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The data gathered at the Tevatron in Runs Ia and Ib have already resulted in many new and rigorous tests of QCD. Several years will be required to exploit fully the data taken with the current D0 detector at present luminosities. In particular, measuring differential cross-sections for jet, photon, and intermediate vector boson production with respect to increased numbers of event variables (momenta, pseudorapidities, etc.) will explore new regions of phase space particularly sensitive to parton distribution functions and higher order QCD calculations. These multi-dimensional cross-sections will also guide the way for establishing non-perturbative descriptions of partonic interactions, which are important at the edges of phase space. The large total luminosities expected for Run II will also encourage searches for new phenomena such as quark compositeness and excited quarks, rare diffractive processes, and vacuum polarization, and will provide accurate tests of all aspects of QCD because the theoretically and experimentally well described W/Z+jet samples will have statistical significance rivaling that of the present dijet samples. As QCD moves into this era of precision, rather than qualitative, tests, confrontation between theory and experiment at higher integrated luminosities and with an upgraded detector will be of great importance. The addition of a central magnetic field will also allow the study of more exclusive final states such as W+charm and gamma+charm. The current QCD program with the D0 detector is rich and imaginative and we are confident that this will continue with the upgraded detector. We have already presented analyses in areas of physics previously unexplored at the Tevatron: rapidity gaps, correlations between jets with large rapidity intervals, the measurement of alpha_s, and energy flow around the jets, as well as the development of a new jet finding algorithm.
Until recently, cross-sections measured at the Tevatron have been used to verify the accuracy of current parton distribution parametrizations. This is one of the best tests of QCD because it requires the perturbative calculation of the QCD hard parton cross-sections AND the QCD evolution equations to extrapolate the parton distributions from low energy fixed target experiments to the Collider energy scales. This is a rigorous test of factorization since the energy scales tested differ by more than an order of magnitude. Measurement of the total inclusive jet or photon cross-sections are examples of such tests.
Until now, however, the Tevatron results (except for the W-asymmetry measurement) have not been used to fix the parton distributions. This will change in the next few years as studies focus on measuring differential cross sections with respect to an increased number of variables for jets, photons, and W/Z final states with larger statistics. For example, consider the triple differential cross-section d3sigma/dpT1 deta1 deta2 where pT1 and eta1 are the leading jet transverse momentum and eta2 the rapidity of the second leading jet [9] At small leading momentum and rapidity, pT1 = 50 GeV and eta1 = 0, and large values of rapidity for the second jet , eta2 = 2.5, the cross-section is sensitive to the product of parton momentum fractions at extreme values of x (between 0.003 and 0.7). As a second example of differential cross-sections, the inclusive photon cross-section d2sigma/dpT(gamma) deta and the gamma+jet inclusive cross section at large rapidities are sensitive to the gluon content of the proton at x=0.001.
Looking ahead further one can anticipate the measurement of specific parton flavors in the proton, by selecting certain exclusive final states. This is very difficult with the current D0 detector, but is made possible by the upgraded tracking system. An example here is the final state W+charm, which directly probes the strange quark distribution. Another example would be gamma+charm or any other process where the final state quark could be tagged. Charm identification will be possible both through reconstruction of the exclusive D decay modes, and through tagging soft muons from the charm decay.
The differential jet, gamma, W and Z cross-sections just discussed also provide precise tests of QCD calculations at order alpha_s cubed (NLO). These calculations for differential jet production are now available [10]. For large jet rapidities, leading order calculations seriously underestimate the cross section. NLO calculations compensate for this shortfall but not completely. Most likely even higher order calculations are necessary and these are currently being worked on. The examination of rare high pT and very forward jets, possible only with high luminosity, will be a further revealing test of NLO calculations. The large pseudorapidity coverage of the DO calorimeter (|eta|<4) is ideally suited to these measurements.
Currently, precision studies of QCD with jets are limited in D0 because the jet energy scale has large systematic errors. This error will be greatly reduced in the upgraded detector, because tracking in a magnetic field will allow a calibration of the hadron energy scale in situ for the first time.
At very low transverse momentum or at the edge of accessible phase space, one expects non-perturbative effects, like primordial parton kT, to play a role. It has been suggested that such effects can explain the discrepancies in direct photon cross sections at different center of mass energies. A universal formulation of such non-perturbative phenomena is being attempted now,[11] and its predictions can be tested in other processes at the Collider. To test the transition from perturbative to non-perturbative calculations, both large acceptance and high luminosities are required. The W and Z pT spectra test a similar transition since the low pT portion of the spectrum is calculated by resummation techniques, with the above mentioned non-perturbative contributions, and matched to the high pT perturbative part of the spectrum.
NLO calculations for di-photon and intermediate vector boson production are available but have not been precisely tested. [12,13] The high statistics samples required for these NLO tests must wait for higher luminosities or, equivalently, higher energies.
Drell-Yan pairs provide a clean probe of QCD processes. The colorless muons or electrons are free of final-state interactions and can be accurately identified without any of the ambiguities of jet identification and measurement. Typically, cross sections are small, and as a result Drell-Yan production has not been used to its full potential. However, the special cases of Z and W production have recently been used to test perturbative, resummed, or parton shower based predictions of QCD. Two examples include the determination of alpha_s from W+jets and the comparison of Z and W pT distributions with resummed predictions.
Z production alone can be considered an outstanding QCD test laboratory. Because the final state Z can be reconstructed very accurately and without background, the measurement of pT, pL, rapidity dependence, and energy flow around the Z can be made in an unambiguous and unique way. This kind of detailed study of QCD is just starting to become feasible with currently available luminosities. With higher luminosities, it can reach the statistical precision of jet cross sections but without any of the hindrance from systematics. To reach this statistical precision one would need a sample of roughly 100,000 Z's, which corresponds to about 1 fb-1 if one uses the Z -> e+e- and Z -> mu mu decays. In fact, the entire menu of differential jet and photon cross-sections can be replaced with differential Z+jet final state cross-sections. This will truly move QCD into the realm of precision physics. An obvious measurement here would be the determination of alpha_s from the ratio of Z + (n jet)/ Z +(n-1 jet) events. This would be similar to what has already been done with W's, but much more precisely determined experimentally.
The special case of Z production can be generalized by introducing the Drell-Yan gamma* -> l+ l- pair mass as a parameter. In particular, measurement of the Drell-Yan pair pT distribution as a function of mass provides a test of resummation techniques. The more interesting measurement though would again be the determination of the strong coupling constant. One employs the same technique as for Z's, but as a function of the lepton pair invariant mass. This results in a measurement of alpha_s as a function of Q^2 scale, and tests both the running of alpha_s and its absolute value in one experiment. With sufficient statistics the angular distribution of the final state leptons may also analyze the polarization state of the vacuum [14] , a possibility that has, as yet, not been investigated at the collider. Including both electron and muon final states, one expects about 60K events in the region 20 < m(gamma*) < 30 GeV.
DO has developed a new jet-finding algorithm based on the successive-combination techniques commonly used in e+e- physics. The same algorithm may be used to find clusters of energy within jets. With large statistics, we hope to be able to statistically separate quark and gluon jets using this approach and thus refine our study of the QCD subprocesses. It should also be possible to measure both alpha_s and observe its running from the dependence of the observed number of jets on the combination scale used in the algorithm.
Dijet production at large rapidity differences, Delta eta > 4, with little or no activity between the jets (rapidity gaps) may signal the presence of the exchange of a colorless object [15] Such events have been observed by D0 in its current run and we want to examine this phenomenon further in the future. Is the exchanged object the Pomeron and is it the same object observed in diffractive scattering? By studying diffractively produced events at the Tevatron the partonic content of the Pomeron may be measured. Is it the same as measured at HERA and at UA8? These questions can partially be answered with events with rapidity gap signatures, but ultimately may require the measurement of the diffractively scattered (anti-)proton. D0 has begun to investigate the potential for pursuing rapidity gap and diffractive physics in Run II.