This week, the LHC has been in its first technical stop of the 2011 run. So far, the performance of the machine has been quite encouraging. Collision rates have already exceeded the highest rates of 2010, and the total number of collisions recorded this year is already about three quarters as much as we got all of last year.

I always find myself writing in vague terms like “total number of collisions” rather than actually giving a number, because the units that particle physicists use to characterize the amount of data, or “integrated luminosity”, collected at a collider are rather obscure. We usually talk in terms of “inverse picobarns.” What on earth is that? Let’s attack it piece by piece. A barn is a unit of area, as in “you can’t hit the side of a barn”; one barn is 10^{-28} m^{2}, which of course is a tiny area. (A picobarn is 10^{-12} barn, even smaller.) Rates for particle production are typically given as “cross sections,” that is, in units of area. This is related to the fact that our experiments are really scattering experiments, in which we shoot a probe (one proton) at a target (another proton), and a cross section is the effective area of the target that will lead to a particular production process. The measure of integrated luminosity is in units of inverse area, such as 1/barn, or 1/picobarn — the inverse picobarn. By multiplying the amount of data recorded (an inverse area) by the cross section for a process (an area), you get the total number of times that process should have occurred. For instance, the cross section for the production of a pair of top quarks at the LHC is roughly 250 picobarns. Since CMS recorded about 35 inverse picobarns last year, you would expect to have 250 * 35 = 8750 top-pair events in the dataset.

All that being said, an inverse picobarn is very hard for most people to visualize. We can imagine what an area — the side of a barn — looks like, but we’re not used to picturing inverse areas. Fortunately, I have a solution to this problem. There is in fact a unit in common usage that is also an inverse area. This is the standard unit of fuel efficiency, the mile per gallon. With a length in the numerator and a volume in the denominator, the mile per gallon does have the dimensions of the reciporical of area. This means that we can express the integrated luminosity of the LHC in miles per gallon, a concept that the typical person on the street, or even an elected official, can understand. So how much mileage has the LHC delivered this year? First, we need to convert the inverse picobarn into miles per gallon:

1 pb^{-1} = 10^{12} b^{-1} * (1 b/10^{-28} m^{2}) * (10^{-3} m^{3}/1 liter) * (1 km/10^{3} m) * 3.79 liters/gallon * 0.621 miles/km = 2.35 x 10^{34} miles/gallon.

The LHC has delivered 26 pb^{-1} in 2011, or 6.1 x 10^{35} MPG. This is a huge number! The LHC is thus by far the most fuel efficient machine on Earth, and thus it should be of great interest to people everywhere who are interested in reducing our use of fossil fuels, protecting the environment and so forth. Such a fabulous device is surely worth supporting with taxpayer dollars.

Now, the number 2.35 x 10^{34} mile pb/gallon is also quite interesting in itself, as it is a dimensionless quantity. Such dimensionless numbers are considered to be fundamental physical quantities. For instance, the atomic fine structure constant, 2 π e^{2}/hc = 1/137 (approximately) is a dimensionless number that determines the strength of electromagnetic interactions, and therefore important physical parameters such as the size of atoms. There are only a few such numbers that occur in particle physics, and we seem to have uncovered a new one through this exercise. So why does the mileage-luminosity conversion constant have that particular value, and why is this value so amazingly large, a factor of 100 billion bigger than Avogadro’s number?

But since the LHC is in Europe, which uses the metric system, we should be computing the integrated luminosity not in miles per gallon, but in kilometers per liter. To get the conversion constant, we do the same calculation as above, but just drop the last two factors to obtain 10^{34} km pb/liter. It is exactly a power of ten! This suggests that the number ten itself must be a fundamental parameter of the universe, which could well explain why humans have ten fingers and ten toes.

Obviously these issues require further investigations, which in turn will require additional grant funding, preferably an amount that will cover my summer salary (itself perhaps a fundamental constant, given the state of the university budget). I am hoping to come up with more answers within a year from today, so that I can submit a paper for journal publication by April 1, 2012.