- #1
kaksmet
- 83
- 0
Hello!
I am trying to calculate the matrix element of the process where an incoming upp quark and gluon interact via an upquark and emit a photon and an upquark.
---u(p1)->--~~gamma(p3)~~
~~g(p2)~~~-------u(p4)-------
from the gluon vertex I get a color factor [tex]t^a[/tex] which I am not sure how to handle. My matrix element then looks like this
[tex]\bar{u}^s(p_4)ig_s \gamma^{mu}t^a\epsilon_{\mu}(p_2)\frac{\gamma^{\alpha}q_{\alpha} + m}{q^2-m^2}\epsilon^*_{\nu}(p_3)iQ_ue\gamma^{\nu}u^s(p_1)[/tex]
But there must be something that I am missing, since [tex]t^a[/tex] is a matrix it seems like my matrix element has the matrix dimensions of [tex]t^a[/tex]. Should I include a color part of the u quark? And if so, how does that work? Any reference where I could read more about it?
Thanks a lot for any imput!
I am trying to calculate the matrix element of the process where an incoming upp quark and gluon interact via an upquark and emit a photon and an upquark.
---u(p1)->--~~gamma(p3)~~
|
|
u(q)
|
|
from the gluon vertex I get a color factor [tex]t^a[/tex] which I am not sure how to handle. My matrix element then looks like this
[tex]\bar{u}^s(p_4)ig_s \gamma^{mu}t^a\epsilon_{\mu}(p_2)\frac{\gamma^{\alpha}q_{\alpha} + m}{q^2-m^2}\epsilon^*_{\nu}(p_3)iQ_ue\gamma^{\nu}u^s(p_1)[/tex]
But there must be something that I am missing, since [tex]t^a[/tex] is a matrix it seems like my matrix element has the matrix dimensions of [tex]t^a[/tex]. Should I include a color part of the u quark? And if so, how does that work? Any reference where I could read more about it?
Thanks a lot for any imput!