# Top anti-top decays and Cabbibo Suppresion

1. Mar 2, 2010

### TFM

1. The problem statement, all variables and given/known data

Consider the following final state topologies for $$t \bar{t}$$
decays:

(i)

$$t\bar{t} \rightarrow b jets + (1 lepton) + (\geq 1 light jet(s) ) + neutrinos (lepton = e or \mu)$$;

(ii)

$$t\bar{t} \rightarrow b jets+(2 leptons)+ neutrinos (lepton = e or \mu)$$;

where the light jets and the leptons come from the decay of the W bosons produced in conjunction with the b-jets in the top-antitop decays.

Some of the final states listed above, while being kinematically allowed, will nevertheless be “Cabibbo suppressed”, and therefore their contribution to the list of possible final states can be neglected to first order. Under these assumptions, show that the fraction of events measured in the final state is 24/81 for topology (i) and 4/81 for topology (ii).

2. Relevant equations

$$d' = d cos\theta_c + s sin\theta_c$$

$$s' = s cos\theta_c - d sin\theta_c$$

$$g_{ud} = g_{cs} = g_Wcos\theta_c$$

$$g_{us} = -g_{cd} = g_Wsin\theta_c$$

3. The attempt at a solution

Hi

I have written done some equations, but I am unsure if they are that useful (the question states some states will be Cabbibo Surppres, so I am assuming some of then will come in somewhere) but I am uncertain how you are supposed to get number valuies from the two equations?