How much is one inverse femtobarn?

Blog readers know this since ages, but today the news was made official.

Last week, the Chamonix workshop once again proved its worth as a place where all the stakeholders in the LHC can come together, take difficult decisions and reach a consensus on important issues for the future of particle physics. The most important decision we reached last week is to run the LHC for 18 to 24 months at a collision energy of 7 TeV (3.5 TeV per beam). After that, we’ll go into a long shutdown in which we’ll do all the necessary work to allow us to reach the LHC’s design collision energy of 14 TeV for the next run. This means that when beams go back into the LHC later this month, we’ll be entering the longest phase of accelerator operation in CERN’s history, scheduled to take us into summer or autumn 2011.

This announcement does not mention the luminosity goal, but both blogs and some Chamonix slides point to 1fb${}^{-1}$. How much is that? The Tevatron by the end of 2011 will have acquired 10-12 inverse femtobarns of luminosity. Using advanced calculus one concludes that 1 inverse femtobarn is less than 10 inverse femtobarns, but at the same time 7 TeV is more than 2 TeV. To unravel this, here is a handful of back-of-a-madgraph estimates of how many interesting events can the colliders get by the end of 2011.

Higgs Boson (120 GeV Higgs produced in gluon fusion)

Tevatron: 10 000 LHC: 11 000

Both experiments will have a similar sensitivity to the Higgs. Although 10k looks like whole lotta events, Higgs signatures are notoriously difficult to search. For example, one promising discovery channel at the LHC is when the Higgs decays into two photons, which happens roughly twice per thousand events for a 120 GeV Higgs. For this and other reasons, neither Tevatron nor the LHC has good prospects of discovering the Higgs, unless in lucky circumstances (e.g. production cross section larger than in the standard model, or Higgs mass sitting close to the sweet spot of 160 GeV).

Top Quark Pairs

Tevatron: 80 000 LHC: 130 000

Similarly as for the Higgs, the Tevatron and the LHC will acquire comparable top samples. There should be some, though not dramatic, improvement in top precision measurements. Who knows, maybe there will emerge some 3-sigmish discrepancies with the standard model. The general lesson is that the LHC will be competitive in measuring the standard model processes, but it cannot beat the Tevatron black and blue. What about beyond the standard model?

500 GeV Quark

Tevatron: 15 LHC: 300

This illustrates the obvious truth: LHC fares much better with particles who sit close to the kinematical limit of the Tevatron. In that case one finds that $7 \gg 2$: the energy advantage trumps the luminosity handicap. However, in that particular case the discovery is not guaranteed because of the large standard model background, for example from the top quark pair production. So let's try something easier.

1 TeV Z' (U(1)' gauge boson coupled to B-L with g'=0.1 and decaying to electrons or muons)

Tevatron: 5 LHC: 25

In this case the standard model background is almost non-existent, so 25 events might be enough to claim a discovery. But there is only a tiny sliver of parameter space which the Tevatron cannot reach but the first LHC run can. Make the Z' mass 1.3 TeV and the number of dilepton events at the LHC drops to 5. The final lesson to take home: the LHC can be lucky if Tevatron is extremely unlucky. Let's then hope for the worst, to some.