QCD Predictions agree with the data – NOT!

February 27, 2010 at 6:31 pm 4 comments

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:

D0 di-jet mass distribution

Double-differential cross section with respect to di-jet mass and rapidity compared to NLO QCD predictions

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:

D0 MJJ ratio

ratio of the measurement 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…


Entry filed under: Particle Physics.

Update of the Higgs Boson Mass p.d.f. Earthquake Resource

4 Comments Add your own

  • 1. Markus Wobisch  |  March 2, 2010 at 10:14 pm

    A very nice summary of the analysis! I just would like to correct two minor errors:
    1) The rapidity which defines the dijet phase space is |y|-max, and not |y-max|. The difference is subtle, but important: |y|-max is defined as the maximum of the absolute rapidities of the two leading pT jets: max(|y1|,|y2|) – and NOT as the rapidity of the more energetic jet. (jets are actually ordered in pT and not in energy, and the rapidity of the higher pT jet would not be an infrared safe observable).
    2) The NLO calculation reduces the dependence on the _renormalization_ scale (not on the “hadronization” scale – there is no such thing in pQCD)

    • 2. Michael Schmitt  |  March 4, 2010 at 10:59 am

      Hi Markus, thanks!

      I corrected the text for the two points you mention. Let’s see what the CTEQ Collaborations comes out with, next…


  • 3. Pavel Nadolsky  |  March 10, 2010 at 1:26 pm

    An excellent measurement; but the figures may mislead

    Michael, thank you for a lucid overview of an interesting measurement. I can comment on some issues that were brought up in regard to the CTEQ PDFs.

    We have not examined yet the brand-new jet pair production data from the Tevatron discussed in your blog. On the other hand, we spent a great deal of time studing a closely related measurement at the same collider, single-inclusive data production of 1 jet plus anything else at energy 1.96 TeV. Single-jet data share many features with dijet production, as both are dominated by the same scattering processes. That study has been documented in arXiv:0904.2424. We produced an (unpublished) CT09 set of PDFs that includes the latest constraints imposed by single-jet cross sections.

    Similarly to the D0 dijet study, the latest CDF and D0 papers on single-jet production tend to create an impression that theory predictions based on CTEQ6.6 PDFs overshoot significantly the data presented in those papers. Our detailed investigation led us to believe that

    this choice of presentation in experimental papers EXAGGERATES the actual disagreement between CT6.6 PDFs and the Run-2 jet data or MSTW08 PDFs.

    In addition, we found that the jet data has less ability to distinguish between different PDF models than might be superficially concluded from experimental publications :(.

    To see what happens, notice first that, without the latest jet data included, the CTEQ6.6 and MSTW’08 PDF models do not exclude one another. There is a substantial uncertainty in the model of the PDFs at the relevant large x values, which covers the central predictions by both groups. A non-expert may conclude the opposite from the figure in the dijet paper, which shows the CTEQ6.6 theory prediction that is way outside of the shown PDF uncertainty band. The issue is the interpretation of the shown quantitative results: the authors chose to show the smallest of the existing estimates of the PDF uncertainty, which, by the way, is contested by other groups.

    The second relevant effect is the dominance of systematic uncertainties in the latest jet production measurements. Because of the systematic effects, all data points can shift up or down by large amounts toward either CTEQ6.6 or MSTW theoretical prediction, i.e., to the theoretical prediction they are compared against. The yellow bands in the figures show the experimentalists’ own estimate of the systematic uncertainty. This estimate varies depending on the chosen procedure. For example, when the published single-jet systematic errors were implemented in the CTEQ fits, the systematic shifts in the single-jet data in these fits were typically larger than those expected based on the yellow bands in the experimental publications. Some combinations of systematic shifts bring the single-jet data quite closely to the CTEQ6.6 prediction. The agreement is not perfect (see the explanation below), but greatly improved. The bottom line is that the jet data have significant flexibility to accommodate either of the two models as much as possible, depending on the setup of the analysis.

    Why are the CTEQ6.6 and MSTW08 predictions different? The gluon parametrization in the CTEQ6.6 PDF set is increased to better accommodate the D0 Run-1 single-jet data, in contrast to the MSTW’08 set. The Run-1 single jet production prefer a harder gluon than the Run-2 single-jet production. In dijet production, the CTEQ6.6 theory prediction is presumably larger than MSTW precisely for the same reason.

    In the latest CT09 fit, the CDF and D0 Run-2 single-jet data are included, as well as the earlier CDF and D0 Run-1 data sets. The CT09 large-x gluon is reduced, becoming more similar to, but not identical with, MSTW gluon. The total PDF uncertainty is reduced marginally; it still covers CT6.6, which is now disfavored, but not significantly.

    In another world, we would probably prefer that the CTEQ6.6 parametrization were not singled out to emphasize the differences that are actually smaller than was suggested. On the other hand, these measurements are important for constraining the proton structure at large x; we hope they will be repeated soon at the LHC, and we plan to implement them quickly in our fits. Meanwhile, stay tuned for the CT10 PDF set that will be released soon and supersede CT09! It will explicitly demonstrate the effect of the new Tevatron single-jet data, as well as the other wonderful new measurements flowing in, on the PDFs and theoretical predictions based on them.

    • 4. Michael Schmitt  |  March 11, 2010 at 6:36 am

      Dear Pavel,

      it is wonderful that you take the time to provide this information. I am not an expert on PDFs so I do not know about the unpublished fits – I should be doing more homework for sure. 😉 I agree that the normalization and jet energy uncertainties plague these comparisons and the visual aspects of some of these plots can fool the reader. I do not think that the authors of the D0 paper, or of CDF papers, intend to embarrass anyone working on PDFs – on the contrary, collider physicists are becoming more and more interested in the subject since it is so very crucial to physics at colliders. My own intention was to draw attention to what someone else might consider a mundane measurement, and to the issue of PDFs in general. Without wanting to denigrate any set of PDFs, I wanted to shine a spotlight on the leading ones, using the D0 paper as the spotlight.

      I’ll keep an eye open for the 2010 version of the CTEQ PDFs and be sure to advertise them here on my blog. 🙂

      thanks again very much


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