## The fascinating b quark cross sections July 10, 2008

Posted by dorigo in news, physics, science.
Tags: , ,

Sometimes I come to think I need a secretary, or even better, a press office. It is such a tough job to keep up to date with the scientific publications popping out on a daily basis, that I sometimes have to completely leave my research aside to foster my own education.

When, however, a new important result escapes my attention for over one year, and the result comes directly from an experiment I am part of, I realize the task is beyond my forces.

Such was indeed the fate of the measurement of correlated b-quark pair production cross section, which CDF published in Phys. Rev. D77, 072004 (2008 ) a couple of months ago (get your preprint here), but which has been around for over a year now. It is especially annoying because it is a very careful measurement which probably settles the issue of b-quark pair cross section, a topic where collider experiments had in the past produced conflicting results. What’s more, the paper is the result of three years of work of a group of friends of mine. Shame on me!

Pairs of b-quarks are produced in hadron collisions by strong interactions (QCD, for Quantum Chromo-Dynamics), typically through the fusion of two gluons. While the production mechanism occurs at an energy high enough to warrant a perturbative calculation -because the strong coupling constant $\alpha_S$ is small enough that it is meaningful to write down the cross section for the hard process as an infinite series of terms in powers of that quantity, the surrounding lower energy phenomena -what happens before the hard scattering, and what happens after it- are non-calculable, and they thus must be evaluated with a fair amount of assumptions.

Before the scattering, you need to “find” in the colliding bodies two suitable partons -mostly gluons, as I said above- of the right energy. The probability to find those partons in the proton and antiproton is a function of their energy, and is described by so-called “parton distribution functions“, which are determined by dedicated experiments.

Similarly non-calculable are the QCD processes responsible for the phase, called “fragmentation” that connects the outgoing b-quarks into a final state with a well-defined observed behavior. The energetic b-quark, leaving the interaction region, extends a color string until the latter “breaks” popping up quark-antiquark pairs which can then bind into color-neutral hadrons – one of them a B-hadron, containing the original b-quark. It is those hadrons which the experiment detects in the tracker and calorimeter system, collectively measuring their energy -or more customarily, their momentum transverse to the beam, $P_T$.

All in all, theoretical calculations of b-quark pair production are a big headache. It is actually surprising that different calculations roughly agree, in fact, once the connection between quark energy and observed B hadron energy is treated with some amount of care. In fact, the comparison of calculations at different level of approximation (at “leading order” or “next-to-leading order” -LO, NLO) present a stable result, which can be therefore trusted to be correct to within 10-20%.

Experimentally, there have been five measurements of the $b \bar b$ production cross section obtained by CDF and D0 in the past. These consider different $P_T$ thresholds for the B hadrons, so to compare them it is meaningful to divide each by the corresponding theoretical prediction. Here are the past results on the experimental/theoretical ratios, based on Run I data:

• $R = 1.2 \pm 0.3$ (CDF, jets with secondary vertex b-tags);
• $R = 1.1 \pm 0.3$ (D0, jets with secondary vertex b-tags);
• $R = 1.5 \pm 0.2$ (CDF, events with one semileptonic muon b-tag jet and the other containing a secondary vertex b-tag);
• $R = 3.0 \pm 0.6$ (CDF, events with two semileptonic muon b-tag jets);
• $R = 2.3 \pm 0.7$ (D0, events with two semileptonic muon b-tag jets).

In total, the average is $R=1.8$ with a 0.8 RMS and a poor overall agreement. Particularly nagging is the dimuon result by CDF, off from unity by more than three standard deviations. With the order-of-magnitude increase of Run II dataset statistics, the matter could and should be straightened!

The new measurement by CDF, based on 740 inverse picobarns of data -roughly eight times more than the former analysis- uses again dimuon events: events where two jets, back-to-back in azimuth, both contain a muon with an impact parameter consistent with the b-quark decay length. The impact parameter is the mismatch between the muon trajectory and the interaction vertex: a large value of $d$ is produced if the muon is not coming from the interaction vertex, but from the decay of a particle that travelled a sizable distance before disintegrating. By fitting the impact parameter distribution of muon tracks in dimuon events, CDF can determine the amount of $b \bar b$ events present in the data sample.

Above, the impact parameter, in centimeters, of muon tracks (black points with error bars) is compared to the sum of contributing processes. The $late x b \bar b$ component is shown in cyan. Ignore the blue bars below the main plot – they just show residuals from the fit results.

The measurement is not over once the sample composition of the data is assessed by the above fit, of course: backgrounds have to be shown to be modeled correctly, and the probability that a light hadron is misidentified as a muon must be taken into account. Checks of all kinds can and should be made to ensure a solid result.

As an example: a sizable amount of muons coming from cosmic rays that happened to cross the detector during collider operation need to be removed -they otherwise spoil the impact parameter distribution- by observing the correlation of the impact parameter of the two muons, as shown in the figure below. On the left you can see a population along the diagonal (cosmic muons) – the two muons have the same impact parameter because they are one single track reconstructed as two opposite ones. On the right, data after the requirement that the azimuthal angle between muons of opposite charge is smaller than 3.135 radians are totally devoid of the nasty background.

Other checks are made: promptly produced muons can be studied, and tails in their impact parameter distribution sized up, by selecting a sample of Upsilon meson decays. Every time I see a plot of the three resonances (see below) I am reminded of why I love particle physics!

So, the analysis is complex, as I said, but we need not delve into the details. So what is the result ? It is found that $R=1.20 \pm 0.21$. The result is not terribly more accurate than the ones quoted above, but the error on R is dominated by the theoretical uncertainty (which is based on a next-to-leading order technique – ok, ignore this detail, and we can both be happy). Therefore, since R should be close to one, or actually exactly one if theory were perfect, can we deduce that the former CDF result ($R=3.0 \pm 0.6$) was plain wrong ? Well, probably yes. In principle, each of the five measurements could be wrong; or all of them, all for the same reason or each for a different one.

The theory predictions could also be the source of deviations from unity in the ratios. What matters, though, is that several of the details with which the present result has been obtained show that the margin for a mistake or a misinterpretation of backgrounds or other instrumental effects, in this case, is really narrow. I have finally -with one year of delay- carefully read the paper, and I am thoroughly convinced that there is no more mystery hiding in the correlated b-quark pair cross section at the Tevatron.

It only remains me to point those of you willing to know more about this measurement to the public page of the analysis, where tens of plots are available together with additional documentation.

1. nige cook - July 11, 2008

It’s interesting that because the alpha_strong coupling parameter falls with increasing collision energy, the perturbative expansion converges more quickly and can be reasonably evaluated for this beauty quark interaction at high energy. The opposite is the case for electromagnetism and mainstream quantum gravity ideas, where the coupling parameter increases with increasing collision energy, instead of falling. I suppose this increase in the ease of evaluating a perturbative expansion for small coupling constants, with the fall in the strong coupling constant with increasing energy, is the reason why so much is known theoretically about QCD at very high energy (asymptotic freedom of quarks and so on).

This paper is a nice test between the QCD theory and experiment for this interaction. But it is a bit scary that an earlier result showed a ratio of R = 3 +/- 0.6 between theory and experiment, and wasn’t headline news! We keep hearing that science is so rational and disciplined that ‘a theory is disproved if even one experiment refutes it’. In practice, this is just hot air and propaganda. In reality, you can get an experimental result which is different from theory by a factor of 3.0 (some 5 times the estimated standard deviation or error bar of +/-0.6), and nobody cares because it’s just a minor anomaly that will be resolved in later research!

The emotional insistence that science refutes any theory that appears to definitely contradict experiment is just a hoax, and only applies to new ideas which haven’t been well funded or fully investigated get. It doesn’t apply to established theories which have plenty of research and publicity behind them.

I’m not a doubter of QCD, because it’s based on very strong observational and theoretical evidence such as the SU(3) symmetry description of particle properties and numerous experiments. But it’s very revealing that an experiment showed such a massive error between theory and experiment, without widespread publicity of the error ‘disproving QCD’, and the disagreement has only recently been cleared up. It’s good news that the latest result shows a ratio between experiment and theory of R = 1.20 with an error bar of +/- 0.21.

2. dorigo - July 11, 2008

Nige, good points, but be careful. As I said in the post, 3.0 +- 0.6 differs from 1.0 by three (precisely 3.33) standard deviations, not by five units.

Cheers,
T.

3. nige cook - July 11, 2008

Thanks for that. So the ratio was off unity by a factor of 3, which is a diference equal to 3-1 = 2 units of ratio. Hence 2/0.6 = 3.33 error bars. My miscalculation is easy for an idiot to do.

(I’ve seen a similar units error made by reporters on TV when discussing election poll forecasts. An poll of 1000 people selected at random from a large population gives a standard deviation of +/- 100/(1000^{1/2}) = +/- 3%. Invariably the TV reporter then says something like ‘the forecast is that party X will get 50% +/- 3% of the vote’, when of course for 3% of 50% is just 1.5%, so the true estimate is 50% +/- 1.5%.)

4. CDF publishes multi-muons!!!! « A Quantum Diaries Survivor - October 31, 2008

[…] cross section for production appears in good agreement with next-to-leading order QCD predictions when b-quarks are tagged by a reconstruction of their […]

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