A Quantum Diaries Survivor

The summer is in full swing, and summer conferences are blossoming all over the place. That means that the CDF and D0 experiments are quite busy approving brand new results on all the most interesting physics measurements and searches, recently obtained with up to two-inverse femtobarn datasets of proton-antiproton collisions provided by the Tevatron collider. Two inverse femtobarns means a whole lot of them: 160,000 billion collisions took place in each detector, and a few billions were written to tape and analyzed.

I am not going to sit here and watch a stream of star new results being published, presented, and consumed without offering my two cents on those that trigger my interest, of course. Unfortunately, I am again going to discuss a new result by D0 today, after two more in the past few days. The fact is, I belong to CDF and have agreed to allow my peers to present their analyses at conferences before discussing them in my blog. So the CDF stuff will be broadcast here with some delay… As for D0, I have no commitment preventing me from discussing their public results, although of course I would like to avoid doing anything they may not like. But the material is public, and this is the internet, baby…

Anyway. The exciting new result by D0 I discuss today is something that arises my interest for at least a couple of different reasons. Make it three.

First, it is about Upsilon mesons - fascinating systems composed of two b-quarks orbiting around each other. I have always had a weak spot for these particles, which were the source of the discovery of the fifth quark by Lederman and colleagues in 1977. There is a whole family of these states, at increasing masses: the Y(1S), Y(2S), Y(3S), Y(4S)… Only the first three of these live long enough to make a narrow resonance when they decay into pairs of muons. The fourth is massive enough to decay to two B hadrons, and in fact low energy electron-positron colliders have exploited the Y(4S) decay to provide a huge amount of B particles. The PEP-II and Kek B-factories have enabled their experiments BaBar and Belle to produce exquisite physics measurements by running “at the Y(4S)”: by adjusting beam energies and crossing angles, these machines can achieve electron-positron collisions with a total center-of-mass energy equal to the mass of the Y(4S) – 10.55 GeV, which maximizes the probability to create that bound state.

Below is a picture worth a thousand words: the invariant mass distribution of pairs of muons reconstructed by CDF in Run 1, showing not just the three narrow. lowest-energy Y states, but also, at far smaller masses, the J/psi and the Psi(2S) - quite similar states composed of two charmed quarks. If you have studied quantum mechanics deep enough to understand bound systems, you cannot help seeing the beauty of this spectrum. The states are called “quarkonium”, underlining the fact that they are not conceptually different from a new state of matter - elemental, in a way, no less than polonium or americium - but actually much closer to positronium, the bound state of an electron-positron pair.

Second (yes, we are still in a list), the result is about Upsilon polarization, and it is a stringent test of NRQCD (non-relativistic quantum chromodynamics). The theory is successful in describing the phenomenology of production and decay of states such as or quarkonium. NRQCD basically works by factoring out effects that depend on the dynamics of the quarks in the meson, which are “non-relativistic” in the sense that they typically move at a few tenths of the speed of light inside the bound state. I studied the matter in some detail years ago, when I searched for a very rare process including Y mesons. Although I since forgot most of it, the physics of quarkonium production has remained a dear topic to me. In particular, the polarization (that is, the angle between the spin of the meson and its direction of flight) is a very intriguing and complex property to study, a property of particles which often puts theories to the test.

Third, and most important: the new measurement by D0 is totally at odds with NRQCD. Not just that: it is also in disagreement with the previous CDF measurement of the same quantity. How’s that for a motivation to read further ?

Indeed, there is not too much to describe about the measurement, which is rather straightforward: a large sample of dimuon decays of the Y mesons is collected by D0 from muon triggered data by applying standard identification cuts to muon candidates, and 420,000 Y decays are isolated in a sample of 1.3 inverse femtobarns. Then they define a variable sensitive to the Y polarization - the angle which the positive decay muon makes with the direction of flight of the Y, in the center of mass of the decaying body. Finally, the data is divided into many subsets depending on the value of Y transverse momentum and (we say that the data is “binned” to describe the slicing and dicing), and for each subset the number of Y(1S), Y(2S), and Y(3S) events is obtained by a fit to the dimuon mass distribution.

The fit is actually not too easy to perform, since the reconstructed invariant mass of pairs of muons in D0 shows a resolution not too simple to model. D0 parametrizes the mass distribution of each Y state with a function which is the sum of two gaussians (the sum of three gaussians is also tried) - so the three Y(1S), Y(2S), and Y(3S) peaks are understood as the sum of three double (or triple) gaussians, as in the plot shown below, which shows the Y candidates for a narrow bin in and Y transverse momentum.

The result of the many fits is the number of Y candidates as a function of the two variables used to bin the data: a differential measurement telling how probable it is for a Y to be produced with a given value of and . These distributions are the starting point of the polarization measurement. If one defines the variable , where are the transverse and longitudinal polarization components of the total cross section, then can be determined from because

.

All the above is to just say that one just needs to measure the angle of the positive muon from the Y direction, and then a few tricks allow the extraction of a measure of how many Y are polarized each way.

Experimentally, after the number of candidates in each bin is known, one uses Monte Carlo signal simulations with different input values of the parameter to find the one which matches the distribution better, for each interval. The result is a determination of alpha as a function of , which can be compared to theoretical expectations of NRQCD and to previous measurements by CDF. You can see the results for the Y(1S) meson below.

This result is quite striking! Not only does the D0 measurement (black points) show a very sharp variation of with the particle momentum, which is totally inconsistent with the predictions of NRQCD (yellow band). The D0 data points are also quite far away from what CDF found in a previous analysis (green points lining at close to zero).

A less conclusive result is found for Y(2S) mesons. For them, the statistical errors in are larger, and NRQCD remains a reasonable interpretation of the momentum trend.

I think the D0 measurement is sufficiently precise to throw the ball in the theoreticians’ court, where it is bound to stay long enough for a better description of Y polarization to become available. CDF is also bound to improve the precision of their own polarization measurement. We have the data, and the means: The mass resolution is much better than that of D0, so the number of candidates is much easier to extract… The challenge is on!

You can find more details on the D0 measurement of Upsilon polarization in the public page of their B physics analyses.

Update: Kea also discusses this result.