input_case nil$ vecdim 3; in "vpack.red"$ mass n=1,f=1,l=1,e=1,p=1,h=1,l1=1,e1=1,n1=1,f1=1; mshell n,f,l,e,p,h,l1,e1,n1,f1; % psi' -> chi1 + photon % --------------------- % n - beams axis % f - psi' polarization % l - photon flight direction % e - photon polarization % h - chi1 polarization M:=E3(h,e,f)$ MM:=M^2$ MM:=trans(e,l,MM)$ MM:=trans(f,n,MM)$ write "distribution n,l ",num(aver(h,MM)); % psi' -> chi1 + photon; chi1 -> meson + meson % -------------------------------------------- % n1 - decay axis MM1:=sub(h=n1,MM)$ write "correlation n,l,n1: ",num(MM1); write "distribution n,n1: ",num(aver(l,MM1)); write "distribution l,n1: ",num(aver(n,MM1)); % psi' -> chi1 + photon; chi1 -> baryon + antibaryon % -------------------------------------------------- MM:=trans(h,n1,MM)$ write "correlation n,l,n1: ",num(MM); write "distribution n,n1: ",num(aver(l,MM)); write "distribution l,n1: ",num(aver(n,MM)); % psi' -> chi1 + photon; chi1 -> psi + photon' % -------------------------------------------- % l1 - photon' flight direction % e1 - photon' polarization % f1 - psi polarization M:=M*E3(h,e1,f1)$ M:=aver(h,M)$ MM:=M^2$ clear M; MM:=trans(e,l,MM)$ MM:=trans(e1,l1,MM)$ MM:=trans(f,n,MM)$ MM1:=aver(f1,MM)$ write "correlation n,l,l1: ",num(MM1); write "distribution n,l1: ",num(aver(l,MM1)); write "distribution l,l1: ",num(aver(n,MM1)); % psi' -> chi1 + photon; chi1 -> psi + photon'; psi -> pi+ pi- % ------------------------------------------------------------ % n1 - decay axis MM1:=sub(f1=n1,MM)$ write "correlation n,l,l1,n1: ",num(MM1); write "distribution n,n1: ",num(aver(l,aver(l1,MM1))); % psi' -> chi1 + photon; chi1 -> psi + photon'; psi -> mu+ mu- % ------------------------------------------------------------ MM:=trans(f1,n1,MM)$ write "correlation n,l,l1,n1: ",num(MM); write "distribution n,n1: ",num(aver(l,aver(l1,MM))); % psi' -> chi2 + photon % --------------------- % chi2 spin projectors: % m = 0 - h0 % m = +-1 - h1 % m = +-2 - h2 % all - hs vector i1,j1,i2,j2; hs:=(i1.i2*j1.j2+i1.j2*j1.i2)/2-i1.j1*i2.j2/3$ h0:=3/2*(n1.i1*n1.j1-i1.j1/3)*(n1.i2*n1.j2-i2.j2/3)$ h1:=1/2*(n1.i1*e.j1+n1.j1*e.i1)*(n1.i2*e.j2+n1.j2*e.i2)$ h1:=trans(e,n1,h1); h2:=hs-h0-h1; M2:=f.i1*e.j1*f.i2*e.j2$ index i1,i2,j1,j2; MM:=M2*hs$ MM:=trans(e,l,MM)$ MM:=trans(f,n,MM)$ write "distribution n,l: ",num(aver(h,MM)); % psi' -> chi2 + photon; chi2 -> meson + meson % -------------------------------------------- MM:=M2*h0$ clear h0; MM:=trans(e,l,MM)$ MM:=trans(f,n,MM)$ write "correlation n,l,n1: ",num(MM); write "distribution n,n1: ",num(aver(l,MM)); write "distribution l,n1: ",num(aver(n,MM)); % psi' -> chi2 + photon; chi2 -> baryon + antibaryon % -------------------------------------------------- MM:=M2*h1$ clear h1; MM:=trans(e,l,MM)$ MM:=trans(f,n,MM)$ write "correlation n,l,n1: ",num(MM); write "distribution n,n1: ",num(aver(l,MM)); write "distribution l,n1: ",num(aver(n,MM)); % psi' -> chi2 + photon; chi2 -> gluon + gluon % -------------------------------------------- MM:=M2*h2$ clear h2; MM:=trans(e,l,MM)$ MM:=trans(f,n,MM)$ write "correlation n,l,n1: ",num(MM); write "distribution n,n1: ",num(aver(l,MM)); write "distribution l,n1: ",num(aver(n,MM)); % psi' -> chi2 + photon; chi2 -> psi + photon' % -------------------------------------------- M:=hs*f.i1*e.j1*f1.i2*e1.j2$ clear hs; MM:=M^2$ clear M; MM:=trans(e,l,MM)$ MM:=trans(e1,l1,MM)$ MM:=trans(f,n,MM)$ MM1:=aver(f1,MM)$ write "correlation n,l,l1: ",num(MM1); write "distribution n,l1: ",num(aver(l,MM1)); write "distribution l,l1: ",num(aver(n,MM1)); % psi' -> chi2 + photon; chi2 -> psi + photon'; psi -> pi+ pi- % ------------------------------------------------------------ MM1:=sub(f1=n1,MM)$ write "correlation n,l,l1,n1: ",num(MM1); write "distribution n,n1: ",num(aver(l,aver(l1,MM1))); % psi' -> chi2 + photon; chi2 -> psi + photon'; psi -> mu+ mu- % ------------------------------------------------------------ MM:=trans(f1,n1,MM)$ write "correlation n,l,l1,n1: ",num(MM); write "distribution n,n1: ",num(aver(l,aver(l1,MM))); end;