Name: Daniel Date: 05/27/19-03:28:02 PM Z
Hello,
I’m trying to calculate a total cross-section for a simples process but I am getting negative values for some input masses:
ScalarProduct[p1, p1] = mx^2;
ScalarProduct[k1, k1] = mx^2;
ScalarProduct[p2, p2] = mq^2;
ScalarProduct[k2, k2] = mq^2;
ScalarProduct[p1, p2] = (s - mx^2 - mq^2)/2;
ScalarProduct[k1, p1] = -((t - 2 mx^2)/2);
ScalarProduct[p2, k1] = -((u - mx^2 - mq^2)/2);
Ma = (yx*yf)/(SP[k1 - p1] - m^2) Spinor[k1,
mx].Spinor[p1, mx] Spinor[
k2, mq].Spinor[p2, mq];
Ma = (yx*yf)/(SP[k1 - p1] - m^2) Spinor[k1,
mx].Spinor[p1, mx] Spinor[
k2, mq].Spinor[p2, mq];
MM = 1/4 Ma2 /. DiracTrace -> Tr /. k2 -> -k1 + p1 + p2 //
ExpandScalarProduct // PropagatorDenominatorExplicit // Simplify
Expand[MM /. u -> mx^2 + mq^2 - t - s ] // ExpandScalarProduct
//
PropagatorDenominatorExplicit // Simplify ;
((-2 mq^2 + t) (-4 mx^2 + t) yf^2 yx^2)/(m^2 - t)^2
Expand[MM /. u -> mx^2 + mq^2 - t - s /. t -> -px^2 (1 - Cos[\[Theta]])] ;
Integrate[(yf^2 yx^2 Sin(\[Theta])(-4 mx^2+px^2 Cos(\[Theta])-px^2) (-3 mq^2+mx^2+px^2 Cos(\[Theta])-px^2))/(m^2-px^2 Cos(\[Theta])+px^2)^2, {\[Theta], 0, Pi}]
The result of the above integral is:
Sol12 = 1 - ((m^2 - 4 mx^2) (m^2 - 3 mq^2 + mx^2))/(
px^2 (m^2 + 2 px^2)) - (-m^4 + 4 mx^2 (-3 mq^2 + mx^2) +
m^2 (3 mq^2 + 3 mx^2 - px^2) +
m^2 (-2 m^2 + 3 (mq^2 + mx^2)) Log[m^2])/(
m^2 px^2) - ((2 m^2 - 3 (mq^2 + mx^2)) Log[m^2 + 2
px^2])/px^2;
Then for some input masses it takes negative values:
N[Sol12 /. mq -> 1 /. mx -> 100 /. m -> 1000 /. px -> 10]
-0.000793574
Thanks in advance for any help.
Daniel