# A Charge-current interaction: linear terms in a given quark

1. Feb 12, 2017

### spaghetti3451

I am trying to figure out the interaction terms in the Lagrangian which are linear in the top quark.

I find that these terms can only be found in the charged-current interaction since the neutral-current interaction and the gluon-fermion couplings are quadratic in the top quark.

Now, I find two interaction terms in the charged-current interaction which are linear in the top quark:

$ie_{W} \left( V_{mn}\bar{u}_{m}\gamma^{\mu}(1+\gamma^{5}) d_{n} + (V^{\dagger})_{mn}\bar{d}_{m}\gamma^{\mu}(1+\gamma^{5})u_{n} \right),$

where $\displaystyle{e_{W} = g_{2}/2\sqrt{2}}$.

Do both of these terms cause the top quark to decay. My hunch is that, since the top quark must be an initial state, only the second term is allowed, because the second term does not have a bar on the top quark.

2. Feb 19, 2017