b jets are hard to count!
b-jets are hard to count – or rather, they are hard to predict? Who knows? There is a major discrepancy reported by CDF in what should be a concrete, direct, basic quantity – the cross section for producing a W-boson and one or two b-quark jets (arXiv:0909.1505):
First Measurement of the b-jet Cross Section in Events with a W Boson in p-pbar Collisions at √s = 1.86 TeV
Noteworthy, already, is the fact that this is the first such measurement… The authors have aimed for a very pure event sample, sacrificing a lot of b-jet efficiency, so a lot of integrated luminosity is required for making the measurement. For this report, 1.9 fb-1 were analyzed.
In a nutshell, the analysis runs as follows. Events with W-bosons are selected in the usual way, by requiring a high-pT electron or muon and significant missing energy. Jets are reconstructed with the cone algorithm with a radius ΔR = 0.4, and a minimal set of jet energy corrections are applied. Events are retained if there are exactly one or two jets satisfying ET>20 GeV and |η|<2, which are reasonably safe cuts in terms of jet reconstruction and acceptance. There are about 175k such event.
The next crucial step is to tag the jets produced from b-quarks. The authors use a super-tight version of the well-known secondary vertex tag. These secondary vertices are reconstructed from at least three well-reconstructed tracks with significant individual impact parameters, and then the position of the reconstructed secondary vertex must be at least 7.5 σ from the primary vertex – this is a very hard cut which reduces the contamination from light quarks and gluons by an order of magnitude, and from charm quarks by a factor of four with respect to the standard cuts. This reduces the number of tagged jets down to 934.
Here is the interesting part, technically. In order to infer the composition of their sample, the authors make the distribution of the vertex mass, that is, the invariant mass of all the tracks coming from the secondary vertex. This quantity is known to be higher, statistically, for heavy flavor jets than for light quark jets, and it was used in the past in jet-shape tagging methods. The distribution is fit to three templates, one for b-jets, one for c-jets, and one for light quark and gluon jets. The b-jet and c-jet templates are taken from simulation, and have been shown to be reliable using a sample of b-jets tagged with muons inside the jet. The light quark and gluon jet template is taken from simulation, and checked using jets that give a negative secondary vertex parameter. In any case, the c-quark and light-quark templates are not crucial since the sample to be fit is so pure, as can be seen from the distribution itself:
(By the way, let me remark that this is the right way to make a plot – use shading with simple colors, large dots for data and a thin line for the sum, include a clear key and the measured quantities all in a fashion and style that is easy to read even if the plot is not large.)
The fraction of b-jets is 71%, which is quite pure in a situation like this. The corresponding number of b-jets is 670±44. Of these, 152±21 b-jets come from physics background processes such as top-quark production, single-top and di-boson production. The QCD contribution (i.e., events with a fake W) is estimated to be 25±8, which is cross checked with a control sample.
In order to compare the number of signal events (493±48) to predictions, the authors convert this yield into a cross section defined by the geometric and kinematic acceptance of the lepton and jets. This eliminates the uncertainty on the acceptance from the experimental number, and forces the theoretical predictions to be done within the cuts chosen for this analysis. Since the authors are able to run the theoretical codes to obtain the predictions, this can be done in a consistent manner. It would be difficult, however, for D0 to check the CDF result since D0 will necessarily use different cuts dictated by their detector.
The CDF result is:
σ×B = 2.74 ± 0.27 ± 0.42 pb
where the B stands for the branching ratio of W-bosons decaying to leptons. A recent NLO calculation by Campell. Febres Cordero and Reina gives
σ×B = 1.22 ± 0.14 pb
which is clearly too low by a factor of 2.25. This is a huge discrepancy. If we compute the difference between the measured and predicted cross sections, we obtain
Δσ×B = 1.54 ± 0.52 pb
which is clearly not consistent with zero.
Where might the experiments gone wrong? Is it hard to see where a factor of two could appear. The plot of the vertex mass above shows that the sample is, basically, b-jets and known at least to 10% or so. The acceptance correction has been minimized so that can’t be off by a factor of two, either. How about the b-tag efficiency? The simulation gives ε=0.177 which must be corrected by a factor of 0.88 to conform to the data. Could this be off by a factor of two? Unlikely, given all the measurements of top quark production already successfully published by CDF and checked by D0. All other efficiencies are in the high nineties in percent.
So the ball is in the theorists’ court. A response has already been published by Febres Cordero, Reina and Wackenroth in arXiv:1001.3362. I know Reina and Wackenroth and they have an established record of very high quality work. As stated above, their best number right now is a factor of 2.25 below the CDF result. More primitive calculations from PYTHIA give 1.10 pb and from ALPGEN, 0.78 pb.
There have been other measurement of the rate of b-jet production, of course. Usually they do not attain the purity and incisiveness of this analysis. A recent measurement of the production of a Z-boson with a pair of b-jets, relative to Z-bosons with a pair of any kind of jets (arXiv:0812.4458″), gave (3.32±0.53±0.42)×10-3 which does not contradict the ALPGEN prediction of 2.1×19-3. Other predictions include 2.3-2.8×10-3 from MCFM and 3.5×10-3 from PYTHIA. Basically, the predictions are correct.
We have a real mystery here. The theorists are investigating this result, and maybe they will find the answer. Meanwhile, the LHC is scheduled to provide collision data later this month, and one can hope that the LHC experiments will make this measurement before the end of the year. Will there be a factor of two discrepancy more events than predicted – which would have major implications for new particle searches – or will the discrepancy be even higher??
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