The ZEUS detector is shown in figure 1. The asymmetric design of the detector reflects the proton energy being significantly higher than that of the electron beam.
The tracking system consists of a vertex detector (VXD) [1] and a central tracking chamber (CTD) [2] enclosed in a 1.43 T solenoidal magnetic field. Immediately surrounding the beampipe is the VXD which consists of 120 radial cells, each with 12 sense wires. The CTD, which encloses the VXD, is a drift chamber consisting of 72 cylindrical layers, arranged in 9 superlayers. Superlayers with wires parallel to the beam axis alternate with those inclined at a small angle to give a stereo view. A forward tracking detector is employed in the forward region to detect tracks in the proton direction and consists of three 12-layer planar drift chambers sandwiched with pairs of transition radiation detectors. In the rear direction there is an additional 12-layer planar drift chamber known as the rear tracking detector (RTD).
Outside the solenoid is the uranium-scintillator calorimeter (CAL) [3], which is divided into three parts: forward, barrel and rear covering the polar regions 2.6° to 36.7°, 36.7° to 129.1° and 129.1° to 176.2°, respectively. The CAL covers 99.7% of the solid angle, with holes of 20 ×20 cm2 in the centres of the forward and rear calorimeters to accommodate the HERA beam pipe. Each of the calorimeter parts is subdivided into towers which are segmented longitudinally into electromagnetic (EMC) and hadronic (HAC) sections. The small angle rear tracking detector (SRTD) [4], which is attached to the front face of the rear calorimeter, measures the impact point of charged particles at small angles with respect to the positron beam direction.
The iron return yoke for the magnet is instrumented with proportional counters. This backing calorimeter (BAC) measures any hadronic energy which `leaks out' out of the main calorimeter. Beyond that and in the forward direction there are further detectors for muon detection.
Downstream of the main detector in the proton direction, six measuring stations are installed in the proton ring for detecting forward scattered protons. Beyond the final station, further downstream, is a forward neutron calorimeter. In the electron direction, two lead scintillator calorimeters placed -35 m and -107 m from the interaction point measure the luminosity and tag events with a small momentum transfer [5].
A fuller description of the ZEUS detector can be found in reference [6]. The H1 detector is of a very similar layout as ZEUS and a description can be found in reference [7].
In QPM there is a 1+1 parton configuration, fig. 2a, which consists of a single struck quark and the proton remnant, denoted by ``+1''. At HERA energies there are significant higher-order Quantum Chromodynamic (QCD) corrections: to leading order in the strong coupling constant, as, these are QCD-Compton scattering (QCDC), where a gluon is radiated by the scattered quark and Boson-Gluon-Fusion (BGF), where the virtual boson and a gluon fuse to form a quark-antiquark pair. Both processes have 2+1 partons in the final state, as shown in fig. 2. There also exists calculations for the higher, next-to-leading (NLO) processes.
Perturbative QCD does not predict the absolute value of the parton densities within the proton but determines how they vary from a given input. For a given initial distribution at a particular scale Altarelli-Parisi (DGLAP) evolution [9] enables the distributions at higher Q2 to be determined. DGLAP evolution resums the leading log(Q2) contributions associated with a chain of gluon emissions. At large enough electron-proton centre-of-mass energies there is a second large variable 1/x and, therefore, it is also necessary to resum the log(1/x) contributions. This is acheived by using the BFKL equation [10].
|
Figures 3a-d show the ZEUS jet rates using data taken in 1994, R1+1, R2+1 and R3+1 as a function of ycut for data compared with the DISJET and PROJET NLO QCD calculations for three Q2 intervals 120 < Q2 < 240 GeV2, 240 < Q2 < 720 GeV2, 720 < Q2 < 3600 GeV2, and the combined region 120 < Q2 < 3600 GeV2. There is good agreement between the corrected 1+1 and 2+1 jet rates and the NLO QCD calculation over most of the range in ycut shown. Both programs agree well in their prediction of the jet-rate dependence as a function of ycut.
The values of as(Q) extracted by the H1 [14] and ZEUS [15] collaboration as a function of Q are shown in Fig. 4. The value of as was determined by varying the L scale parameter in the QCD calculation until the best fit to the ratio R2+1 was obtained at a particular value of ycut. The measured as decreases with increasing Q, consistent with the running of the strong coupling constant, with Q2 taken as the scale. In addition the figure shows the curves for L[`MS](5) = 100, 200, and 300 MeV. An extrapolation to as(Mz) yields:
|
Recently two new, more flexible NLO calculations (MEPJET [17] and DISENT [18]) have become available allowing the experiments to analyze the data using any particular jet algorithm. The kT algorithm [19] is particularly suited for DIS as it allows factorization between the beam fragmentation and the hard process [20]. The ZEUS collaboration has reanalyzed [21] their 1994 data using this algorithm. The preliminary values of as(Q) obtained in the three bins of Q are shown (with statistical errors only) in Fig. 4 and are consistent with the results obtained with the JADE algorithm.
A natural frame in which to study the dynamics of the hadronic final state in DIS is the Breit frame [22]. In this frame the exchanged virtual boson is purely space-like with 3-momentum q = (0,0,-Q), the incident quark carries momentum Q/2 in the positive Z direction, and the outgoing struck quark carries Q/2 in the negative Z direction. A final state particle has a 4-momentum pB in this frame, and is assigned to the current region if pBZ is negative, and to the target frame if pBZ is positive. The advantage of this frame lies in the maximal separation of the outgoing parton from radiation associated with the incoming parton and the proton remnant, thus providing the optimal environment for the study of the fragmentation of the outgoing parton.
Event shape variables have been investigated in e+e- experiments and used to extract the strong coupling constant as(MZ) independent of any jet algorithm, see eg ref. [23]. H1 have recently performed a similar analysis [24] in deep inelastic scattering in the current fragmentation region of the Breit frame.
The event shape dependence on Q (or energy dependence) can be due to the logarithmic change of the strong coupling constant as(Q) µ 1/lnQ, and/or power corrections (hadronisation effects) which are expected to behave like 1/Q. Recent theoretical developments suggest that 1/Q corrections are not necessarily related to hadronisation, but may instead be a universal soft gluon phenomenon associated with the behaviour of the running coupling at small momentum scales [25,26].
H1 have analysed a number of infrared safe (ie independent of the number of partons produced) event shape variables. Their definitions are given below, where the sums extend over all hadrons h (being a calorimetric cluster in the detector or a parton in the QCD calculations) with four-momentum pBh = { EBh, pBh } The current hemisphere axis n = {0, 0, -1 } coincides with the virtual boson direction.
|
|
|
|
A common characteristic of the mean event shape values á1 - Tc ñ, á1 - Tz ñ, á Bcñ and árc ñ is the fact that they exhibit a clear decrease with rising Q, fig. 5. This is due to fact that the energy flow becomes more collimated along the event shape axis as Q increases, a phenomenon also observed in e+e-\ annihilation experiments.
H1 showed by fitting to the data in fig. 5 all the event shape variables can be well described by just the first order power corrections µ 1/Q, without the need for any higher order corrections. The second order perturbative QCD parton predictions are also shown and their discrepancies with the data show that the power corrections are substantial at low values of Q, but become less important with increasing energy.
The analysis of the event shapes give results consistent with each other for [`(a)]0, the power correction parameter thus supporting the prediction of universality [25], and also gives consistent values of as(MZ). The results of the fit are [`(a)]0 = 0.491 ±0.003 (exp) +0.079-0.042 (theory) for the power correction parameter and as(MZ) = 0.118 ±0.001 (exp) +0.007-0.006 (theory) for the strong coupling constant in the [`MS] scheme. These values are compatible with those extracted by e+e- experiments [27]
In e+e- annihilation the two quarks are produced with equal and opposite momenta, ±Ös/2. This can be compared with a quark struck from within the proton with outgoing momentum -Q/2 in the Breit frame. In the direction of the struck quark (the current fragmentation region) the particle momentum spectra, xp = 2pB/Q, are expected to have a dependence on Q similar to those observed in e+e- annihilation [30,31,32] at energy Ös = Q.
The inclusive charged particle distributions [33,34], (1/stot)ds/d xp, are shown in figure 6 plotted in bins of fixed xp as a function of Q2. For Q2 > 80 GeV2 the distributions rise with Q2 at low xp and fall-off at high xp and high Q2. By measuring the amount of scaling violation one can ultimately measure the amount of parton radiation and thus determine as. Below Q2 = 80 GeV2 the fall off is due to depopulation of the current region.
The results can be compared to the next-to-leading order (NLO) QCD calculations, as implemented in CYCLOPS [35], of the charged particle inclusive distributions in the restricted region Q2 > 80 GeV2 and xp > 0.1 , where the theoretical uncertainties are small, unaffected by the hadron mass effects which are not included in the fragmentation function. This comparison is shown in figure 6. The NLO calculation combines a full next-to-leading order matrix element with the MRSA¢ parton densities (with a LQCD = 230 MeV) and NLO fragmentation functions derived by Binnewies et al. from fits to e+e- data [36]. The data and the NLO calculations are in good agreement, supporting the idea of universality of quark fragmentation.
The peak position of the x = ln(1/xp) distributions, xpeak, was evaluated. Figure 7 shows the distribution of xpeak as a function of Q for the HERA data [33,37,38] and of Ös for the e+e- data. Over the range shown the peak moves from @ 1.5 to 3.0, equivalent to the position of the maximum of the corresponding momentum spectrum increasing from @ 400 to 900 MeV. The HERA data points are consistent with those from TASSO [39] data and a clear agreement in the rate of growth of the HERA points with the e+e- data [39,40] is observed.
The increase of xpeak can be approximated phenomenologically by the straight line fit xpeak = b ln(Q)+c also shown in figure 7. Also shown is the statistical fit to the data when b = 1 which would be the case if the QCD cascade was of an incoherent nature, dominated by cylindrical phase space. (A discussion of phase space effects is given in [41].) In such a case, the logarithmic particle momentum spectrum would be peaked at a constant value of momentum, independent of Q. The observed gradient is clearly inconsistent with b = 1 and therefore inconsistent with cylindrical phase space thus supporting the coherent nature of gluon radiation.
BFKL evolution can be enhanced by studying DIS events which contain an identified jet of longitudinal momentum fraction xjet = pz(j)/Eproton (in the proton direction) which is large compared to Bjorken x [42]. By tagging a forward jet with pT(j) @ Q this allows minimal phase space for DGLAP evolution while the condition xjet >> x leaves BFKL evolution active. This leads to the forward jet production cross section in BFKL dynamics being larger than that of the \cal O(aS2) QCD calculation with DGLAP evolution [43].
In Fig. 8, recent data from H1 [44] and ZEUS [45] are compared with BFKL predictions [46] and fixed order QCD predictions as calculated with the MEPJET [17] program at NLO. The conditions pT(j) @ Q and xjet >> x are satisfied in the two experiments by slightly different selection cuts. H1 selects events with a forward jet of pT(j) > 3.5 GeV (in the angular region 7o < q(j) < 20o) with
| (7) |
| (8) |
Fig. 8 shows that both experiments observe substantially more forward jet events than expected from NLO QCD. A very rough estimate of the uncertainty of the NLO calculation is provided by the two dotted lines, which correspond to variations by a factor 10 of the renormalisation and factorisation scales mR2 and mF2. A recent BFKL calculation (dashed lines) gives a better agreement with the data. The overall normalisation in this calculation is uncertain and the agreement may be fortuitous, indeed it should also be noted that both experiments observe more centrally produced dijet events than predicted by the NLO QCD calculations. Further careful investigation is necessary before claiming that BFKL is the mechanism for this enhanced forward jet production.