How Many Higgs Bosons Are Produced in an 8-Hour LHC Run?

[Kara386]

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?

Homework Equations

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.

 

[Kara386]

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.

 

[mfb]

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.