MsT^2)-2 (metaP^2) (4 (MsT^4)-2 (MsT^2) t+(t^2))+(MsT^2) ((t^2)+(MsT^2) (6 s+t))))-gT ((MsT^2)-t) ((meta^4) (2 (metaP^2)-t)-(meta^2) (4 (metaP^4)-2 (metaP^2) (2 (MsT^2)+t)+t (2 (MsT^2)+t))+((metaP^2)-t) (2 (metaP^4)-2 t ((MsT^2)+t)+(metaP^2) (4 (MsT^2)+t))) βT+((meta^2)+(metaP^2)-t) (2 (metaP^2)-t) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2))-(1/(-(meta^2)-3 (metaP^2)+(MsT^2)+s+t))2 ((Sqrt[2]) ((Cθ)^4)-5 ((Cθ)^3) Sθ+3 (Sqrt[2]) ((Cθ)^2) ((Sθ)^2)+2 Cθ ((Sθ)^3)-2 (Sqrt[2]) ((Sθ)^4)) ((gT^2) (72 (metaP^8)+(MsT^4) (s^2)+(MsT^2) (s^3)+(s^4)-4 (MsT^4) s t+3 (MsT^2) (s^2) t+4 (s^3) t+(MsT^4) (t^2)+3 (MsT^2) s (t^2)+6 (s^2) (t^2)+(MsT^2) (t^3)+4 s (t^3)+(t^4)+(meta^6) (8 (metaP^2)-2 (s+t))-3 (metaP^2) (s+t) ((((MsT^2)+2 (s+t)))^2)-2 (metaP^6) (23 (MsT^2)+51 (s+t))+(metaP^4) (8 (MsT^4)+43 (MsT^2) (s+t)+53 (((s+t))^2))+(meta^4) (56 (metaP^4)+(s+t) (3 (MsT^2)+5 (s+t))-2 (metaP^2) (7 (MsT^2)+17 (s+t)))+(meta^2) (120 (metaP^6)-(s+t) ((((MsT^2)+2 (s+t)))^2)-2 (metaP^4) (34 (MsT^2)+59 (s+t))+(metaP^2) (8 (MsT^4)+34 (MsT^2) (s+t)+38 (((s+t))^2))))-gT (-(meta^2)-3 (metaP^2)+(MsT^2)+s+t) ((meta^4) (10 (metaP^2)-3 (s+t))+(2 (metaP^2)-s-t) (13 (metaP^4)-2 ((MsT^2)-s-t) (s+t)+(metaP^2) (2 (MsT^2)-11 (s+t)))+(meta^2) (28 (metaP^4)+(metaP^2) (4 (MsT^2)-26 (s+t))+(s+t) (-2 (MsT^2)+5 (s+t)))) βT+(-2 (metaP^2)+s+t) (-(meta^2)-(metaP^2)+s+t) (-2 (MsT^4)+(MsT^2) ((meta^2)+3 (metaP^2)-s-t)+(((-(meta^2)-3 (metaP^2)+s+t))^2)) ((βT)^2))+(1/(-(meta^2)-3 (metaP^2)+(MsT^2)+s+t))(2 (Sqrt[2]) ((Cθ)^4)+2 ((Cθ)^3) Sθ-3 (Sqrt[2]) ((Cθ)^2) ((Sθ)^2)-5 Cθ ((Sθ)^3)-(Sqrt[2]) ((Sθ)^4)) ((gT^2) (72 (metaP^8)+(MsT^4) (s^2)+(MsT^2) (s^3)+(s^4)-4 (MsT^4) s t+3 (MsT^2) (s^2) t+4 (s^3) t+(MsT^4) (t^2)+3 (MsT^2) s (t^2)+6 (s^2) (t^2)+(MsT^2) (t^3)+4 s (t^3)+(t^4)+(meta^6) (8 (metaP^2)-2 (s+t))-3 (metaP^2) (s+t) ((((MsT^2)+2 (s+t)))^2)-2 (metaP^6) (23 (MsT^2)+51 (s+t))+(metaP^4) (8 (MsT^4)+43 (MsT^2) (s+t)+53 (((s+t))^2))+(meta^4) (56 (metaP^4)+(s+t) (3 (MsT^2)+5 (s+t))-2 (metaP^2) (7 (MsT^2)+17 (s+t)))+(meta^2) (120 (metaP^6)-(s+t) ((((MsT^2)+2 (s+t)))^2)-2 (metaP^4) (34 (MsT^2)+59 (s+t))+(metaP^2) (8 (MsT^4)+34 (MsT^2) (s+t)+38 (((s+t))^2))))-gT (-(meta^2)-3 (metaP^2)+(MsT^2)+s+t) ((meta^4) (10 (metaP^2)-3 (s+t))+(2 (metaP^2)-s-t) (13 (metaP^4)-2 ((MsT^2)-s-t) (s+t)+(metaP^2) (2 (MsT^2)-11 (s+t)))+(meta^2) (28 (metaP^4)+(metaP^2) (4 (MsT^2)-26 (s+t))+(s+t) (-2 (MsT^2)+5 (s+t)))) βT+(-2 (metaP^2)+s+t) (-(meta^2)-(metaP^2)+s+t) (-2 (MsT^4)+(MsT^2) ((meta^2)+3 (metaP^2)-s-t)+(((-(meta^2)-3 (metaP^2)+s+t))^2)) ((βT)^2)));


  f13TensorSD[s_,t_]:=  -((2 Sθ (4 ((Cθ)^3)-3 (Sqrt[2]) ((Cθ)^2) Sθ-12 Cθ ((Sθ)^2)+(Sqrt[2]) ((Sθ)^3)) (3 (metaP^4)+(s^2)+(meta^2) (3 (metaP^2)-s-t)+s t+(t^2)-3 (metaP^2) (s+t)) β13SD)/(Fpi^4))+((24 Cθ Sθ (((Cθ)^2)+((Sθ)^2)) (3 (metaP^4)+(s^2)+(meta^2) (3 (metaP^2)-s-t)+s t+(t^2)-3 (metaP^2) (s+t)) β14SD)/(Fpi^4))+((24 Cθ Sθ (((Cθ)^2)+((Sθ)^2)) (3 (metaP^4)+(s^2)+(meta^2) (3 (metaP^2)-s-t)+s t+(t^2)-3 (metaP^2) (s+t)) β15SD)/(Fpi^4))-((144 ((Cθ)^3) Sθ (3 (metaP^4)+(s^2)+(meta^2) (3 (metaP^2)-s-t)+s t+(t^2)-3 (metaP^2) (s+t)) β16SD)/(Fpi^4))+((8 Sθ (4 ((Cθ)^3)-3 (Sqrt[2]) ((Cθ)^2) Sθ-3 Cθ ((Sθ)^2)+(Sqrt[2]) ((Sθ)^3)) (3 (metaP^4)+(s^2)+(meta^2) (3 (metaP^2)-s-t)+s t+(t^2)-3 (metaP^2) (s+t)) β3SD)/(3 (Fpi^4)));

η' η' -> η' η'

f14PsR[s_,t_]:=-(1/(9 (Fpi^4) (MpR1^2)))32 (dmt^2) (2 ((Cθ)^4) (((2 (mk^2)+(mpi^2)))^2)+16 (Sqrt[2]) ((Cθ)^3) (-2 (mk^4)+(mk^2) (mpi^2)+(mpi^4)) Sθ+6 ((Cθ)^2) (16 (mk^4)-14 (mk^2) (mpi^2)+7 (mpi^4)) ((Sθ)^2)+(Sqrt[2]) Cθ (-64 (mk^4)+62 (mk^2) (mpi^2)-7 (mpi^4)) ((Sθ)^3)+4 (8 (mk^4)-13 (mk^2) (mpi^2)+5 (mpi^4)) ((Sθ)^4))-(1/(27 (Fpi^4) (MpR8^2)))8 (dm^2) (2 ((Cθ)^4) (26 (mk^4)-64 (mk^2) (mpi^2)+29 (mpi^4))-16 (Sqrt[2]) ((Cθ)^3) (13 (mk^4)-20 (mk^2) (mpi^2)+7 (mpi^4)) Sθ+12 ((Cθ)^2) (52 (mk^4)-68 (mk^2) (mpi^2)+25 (mpi^4)) ((Sθ)^2)-8 (Sqrt[2]) Cθ (52 (mk^4)-65 (mk^2) (mpi^2)+22 (mpi^4)) ((Sθ)^3)+(208 (mk^4)-176 (mk^2) (mpi^2)+49 (mpi^4)) ((Sθ)^4)) ;

  f14δL8[s_,t_]:= (1/(9 (Fpi^4)))16 (((Cθ)^4) (28 (mk^4)-32 (mk^2) (mpi^2)+22 (mpi^4))-16 (Sqrt[2]) ((Cθ)^3) (7 (mk^4)-8 (mk^2) (mpi^2)+(mpi^4)) Sθ+12 ((Cθ)^2) (28 (mk^4)-32 (mk^2) (mpi^2)+13 (mpi^4)) ((Sθ)^2)-4 (Sqrt[2]) Cθ (56 (mk^4)-64 (mk^2) (mpi^2)+17 (mpi^4)) ((Sθ)^3)+(112 (mk^4)-128 (mk^2) (mpi^2)+43 (mpi^4)) ((Sθ)^4)) δL8 ;

  f14TensorResonance[s_,t_]:= (1/(27 (Fpi^4) (MsT^4)))4 ((1/((MsT^2)-s))(4 ((Cθ)^4)+8 (Sqrt[2]) ((Cθ)^3) Sθ+12 ((Cθ)^2) ((Sθ)^2)+4 (Sqrt[2]) Cθ ((Sθ)^3)+((Sθ)^4)) ((gT^2) (16 (metaP^4) (MsT^4)-(MsT^2) (s^3)+(s^4)+(MsT^4) ((s^2)+6 s t+6 (t^2))-4 (metaP^2) (MsT^2) ((s^2)+(MsT^2) (s+6 t)))-2 gT (2 (metaP^2)-s) ((MsT^2)-s) (2 (metaP^2) (MsT^2)-s ((MsT^2)+s)) βT+(((-2 (metaP^2)+s))^2) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))+(1/((MsT^2)-s))2 (((Cθ)^4)-4 (Sqrt[2]) ((Cθ)^3) Sθ+12 ((Cθ)^2) ((Sθ)^2)-8 (Sqrt[2]) Cθ ((Sθ)^3)+4 ((Sθ)^4)) ((gT^2) (16 (metaP^4) (MsT^4)-(MsT^2) (s^3)+(s^4)+(MsT^4) ((s^2)+6 s t+6 (t^2))-4 (metaP^2) (MsT^2) ((s^2)+(MsT^2) (s+6 t)))-2 gT (2 (metaP^2)-s) ((MsT^2)-s) (2 (metaP^2) (MsT^2)-s ((MsT^2)+s)) βT+(((-2 (metaP^2)+s))^2) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))+(1/((MsT^2)-t))(4 ((Cθ)^4)+8 (Sqrt[2]) ((Cθ)^3) Sθ+12 ((Cθ)^2) ((Sθ)^2)+4 (Sqrt[2]) Cθ ((Sθ)^3)+((Sθ)^4)) ((gT^2) (16 (metaP^4) (MsT^4)-(MsT^2) (t^3)+(t^4)+(MsT^4) (6 (s^2)+6 s t+(t^2))-4 (metaP^2) (MsT^2) ((t^2)+(MsT^2) (6 s+t)))-2 gT (2 (metaP^2)-t) ((MsT^2)-t) (2 (metaP^2) (MsT^2)-t ((MsT^2)+t)) βT+(((-2 (metaP^2)+t))^2) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2))+(1/((MsT^2)-t))2 (((Cθ)^4)-4 (Sqrt[2]) ((Cθ)^3) Sθ+12 ((Cθ)^2) ((Sθ)^2)-8 (Sqrt[2]) Cθ ((Sθ)^3)+4 ((Sθ)^4)) ((gT^2) (16 (metaP^4) (MsT^4)-(MsT^2) (t^3)+(t^4)+(MsT^4) (6 (s^2)+6 s t+(t^2))-4 (metaP^2) (MsT^2) ((t^2)+(MsT^2) (6 s+t)))-2 gT (2 (metaP^2)-t) ((MsT^2)-t) (2 (metaP^2) (MsT^2)-t ((MsT^2)+t)) βT+(((-2 (metaP^2)+t))^2) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2))+(1/(-4 (metaP^2)+(MsT^2)+s+t))(4 ((Cθ)^4)+8 (Sqrt[2]) ((Cθ)^3) Sθ+12 ((Cθ)^2) ((Sθ)^2)+4 (Sqrt[2]) Cθ ((Sθ)^3)+((Sθ)^4)) ((gT^2) (16 (metaP^4) (MsT^4)+(MsT^2) (((-4 (metaP^2)+s+t))^3)+(((-4 (metaP^2)+s+t))^4)+(MsT^4) (16 (metaP^4)+(s^2)+8 (metaP^2) (2 s-t)-4 s t+(t^2))-4 (metaP^2) (MsT^2) ((MsT^2) (4 (metaP^2)+5 s-t)+(((-4 (metaP^2)+s+t))^2)))-2 gT (-2 (metaP^2)+s+t) (-4 (metaP^2)+(MsT^2)+s+t) (-16 (metaP^4)+((MsT^2)-s-t) (s+t)+(metaP^2) (-2 (MsT^2)+8 (s+t))) βT+(((-2 (metaP^2)+s+t))^2) (-2 (MsT^4)+(MsT^2) (4 (metaP^2)-s-t)+(((-4 (metaP^2)+s+t))^2)) ((βT)^2))+(1/(-4 (metaP^2)+(MsT^2)+s+t))2 (((Cθ)^4)-4 (Sqrt[2]) ((Cθ)^3) Sθ+12 ((Cθ)^2) ((Sθ)^2)-8 (Sqrt[2]) Cθ ((Sθ)^3)+4 ((Sθ)^4)) ((gT^2) (16 (metaP^4) (MsT^4)+(MsT^2) (((-4 (metaP^2)+s+t))^3)+(((-4 (metaP^2)+s+t))^4)+(MsT^4) (16 (metaP^4)+(s^2)+8 (metaP^2) (2 s-t)-4 s t+(t^2))-4 (metaP^2) (MsT^2) ((MsT^2) (4 (metaP^2)+5 s-t)+(((-4 (metaP^2)+s+t))^2)))-2 gT (-2 (metaP^2)+s+t) (-4 (metaP^2)+(MsT^2)+s+t) (-16 (metaP^4)+((MsT^2)-s-t) (s+t)+(metaP^2) (-2 (MsT^2)+8 (s+t))) βT+(((-2 (metaP^2)+s+t))^2) (-2 (MsT^4)+(MsT^2) (4 (metaP^2)-s-t)+(((-4 (metaP^2)+s+t))^2)) ((βT)^2))) ;


  f14TensorSD[s_,t_]:=((16 (((((Cθ)^2)+((Sθ)^2)))^2) (6 (metaP^4)+(s^2)+s t+(t^2)-4 (metaP^2) (s+t)) β1SD)/(Fpi^4))-((8 Cθ (2 ((Cθ)^3)+6 Cθ ((Sθ)^2)-(Sqrt[2]) ((Sθ)^3)) (6 (metaP^4)+(s^2)+s t+(t^2)-4 (metaP^2) (s+t)) β13SD)/(Fpi^4))-((48 ((Cθ)^2) (((Cθ)^2)+((Sθ)^2)) (6 (metaP^4)+(s^2)+s t+(t^2)-4 (metaP^2) (s+t)) β14SD)/(Fpi^4))-((48 ((Cθ)^2) (((Cθ)^2)+((Sθ)^2)) (6 (metaP^4)+(s^2)+s t+(t^2)-4 (metaP^2) (s+t)) β15SD)/(Fpi^4))+((144 ((Cθ)^4) (6 (metaP^4)+(s^2)+s t+(t^2)-4 (metaP^2) (s+t)) β16SD)/(Fpi^4))+((16 (((((Cθ)^2)+((Sθ)^2)))^2) (6 (metaP^4)+(s^2)+s t+(t^2)-4 (metaP^2) (s+t)) β2SD)/(Fpi^4))+((8 (2 ((Cθ)^4)+12 ((Cθ)^2) ((Sθ)^2)-4 (Sqrt[2]) Cθ ((Sθ)^3)+3 ((Sθ)^4)) (6 (metaP^4)+(s^2)+s t+(t^2)-4 (metaP^2) (s+t)) β3SD)/(3 (Fpi^4)))  ;

(SuperPlus[K])(π^0)->(SuperPlus[K]) η

f15PsR[s_,t_]:=((4 (dmt^2) (2 (mk^2)+(mpi^2)) (4 Cθ ((mk^2)-(mpi^2))+(Sqrt[2]) (2 (mk^2)+(mpi^2)) Sθ))/(3 (Sqrt[3]) (Fpi^4) (MpR1^2)))+((8 (dm^2) (Cθ (2 (mk^4)-(mk^2) (mpi^2)-(mpi^4))+(Sqrt[2]) ((mk^4)+10 (mk^2) (mpi^2)-2 (mpi^4)) Sθ))/(9 (Sqrt[3]) (Fpi^4) (MpR8^2)))  ;

  f15δL8[s_,t_]:=  -((8 (Cθ (4 (mk^4)-2 (mk^2) (mpi^2)-2 (mpi^4))+(Sqrt[2]) (2 (mk^4)+8 (mk^2) (mpi^2)-(mpi^4)) Sθ) δL8)/(3 (Sqrt[3]) (Fpi^4)));

  f15TensorResonance[s_,t_]:=  (1/(3 (Sqrt[3]) (Fpi^4) (MsT^4)))(-(1/((MsT^2)-s))(Cθ+2 (Sqrt[2]) Sθ) ((gT^2) ((mk^8)-2 (mk^6) ((mpi^2)+2 (MsT^2))+2 (mpi^4) (MsT^2) s-(mpi^2) (MsT^4) s-(mpi^4) (s^2)-(mpi^2) (MsT^2) (s^2)+(MsT^4) (s^2)-(MsT^2) (s^3)+(s^4)+(meta^4) ((mk^4)-2 (mk^2) ((mpi^2)-2 (MsT^2))+((mpi^2)-s) ((mpi^2)-2 (MsT^2)+s))-6 (mpi^2) (MsT^4) t+6 (MsT^4) s t+6 (MsT^4) (t^2)+(mk^4) ((mpi^4)+(MsT^4)-2 (s^2)+(MsT^2) (2 (mpi^2)+7 s+6 t))+(mk^2) (4 (mpi^4) (MsT^2)-2 (MsT^2) ((s^2)+(MsT^2) (s+6 t))+(mpi^2) (7 (MsT^4)+2 (s^2)-(MsT^2) (7 s+6 t)))-(meta^2) (2 (mk^6)-2 (mk^4) (2 (mpi^2)+(MsT^2))+(MsT^2) (2 (mpi^4)+(s^2)+(MsT^2) (s+6 t)-(mpi^2) ((MsT^2)+3 s+6 t))+(mk^2) (-7 (MsT^4)+2 ((mpi^4)-(s^2))+(MsT^2) (4 (mpi^2)+7 s+6 t))))-gT ((MsT^2)-s) ((meta^4) ((mk^2)+(mpi^2)-s)-(meta^2) ((mk^4)-2 (mk^2) (-2 (mpi^2)+(MsT^2)+s)-((mpi^2)-s) ((mpi^2)+2 (MsT^2)+s))+((mk^2)-s) (2 (mk^4)-(mk^2) ((mpi^2)-2 (MsT^2))+((mpi^2)-s) ((mpi^2)+2 ((MsT^2)+s)))) βT+((meta^2)+(mk^2)-s) ((mk^2)+(mpi^2)-s) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))-(1/(-(meta^2)-2 (mk^2)-(mpi^2)+(MsT^2)+s+t))(Cθ+2 (Sqrt[2]) Sθ) ((gT^2) ((mk^8)-2 (mk^6) ((mpi^2)-4 (MsT^2))-6 (mpi^2) (MsT^4) s+6 (MsT^4) (s^2)-(meta^2) (2 (mk^6)+4 (mk^4) (-(mpi^2)+(MsT^2))+(mk^2) (-7 (MsT^4)+2 ((mpi^4)-((((meta^2)+2 (mk^2)+(mpi^2)-s-t))^2))+(MsT^2) ((meta^2)+2 (mk^2)+5 (mpi^2)-7 s-t))+(MsT^2) (-4 (mpi^4)+((((meta^2)+2 (mk^2)+(mpi^2)-s-t))^2)+3 (mpi^2) ((meta^2)+2 (mk^2)+(mpi^2)+s-t)+(MsT^2) ((meta^2)+2 (mk^2)+5 s-t)))+(mk^4) ((mpi^4)+(MsT^4)+(MsT^2) ((meta^2)+2 (mk^2)-3 (mpi^2)-7 s-t)-2 ((((meta^2)+2 (mk^2)+(mpi^2)-s-t))^2))+(meta^4) ((mk^4)+(mpi^4)-2 (mk^2) ((mpi^2)+(MsT^2))-((((meta^2)+2 (mk^2)+(mpi^2)-s-t))^2)+2 (MsT^2) ((meta^2)+2 (mk^2)+3 (mpi^2)-s-t))+2 (mpi^4) (MsT^2) ((meta^2)+2 (mk^2)+(mpi^2)-s-t)-(mpi^2) (MsT^4) ((meta^2)+2 (mk^2)+(mpi^2)-s-t)+6 (MsT^4) s ((meta^2)+2 (mk^2)+(mpi^2)-s-t)-(mpi^4) ((((meta^2)+2 (mk^2)+(mpi^2)-s-t))^2)-(mpi^2) (MsT^2) ((((meta^2)+2 (mk^2)+(mpi^2)-s-t))^2)+(MsT^4) ((((meta^2)+2 (mk^2)+(mpi^2)-s-t))^2)-(MsT^2) ((((meta^2)+2 (mk^2)+(mpi^2)-s-t))^3)+((((meta^2)+2 (mk^2)+(mpi^2)-s-t))^4)+(mk^2) (-(MsT^2) (2 (mpi^4)+(mpi^2) ((meta^2)+2 (mk^2)+(mpi^2)-7 s-t)+2 ((((meta^2)+2 (mk^2)+(mpi^2)-s-t))^2))+2 (mpi^2) ((((meta^2)+2 (mk^2)+(mpi^2)-s-t))^2)+(MsT^4) (-2 (meta^2)-4 (mk^2)+5 (mpi^2)-10 s+2 t)))-gT (-(meta^2)-2 (mk^2)-(mpi^2)+(MsT^2)+s+t) ((meta^4) (-(meta^2)-(mk^2)+s+t)-(meta^2) ((meta^4)+(mk^4)+2 (meta^2) ((mk^2)+(mpi^2)+(MsT^2)-s-t)+2 (mk^2) (3 (mpi^2)+(MsT^2)-s-t)-(2 (mpi^2)+2 (MsT^2)-s-t) (s+t))+(-(meta^2)-(mk^2)-(mpi^2)+s+t) (2 (mk^4)-(mk^2) ((mpi^2)-2 (MsT^2))+(2 (meta^2)+4 (mk^2)+3 (mpi^2)+2 (MsT^2)-2 s-2 t) (-(meta^2)-2 (mk^2)+s+t))) βT+(-2 (MsT^4)+(MsT^2) ((meta^2)+2 (mk^2)+(mpi^2)-s-t)+((((meta^2)+2 (mk^2)+(mpi^2)-s-t))^2)) (-(meta^2)-(mk^2)+s+t) (-(mk^2)-(mpi^2)+s+t) ((βT)^2))+(1/((MsT^2)-t))2 (Cθ-(Sqrt[2]) Sθ) ((gT^2) ((t^2) (-(meta^4)+2 (meta^2) (mpi^2)-(mpi^4)+(t^2))+(MsT^4) (6 (mk^4)-6 (mpi^2) s+6 (s^2)+2 (mk^2) ((mpi^2)-6 s-t)+(meta^2) (2 (mk^2)+6 (mpi^2)-6 s-t)-(mpi^2) t+6 s t+(t^2))+(MsT^2) (2 (meta^4) ((mk^2)+t)+((mpi^2)-t) (2 (mk^2) ((mpi^2)+t)+t (2 (mpi^2)+t))-(meta^2) (4 (mk^2) (mpi^2)+t (4 (mpi^2)+t))))-gT ((MsT^2)-t) ((meta^4) (2 (mk^2)-t)-(meta^2) (4 (mk^2) ((mpi^2)-(MsT^2))+t (-2 (mpi^2)+2 (MsT^2)+t))+((mpi^2)-t) (2 (mk^2) ((mpi^2)+2 (MsT^2)+t)-t ((mpi^2)+2 ((MsT^2)+t)))) βT-(2 (mk^2)-t) (-(meta^2)-(mpi^2)+t) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2)));


  f15TensorSD[s_,t_]:=  (((Sqrt[6]) Sθ ((mk^4)-(mpi^2) s+(s^2)+2 (mk^2) ((mpi^2)-s-t)+(meta^2) (2 (mk^2)+(mpi^2)-s-t)-(mpi^2) t+s t+(t^2)) β13SD)/(Fpi^4))-(1/((Sqrt[3]) (Fpi^4)))(4 (Sqrt[2]) Sθ ((mk^4)-(mpi^2) s+(s^2)+2 (mk^2) ((mpi^2)-s-t)+(meta^2) (2 (mk^2)+(mpi^2)-s-t)-(mpi^2) t+s t+(t^2))+Cθ (2 (mk^4)-2 (mpi^2) s+2 (s^2)-2 (mk^2) ((mpi^2)+2 s-t)+(mpi^2) t+2 s t-(t^2)+(meta^2) (-2 (mk^2)+2 (mpi^2)-2 s+t))) β3SD;

(SuperPlus[K])(π^0)->(SuperPlus[K]) η'

f16PsR[s_,t_]:= -((4 (dmt^2) (2 (mk^2)+(mpi^2)) ((Sqrt[2]) Cθ (2 (mk^2)+(mpi^2))+4 (-(mk^2)+(mpi^2)) Sθ))/(3 (Sqrt[3]) (Fpi^4) (MpR1^2)))-((8 (dm^2) ((Sqrt[2]) Cθ ((mk^4)+10 (mk^2) (mpi^2)-2 (mpi^4))+(-2 (mk^4)+(mk^2) (mpi^2)+(mpi^4)) Sθ))/(9 (Sqrt[3]) (Fpi^4) (MpR8^2)));

  f16δL8[s_,t_]:= ((8 ((Sqrt[2]) Cθ (2 (mk^4)+8 (mk^2) (mpi^2)-(mpi^4))+2 (-2 (mk^4)+(mk^2) (mpi^2)+(mpi^4)) Sθ) δL8)/(3 (Sqrt[3]) (Fpi^4))) ;

  f16TensorResonance[s_,t_]:=  (1/(3 (Sqrt[3]) (Fpi^4) (MsT^4)))((1/((MsT^2)-s))(2 (Sqrt[2]) Cθ-Sθ) ((gT^2) ((mk^8)-2 (mk^6) ((mpi^2)+2 (MsT^2))+2 (mpi^4) (MsT^2) s-(mpi^2) (MsT^4) s-(mpi^4) (s^2)-(mpi^2) (MsT^2) (s^2)+(MsT^4) (s^2)-(MsT^2) (s^3)+(s^4)+(metaP^4) ((mk^4)-2 (mk^2) ((mpi^2)-2 (MsT^2))+((mpi^2)-s) ((mpi^2)-2 (MsT^2)+s))-6 (mpi^2) (MsT^4) t+6 (MsT^4) s t+6 (MsT^4) (t^2)+(mk^4) ((mpi^4)+(MsT^4)-2 (s^2)+(MsT^2) (2 (mpi^2)+7 s+6 t))+(mk^2) (4 (mpi^4) (MsT^2)-2 (MsT^2) ((s^2)+(MsT^2) (s+6 t))+(mpi^2) (7 (MsT^4)+2 (s^2)-(MsT^2) (7 s+6 t)))-(metaP^2) (2 (mk^6)-2 (mk^4) (2 (mpi^2)+(MsT^2))+(MsT^2) (2 (mpi^4)+(s^2)+(MsT^2) (s+6 t)-(mpi^2) ((MsT^2)+3 s+6 t))+(mk^2) (-7 (MsT^4)+2 ((mpi^4)-(s^2))+(MsT^2) (4 (mpi^2)+7 s+6 t))))-gT ((MsT^2)-s) ((metaP^4) ((mk^2)+(mpi^2)-s)-(metaP^2) ((mk^4)-2 (mk^2) (-2 (mpi^2)+(MsT^2)+s)-((mpi^2)-s) ((mpi^2)+2 (MsT^2)+s))+((mk^2)-s) (2 (mk^4)-(mk^2) ((mpi^2)-2 (MsT^2))+((mpi^2)-s) ((mpi^2)+2 ((MsT^2)+s)))) βT+((metaP^2)+(mk^2)-s) ((mk^2)+(mpi^2)-s) (-2 (MsT^4)+(MsT^2) s+(s^2)) ((βT)^2))+(1/(-(metaP^2)-2 (mk^2)-(mpi^2)+(MsT^2)+s+t))(2 (Sqrt[2]) Cθ-Sθ) ((gT^2) ((mk^8)-2 (mk^6) ((mpi^2)-4 (MsT^2))-6 (mpi^2) (MsT^4) s+6 (MsT^4) (s^2)-(metaP^2) (2 (mk^6)+4 (mk^4) (-(mpi^2)+(MsT^2))+(mk^2) (-7 (MsT^4)+2 ((mpi^4)-((((metaP^2)+2 (mk^2)+(mpi^2)-s-t))^2))+(MsT^2) ((metaP^2)+2 (mk^2)+5 (mpi^2)-7 s-t))+(MsT^2) (-4 (mpi^4)+((((metaP^2)+2 (mk^2)+(mpi^2)-s-t))^2)+3 (mpi^2) ((metaP^2)+2 (mk^2)+(mpi^2)+s-t)+(MsT^2) ((metaP^2)+2 (mk^2)+5 s-t)))+(mk^4) ((mpi^4)+(MsT^4)+(MsT^2) ((metaP^2)+2 (mk^2)-3 (mpi^2)-7 s-t)-2 ((((metaP^2)+2 (mk^2)+(mpi^2)-s-t))^2))+(metaP^4) ((mk^4)+(mpi^4)-2 (mk^2) ((mpi^2)+(MsT^2))-((((metaP^2)+2 (mk^2)+(mpi^2)-s-t))^2)+2 (MsT^2) ((metaP^2)+2 (mk^2)+3 (mpi^2)-s-t))+2 (mpi^4) (MsT^2) ((metaP^2)+2 (mk^2)+(mpi^2)-s-t)-(mpi^2) (MsT^4) ((metaP^2)+2 (mk^2)+(mpi^2)-s-t)+6 (MsT^4) s ((metaP^2)+2 (mk^2)+(mpi^2)-s-t)-(mpi^4) ((((metaP^2)+2 (mk^2)+(mpi^2)-s-t))^2)-(mpi^2) (MsT^2) ((((metaP^2)+2 (mk^2)+(mpi^2)-s-t))^2)+(MsT^4) ((((metaP^2)+2 (mk^2)+(mpi^2)-s-t))^2)-(MsT^2) ((((metaP^2)+2 (mk^2)+(mpi^2)-s-t))^3)+((((metaP^2)+2 (mk^2)+(mpi^2)-s-t))^4)+(mk^2) (-(MsT^2) (2 (mpi^4)+(mpi^2) ((metaP^2)+2 (mk^2)+(mpi^2)-7 s-t)+2 ((((metaP^2)+2 (mk^2)+(mpi^2)-s-t))^2))+2 (mpi^2) ((((metaP^2)+2 (mk^2)+(mpi^2)-s-t))^2)+(MsT^4) (-2 (metaP^2)-4 (mk^2)+5 (mpi^2)-10 s+2 t)))-gT (-(metaP^2)-2 (mk^2)-(mpi^2)+(MsT^2)+s+t) ((metaP^4) (-(metaP^2)-(mk^2)+s+t)-(metaP^2) ((metaP^4)+(mk^4)+2 (metaP^2) ((mk^2)+(mpi^2)+(MsT^2)-s-t)+2 (mk^2) (3 (mpi^2)+(MsT^2)-s-t)-(2 (mpi^2)+2 (MsT^2)-s-t) (s+t))+(-(metaP^2)-(mk^2)-(mpi^2)+s+t) (2 (mk^4)-(mk^2) ((mpi^2)-2 (MsT^2))+(2 (metaP^2)+4 (mk^2)+3 (mpi^2)+2 (MsT^2)-2 s-2 t) (-(metaP^2)-2 (mk^2)+s+t))) βT+(-2 (MsT^4)+(MsT^2) ((metaP^2)+2 (mk^2)+(mpi^2)-s-t)+((((metaP^2)+2 (mk^2)+(mpi^2)-s-t))^2)) (-(metaP^2)-(mk^2)+s+t) (-(mk^2)-(mpi^2)+s+t) ((βT)^2))+(1/((MsT^2)-t))2 ((Sqrt[2]) Cθ+Sθ) ((gT^2) ((t^2) (-(metaP^4)+2 (metaP^2) (mpi^2)-(mpi^4)+(t^2))+(MsT^4) (6 (mk^4)-6 (mpi^2) s+6 (s^2)+2 (mk^2) ((mpi^2)-6 s-t)+(metaP^2) (2 (mk^2)+6 (mpi^2)-6 s-t)-(mpi^2) t+6 s t+(t^2))+(MsT^2) (2 (metaP^4) ((mk^2)+t)+((mpi^2)-t) (2 (mk^2) ((mpi^2)+t)+t (2 (mpi^2)+t))-(metaP^2) (4 (mk^2) (mpi^2)+t (4 (mpi^2)+t))))-gT ((MsT^2)-t) ((metaP^4) (2 (mk^2)-t)-(metaP^2) (4 (mk^2) ((mpi^2)-(MsT^2))+t (-2 (mpi^2)+2 (MsT^2)+t))+((mpi^2)-t) (2 (mk^2) ((mpi^2)+2 (MsT^2)+t)-t ((mpi^2)+2 ((MsT^2)+t)))) βT-(2 (mk^2)-t) (-(metaP^2)-(mpi^2)+t) (-2 (MsT^4)+(MsT^2) t+(t^2)) ((βT)^2)));


  f16TensorSD[s_,t_]:=  -(((Sqrt[6]) Cθ ((mk^4)-(mpi^2) s+(s^2)+2 (mk^2) ((mpi^2)-s-t)+(metaP^2) (2 (mk^2)+(mpi^2)-s-t)-(mpi^2) t+s t+(t^2)) β13SD)/(Fpi^4))+(1/((Sqrt[3]) (Fpi^4)))(Sθ (-2 (mk^4)+2 (mpi^2) s-2 (s^2)+(metaP^2) (2 (mk^2)-2 (mpi^2)+2 s-t)+2 (mk^2) ((mpi^2)+2 s-t)-(mpi^2) t-2 s t+(t^2))+4 (Sqrt[2]) Cθ ((mk^4)-(mpi^2) s+(s^2)+2 (mk^2) ((mpi^2)-s-t)+(metaP^2) (2 (mk^2)+(mpi^2)-s-t)-(mpi^2) t+s t+(t^2))) β3SD;

Analytical Results for the Scalar Form-Factor within U(3) χPT

In this secotr, we provide the analytical results for the scalar form-factors of the pseudo-Goldstone boson pairs, i.e. (Subscript[F, PQ]^a)  defined in Eq.(18) in the article.  A mini-manual is given below.

1.   The title for each cell, i.e. sN -> PQ,  denotes the form factor of the boson pair PQ in the case of the scalar source with the Gell-Mann matrix index a=N, being N=0,8,3. 
E.g.  inside the cell s0 -> (π^0)(π^0), we give the result  (Subscript[F, (π^0)(π^0)]^(a=0)). 

2.  Within each cell,  there are formulae that correspond to different contributions.  Taking the cell s0 -> (π^0)(π^0) for example, fs0p0p0CA  denotes the leading order contribution from the Lagrangian in Eq.(1) (see the article) to  (Subscript[F, (π^0)(π^0)]^(a=0)).   fs0p0p0Loop, fs0p0p0Res, fs0p0p0δL8Lam2 and fs0p0p0mixing correspond to the contributions from the chiral loops, resonances, the δL8 and Λ2 operators and (OverBar[η])-(OverBar[η])' mixing terms to the form-factor  (Subscript[F, (π^0)(π^0)]^(a=0)) .  Similar notations apply to the other cases. 

3.  To get the form-factors in isospin base, one also needs the corresponding formulae of the charged pseudo-Goldstone boson pairs: (Subscript[F, (SuperPlus[π])(SuperMinus[π])]^(a=0,8)),  (Subscript[F, (SuperMinus[π])(SuperPlus[π])]^(a=0,8)), (Subscript[F, (SuperPlus[K])(SuperMinus[K])]^(a=0,8,3)).  The relations between the neutral and charged pairs are : (Subscript[F, (SuperPlus[π])(SuperMinus[π])]^(a=0,8)) =(Subscript[F, (SuperMinus[π])(SuperPlus[π])]^(a=0,8))= (Subscript[F, (π^0)(π^0)]^(a=0,8)) , (Subscript[F, (SuperPlus[K])(SuperMinus[K])]^(a=0,8))=(Subscript[F, (K^0)((OverBar[K])^0)]^(a=0,8)) , (Subscript[F, (SuperPlus[K])(SuperMinus[K])]^(a=3))= -(Subscript[F, (K^0)((OverBar[K])^0)]^(a=3)).  

4. About the second multiplet of scalar resonances, their contributions share the same forms as these from the lowest multiplet. Of course, one has to correspondingly replace the resonances parameters. We do not show their contributions explicitly.

s0 -> (π^0)(π^0)

fs0p0p0CA[s_]:=2 (Sqrt[(2/3)]);

fs0p0p0Loop[s_]:=(1/(16 (π^2)))(((((Sqrt[2]) ((Cθ)^2)-4 Cθ Sθ+2 (Sqrt[2]) ((Sθ)^2)) A0[(meta^2)])/(3 (Sqrt[3]) (Fpi^2)))+(((2 (Sqrt[2]) ((Cθ)^2)+4 Cθ Sθ+(Sqrt[2]) ((Sθ)^2)) A0[(metaP^2)])/(3 (Sqrt[3]) (Fpi^2)))-(((Sqrt[(2/3)]) A0[(mpi^2)])/(Fpi^2))+(((Sqrt[(2/3)]) (mpi^2) (((Cθ)^2)-2 (Sqrt[2]) Cθ Sθ+2 ((Sθ)^2)) B0eq[s,(meta^2)])/(3 (Fpi^2)))+(((Sqrt[(2/3)]) (mpi^2) (2 ((Cθ)^2)+2 (Sqrt[2]) Cθ Sθ+((Sθ)^2)) B0eq[s,(metaP^2)])/(3 (Fpi^2)))+(((Sqrt[(2/3)]) s B0eq[s,(mk^2)])/(Fpi^2))-(((Sqrt[(2/3)]) ((mpi^2)-2 s) B0eq[s,(mpi^2)])/(Fpi^2)));

fs0p0p0Res[s_]:=-((32 (Sqrt[(2/3)]) (dm^2) (mpi^2))/((Fpi^2) (MpR8^2)))-((16 (Sqrt[(2/3)]) (cdt-cmt) cmt (2 (mk^2)+(mpi^2)))/((Fpi^2) (Ms1^2)))+((32 (Sqrt[(2/3)]) (cd-cm) cm ((mk^2)-(mpi^2)))/(3 (Fpi^2) (Ms8^2)))+((8 (Sqrt[6]) cmt (2 cmt (mpi^2)+cdt (-2 (mpi^2)+s)))/((Fpi^2) ((Ms1^2)-s)));

fs0p0p0δL8Lam2[s_]:=((64 (Sqrt[(2/3)]) (mpi^2) δL8)/(Fpi^2));

fs0p0p0mixing[s_]:=0;

s0 -> (K^0) (OverBar[(K^0)])

fs0k0k0bCA[s_]:=2 (Sqrt[(2/3)]);

fs0k0k0bLoop[s_]:=(1/(16 (π^2)))(((2 (-(Sqrt[2]) ((Cθ)^2)+Cθ Sθ+(Sqrt[2]) ((Sθ)^2)) A0[(meta^2)])/(3 (Sqrt[3]) (Fpi^2)))-((2 (-(Sqrt[2]) ((Cθ)^2)+Cθ Sθ+(Sqrt[2]) ((Sθ)^2)) A0[(metaP^2)])/(3 (Sqrt[3]) (Fpi^2)))-(((((Cθ)^2) (6 (meta^2)+2 (mpi^2)-9 s)+4 (Sqrt[2]) Cθ (-2 (mk^2)+(mpi^2)) Sθ-8 (mk^2) ((Sθ)^2)) B0eq[s,(meta^2)])/(6 (Sqrt[6]) (Fpi^2)))+(((8 ((Cθ)^2) (mk^2)+4 (Sqrt[2]) Cθ (-2 (mk^2)+(mpi^2)) Sθ+(-6 (metaP^2)-2 (mpi^2)+9 s) ((Sθ)^2)) B0eq[s,(metaP^2)])/(6 (Sqrt[6]) (Fpi^2)))+(((Sqrt[(3/2)]) s B0eq[s,(mk^2)])/(Fpi^2))+(((Sqrt[(3/2)]) s B0eq[s,(mpi^2)])/(2 (Fpi^2))));

fs0k0k0bRes[s_]:=-((32 (Sqrt[(2/3)]) (dm^2) (mk^2))/((Fpi^2) (MpR8^2)))-((16 (Sqrt[(2/3)]) (cdt-cmt) cmt (2 (mk^2)+(mpi^2)))/((Fpi^2) (Ms1^2)))-((16 (Sqrt[(2/3)]) (cd-cm) cm ((mk^2)-(mpi^2)))/(3 (Fpi^2) (Ms8^2)))+((8 (Sqrt[6]) cmt (2 cmt (mk^2)+cdt (-2 (mk^2)+s)))/((Fpi^2) ((Ms1^2)-s)));

fs0k0k0bδL8Lam2[s_]:=((64 (Sqrt[(2/3)]) (mk^2) δL8)/(Fpi^2));

fs0k0k0bmixing[s_]:=0;

s0 -> η η

fs0etetCA[s_]:=2 (Sqrt[(2/3)]);

fs0etetLoop[s_]:=(1/(16 (π^2)))((((3 (Sqrt[2]) ((Cθ)^4)+8 ((Cθ)^3) Sθ+12 (Sqrt[2]) ((Cθ)^2) ((Sθ)^2)+2 (Sqrt[2]) ((Sθ)^4)) A0[(meta^2)])/(3 (Sqrt[3]) (Fpi^2)))+(((2 (Sqrt[2]) ((Cθ)^4)-4 ((Cθ)^3) Sθ-3 (Sqrt[2]) ((Cθ)^2) ((Sθ)^2)+4 Cθ ((Sθ)^3)+2 (Sqrt[2]) ((Sθ)^4)) A0[(metaP^2)])/(3 (Sqrt[3]) (Fpi^2)))+((8 (-(Sqrt[2]) ((Cθ)^2)+Cθ Sθ+(Sqrt[2]) ((Sθ)^2)) A0[(mk^2)])/(3 (Sqrt[3]) (Fpi^2)))+((((Sqrt[2]) ((Cθ)^2)-4 Cθ Sθ+2 (Sqrt[2]) ((Sθ)^2)) A0[(mpi^2)])/((Sqrt[3]) (Fpi^2)))+(1/(9 (Fpi^2)))(Sqrt[(2/3)]) (((Cθ)^4) (16 (mk^2)-7 (mpi^2))+4 (Sqrt[2]) ((Cθ)^3) (8 (mk^2)-5 (mpi^2)) Sθ+12 ((Cθ)^2) (4 (mk^2)-(mpi^2)) ((Sθ)^2)+16 (Sqrt[2]) Cθ ((mk^2)-(mpi^2)) ((Sθ)^3)+2 (2 (mk^2)+(mpi^2)) ((Sθ)^4)) B0eq[s,(meta^2)]+(((Sqrt[(2/3)]) (4 (mk^2)-(mpi^2)) (2 ((Cθ)^4)-2 (Sqrt[2]) ((Cθ)^3) Sθ-3 ((Cθ)^2) ((Sθ)^2)+2 (Sqrt[2]) Cθ ((Sθ)^3)+2 ((Sθ)^4)) B0eq[s,(metaP^2)])/(9 (Fpi^2)))-(((Sqrt[(2/3)]) (((Cθ)^2) (6 (meta^2)+2 (mpi^2)-9 s)+4 (Sqrt[2]) Cθ (-2 (mk^2)+(mpi^2)) Sθ-8 (mk^2) ((Sθ)^2)) B0eq[s,(mk^2)])/(3 (Fpi^2)))+(((Sqrt[(2/3)]) (mpi^2) (((Cθ)^2)-2 (Sqrt[2]) Cθ Sθ+2 ((Sθ)^2)) B0eq[s,(mpi^2)])/(Fpi^2)));

fs0etetRes[s_]:=-((32 Cθ (dm^2) ((Sqrt[2]) Cθ (4 (mk^2)-(mpi^2))+4 ((mk^2)-(mpi^2)) Sθ))/(3 (Sqrt[3]) (Fpi^2) (MpR8^2)))-((32 (dmt^2) Sθ (4 Cθ ((mk^2)-(mpi^2))+(Sqrt[2]) (2 (mk^2)+(mpi^2)) Sθ))/((Sqrt[3]) (Fpi^2) (MpR1^2)))+((32 cm Cθ ((mk^2)-(mpi^2)) ((Sqrt[2]) cm Cθ+4 cm Sθ-cd ((Sqrt[2]) Cθ+4 Sθ)))/(3 (Sqrt[3]) (Fpi^2) (Ms8^2)))+((16 (Sqrt[2]) cmt (2 (mk^2)+(mpi^2)) ((Sqrt[3]) cmt-(Sqrt[3]) cdt (((Cθ)^2)+((Sθ)^2))))/(3 (Fpi^2) (Ms1^2)))+((8 cmt (-3 (Sqrt[6]) cdt (2 (meta^2)-s) (((Cθ)^2)+((Sθ)^2))+2 (Sqrt[3]) cmt ((Sqrt[2]) ((Cθ)^2) (4 (mk^2)-(mpi^2))+8 Cθ ((mk^2)-(mpi^2)) Sθ+(Sqrt[2]) (2 (mk^2)+(mpi^2)) ((Sθ)^2))))/(3 (Fpi^2) ((Ms1^2)-s)));

fs0etetδL8Lam2[s_]:=((64 ((Sqrt[2]) ((Cθ)^2) (4 (mk^2)-(mpi^2))+8 Cθ ((mk^2)-(mpi^2)) Sθ+(Sqrt[2]) (2 (mk^2)+(mpi^2)) ((Sθ)^2)) δL8)/(3 (Sqrt[3]) (Fpi^2)))+4 (Sqrt[(2/3)]) ((Sθ)^2) Λ2;

fs0etetmixing[s_]:=0;

s0 -> η η'

fs0etetpCA[s_]:=0;

fs0etetpLoop[s_]:=(1/(16 (π^2)))(-((Cθ (2 ((Cθ)^3)+3 (Sqrt[2]) ((Cθ)^2) Sθ-6 Cθ ((Sθ)^2)-4 (Sqrt[2]) ((Sθ)^3)) A0[(meta^2)])/(3 (Sqrt[3]) (Fpi^2)))+((Sθ (4 (Sqrt[2]) ((Cθ)^3)-6 ((Cθ)^2) Sθ-3 (Sqrt[2]) Cθ ((Sθ)^2)+2 ((Sθ)^3)) A0[(metaP^2)])/(3 (Sqrt[3]) (Fpi^2)))-((2 (2 ((Cθ)^2)+5 (Sqrt[2]) Cθ Sθ-2 ((Sθ)^2)) A0[(mk^2)])/(3 (Sqrt[3]) (Fpi^2)))+(((2 ((Cθ)^2)-(Sqrt[2]) Cθ Sθ-2 ((Sθ)^2)) A0[(mpi^2)])/((Sqrt[3]) (Fpi^2)))-(1/(9 (Fpi^2)))(Sqrt[(2/3)]) ((Sqrt[2]) ((Cθ)^4) (8 (mk^2)-5 (mpi^2))+((Cθ)^3) (8 (mk^2)+(mpi^2)) Sθ+3 (Sqrt[2]) ((Cθ)^2) (-4 (mk^2)+(mpi^2)) ((Sθ)^2)+4 Cθ (-5 (mk^2)+2 (mpi^2)) ((Sθ)^3)+4 (Sqrt[2]) (-(mk^2)+(mpi^2)) ((Sθ)^4)) B0eq[s,(meta^2)]-(1/(9 (Fpi^2)))(Sqrt[(2/3)]) (4 (Sqrt[2]) ((Cθ)^4) ((mk^2)-(mpi^2))+3 (Sqrt[2]) ((Cθ)^2) (4 (mk^2)-(mpi^2)) ((Sθ)^2)+Cθ (8 (mk^2)+(mpi^2)) ((Sθ)^3)+(Sqrt[2]) (-8 (mk^2)+5 (mpi^2)) ((Sθ)^4)+((Cθ)^3) (-20 (mk^2) Sθ+8 (mpi^2) Sθ)) B0eq[s,(metaP^2)]-(((Sqrt[(2/3)]) (2 (Sqrt[2]) ((Cθ)^2) (2 (mk^2)-(mpi^2))+Cθ (3 (meta^2)+3 (metaP^2)+8 (mk^2)+2 (mpi^2)-9 s) Sθ+2 (Sqrt[2]) (-2 (mk^2)+(mpi^2)) ((Sθ)^2)) B0eq[s,(mk^2)])/(3 (Fpi^2)))+(((Sqrt[(2/3)]) (mpi^2) ((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2)) B0eq[s,(mpi^2)])/(Fpi^2)));

fs0etetpRes[s_]:=-((32 (cm^2) ((mk^2)-(mpi^2)) (2 ((Cθ)^2)-(Sqrt[2]) Cθ Sθ-2 ((Sθ)^2)))/(3 (Sqrt[3]) (Fpi^2) (Ms8^2)))-((32 (cmt^2) ((mk^2)-(mpi^2)) (2 ((Cθ)^2)-(Sqrt[2]) Cθ Sθ-2 ((Sθ)^2)))/((Sqrt[3]) (Fpi^2) ((Ms1^2)-s)))+((32 (dm^2) (2 ((Cθ)^2) ((mk^2)-(mpi^2))+(Sqrt[2]) Cθ (-4 (mk^2)+(mpi^2)) Sθ+2 (-(mk^2)+(mpi^2)) ((Sθ)^2)))/(3 (Sqrt[3]) (Fpi^2) (MpR8^2)))+((32 (dmt^2) (2 ((Cθ)^2) ((mk^2)-(mpi^2))+(Sqrt[2]) Cθ (2 (mk^2)+(mpi^2)) Sθ+2 (-(mk^2)+(mpi^2)) ((Sθ)^2)))/((Sqrt[3]) (Fpi^2) (MpR1^2)));

fs0etetpδL8Lam2[s_]:=-((128 ((mk^2)-(mpi^2)) (2 ((Cθ)^2)-(Sqrt[2]) Cθ Sθ-2 ((Sθ)^2)) δL8)/(3 (Sqrt[3]) (Fpi^2)))-4 (Sqrt[(2/3)]) Cθ Sθ Λ2;

fs0etetpmixing[s_]:=-2 (Sqrt[(2/3)]) δk;

s0 -> η' η'

fs0etpetpCA[s_]:=2 (Sqrt[(2/3)]);

fs0etpetpLoop[s_]:=(1/(16 (π^2)))((((2 (Sqrt[2]) ((Cθ)^4)-4 ((Cθ)^3) Sθ-3 (Sqrt[2]) ((Cθ)^2) ((Sθ)^2)+4 Cθ ((Sθ)^3)+2 (Sqrt[2]) ((Sθ)^4)) A0[(meta^2)])/(3 (Sqrt[3]) (Fpi^2)))+(((2 (Sqrt[2]) ((Cθ)^4)+12 (Sqrt[2]) ((Cθ)^2) ((Sθ)^2)-8 Cθ ((Sθ)^3)+3 (Sqrt[2]) ((Sθ)^4)) A0[(metaP^2)])/(3 (Sqrt[3]) (Fpi^2)))-((8 (-(Sqrt[2]) ((Cθ)^2)+Cθ Sθ+(Sqrt[2]) ((Sθ)^2)) A0[(mk^2)])/(3 (Sqrt[3]) (Fpi^2)))+(((2 (Sqrt[2]) ((Cθ)^2)+4 Cθ Sθ+(Sqrt[2]) ((Sθ)^2)) A0[(mpi^2)])/((Sqrt[3]) (Fpi^2)))+(((Sqrt[(2/3)]) (4 (mk^2)-(mpi^2)) (2 ((Cθ)^4)-2 (Sqrt[2]) ((Cθ)^3) Sθ-3 ((Cθ)^2) ((Sθ)^2)+2 (Sqrt[2]) Cθ ((Sθ)^3)+2 ((Sθ)^4)) B0eq[s,(meta^2)])/(9 (Fpi^2)))-(1/(9 (Fpi^2)))(Sqrt[(2/3)]) (-2 ((Cθ)^4) (2 (mk^2)+(mpi^2))+16 (Sqrt[2]) ((Cθ)^3) ((mk^2)-(mpi^2)) Sθ+12 ((Cθ)^2) (-4 (mk^2)+(mpi^2)) ((Sθ)^2)+4 (Sqrt[2]) Cθ (8 (mk^2)-5 (mpi^2)) ((Sθ)^3)+(-16 (mk^2)+7 (mpi^2)) ((Sθ)^4)) B0eq[s,(metaP^2)]-(((Sqrt[(2/3)]) (-8 ((Cθ)^2) (mk^2)+4 (Sqrt[2]) Cθ (2 (mk^2)-(mpi^2)) Sθ+(6 (metaP^2)+2 (mpi^2)-9 s) ((Sθ)^2)) B0eq[s,(mk^2)])/(3 (Fpi^2)))+(((Sqrt[(2/3)]) (mpi^2) (2 ((Cθ)^2)+2 (Sqrt[2]) Cθ Sθ+((Sθ)^2)) B0eq[s,(mpi^2)])/(Fpi^2)));

fs0etpetpRes[s_]:=((32 cm ((mk^2)-(mpi^2)) Sθ (4 cd Cθ-4 cm Cθ-(Sqrt[2]) cd Sθ+(Sqrt[2]) cm Sθ))/(3 (Sqrt[3]) (Fpi^2) (Ms8^2)))+((32 (dm^2) Sθ (4 Cθ ((mk^2)-(mpi^2))+(Sqrt[2]) (-4 (mk^2)+(mpi^2)) Sθ))/(3 (Sqrt[3]) (Fpi^2) (MpR8^2)))-((32 Cθ (dmt^2) ((Sqrt[2]) Cθ (2 (mk^2)+(mpi^2))+4 (-(mk^2)+(mpi^2)) Sθ))/((Sqrt[3]) (Fpi^2) (MpR1^2)))+((16 (Sqrt[2]) cmt (2 (mk^2)+(mpi^2)) ((Sqrt[3]) cmt-(Sqrt[3]) cdt (((Cθ)^2)+((Sθ)^2))))/(3 (Fpi^2) (Ms1^2)))+((8 cmt (-3 (Sqrt[2]) cdt (2 (metaP^2)-s)+2 cmt ((Sqrt[2]) ((Cθ)^2) (2 (mk^2)+(mpi^2))+8 Cθ (-(mk^2)+(mpi^2)) Sθ+(Sqrt[2]) (4 (mk^2)-(mpi^2)) ((Sθ)^2))))/((Sqrt[3]) (Fpi^2) ((Ms1^2)-s)));

fs0etpetpδL8Lam2[s_]:=((64 ((Sqrt[2]) ((Cθ)^2) (2 (mk^2)+(mpi^2))+8 Cθ (-(mk^2)+(mpi^2)) Sθ+(Sqrt[2]) (4 (mk^2)-(mpi^2)) ((Sθ)^2)) δL8)/(3 (Sqrt[3]) (Fpi^2)))+4 (Sqrt[(2/3)]) ((Cθ)^2) Λ2;

fs0etpetpmixing[s_]:=0;

s8 -> (π^0)(π^0)

fs8p0p0CA[s_]:=(2/(Sqrt[3]));

fs8p0p0Loop[s_]:=(1/(16 (π^2)))((((((Cθ)^2)-2 (Sqrt[2]) Cθ Sθ+2 ((Sθ)^2)) A0[(meta^2)])/(3 (Sqrt[3]) (Fpi^2)))+(((2 ((Cθ)^2)+2 (Sqrt[2]) Cθ Sθ+((Sθ)^2)) A0[(metaP^2)])/(3 (Sqrt[3]) (Fpi^2)))-((A0[(mpi^2)])/((Sqrt[3]) (Fpi^2)))+((2 (mpi^2) (((-(Sqrt[2]) ((Cθ)^2)+Cθ Sθ+(Sqrt[2]) ((Sθ)^2)))^2) B0[s,(meta^2),(metaP^2)])/(3 (Sqrt[3]) (Fpi^2)))-((Cθ (mpi^2) (Cθ+2 (Sqrt[2]) Sθ) (((Cθ)^2)-2 (Sqrt[2]) Cθ Sθ+2 ((Sθ)^2)) B0eq[s,(meta^2)])/(3 (Sqrt[3]) (Fpi^2)))+(((mpi^2) (2 (Sqrt[2]) Cθ-Sθ) Sθ (2 ((Cθ)^2)+2 (Sqrt[2]) Cθ Sθ+((Sθ)^2)) B0eq[s,(metaP^2)])/(3 (Sqrt[3]) (Fpi^2)))-((s B0eq[s,(mk^2)])/(2 (Sqrt[3]) (Fpi^2)))-((((mpi^2)-2 s) B0eq[s,(mpi^2)])/((Sqrt[3]) (Fpi^2))));

fs8p0p0Res[s_]:=-((32 (dm^2) (mpi^2))/((Sqrt[3]) (Fpi^2) (MpR8^2)))-((16 (cdt-cmt) cmt (2 (mk^2)+(mpi^2)))/((Sqrt[3]) (Fpi^2) (Ms1^2)))+((32 (cd-cm) cm ((mk^2)-(mpi^2)))/(3 (Sqrt[3]) (Fpi^2) (Ms8^2)))+((8 cm (2 cm (mpi^2)+cd (-2 (mpi^2)+s)))/((Sqrt[3]) (Fpi^2) ((Ms8^2)-s)));

fs8p0p0δL8Lam2[s_]:=((64 (mpi^2) δL8)/((Sqrt[3]) (Fpi^2)));

fs8p0p0mixing[s_]:=0;

s8 -> (K^0) (OverBar[(K^0)])

fs8k0k0bCA[s_]:=-(1/(Sqrt[3]));

fs8k0k0bLoop[s_]:=(1/(16 (π^2)))((((3 ((Cθ)^4)+3 (Sqrt[2]) ((Cθ)^3) Sθ-2 ((Sθ)^2)+(Sqrt[2]) Cθ Sθ (-4+3 ((Sθ)^2))+((Cθ)^2) (-1+3 ((Sθ)^2))) A0[(meta^2)])/(6 (Sqrt[3]) (Fpi^2)))-(((3 (Sqrt[2]) ((Cθ)^3) Sθ+((Sθ)^2)-3 ((Sθ)^4)+((Cθ)^2) (2-3 ((Sθ)^2))+(Sqrt[2]) Cθ Sθ (-4+3 ((Sθ)^2))) A0[(metaP^2)])/(6 (Sqrt[3]) (Fpi^2)))-(1/(6 (Sqrt[3]) (Fpi^2)))((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2)) (2 (Sqrt[2]) ((Cθ)^2) (2 (mk^2)-(mpi^2))+Cθ (3 (meta^2)+3 (metaP^2)+8 (mk^2)+2 (mpi^2)-9 s) Sθ+2 (Sqrt[2]) (-2 (mk^2)+(mpi^2)) ((Sθ)^2)) B0[s,(meta^2),(metaP^2)]+((Cθ (Cθ+2 (Sqrt[2]) Sθ) (((Cθ)^2) (6 (meta^2)+2 (mpi^2)-9 s)+4 (Sqrt[2]) Cθ (-2 (mk^2)+(mpi^2)) Sθ-8 (mk^2) ((Sθ)^2)) B0eq[s,(meta^2)])/(12 (Sqrt[3]) (Fpi^2)))-(((2 (Sqrt[2]) Cθ-Sθ) Sθ (-8 ((Cθ)^2) (mk^2)+4 (Sqrt[2]) Cθ (2 (mk^2)-(mpi^2)) Sθ+(6 (metaP^2)+2 (mpi^2)-9 s) ((Sθ)^2)) B0eq[s,(metaP^2)])/(12 (Sqrt[3]) (Fpi^2)))-(((Sqrt[3]) s B0eq[s,(mk^2)])/(4 (Fpi^2)))+(((Sqrt[3]) s B0eq[s,(mpi^2)])/(4 (Fpi^2))));

fs8k0k0bRes[s_]:=((16 (dm^2) (mk^2))/((Sqrt[3]) (Fpi^2) (MpR8^2)))+((8 (cdt-cmt) cmt (2 (mk^2)+(mpi^2)))/((Sqrt[3]) (Fpi^2) (Ms1^2)))+((8 (cd-cm) cm ((mk^2)-(mpi^2)))/(3 (Sqrt[3]) (Fpi^2) (Ms8^2)))-((4 cm (2 cm (mk^2)+cd (-2 (mk^2)+s)))/((Sqrt[3]) (Fpi^2) ((Ms8^2)-s)));

fs8k0k0bδL8Lam2[s_]:=-((32 (mk^2) δL8)/((Sqrt[3]) (Fpi^2)));

fs8k0k0bmixing[s_]:=0;

s8 -> η η

fs8etetCA[s_]:=-((2 Cθ (Cθ+2 (Sqrt[2]) Sθ))/(Sqrt[3]));

fs8etetLoop[s_]:=(1/(16 (π^2)))(-((Cθ (5 ((Cθ)^3)+12 (Sqrt[2]) ((Cθ)^2) Sθ+12 Cθ ((Sθ)^2)+8 (Sqrt[2]) ((Sθ)^3)) A0[(meta^2)])/(3 (Sqrt[3]) (Fpi^2)))-(((2 ((Cθ)^4)-2 (Sqrt[2]) ((Cθ)^3) Sθ-3 ((Cθ)^2) ((Sθ)^2)+2 (Sqrt[2]) Cθ ((Sθ)^3)+2 ((Sθ)^4)) A0[(metaP^2)])/(3 (Sqrt[3]) (Fpi^2)))+((2 (-((Cθ)^2)+3 ((Cθ)^4)-4 (Sqrt[2]) Cθ Sθ+6 (Sqrt[2]) ((Cθ)^3) Sθ-2 ((Sθ)^2)) A0[(mk^2)])/(3 (Sqrt[3]) (Fpi^2)))+(((((Cθ)^2)-2 (Sqrt[2]) Cθ Sθ+2 ((Sθ)^2)) A0[(mpi^2)])/((Sqrt[3]) (Fpi^2)))-(1/(9 (Sqrt[3]) (Fpi^2)))2 ((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2)) ((Sqrt[2]) ((Cθ)^4) (8 (mk^2)-5 (mpi^2))+((Cθ)^3) (8 (mk^2)+(mpi^2)) Sθ+3 (Sqrt[2]) ((Cθ)^2) (-4 (mk^2)+(mpi^2)) ((Sθ)^2)+4 Cθ (-5 (mk^2)+2 (mpi^2)) ((Sθ)^3)+4 (Sqrt[2]) (-(mk^2)+(mpi^2)) ((Sθ)^4)) B0[s,(meta^2),(metaP^2)]-(1/(9 (Sqrt[3]) (Fpi^2)))Cθ (Cθ+2 (Sqrt[2]) Sθ) (((Cθ)^4) (16 (mk^2)-7 (mpi^2))+4 (Sqrt[2]) ((Cθ)^3) (8 (mk^2)-5 (mpi^2)) Sθ+12 ((Cθ)^2) (4 (mk^2)-(mpi^2)) ((Sθ)^2)+16 (Sqrt[2]) Cθ ((mk^2)-(mpi^2)) ((Sθ)^3)+2 (2 (mk^2)+(mpi^2)) ((Sθ)^4)) B0eq[s,(meta^2)]+(((4 (mk^2)-(mpi^2)) (2 (Sqrt[2]) Cθ-Sθ) Sθ (2 ((Cθ)^4)-2 (Sqrt[2]) ((Cθ)^3) Sθ-3 ((Cθ)^2) ((Sθ)^2)+2 (Sqrt[2]) Cθ ((Sθ)^3)+2 ((Sθ)^4)) B0eq[s,(metaP^2)])/(9 (Sqrt[3]) (Fpi^2)))+(((((Cθ)^2) (6 (meta^2)+2 (mpi^2)-9 s)+4 (Sqrt[2]) Cθ (-2 (mk^2)+(mpi^2)) Sθ-8 (mk^2) ((Sθ)^2)) B0eq[s,(mk^2)])/(6 (Sqrt[3]) (Fpi^2)))+(((mpi^2) (((Cθ)^2)-2 (Sqrt[2]) Cθ Sθ+2 ((Sθ)^2)) B0eq[s,(mpi^2)])/((Sqrt[3]) (Fpi^2))));

fs8etetRes[s_]:=((32 Cθ (dmt^2) (4 Cθ ((mk^2)-(mpi^2))+(Sqrt[2]) (2 (mk^2)+(mpi^2)) Sθ))/((Sqrt[3]) (Fpi^2) (MpR1^2)))+((32 (dm^2) (((Cθ)^2) (4 (mk^2)-(mpi^2))+3 (Sqrt[2]) Cθ (2 (mk^2)-(mpi^2)) Sθ+4 ((mk^2)-(mpi^2)) ((Sθ)^2)))/(3 (Sqrt[3]) (Fpi^2) (MpR8^2)))+((16 cmt Cθ (2 (mk^2)+(mpi^2)) (Cθ+2 (Sqrt[2]) Sθ) (-(Sqrt[3]) cmt+(Sqrt[3]) cdt (((Cθ)^2)+((Sθ)^2))))/(3 (Fpi^2) (Ms1^2)))-((32 cm ((mk^2)-(mpi^2)) (cm (3 ((Cθ)^2)+2 (Sqrt[2]) Cθ Sθ+2 ((Sθ)^2))-cd ((Cθ)^2) (((Cθ)^2)+4 (Sqrt[2]) Cθ Sθ+8 ((Sθ)^2))))/(3 (Sqrt[3]) (Fpi^2) (Ms8^2)))-((8 cm (-3 cd Cθ (2 (meta^2)-s) (Cθ+2 (Sqrt[2]) Sθ)+2 cm (((Cθ)^2) (8 (mk^2)-5 (mpi^2))+2 (Sqrt[2]) Cθ (4 (mk^2)-(mpi^2)) Sθ+4 ((mk^2)-(mpi^2)) ((Sθ)^2))))/(3 (Sqrt[3]) (Fpi^2) ((Ms8^2)-s)));

fs8etetδL8Lam2[s_]:=-((64 (((Cθ)^2) (8 (mk^2)-5 (mpi^2))+2 (Sqrt[2]) Cθ (4 (mk^2)-(mpi^2)) Sθ+4 ((mk^2)-(mpi^2)) ((Sθ)^2)) δL8)/(3 (Sqrt[3]) (Fpi^2)))-4 (Sqrt[(2/3)]) Cθ Sθ Λ2;

fs8etetmixing[s_]:=-((2 ((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2)) (2 sδ+δk))/(Sqrt[3]));

s8 -> η η'

fs8etetpCA[s_]:=((2 ((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2)))/(Sqrt[3]));

fs8etetpLoop[s_]:=(1/(16 (π^2)))((((3 (Sqrt[2]) ((Cθ)^4)+((Cθ)^3) Sθ-3 (Sqrt[2]) ((Cθ)^2) ((Sθ)^2)-6 Cθ ((Sθ)^3)-2 (Sqrt[2]) ((Sθ)^4)) A0[(meta^2)])/(3 (Sqrt[3]) (Fpi^2)))+(((2 (Sqrt[2]) ((Cθ)^4)-6 ((Cθ)^3) Sθ+3 (Sqrt[2]) ((Cθ)^2) ((Sθ)^2)+Cθ ((Sθ)^3)-3 (Sqrt[2]) ((Sθ)^4)) A0[(metaP^2)])/(3 (Sqrt[3]) (Fpi^2)))-(((-4 (Sqrt[2]) ((Cθ)^2)+3 (Sqrt[2]) ((Cθ)^4)-3 ((Cθ)^3) Sθ+(Sqrt[2]) ((Sθ)^2) (4-3 ((Sθ)^2))-Cθ Sθ (2+3 ((Sθ)^2))) A0[(mk^2)])/(3 (Sqrt[3]) (Fpi^2)))+((((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2)) A0[(mpi^2)])/((Sqrt[3]) (Fpi^2)))+((2 (4 (mk^2)-(mpi^2)) ((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2)) (2 ((Cθ)^4)-2 (Sqrt[2]) ((Cθ)^3) Sθ-3 ((Cθ)^2) ((Sθ)^2)+2 (Sqrt[2]) Cθ ((Sθ)^3)+2 ((Sθ)^4)) B0[s,(meta^2),(metaP^2)])/(9 (Sqrt[3]) (Fpi^2)))+(1/(9 (Sqrt[3]) (Fpi^2)))Cθ (Cθ+2 (Sqrt[2]) Sθ) ((Sqrt[2]) ((Cθ)^4) (8 (mk^2)-5 (mpi^2))+((Cθ)^3) (8 (mk^2)+(mpi^2)) Sθ+3 (Sqrt[2]) ((Cθ)^2) (-4 (mk^2)+(mpi^2)) ((Sθ)^2)+4 Cθ (-5 (mk^2)+2 (mpi^2)) ((Sθ)^3)+4 (Sqrt[2]) (-(mk^2)+(mpi^2)) ((Sθ)^4)) B0eq[s,(meta^2)]-(1/(9 (Sqrt[3]) (Fpi^2)))(2 (Sqrt[2]) Cθ-Sθ) Sθ (4 (Sqrt[2]) ((Cθ)^4) ((mk^2)-(mpi^2))+3 (Sqrt[2]) ((Cθ)^2) (4 (mk^2)-(mpi^2)) ((Sθ)^2)+Cθ (8 (mk^2)+(mpi^2)) ((Sθ)^3)+(Sqrt[2]) (-8 (mk^2)+5 (mpi^2)) ((Sθ)^4)+((Cθ)^3) (-20 (mk^2) Sθ+8 (mpi^2) Sθ)) B0eq[s,(metaP^2)]+(((2 (Sqrt[2]) ((Cθ)^2) (2 (mk^2)-(mpi^2))+Cθ (3 (meta^2)+3 (metaP^2)+8 (mk^2)+2 (mpi^2)-9 s) Sθ+2 (Sqrt[2]) (-2 (mk^2)+(mpi^2)) ((Sθ)^2)) B0eq[s,(mk^2)])/(6 (Sqrt[3]) (Fpi^2)))+(((mpi^2) ((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2)) B0eq[s,(mpi^2)])/((Sqrt[3]) (Fpi^2))));

fs8etetpRes[s_]:=((8 cmt (-2 (Sqrt[3]) cdt+2 (Sqrt[3]) cmt) (2 (mk^2)+(mpi^2)) ((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2)))/(3 (Fpi^2) (Ms1^2)))+((16 cm (-cd+2 cm) ((mk^2)-(mpi^2)) ((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2)))/(3 (Sqrt[3]) (Fpi^2) (Ms8^2)))-((16 (dm^2) ((Sqrt[6]) ((Cθ)^2) (2 (mk^2)-(mpi^2))-2 (Sqrt[3]) Cθ (mpi^2) Sθ+(Sqrt[6]) (-2 (mk^2)+(mpi^2)) ((Sθ)^2)))/(3 (Fpi^2) (MpR8^2)))-((16 (dmt^2) ((Sqrt[2]) ((Cθ)^2) (2 (mk^2)+(mpi^2))+8 Cθ (-(mk^2)+(mpi^2)) Sθ-(Sqrt[2]) (2 (mk^2)+(mpi^2)) ((Sθ)^2)))/((Sqrt[3]) (Fpi^2) (MpR1^2)))+((4 cm (4 cm (4 (mk^2)-(mpi^2)) ((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2))-6 cd ((meta^2)+(metaP^2)-s) ((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2))))/(3 (Sqrt[3]) (Fpi^2) ((Ms8^2)-s)));

fs8etetpδL8Lam2[s_]:=((64 (4 (mk^2)-(mpi^2)) ((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2)) δL8)/(3 (Sqrt[3]) (Fpi^2)))+2 (Sqrt[(2/3)]) (((Cθ)^2)-((Sθ)^2)) Λ2;

fs8etetpmixing[s_]:=((-8 (Sqrt[2]) Cθ sδ Sθ+((Cθ)^2) (-2 sδ+δk)+((Sθ)^2) (2 sδ+δk))/(Sqrt[3]));

s8 -> η' η'

fs8etpetpCA[s_]:=((2 (2 (Sqrt[2]) Cθ-Sθ) Sθ)/(Sqrt[3]));

fs8etpetpLoop[s_]:=(1/(16 (π^2)))(-(((2 ((Cθ)^4)-2 (Sqrt[2]) ((Cθ)^3) Sθ-3 ((Cθ)^2) ((Sθ)^2)+2 (Sqrt[2]) Cθ ((Sθ)^3)+2 ((Sθ)^4)) A0[(meta^2)])/(3 (Sqrt[3]) (Fpi^2)))+((Sθ (8 (Sqrt[2]) ((Cθ)^3)-12 ((Cθ)^2) Sθ+12 (Sqrt[2]) Cθ ((Sθ)^2)-5 ((Sθ)^3)) A0[(metaP^2)])/(3 (Sqrt[3]) (Fpi^2)))-((2 (2 ((Cθ)^2)+((Sθ)^2)-3 ((Sθ)^4)+2 (Sqrt[2]) Cθ Sθ (-2+3 ((Sθ)^2))) A0[(mk^2)])/(3 (Sqrt[3]) (Fpi^2)))+(((2 ((Cθ)^2)+2 (Sqrt[2]) Cθ Sθ+((Sθ)^2)) A0[(mpi^2)])/((Sqrt[3]) (Fpi^2)))-(1/(9 (Sqrt[3]) (Fpi^2)))2 ((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2)) (4 (Sqrt[2]) ((Cθ)^4) ((mk^2)-(mpi^2))+3 (Sqrt[2]) ((Cθ)^2) (4 (mk^2)-(mpi^2)) ((Sθ)^2)+Cθ (8 (mk^2)+(mpi^2)) ((Sθ)^3)+(Sqrt[2]) (-8 (mk^2)+5 (mpi^2)) ((Sθ)^4)+((Cθ)^3) (-20 (mk^2) Sθ+8 (mpi^2) Sθ)) B0[s,(meta^2),(metaP^2)]-((Cθ (4 (mk^2)-(mpi^2)) (Cθ+2 (Sqrt[2]) Sθ) (2 ((Cθ)^4)-2 (Sqrt[2]) ((Cθ)^3) Sθ-3 ((Cθ)^2) ((Sθ)^2)+2 (Sqrt[2]) Cθ ((Sθ)^3)+2 ((Sθ)^4)) B0eq[s,(meta^2)])/(9 (Sqrt[3]) (Fpi^2)))-(1/(9 (Sqrt[3]) (Fpi^2)))(2 (Sqrt[2]) Cθ-Sθ) Sθ (-2 ((Cθ)^4) (2 (mk^2)+(mpi^2))+16 (Sqrt[2]) ((Cθ)^3) ((mk^2)-(mpi^2)) Sθ+12 ((Cθ)^2) (-4 (mk^2)+(mpi^2)) ((Sθ)^2)+4 (Sqrt[2]) Cθ (8 (mk^2)-5 (mpi^2)) ((Sθ)^3)+(-16 (mk^2)+7 (mpi^2)) ((Sθ)^4)) B0eq[s,(metaP^2)]-(((8 ((Cθ)^2) (mk^2)+4 (Sqrt[2]) Cθ (-2 (mk^2)+(mpi^2)) Sθ+(-6 (metaP^2)-2 (mpi^2)+9 s) ((Sθ)^2)) B0eq[s,(mk^2)])/(6 (Sqrt[3]) (Fpi^2)))+(((mpi^2) (2 ((Cθ)^2)+2 (Sqrt[2]) Cθ Sθ+((Sθ)^2)) B0eq[s,(mpi^2)])/((Sqrt[3]) (Fpi^2))));

fs8etpetpRes[s_]:=((16 cmt (-(Sqrt[3]) cdt+(Sqrt[3]) cmt) (2 (mk^2)+(mpi^2)) (2 (Sqrt[2]) Cθ-Sθ) Sθ)/(3 (Fpi^2) (Ms1^2)))-((32 (dmt^2) Sθ ((Sqrt[2]) Cθ (2 (mk^2)+(mpi^2))+4 (-(mk^2)+(mpi^2)) Sθ))/((Sqrt[3]) (Fpi^2) (MpR1^2)))+((32 (dm^2) (4 ((Cθ)^2) ((mk^2)-(mpi^2))+3 (Sqrt[2]) Cθ (-2 (mk^2)+(mpi^2)) Sθ+(4 (mk^2)-(mpi^2)) ((Sθ)^2)))/(3 (Sqrt[3]) (Fpi^2) (MpR8^2)))-((32 cm ((mk^2)-(mpi^2)) (-cd ((Sθ)^2) (8 ((Cθ)^2)-4 (Sqrt[2]) Cθ Sθ+((Sθ)^2))+cm (2 ((Cθ)^2)-2 (Sqrt[2]) Cθ Sθ+3 ((Sθ)^2))))/(3 (Sqrt[3]) (Fpi^2) (Ms8^2)))+((8 cm (3 cd (2 (metaP^2)-s) Sθ (-2 (Sqrt[2]) Cθ+Sθ)-2 cm (4 ((Cθ)^2) ((mk^2)-(mpi^2))+2 (Sqrt[2]) Cθ (-4 (mk^2)+(mpi^2)) Sθ+(8 (mk^2)-5 (mpi^2)) ((Sθ)^2))))/(3 (Sqrt[3]) (Fpi^2) ((Ms8^2)-s)));

fs8etpetpδL8Lam2[s_]:=-((64 (4 ((Cθ)^2) ((mk^2)-(mpi^2))+2 (Sqrt[2]) Cθ (-4 (mk^2)+(mpi^2)) Sθ+(8 (mk^2)-5 (mpi^2)) ((Sθ)^2)) δL8)/(3 (Sqrt[3]) (Fpi^2)))+4 (Sqrt[(2/3)]) Cθ Sθ Λ2;

fs8etpetpmixing[s_]:=((2 ((Sqrt[2]) ((Cθ)^2)-Cθ Sθ-(Sqrt[2]) ((Sθ)^2)) (2 sδ-δk))/(Sqrt[3]));

s3 -> (π^0) η

fs3p0etCA[s_]:=((2 (Cθ-(Sqrt[2]) Sθ))/(Sqrt[3]));

fs3p0etLoop[s_]:=(1/(16 (π^2)))((((((Cθ)^3)-3 (Sqrt[2]) ((Cθ)^2) Sθ+6 Cθ ((Sθ)^2)-2 (Sqrt[2]) ((Sθ)^3)) A0[(meta^2)])/(3 (Sqrt[3]) (Fpi^2)))+(((2 ((Cθ)^3)-3 Cθ ((Sθ)^2)-(Sqrt[2]) ((Sθ)^3)) A0[(metaP^2)])/(3 (Sqrt[3]) (Fpi^2)))-(((Cθ+((Cθ)^3)+(Sqrt[2]) Sθ-(Sqrt[2]) ((Cθ)^2) Sθ) A0[(mk^2)])/((Sqrt[3]) (Fpi^2)))+(((Cθ-(Sqrt[2]) Sθ) A0[(mpi^2)])/((Sqrt[3]) (Fpi^2)))+((2 (mpi^2) (Cθ-(Sqrt[2]) Sθ) (((Cθ)^2)-2 (Sqrt[2]) Cθ Sθ+2 ((Sθ)^2)) B0[s,(meta^2),(mpi^2)])/(3 (Sqrt[3]) (Fpi^2)))+((2 (mpi^2) (2 ((Cθ)^3)-3 Cθ ((Sθ)^2)-(Sqrt[2]) ((Sθ)^3)) B0[s,(metaP^2),(mpi^2)])/(3 (Sqrt[3]) (Fpi^2)))-(((Cθ (3 (meta^2)+8 (mk^2)+(mpi^2)-9 s)+2 (Sqrt[2]) (2 (mk^2)+(mpi^2)) Sθ) B0eq[s,(mk^2)])/(6 (Sqrt[3]) (Fpi^2))));

fs3p0etRes[s_]:=-((16 (dm^2) (2 Cθ (2 (mk^2)+(mpi^2))+(Sqrt[2]) (2 (mk^2)-5 (mpi^2)) Sθ))/(3 (Sqrt[3]) (Fpi^2) (MpR8^2)))+((16 (dmt^2) (4 Cθ ((mk^2)-(mpi^2))+(Sqrt[2]) (2 (mk^2)+(mpi^2)) Sθ))/((Sqrt[3]) (Fpi^2) (MpR1^2)))+((4 cm (4 cm (mpi^2) (Cθ-(Sqrt[2]) Sθ)-2 cd ((meta^2)+(mpi^2)-s) (Cθ-(Sqrt[2]) Sθ)))/((Sqrt[3]) (Fpi^2) ((Ma^2)-s)))-((8 cmt (2 (mk^2)+(mpi^2)) (Cθ-(Sqrt[2]) Sθ) (-2 (Sqrt[3]) cmt+(Sqrt[3]) cdt (1+((Cθ)^2)+((Sθ)^2))))/(3 (Fpi^2) (Ms1^2)))-((16 cm ((mk^2)-(mpi^2)) (2 cm (Cθ-(Sqrt[2]) Sθ)+cd (((Cθ)^3)+(Sqrt[2]) Sθ+(Sqrt[2]) ((Cθ)^2) Sθ-Cθ (1+4 ((Sθ)^2)))))/(3 (Sqrt[3]) (Fpi^2) (Ms8^2)));

fs3p0etδL8Lam2[s_]:=((64 (mpi^2) (Cθ-(Sqrt[2]) Sθ) δL8)/((Sqrt[3]) (Fpi^2)))-2 (Sqrt[(2/3)]) Sθ Λ2;

fs3p0etmixing[s_]:=-((((Sqrt[2]) Cθ+Sθ) (2 sδ+δk))/(Sqrt[3]));

s3 -> (K^0) (OverBar[(K^0)])

fs3k0k0bCA[s_]:=-1;

fs3k0k0bLoop[s_]:=(1/(16 (π^2)))((((2 ((Cθ)^2)-(Sqrt[2]) Cθ Sθ-2 ((Sθ)^2)) A0[(meta^2)])/(6 (Fpi^2)))+(((-2 ((Cθ)^2)+(Sqrt[2]) Cθ Sθ+2 ((Sθ)^2)) A0[(metaP^2)])/(6 (Fpi^2)))+(((Cθ-(Sqrt[2]) Sθ) (Cθ (3 (meta^2)+8 (mk^2)+(mpi^2)-9 s)+2 (Sqrt[2]) (2 (mk^2)+(mpi^2)) Sθ) B0[s,(meta^2),(mpi^2)])/(18 (Fpi^2)))-((((Sqrt[2]) Cθ+Sθ) (2 (Sqrt[2]) Cθ (2 (mk^2)+(mpi^2))-(3 (metaP^2)+8 (mk^2)+(mpi^2)-9 s) Sθ) B0[s,(metaP^2),(mpi^2)])/(18 (Fpi^2)))-((s B0eq[s,(mk^2)])/(4 (Fpi^2))));

fs3k0k0bRes[s_]:=((16 (dm^2) (mk^2))/((Fpi^2) (MpR8^2)))+((8 (cdt-cmt) cmt (2 (mk^2)+(mpi^2)))/((Fpi^2) (Ms1^2)))+((8 (cd-cm) cm ((mk^2)-(mpi^2)))/(3 (Fpi^2) (Ms8^2)))-((4 cm (2 cm (mk^2)+cd (-2 (mk^2)+s)))/((Fpi^2) ((Ma^2)-s)));

fs3k0k0bδL8Lam2[s_]:=-((32 (mk^2) δL8)/(Fpi^2));

fs3k0k0bmixing[s_]:=0;

s3 -> (π^0) η'

fs3p0etpCA[s_]:=((2 ((Sqrt[2]) Cθ+Sθ))/(Sqrt[3]));

fs3p0etpLoop[s_]:=(1/(16 (π^2)))(((((Sqrt[2]) ((Cθ)^3)-3 ((Cθ)^2) Sθ+2 ((Sθ)^3)) A0[(meta^2)])/(3 (Sqrt[3]) (Fpi^2)))+(((2 (Sqrt[2]) ((Cθ)^3)+6 ((Cθ)^2) Sθ+3 (Sqrt[2]) Cθ ((Sθ)^2)+((Sθ)^3)) A0[(metaP^2)])/(3 (Sqrt[3]) (Fpi^2)))-(((Sθ+((Sθ)^3)+(Sqrt[2]) Cθ (-1+((Sθ)^2))) A0[(mk^2)])/((Sqrt[3]) (Fpi^2)))+((((Sqrt[2]) Cθ+Sθ) A0[(mpi^2)])/((Sqrt[3]) (Fpi^2)))+((2 (mpi^2) ((Sqrt[2]) ((Cθ)^3)-3 ((Cθ)^2) Sθ+2 ((Sθ)^3)) B0[s,(meta^2),(mpi^2)])/(3 (Sqrt[3]) (Fpi^2)))+((2 (mpi^2) ((Sqrt[2]) Cθ+Sθ) (2 ((Cθ)^2)+2 (Sqrt[2]) Cθ Sθ+((Sθ)^2)) B0[s,(metaP^2),(mpi^2)])/(3 (Sqrt[3]) (Fpi^2)))-(((-2 (Sqrt[2]) Cθ (2 (mk^2)+(mpi^2))+(3 (metaP^2)+8 (mk^2)+(mpi^2)-9 s) Sθ) B0eq[s,(mk^2)])/(6 (Sqrt[3]) (Fpi^2))));

fs3p0etpRes[s_]:=-((16 (dmt^2) ((Sqrt[2]) Cθ (2 (mk^2)+(mpi^2))+4 (-(mk^2)+(mpi^2)) Sθ))/((Sqrt[3]) (Fpi^2) (MpR1^2)))+((16 (dm^2) ((Sqrt[2]) Cθ (2 (mk^2)-5 (mpi^2))-2 (2 (mk^2)+(mpi^2)) Sθ))/(3 (Sqrt[3]) (Fpi^2) (MpR8^2)))-((4 cm (-4 cm (mpi^2) ((Sqrt[2]) Cθ+Sθ)+2 cd ((metaP^2)+(mpi^2)-s) ((Sqrt[2]) Cθ+Sθ)))/((Sqrt[3]) (Fpi^2) ((Ma^2)-s)))+((8 cmt (2 (mk^2)+(mpi^2)) ((Sqrt[2]) Cθ+Sθ) (2 (Sqrt[3]) cmt-(Sqrt[3]) cdt (1+((Cθ)^2)+((Sθ)^2))))/(3 (Fpi^2) (Ms1^2)))+((16 cm ((mk^2)-(mpi^2)) (-2 cm ((Sqrt[2]) Cθ+Sθ)+cd (Sθ+4 ((Cθ)^2) Sθ-((Sθ)^3)+(Sqrt[2]) Cθ (1+((Sθ)^2)))))/(3 (Sqrt[3]) (Fpi^2) (Ms8^2)));

fs3p0etpδL8Lam2[s_]:=((64 (mpi^2) ((Sqrt[2]) Cθ+Sθ) δL8)/((Sqrt[3]) (Fpi^2)))+2 (Sqrt[(2/3)]) Cθ Λ2;

fs3p0etpmixing[s_]:=(((Cθ-(Sqrt[2]) Sθ) (2 sδ-δk))/(Sqrt[3]));

Analytical Results for the Pseudoscalar Form-Factor within U(3) χPT

In this sector, we provide the analytical results for the pseudoscalar form-factors of the pseudo-Goldstone boson and pseudoscalar resonances, i.e. (Subscript[H, P]^a) defined in Eq.(34) in the article.  See the mini-manual in the scalar form-factor for details.

p0 ->  η

fps0etCA[s_]:= -2 Fpi Sθ;

fps0etLoop[s_]:= ((-((((Sqrt[2]) ((Cθ)^3)+6 ((Cθ)^2) Sθ+2 ((Sθ)^3)) A0[(meta^2)])/(3 Fpi))-((Sθ (-2 ((Cθ)^2)+(Sqrt[2]) Cθ Sθ+2 ((Sθ)^2)) A0[(metaP^2)])/(3 Fpi))-(((2 (Sqrt[2]) Cθ+5 Sθ-3 ((Cθ)^2) Sθ) A0[(mk^2)])/(3 Fpi))+(((Sqrt[2]) Cθ A0[(mpi^2)])/Fpi))/(16 (π^2)));

fps0etRes[s_]:= ((16 (dmt^2) (2 (Sqrt[2]) Cθ ((mk^2)-(mpi^2))+(2 (mk^2)+(mpi^2)) Sθ))/(Fpi (MpR1^2)))-((16 cm ((mk^2)-(mpi^2)) (2 (Sqrt[2]) cm Cθ-cd Sθ (-1+((Cθ)^2)+2 (Sqrt[2]) Cθ Sθ)))/(3 Fpi (Ms8^2)))+((8 cmt (2 (mk^2)+(mpi^2)) Sθ (-2 cmt+cdt (1+((Cθ)^2)+((Sθ)^2))))/(Fpi (Ms1^2)));

fps0etδL8Lam2[s_]:=-((32 (2 (Sqrt[2]) Cθ ((mk^2)-(mpi^2))+(2 (mk^2)+(mpi^2)) Sθ) δL8)/(3 Fpi))-2 Fpi Sθ Λ2 ;

fps0etmixing[s_]:=-Cθ Fpi (2 sδ+δk);

p0 ->  η'

fps0etpCA[s_]:=2 Cθ Fpi;

fps0etpLoop[s_]:=((((Cθ (2 ((Cθ)^2)-(Sqrt[2]) Cθ Sθ-2 ((Sθ)^2)) A0[(meta^2)])/(3 Fpi))+(((2 ((Cθ)^3)+6 Cθ ((Sθ)^2)-(Sqrt[2]) ((Sθ)^3)) A0[(metaP^2)])/(3 Fpi))-(((2 (Sqrt[2]) Sθ+Cθ (-5+3 ((Sθ)^2))) A0[(mk^2)])/(3 Fpi))+(((Sqrt[2]) Sθ A0[(mpi^2)])/Fpi))/(16 (π^2)));

fps0etpRes[s_]:=-((16 (dmt^2) (Cθ (2 (mk^2)+(mpi^2))+2 (Sqrt[2]) (-(mk^2)+(mpi^2)) Sθ))/(Fpi (MpR1^2)))+((16 cm ((mk^2)-(mpi^2)) (-2 (Sqrt[2]) cm Sθ+cd Cθ (1+2 (Sqrt[2]) Cθ Sθ-((Sθ)^2))))/(3 Fpi (Ms8^2)))-((8 cmt Cθ (2 (mk^2)+(mpi^2)) (-2 cmt+cdt (1+((Cθ)^2)+((Sθ)^2))))/(Fpi (Ms1^2)));

fps0etpδL8Lam2[s_]:= ((32 (Cθ (2 (mk^2)+(mpi^2))+2 (Sqrt[2]) (-(mk^2)+(mpi^2)) Sθ) δL8)/(3 Fpi))+2 Cθ Fpi Λ2;

fps0etpmixing[s_]:=Fpi Sθ (-2 sδ+δk);

p8 ->  η

fps8etCA[s_]:=2 Cθ Fpi;

fps8etLoop[s_]:=((((Cθ (((Cθ)^2)+(Sqrt[2]) Cθ Sθ+2 ((Sθ)^2)) A0[(meta^2)])/Fpi)+(((Cθ-(Sqrt[2]) Sθ) (2 ((Cθ)^2)-((Sθ)^2)) A0[(metaP^2)])/(3 Fpi))+(((Cθ-3 ((Cθ)^3)+2 (Sqrt[2]) Sθ) A0[(mk^2)])/(3 Fpi))-(((Cθ+(Sqrt[2]) Sθ) A0[(mpi^2)])/Fpi))/(16 (π^2)));

fps8etRes[s_]:=-((16 (dm^2) (Cθ (4 (mk^2)-(mpi^2))+2 (Sqrt[2]) ((mk^2)-(mpi^2)) Sθ))/(3 Fpi (MpR8^2)))-((16 cm ((mk^2)-(mpi^2)) (-2 cm (Cθ+(Sqrt[2]) Sθ)+cd Cθ (-1+((Cθ)^2)+2 (Sqrt[2]) Cθ Sθ)))/(3 Fpi (Ms8^2)))-((8 cmt Cθ (2 (mk^2)+(mpi^2)) (-2 cmt+cdt (1+((Cθ)^2)+((Sθ)^2))))/(Fpi (Ms1^2)));

fps8etδL8Lam2[s_]:= ((32 (Cθ (4 (mk^2)-(mpi^2))+2 (Sqrt[2]) ((mk^2)-(mpi^2)) Sθ) δL8)/(3 Fpi));

fps8etmixing[s_]:=-Fpi Sθ (2 sδ+δk);

p8 ->  η'

fps8etpCA[s_]:=2 Fpi Sθ;

fps8etpLoop[s_]:=((-((((Sqrt[2]) Cθ+Sθ) (((Cθ)^2)-2 ((Sθ)^2)) A0[(meta^2)])/(3 Fpi))+((Sθ (2 ((Cθ)^2)-(Sqrt[2]) Cθ Sθ+((Sθ)^2)) A0[(metaP^2)])/Fpi)+(((-2 (Sqrt[2]) Cθ+Sθ-3 ((Sθ)^3)) A0[(mk^2)])/(3 Fpi))+((((Sqrt[2]) Cθ-Sθ) A0[(mpi^2)])/Fpi))/(16 (π^2)));

fps8etpRes[s_]:=((16 (dm^2) (2 (Sqrt[2]) Cθ ((mk^2)-(mpi^2))+(-4 (mk^2)+(mpi^2)) Sθ))/(3 Fpi (MpR8^2)))-((8 cmt (2 (mk^2)+(mpi^2)) Sθ (-2 cmt+cdt (1+((Cθ)^2)+((Sθ)^2))))/(Fpi (Ms1^2)))-((16 cm ((mk^2)-(mpi^2)) (2 cm ((Sqrt[2]) Cθ-Sθ)+cd Sθ (-1-2 (Sqrt[2]) Cθ Sθ+((Sθ)^2))))/(3 Fpi (Ms8^2)));

fps8etpδL8Lam2[s_]:= -((32 (2 (Sqrt[2]) Cθ ((mk^2)-(mpi^2))+(-4 (mk^2)+(mpi^2)) Sθ) δL8)/(3 Fpi));

fps8etpmixing[s_]:=Cθ Fpi (2 sδ-δk);

p3 ->  (π^0)

fps3p0CA[s_]:=2 Fpi;

fps3p0Loop[s_]:=(((((((Cθ)^2)-2 (Sqrt[2]) Cθ Sθ+2 ((Sθ)^2)) A0[(meta^2)])/(3 Fpi))+(((2 ((Cθ)^2)+2 (Sqrt[2]) Cθ Sθ+((Sθ)^2)) A0[(metaP^2)])/(3 Fpi))-((A0[(mpi^2)])/Fpi))/(16 (π^2)));

fps3p0Res[s_]:=-((16 (dm^2) (mpi^2))/(Fpi (MpR8^2)))-((16 (cdt-cmt) cmt (2 (mk^2)+(mpi^2)))/(Fpi (Ms1^2)))+((32 (cd-cm) cm ((mk^2)-(mpi^2)))/(3 Fpi (Ms8^2)));

fps3p0δL8Lam2[s_]:=((32 (mpi^2) δL8)/Fpi) ;

fps3p0mixing[s_]:=0;

p0 ->  Pseudoscalar Resonances

fps0PS=-4 (Sqrt[6])  dmt;

p8 ->  Pseudoscalar Resonances

fps8PS=-4 (Sqrt[2]) dm;

p3 ->  Pseudoscalar Resonances

fps3PS=-4 (Sqrt[2]) dm;