Name: Daniel (email_not_shown)
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

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