> 
# Berechnung des top Zerfalls
# 
> restart;
> read `d:/Programme/Maple V release 5/hep/heppack5.txt`;
Warning, new definition for norm
Warning, new definition for trace
> top:=[Mt,Mt,0,0];

                        top := [Mt, Mt, 0, 0]

> bot:=[Eb,0,theta,0];

                       bot := [Eb, 0, theta, 0]

> Wb:=[Ew,Mw,Pi-theta,Pi];

                    Wb := [Ew, Mw, Pi - theta, Pi]

> j1:=ubuw(top,1,bot,-1);

  j1 := [-sqrt(2) sqrt(Mt) sqrt(Eb) sin(1/2 theta),

        -sqrt(2) sqrt(Mt) sqrt(Eb) cos(1/2 theta),

        I sqrt(2) sqrt(Mt) sqrt(Eb) cos(1/2 theta),

        sqrt(2) sqrt(Mt) sqrt(Eb) sin(1/2 theta)]

# Zunaechst werden die Amplituden (ohne den Faktor g/sqrt(2) fuer die
# moeglichen Spineinstellungen berechnet.
> t[1]:=dotprod(j1,polbar(Wb,1));

              t[1] := 2 sqrt(Mt) sqrt(Eb) cos(1/2 theta)

> t[2]:=dotprod(j1,polbar(Wb,0));

                                                             2     2
  t[2] := - sqrt(2) sqrt(Mt) sqrt(Eb) (sin(1/2 theta) sqrt(Ew  - Mw )

         + cos(1/2 theta) Ew sin(theta)

         - sin(1/2 theta) Ew cos(theta))/Mw

> subs(cos(theta)=cos(theta/2)^2-sin(theta/2)^2,sin(theta)=2*sin(theta/2
> )*cos(theta/2),%);

                                                     2     2
  - sqrt(2) sqrt(Mt) sqrt(Eb) (sin(1/2 theta) sqrt(Ew  - Mw )

                           2
         + 2 cos(1/2 theta)  Ew sin(1/2 theta)

                                            2                 2
         - sin(1/2 theta) Ew (cos(1/2 theta)  - sin(1/2 theta) ))/Mw

> t[2]:=simplify(%);

  t[2] := - sqrt(2) sqrt(Mt) sqrt(Eb) sin(1/2 theta)

                2     2
        (sqrt(Ew  - Mw ) + Ew)/Mw

> t[3]:=dotprod(j1,polbar(Wb,-1));

                              t[3] := 0

> j2:=ubuw(top,-1,bot,-1);

  j2 := [sqrt(2) sqrt(Mt) sqrt(Eb) cos(1/2 theta),

        sqrt(2) sqrt(Mt) sqrt(Eb) sin(1/2 theta),

        I sqrt(2) sqrt(Mt) sqrt(Eb) sin(1/2 theta),

        sqrt(2) sqrt(Mt) sqrt(Eb) cos(1/2 theta)]

> t[4]:=dotprod(j2,polbar(Wb,1));

              t[4] := 2 sqrt(Mt) sqrt(Eb) sin(1/2 theta)

> t[5]:=dotprod(j2,polbar(Wb,0));

                                                           2     2
  t[5] := sqrt(2) sqrt(Mt) sqrt(Eb) (cos(1/2 theta) sqrt(Ew  - Mw )

         + sin(1/2 theta) Ew sin(theta)

         + cos(1/2 theta) Ew cos(theta))/Mw

> subs(cos(theta)=cos(theta/2)^2-sin(theta/2)^2,sin(theta)=2*sin(theta/2
> )*cos(theta/2),%);

                                                   2     2
  sqrt(2) sqrt(Mt) sqrt(Eb) (cos(1/2 theta) sqrt(Ew  - Mw )

                           2
         + 2 sin(1/2 theta)  Ew cos(1/2 theta)

                                            2                 2
         + cos(1/2 theta) Ew (cos(1/2 theta)  - sin(1/2 theta) ))/Mw

> t[5]:=simplify(%);

  t[5] := sqrt(2) sqrt(Mt) sqrt(Eb) cos(1/2 theta)

                2     2
        (sqrt(Ew  - Mw ) + Ew)/Mw

> t[6]:=dotprod(j2,polbar(Wb,-1));

                              t[6] := 0

> sumquadrat:=sum(t[i]*t[i],i=1..6):
> simplify(%);

                        2       2            2     2
               Mt Eb (Mw  + 2 Ew  + 2 sqrt(Ew  - Mw ) Ew)
             2 ------------------------------------------
                                    2
                                  Mw

# Fuer die  Wurzel gilt steht pw=Eb, also gilt nach Multiplaktion mit
# g^2/2 fuer die Summe der quadrierten Matrixelemente
> tsumquadrat:=g^2/2*2*Mt*Eb*(2*Ew^2+Mw^2+2*Eb*Ew)/Mw^2;

                           2            2     2
                          g  Mt Eb (2 Ew  + Mw  + 2 Eb Ew)
           tsumquadrat := --------------------------------
                                          2
                                        Mw

> simplify(subs(Ew=(Mt^2+Mw^2)/2/Mt,Eb=(Mt^2-Mw^2)/2/Mt,%));

                        2    2     2     2       2
                       g  (Mt  - Mw ) (Mt  + 2 Mw )
                   1/2 ----------------------------
                                     2
                                   Mw

>