- 208

- 2

**1. Homework Statement**

In 2011 the ATLAS experiment had a total integrated recorded luminosity of ##5.08fb^{-1}## at 7TeV, and in 2012 of ##21.3fb^{-1}## at 8TeV. Under these conditions Higgs bosons can be produced in several ways including gluon-gluon fusion and vector boson fusion, which have the cross sections ##\sigma_{ggf} = 19.0 \pm 7.5pb## and ##\sigma_{vbf} = 1.6 \pm 0.3 pb## respectively.

The branching ratio of ##H \rightarrow ZZ## is 2.87%, and for ##Z \rightarrow l^{+}l_{-}## is 3.37% where l is a lepton. How many Higgs, produced by the two processes listed above, could have been detected in the decay mode

##H \rightarrow ZZ^* \rightarrow 4l## where l is electrons or muons?

**2. Homework Equations**

**3. The Attempt at a Solution**

Integrated luminosity 2012 = ##L_{12}## and for 2011 = ##L_{11}##. I calculated the total number of Higgs produced while the detector was recording by multiplying integrated luminosities for every year by the cross sections for the processes, then adding:

##N = \sigma_{ggf}L_{12} + \sigma_{vbf}L_{12} + \sigma_{ggf}L_{11} + \sigma_{vbf}L_{11}##

##=1.9\times 10^4 fb \times 21.3 fb^{-1} +1.6\times 10^3 fb \times 21.3 fb^{-1} +1.9\times 10^4 fb \times 5.08 fb^{-1} +1.6\times 10^3 fb \times 5.08 fb^{-1}##

##= 543,748## Higgs produced in total.

I don't know how to find the number of detections. I don't have the total decay width and the only equation I know involving branching ratios is ##BF(i) = \frac{\Gamma_i}{\Gamma}##. I thought about just multiplying the probabilities but I think that's probably wrong, and anyway I'm given the branching ratio of Z to any leptons where I need specifically Z to electrons or muons, so I assume that has to be calculated somehow. Can anyone give me some pointers?

Thanks for any help!