 #1
Thyrac
 1
 0
 Homework Statement:
 I’m wondering what the matrix element is for electron muon scattering for right helicity particles. I got $$e^2(1 + cos(\theta))$$. Is this correct?
 Relevant Equations:

$$u(p_2)\sigma^{\mu}u(p_1)\frac{e^2}{q^2}
u^{\dagger}(p_3)\sigma_{\mu}u^{\dagger}(p_4)$$
The current I have found for the incoming electron and muon is
$$u(p_2)\sigma^{\mu}u(p_1)$$ = $$E_{cm}(0, i, 1, 0)^\mu$$
The current I have found for the outgoing particles are
$$u^{\dagger}(p_3)\sigma_{\mu}u^{\dagger}(p_4)$$ = $$E_{cm}(0, i\cos(\theta), 1, i\sin(\theta))_{\mu}$$
Multiplying these 4vectors together give me $$E_{cm}^2(1+\cos(\theta))$$
And multiplying it by the photon propagator with vertices $$\frac{e^2}{q^2}$$ give us
$$e^2(1 + \cos(\theta))$$
(Note that again all particles involved are right helicity)
Now I haven’t found any source confirming that the matrix element for the process is what I calculated, but I checked my work and can’t see any possible errors. So my question is, is $$e^2(1 + \cos(\theta))$$ the correct matrix element of electron muon scattering?
$$u(p_2)\sigma^{\mu}u(p_1)$$ = $$E_{cm}(0, i, 1, 0)^\mu$$
The current I have found for the outgoing particles are
$$u^{\dagger}(p_3)\sigma_{\mu}u^{\dagger}(p_4)$$ = $$E_{cm}(0, i\cos(\theta), 1, i\sin(\theta))_{\mu}$$
Multiplying these 4vectors together give me $$E_{cm}^2(1+\cos(\theta))$$
And multiplying it by the photon propagator with vertices $$\frac{e^2}{q^2}$$ give us
$$e^2(1 + \cos(\theta))$$
(Note that again all particles involved are right helicity)
Now I haven’t found any source confirming that the matrix element for the process is what I calculated, but I checked my work and can’t see any possible errors. So my question is, is $$e^2(1 + \cos(\theta))$$ the correct matrix element of electron muon scattering?