# How many Higgs bosons in 8 hours?

1. Nov 4, 2016

### Kara386

1. The problem statement, all variables and given/known data
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?
2. Relevant equations

3. 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.

Last edited: Nov 4, 2016
2. Nov 4, 2016

### 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.

Last edited: Nov 4, 2016
3. Nov 8, 2016

### Staff: 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.