# How many Higgs bosons in 8 hours?

## Homework Statement

In 2012, the LHC ran with peak luminosity ##7.73\times 10^33## and at c.o.m. energy at 8TeV. The Higgs can be produced by a number of processes including ##\sigma_{ggf} = 19.0 \pm 7.5##pb and ##\sigma_{VBF}=1.6 \pm 0.3##pb. In 2011 a total integrated luminosity of ##5.08fb^{-1}## was found, and ##21.3fb^{-1}## in 2012.

How many Higgs are produced in an 8 hour run at 2012 peak luminosity? How many were produced in total by these production modes at ATLAS while the detector was recording data?

## The Attempt at a Solution

I don't know how to integrate luminosity w.r.t. time - I thought it was a constant, but then why would you need total integrated luminosity? What I did was
##N_{ggf} = \sigma_{ggf} \int_{0}^{8hrs} L dt## where L is luminosity.
Treating ##L## as a constant, then ##N_{ggf} = 1.9 \times 10^4 \times 7.73 \times 10^{33} t |^{28800s}_{0}##
##=2.2\times 10^{38}## and that has to be repeated for ##\sigma_{vbf}## which gives a number that seems way too high. If ##L## isn't constant I don't know the time dependence, but possibly my mistake is that I'm calculating events and assuming they'll all result in the Higgs?

Then I thought for the second part maybe you had to use total integrated recorded luminosity so ##N_{ggf} = 1.9 \times 10^4 fb\times 21.3 fb^{-1}## and repeat the process for ##N_{vbf}## and repeat the calculation with 2011 integrated luminosities and add them all, but unfortunately that gives an answer less than my first one.

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Wait this might be a units thing. I should work out units properly.

So 1 barn = ##1 \times 10^{-28}m^2##
1 femtobarn = ##1 \times 10^{-43}m^2##
1 picobarn = ##1 \times 10^{-40} m^2##
##7.73 \times 10^{33}cm^{-2}s^{-1} = 7.73 \times 10^{37}m^{-2}s^{-1}##

Redoing it with proper units actually gives 4230 events i.e. Higgs bosons produced in the 8 hours.

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mfb
Mentor
Don't forget the other production process. 4230 is right for gluon-gluon fusion.

During actual operation, the luminosity is not constant (at least not for the experiments measuring the Higgs) - it starts at a high value and then gradually goes down as the number of protons decreases and the beam quality goes down.