LHCb clocks up 8 Inverse femtobarns

The LHCb experiment has just announced that it’s accumulated 8 inverse femtobarns of data. The screen shows the result and the ongoing totals.

It’s obviously a cause for celebration, but maybe this is an opportunity to explain the rather obscure ‘inverse femtobarn’ unit.

Let’s start with the barn. It’s a unit of area. 10 -28 square metres, so rather small. It was invented by the nuclear physicists to describe the effective target-size corresponding to a particular nuclear reaction. When you fire beam particles at target particles then all sorts of things can happen, with probabilities predicted by complicated quantum mechanical calculations,  but those probabilities can be considered as if each reaction had its own area on the target nucleus: the bigger the area the more likely the reaction. It’s not literally true, of course, but the dimensions are right and you can use it as a model if you don’t push it too far.  Nuclear cross sections, usually called σ, are typically  few barns, or fractions of a barn, so it’s a handy unit.

No, it’s not named after some Professor Barn – it’s probably linked to expressions like “Couldn’t hit the broad side of a barn” or even “Couldn’t hit a barn door with a banjo!”

Particle physicists took this over, though our cross sections were typically smaller – millibarns (10-3 barns) for strong interaction processes, microbarns (10-6) and nanobarns (10-9) for electromagnetic processes such as were measured at PETRA and LEP.  Beyond that lie picobarns (10-12) and femtobarns(10-15).   Only the neutrino physicists stuck with m2 or cm2 as their cross sections are so small that even using attobarns can’t give you a sensible number. So a femtobarn is just a cross section or area, 10-43 , square metres.

In a colliding beam storage ring like the LHC, Luminosity measures the useful collision rate, how many particles are in the beams, how tightly the beams have been focussed and how well they are aligned when they collide.  The event rate is the produce of the cross section and the luminosity, R=Lσ so luminosity is what accelerator designers set out to deliver. Integrated luminosity is just  luminosity integrated over time, and ∫L dt = N/σ, as  the integrated rate is just the total number of events,∫R dt = N

So there we have it.  An integrated luminosity of 8 inverse femtobarns (written 8 fb-1  or 8 (1/fb) ) means that for a cross section as tiny as 8 fb, one would expect to see, on average,  8 events. 8 is a measurable number – though that depends on backgrounds –  but what this is saying is that we can detect (if they’re there) rare processes that have cross sections of order 1 fb.   That’s the sort of number that many Beyond-the-Standard-Model theories come up with. It’s pushing back the frontier.

If you look at the screen you can see the recorded number as 8000 pb-1. Yes, an inverse femtobarn is bigger than an inverse picobarn. Which is obvious if you think about it, but disconcerting until you do.

Another point to take from the picture is that the LHC accelerator actually delivered more. 8769.76 pb-1 were delivered to get the 8000 taken. The loss is inevitable due to time lost to ramping voltages,  detector calibration and the overall efficiency of over 90% is pretty good.

So it’s a landmark.  But these BSM processes havn’t shown up yet and until they do we need to keep taking data – and increase the luminosity. Both the LHCb  detector and the LHC accelerator are working hard to achieve this – both are needed, as the detector has to be able to handle the increased data it’s being given. So we’ve passed a milestone, but there’s still a long and exciting road ahead.