QCD Predictions agree with the data – NOT!
The D0 Collaboration just released a nice short paper on the measurement of the di-jet invariant mass (arXiv:1002.4594):
Measurement of the dijet invariant mass cross section in p-pbar collisions at √s = 1.96 TeV
This is a bread-and-butter measurement performed many times at hadron colliders, and it will surely be repeated at the LHC in the coming months. Conceptually, there is not a lot to the measurement: one selects events with two or more jets passing quality requirements; cuts on the missing energy reduce backgrounds to a negligible level. Some art is needed in the handling of jet energy corrections, and the authors of the paper have made careful and conservative choices to reduce the possibility of systematic biases due to these corrections or the unfolding of the spectrum.
The interesting feature of this analysis is the use of a large rapidity range. Jets are used out to a rapidity |y| of 2.4; older analyses tended to stick to the central region |y|≤1. The D0 Collaboration thereby publishes a very pretty double-differential cross section:
The horizontal axis is the di-jet invariant mass, and the six sets of points correspond to six ranges in rapidity, |y|max, for the most energetic of the jets in each event. (Most events have only two jets, in fact.)
The smooth curves appear to go directly through the points – a triumph of pQCD calculations! These are serious calculations, incorporating next-to-leading-order (“NLO”) radiative corrections, which reduce the dependence of the theoretical prediction on arbitrarily chosen factorization scale. Credit goes to Zoltan Nagy for these calculations (arXiv:0307268).
Let’s take a closer look. The D0 Collaboration provides nice plots of the ratio of their measurements to the theoretical prediction:
Now the agreement does not look so perfect, so let’ s explain what is in these plots.
Each panel corresponds to the ratio (data/theory) as a function of the di-jet invariant mass, MJJ, so perfect agreement would be a series of dots with error bars, at one. Uncertainties on the jet corrections (energy scale, resolution, and unfolding) lead to correlated uncertainties indicated by the yellow bands. These are uncertainties on the expectation, in contrast to the actual observed values, so the authors center those bands on one, not on the dots – something that I personally approve of. The calculation done by Nagy has NLO corrections, which make them much more accurate than leading-order calculations, but still some theoretical uncertainties remain, as indicated by the pairs of blue lines. Finally, the cross-section calculation depends on empirical knowledge of the parton distribution functions (p.d.f.s), and since that knowledge is imperfect, there is an associated uncertainty indicated by the dashed red lines.
For the central rapidity bins (top three rows), the dots fall within the yellow bands, the blue lines, and more-or-less between the dashed red lines. This means that the uncertainties, from the experimental measurement, the theoretical prediction and the pdfs cover the deviation of the ratio from one.
For the high rapidity bins, however, things don’t look as nice. Still, collider physicists are conservative and tolerate such discrepancies – measurements at high rapidity and high jet energies are difficult to control, so few people would claim that there is a serious problem, even in the highest rapidity bin. Hence the statement in the abstract: Next-to-leading perturbative QCD predictions are found to be in agreement with the data.
But that’s not the end of the story. The D0 Collaboration used a very up-to-date parametrization for the pdfs, called MSTW2008NLO (arXiv:0901.002). Another recent parametrization, called CTEQ6.6 (arXiv:0802.0007), also from 2008, was considered, leading to a very different result. If the theory prediction is computed using CTEQ6.6, and the ratio (data/MC) is re-computed, a large deviation at high rapidity is observed. See the dot-dashed lines in the ratio plots above – this is the ratio of the CTEQ6.6-based prediction to the MSTW2008NLO prediction. It appears that the prediction is off by nearly a factor of two in the high-mass, high-rapidity region, if CTEQ6.6 is used.
Normally, predictions based on these two competing pdf parametrizations agree pretty well. But the Tevatron experiments are entering a regime in which real differences can be sniffed out. The measurement, while bread-and-butter, is not an easy one, and I am sure the authors worked long and hard on it. The result is that the two most popular pdf parametrizations can be cuttingly compared.
The D0 Collaboration point out some important facts about CTEQ6.6 and MSTW2008NLO. Even though both appeared around 2008, MSTW2008NLO incorporates more recent Tevatron data than CTEQ6.6. In fact, the D0 jet energy spectra, which are correlated with the measurements in this latest paper, were used, so one should expect agreement. Meanwhile, CTEQ have produced new parametrizations – I do not know whether they would agree better with these D0 measurements. One can infer, though, that there has been a significant evolution of the pdfs (sorry for the pun) since the Tevatron Run I era, and the pdf fits are determined in a significant way by measurements like this one. Several other Tevatron measurements wait to be included in the pdf fits.
Finally, let me point out that predictions for the LHC employ pdf sets, often rather old versions of the MSTW or CTEQ fits. Will we see factors-of-two changes in such predictions, once newer parametrizations are used? Maybe we should expect rather large discrepancies when the first jet spectra are measured…
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