VERY HIGH MULTIPLICITY PHYSICS
QCD PHYSICS AT TEVATRON AND LHC
© 2004 A. Korytov*
University of Florida, USA Received May 28, 2003
Presented are the Tevatron Run I QCD results that have been known for certain controversy associated with them. Also, the prospects for the QCD motivated studies at Tevatron Run II and LHC are briefly discussed.
INTRODUCTION
QCD is extremely rich in various phenomena and very challenging both theoretically and experimentally. Within the hard QCD domain (processes involving large momentum transfers), one deals with production of jets, photons, W and Z bosons, and heavy flavor quarks. Perturbative QCD calculations are straightforward, but, if the precision of better than 10% is desired, must typically go beyond the leading order and soon become very difficult. The soft QCD phenomena are usually associated with jet fragmentation, hadronization, diffractive processes, underlying event structure, etc. Perturbative calculations here are even more problematic, if possible at all, and, often, one needs to make a leap to new, preferably QCD motivated, constructs (e.g., Pomeron) or come up with approximate methods of resummation of perturbative terms in all orders (e.g., MLLA (Modified Leading Log Approximation) and BFKL) or, as the last resort, develop completely phe-nomenological tools such as hadronization schemes in various Monte Carlo models.
Also, QCD can be viewed in a broader context of the Standard Model (SM) and its various extensions. Measurements of the key SM parameters, at first glance not directly connected to QCD, are, nevertheless, often limited by the level of our understanding of QCD processes (e.g., MW, (g — 2),e'/e). Even more intriguing, the new physics at hadron colliders, if any, is likely to be born via QCD processes (e.g., consider production mechanisms for Higgs and SUSY particles), and, at the same time, the background to this new physics is likely to be from QCD processes as well. So learning and understanding details of the QCD phenomena is vital in searching for signs of what might be beyond the SM.
E-mail: korytov@phys.ufl.edu
TEVATRON Run I
I will start from the ¿-quark production cross section in proton—antiproton collisions. Figure 1 shows the CDF results and the theoretical prediction as they stood in 2001 [1]. The discrepancy between experiment and the NLO QCD calculations was a factor of 2.9 ± 0.2 ± 0.4, or ~4.2a, which, naturally, prompted for searching explanations beyond the SM [2]. Since then, the NLO calculations of the 6-quark production were extended to include the NLL resummation as well as the improved 5-meson fragmentation function as obtained at LEP. The net result is shown in Fig. 2 [3]. One can see that the data points stay where they were two years ago, while the theoretical curve moved up and the discrepancy is now 1.7.
Another highly controversial result that even made newspaper headlines was the apparent excess of high-ET jets reported by CDF. The inclusive jet cross section da/dET agreed with the pQCD calculation for ET = 50—300 GeV (overs six orders magnitude in cross section), but seemed to start departing from the theory at higher transverse jet energies — Fig. 3 [4]. To make the situation even more entangled, the D0 data [5] fell right in between the CDF and theory points and were consistent with the theory and, at the same time, with CDF. Immediately, it was pointed out that the angular distributions of dijets (Fig. 4 [6]) did not call for the presence of any, albeit very exotic, new physics such as quark compositeness. At the same time, it was also shown that the poor knowledge of gluon PDF at large-^ might be responsible for the discrepancy. Recently, the CTEQ Collaboration released a new set of PDF fits, CTEQ6M, that included H1, ZEUS, CDF, and ^-dependent D0 results, and, also, the new methods of treating the experimental systematic errors. As a result, both the D0 and CDF data from Run I are now in an amazingly good agreement with the theory and each other (Figs. 5 and 6 [7]).
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Fig. 2. B+ meson cross section and theoretical predictions as of 2002 [3].
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Fig. 3. Inclusive differential jet cross section and the NLO predictions as of 2001 [4].
Now I will turn to a few examples of QCD results still awaiting resolution. The first example is a large excess of 3- and 4-jets events with all jets being relatively soft as reported by D0 (Fig. 7 [8]). In addition to the excess, the jets seem to have different spectrum of the overall misbalance in comparison to Monte Carlo predictions (Fig. 8 [8]). However, these discrepancies apparently can be removed by tweaking some of the Monte Carlo parameters [9], but there are no guarantees that such tuning would not cause problems somewhere else.
Another troublesome measurement is a too small inclusive jet cross section in proton—antiproton collisions with a center-of-mass energy of 630 GeV. To reduce the sensitivity to PDFs, one can con-
sider a ratio of inclusive cross sections at y/s = 630 and 1800 GeV r = [da/dxT(630)]/[da/dxT(1800)], where xt = Et/(t/s/2), Fig. 9 [10]. In addition to being systematically ~15% below the theory, the CDF and D0 data seem to have very different trends at xT < 0.1.
These two last discrepancies might be linked to the uncertainties in relating the experimental and theoretical definitions of jets — inherently different entities, given our limited abilities in handling mul-tiparton states within the pQCD framework. A good illustration for this issue is the recent CDF and D0 attempts to switch to the kT-jet-finding algorithm [11] as an alternative to the cone-algorithm [12] commonly used for Run I data analyses. The kT-
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Fig. 4. Angular distribution of the leading jet in the dijet center-of-mass frame, da/dx, where x = (1 _ cos 0cm)/(1 +
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algorithm was a standard at LEP and HERA and proved to be very successful. Unexpectedly, both CDF and D0 encountered a problem that still remains: despite the fact that both the kT-algorithm with D = 1 and the cone-algorithm with R = 0.7 give nearly identical inclusive jet cross sections within the NLO framework, when applied to data, the kT-algorithm give a substantially larger cross section and strongly disagrees with NLO QCD (Fig. 10 [13]). The work on understanding this setback is in progress.
The inclusive photon cross section provides for means to study QCD physics without having to deal with the problems associated with the jet-finding algorithms. However, the results here do not seem to follow the theory either. Both CDF and D0 data indicate that the photon ET spectrum is noticeably steeper than predicted by the theory (Fig. 11 [14]) — the fact also observed way back by the UA2 Collaboration [15]. Varying PDFs and renormaliza-tion/factorization scales does not seem to help in this case. New ad hoc ideas (e.g., kT-smearing of
the primary partons due to soft-gluon radiation) have been put forward to help consolidate the theory and experiment. Nevertheless, it is clear that more work needs to be done.
Switching gears to soft QCD physics, I will continue with jet fragmentation phenomena, the inherently soft process largely driven by gluon emissions off a primary parton and giving rise to a jet. Such gluons typically have transverse momenta of 200—300 MeV with respect to the jet direction. The controversy here is just opposite to the examples discussed earlier — it is in the amazingly good agreement of the experiment and the resumed pQCD calculations, also known as MLLA. The fit of data yields the value for the MLLA phenomenological kT-cutoff scale as low as -200 MeV (Figs. 12 and 13 [16]) - the scale, at which pQCD language is hardly applicable at all.
The ratio of hadron multiplicities in gluon and quark jets is yet another example of the 10 year long odyssey that began at LEP in 1991 [17] and have lasted since then with more than 10 papers
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Fig. 5. Inclusive differential jet cross section for five ^-bins and the NLO predictions with CTEQ6M PDFs (D0 data [7]). The insert shows the relative discrepancy of data and theory: (data — theory)/theory.
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Fig. 6. Inclusive differential jet cross section and the NLO predictions with CTEQ6M PDFs (CDF data [7]). The insert shows the relative discrepancy of data and theory: (data — theory)/theory.
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