# Casimir trick in e+e->H->ffbar

1. Jun 16, 2012

### dingo_d

Casimir trick in e+e-->H->ffbar

1. The problem statement, all variables and given/known data
I have the process:

$e^+e^-\to H\to f\bar{f}$

I have calculated the amplitude and it's conjugate, and now I want to find the averaged, unpolarized square of the invariant amplitude $\langle|M|^2\rangle$.

I average over the initial spins and sum over the final and usually in some simple processes like Moller scattering, I would play with Casimir trick and traces. But here I have:

$\langle|M|^2\rangle=\frac{1}{2}\frac{1}{2}\left( \frac{g_w^2}{4m_w^2} m_e m_f\right)^2\sum_{spins} \bar{u}_4v_2\bar{v}_1u_3\bar{v}_2u_4\bar{u}_3v_1$

Where $\bar{v}_1$ is the incoming positron with impulse p_1 and spin s_1, $u_3$ is the incoming electron, $v_2$ is the outgoing anti fermion, and $\bar{u}_4$ is the outgoing fermion.

If I look at the spinor components, I can arrange them into pairs and use the relations:

$\sum_{s_1}u_{1\delta}\bar{u}_{1\alpha}=({\not} p_1+m_1)_{\delta\alpha}$ and $\sum_{s_2}v_{2\beta}\bar{v}_{2\gamma}=({\not} p_2-m_2)_{\beta\gamma}$

But I'm not getting any trace out of this :\

What am I doing wrong?