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### Why don’t we just say collision rate?

The LHC run for 2011 is just getting underway, and it’s poised to serve up a menu of exciting new physics. While 2010 was a learning year, with an equitable divide between physics running and machine development, 2011 is a physics year. The aim is to establish good running conditions as quickly as possible, and then to run solidly for physics until the end of the year. The beam energy will remain at 3.5 TeV in 2011, but there will be a big drive to increase the luminosity by at least a factor of three compared to what was achieved in 2010. I guess that makes now a good time for that post I promised on luminosity…

Luminosity gives a measure of how many collisions are happening in a particle accelerator, so we’re often asked why we don’t just say collision rate. It’s a very reasonable question. The answer is because luminosity isn’t strictly speaking the collision rate: it measures how many particles we’re able to squeeze through a given space in a given time. That doesn’t mean that those particles will all collide, but the more we can squeeze into a given space, the more likely they are to collide.

The best place to start is with what physicists refer to as a cross-section. Usually, a cross-section is a measure of the size of something. For example, a barn door has a bigger cross-section – it covers a larger area – than a cat flap. In particle physics, a cross-section is a measure of the probability of something happening, and it’s measured in units called…. barns. In reality, a barn is a huge cross-section and most processes have cross-sections measured in tiny fractions of a barn.

When protons collide in the LHC, many things can happen: the protons can just glance off each other, or they can collide more violently producing any of a range of new particles. Each of these processes has its own cross-section. The cross-section for the production of a Higgs particle, for example, is very small at the scale of nanobarns – billionths of a barn  – which means that Higgs particles, if they exist, will be produced very rarely.

When looking for something that rare, the more collisions you have, the more likely it is that the rare thing will happen, and that’s why particle physicists care so much about luminosity. It works a bit like this: if you multiply the luminosity of the beam by the cross-section for any process, such as Higgs production, you get the rate at which you can expect that process to happen. If you multiply the luminosity by the sum of the cross-sections for all possible processes, you get the total number of collisions.

To help figure out the different ways that luminosity contributes to the collision rate, think of rolling marbles from opposite ends of a corridor. If you’ve just got one person at each end of the corridor, the chances they’ll get their marbles to collide are small: the luminosity is pretty low. But put lots of people at each end and the luminosity goes up. Similarly, if you increase the cross-section by rolling footballs down the corridor, the luminosity remains the same, but since a football has a bigger cross-section than a marble, the number of collisions goes up. It’s not a perfect analogy, but I hope you get the idea.

The LHC’s design luminosity is 1034 per square centimetre per second. That’s a big number, and although we can’t say exactly how many collisions it equates to, we can say that and it’s around 600 million collisions per second on average. When the LHC run ended in 2010, the luminosity was around 2×1032 per square centimetre per second, giving a few million proton collisions per second.

The other way that physicists use luminosity is to add it all up, or integrate it. If you do that, you get a measure of the total number of collisions that have happened. So, for example, the integrated luminosity recorded by the ATLAS and CMS experiments in 2010 was around 45 inverse picobarns, which translates to over 3000 billion collisions recorded.  And what about the Higgs particle? With the peak luminosity reached by the LHC last year, we might have expected Higgs particles to be produced at the rate of a handful a day, which is not yet enough for us to see a signal above the background from known and well-understood physics. To claim a discovery, physicists need to see a statistically significant excess over and above what they expect to see from known physics, and they measure the degree of significance using a quantity called a standard deviation, or sigma for short…. But that’s a subject for another post…

James Gillies

### 18 Responses to “Why don’t we just say collision rate?”

1. Chuck McGuire says:

Mr. Gillies, I can tell you are of European descent. American footballs don’t roll worth a darn. I really appreciate the insight that you and the other bloggers at CERN are giving us into the missions and objectives of your organization.

2. CERN says:

You are right, Mr McGuire. I’ll try to remember to use the universally accepted ‘soccer’ to refer to the beautiful game in future…

3. ahmed elabasy says:

brookhaven has acheived an important discover it is the production of anti helium 4 through lead gold collisions could cern by this amazing luminosity be the first to create anti lithium

• CERN says:

The ALICE experiment at CERN has also observed a few anti helium 4s. Making anti-helium nuclei in the laboratory is an experimental tour de force rather than a fundamental discovery. It is synthesized when the quark gluon plasma is formed in heavy-ion collisions. The quark gluon plasma is a hot and dense substance containing an equal number of quarks and anti quarks. As it cools down, the quarks and anti quarks condense into hadrons, such as protons, neutrons, helium, and their anti particles including now anti-helium which is the heaviest anti nucleus observed so far. Making anti lithium will be tough even at the LHC. Observing anti helium in space, however, would be interesting…

4. Louis Schreurs says:

Hi guys,

LHC at CERN resides in EUROPE. In ENGLISH football or soccer is the same game. See Liverpool FC home page, e.g..

Thus Americans are obliged to translate football to soccer to suit their own understanding. Also football isn’t the per se same as American Football.

So I strongly believe that when a European citizen thinks that a football ball rolls like a sphere, he’s thinking a true thought.

by to y’all (LOL), Louis Schreurs, The Netherlands

5. mos says:

so.. 7 TeV = rediculous luminosity??

with the beam at that energy.. i suppose i understand why the people at cern want to take their time at this energy level. it’s going to be a while before 7 TeV huh?

it’s really excciting to see the LHC sailing along without problems though. best wishes with the physics this year.

6. thanks for the detailed explanation. makes it easier for people like me with very little science background to understand and appreciate what you guys are doing.

7. Anirudh says:

Fundamental doubt .. An eV = 1.6 x 10^-19 V, right? So a TeV is just 1eV x 10^12, right? Which translates to about 1.6 x 10^-7 V .. I’m sorry I fail to see the significance. Can you elucidate?

8. Paul says:

so in a nutshell we can look forward to 2012….your not going to do anything Earth shattering.Rite
The LHC’s design luminosity is 10.34 per square centimetre per second. That’s a big number…..YEP

9. Stephen Brooks says:

Anirudh said: Fundamental doubt .. An eV = 1.6 x 10^-19 V, right?

An eV is 1.602 x 10^-19 Joules. It’s a measure of energy, not voltage. Namely, it’s the energy that a single-charged particle (like an electron or proton) would have after being accelerated by 1 Volt.

So the 7TeV of the LHC is either 1.1 x 10^-6 Joules per *proton*, or 7 trillion Volts equivalent acceleration.

10. Pablo says:

Thanks for such an illustrating article. As I read above, i’m also grateful to you for taking the time to explain in simpler words what’s going at CERN.

As for the citizens of the U.S., I think you might have to create some sort of conversion/translation chart for them. I mean, not only they mistake football for soccer, but also use a different measuring system (i.e. centimetre => inches) =P

Great article!

11. Anirudh says:

So the big deal is that you’re able to give all this energy to a single particle? Thanks for clearing that

12. Khoyo says:

@Pablo: Actually, the scientific community stated on the units people have to use when they do science, to avoid having in the same team people thinking in meters, others in miles, and others in yards…
And the international distance unit is the meter.
See http://en.wikipedia.org/wiki/International_System_of_Units

13. Tony says:

Thanks for this explanation which did a great job of explaining something that is more complex than many of us would ever understand if you spoke in technical terms. Yes I was confused with the football reference but hopefully most will realize that soccer is more commonly called football everywhere else but in the US. Keep the explanations coming as it is very rare to see such a well written explanation as yours.

14. Stephen says:

Whether the game is called soccer or football, any such statements can only be ‘globaly’ accepted on this planet alone or we have a freudian slip here.

To suggest anything is ‘universely’ accepted can only mean you have a number of ETs from not only this galaxy but many many others secreted away at your CERN facilty that are all in agreement the game is called soccer.

Hypothesis: The Stargate is fully operational.

15. Jasper says:

Ahhhh, I wish I would be able to work at the CERN. Unfortunately I’m not quite the best student on the planet.
Anyway, I really appreciate that you share your work at CERN, and actually give interesting information.
The only thing I don’t really understand is, what IF you’re able to get your hands on Higgs particles? What’ll happen with them?

16. David in Cincinnati says:

So why is the beam area (in the luminosity’s denominator) equal to 4 pi r^2?

17. I read that 99.999% of the data collected during proton-proton collisions are (almost) immediately discarded. Is the number for the luminosity you are giving based on the 0.001% data of interest or on the data for all collisions? Or in other words the 5.15 inverse femtobarns of the 2011 data run, is that the 100% or just the 0.001%? My guess would be the 0.001%, but decided its better to ask the pros.