[0] GLASPPE/980327^{th} June 1998
HERA Progress: Since last year's DIS workshop, the data available for analysis at ZEUS has more than doubled, corresponding to an integrated luminosity from the 199497 datataking periods of 46.6 pb^{1}. This large data sample presents a significant challenge to the experimentalists in providing precise data in the many areas which HERA can uniquely access. The understanding of the ZEUS detector is being improved using the large data samples to calibrate in situ. To illustrate the current level of understanding of the detector: the integrated luminosity is currently known to better than ±1.5%; the overall momentum scale of the central tracking detector has been established at below the 0.3% level following calibration using elastic J/y data; the electron energy scale in the barrel calorimeter has been calibrated to ±1% using DIS data; and, the hadronic energy scale has been determined within ±3% using DIS data and crosschecked using dijet events. Developments in the calibration of the detector, combined with the improved statistics, enable increasingly precise as well as new measurements to be performed, as discussed below.
Photon Structure: [1] Before discussing the latest preliminary measurements, it is worthwhile to note the uncertainties, as discussed in recently published results on inclusive jet production using the cone algorithm. [2] Experimentally the uncertainty on the jet energy scale of ±3% dominates the uncertainty on the crosssections. Theoretically, the scale dependence on the renormalisation and factorisation scales varied between E_{T}^{jet}/4 < m_{F} = m_{R} < E_{T}^{jet}, is minimised for a cone radius R ~ 0.6, as observed earlier at the Tevatron. The variation of R_{sep}, the twojet merging parameter, leads to similar uncertainties on the crosssection for R < R_{sep} < 2R. In order to minimise the theoretical uncertainties due to merging/seedfinding ambiguities, the iterative k_{T}algorithm has been adopted. An inclusive dijet analysis was performed requiring E_{T}^{jet1} > 14 GeV and E_{T}^{jet2} > 11 GeV.
At these E_{T}^{jet} values, comparisons with Monte Carlo indicate that multiple interactions (not included in the NLO calculations) are not required to describe the observed x_{g} distributions or the jet profiles. To gain greater sensitivity to the internal structure of the photon the measurements are made at highy (0.5 < y < 0.85), corresponding to the highest accessible photon energies. In Fig. 1 the ds/dh_{2} distribution for the secondhighest energy jet is presented for fixed intervals of h_{1}. The shaded band represents the hadronic energy scale uncertainty. The hadronisation uncertainties have been estimated to be ~ 10%, the scale uncertainties are estimated at ~ 10% while the proton parton densities are well constrained in the probed x region (x ~ 10^{2}). The data are thus sensitive to the choice of photon parton densities, as illustrated by the comparison of the the data with the GS96 and GRV parameterisations. The ZEUS data has now reached a level of precision where the photon parton densities can be discriminated: a global analysis of photon parton densities incorporating such data is therefore required.
Multijet Structure: [3] In order to probe the QCD matrix elements at a deeper level, an inclusive threejet analysis has been performed using the k_{T}algorithm for jets with E_{T}^{jet} > 6 GeV. The crosssection for such processes can be written as:

Here, the measured invariant mass distribution, M^{\sf jjj}, is governed by the photon and proton parton densities, f_{\sf 1/\sf g}(x_{\sf g}) and f_{\sf 2/\sf p}(x_{\sf p}), whereas the scaled energies of the jets, X_{3} and X_{4}, are controlled largely by phase space. The measured angular distributions in the threejet centre of mass are cosq_{3}, where q_{3} is the angle the highestenergy jet makes w.r.t. the beam axis, and y_{3}, the angle of the threejet plane w.r.t. the beam axis. The cosq_{3} distribution is determined by the spin of the primary exchange and the distribution of y_{3} is related to the coherence property of the radiated (lowestenergy) jet to lie in the plane of the beam and the highestenergy jet. These are shown in Fig. 2, compared to O(aa_{S}^{2}) calculations (thick line) as well as to a phase space calculation (thin line) where the spin of the partons is ignored. The comparisons constitute a refined test of the photoproduction QCD matrix elements M_{\sf 12® \sf 345}.
Charm in Photoproduction: [4] Heavy flavour production introduces a new scale with which to test perturbative QCD. Measurements of the D^{*}® (K p) p_{s} and D^{*}® (K ppp) p_{s} channels are shown to be in good agreement in Fig. 3(a).
Two approaches have been taken in the calculations: the ``massive" approach (dashed lines) where charm is generated dynamically and divergences are regulated by the charm mass; and the ``massless" approach (full lines) where charm production is activated at the m_{c} threshold and massless approximations are used. Uncertainties arise due to the choice of the effective charm mass, and renormalisation and factorisation scales (here m_{R} = Ö{m_{c}^{2} + p_{^}^{2}} = m_{F}/2) as well as the hardness of the charm decay to D^{*}, characterised in terms of e_{c} in the Peterson fragmentation function for the ``massive" calculations. The measured crosssection is typically underestimated in the calculations. In Fig. 3(b) this excess is observed to be predominantly in the forward direction. The open question is whether the data are more sensitive to the choice of input photon structure function or to the D^{*} fragmentation dynamics as we approach the proton fragmentation region or, perhaps, anomalously large contributions from b® c decays.
Further information is provided by the measurement of associated dijets with E_{T}^{jet1} > 7 GeV and E_{T}^{jet2} > 6 GeV shown in Fig. 4. Here the measurement of x_{g}^{OBS} has a relatively large contribution at lowx_{g} whereas the ``massive" NLO calculation is significantly more peaked towards one, underestimating the lowx_{g} part of the crosssection. The question here is whether the dynamical generation of charm in photoproduction is sufficient, assuming that jet hadronisation effects, estimated at ~ 10% using Monte Carlo simulations, are relatively less important.
Charm in DIS: [5]
D^{*}® (K p) p_{s} measurements in DIS provide a
significant test of the gluon density of the proton
determined from the scaling violations of F_{2}.
They will also help to constrain theoretical uncertainties in the
fits to F_{2} where different prescriptions for heavy flavour effects
are adopted.
Compared to the photoproduction case, they remove the uncertainty
due to the choice of photon PDFs
and hence reduce the number of open question posed above.
The preliminary crosssection
s^{ep® D*X} = 8.55 ±0.40 ^{+0.30}_{0.24} nb
is measured in the range
1 < Q^{2} < 600 GeV^{2},
0.02 < y < 0.7,1.5 < p_{T}(D^{*}) < 15 GeV, and h(D^{*}) < 1.5.
In Fig. 5, the upper plots show the measurements
of the hadronic final state variables p_{T}(D^{*}), h(D^{*}) and x_{D*},
the fractional momentum the D^{*} in the g^{*} p rest frame:
the data agree with the massive NLO calculations where
e_{c} = 0.035, except perhaps at lower
x_{D*} corresponding to higher h(D^{*}).
In addition the kinematic variables, W, Q^{2} and x shown in the
lower plots are in good agreement with the NLO calculations:
it is therefore reasonable to extrapolate the measured crosssection
to the full {h(D^{*}), p_{T}(D^{*}) } range
^{2}
to determine F_{2}^{c}(x, Q^{2}) via the expression

Transition Region: [6] The corresponding rise of F_{2} with decreasing x, or equivalently the rise of s^{tot}_{g* p} with increasing W, has stimulated significant theoretical developments in the understanding of QCD at high energies. One challenge is to explore how and where the transition occurs from soft to hard physics and interpret lowQ^{2} data. In order to relate the lowQ^{2} and Q^{2} = 0 data, a GVMD (Generalised Vector Meson Dominance) analysis has been performed. This analysis relates the virtual photon crosssection to the real crosssection via
s^{tot}_{g* p} = s^{tot}_{gp}·M^{2}_{0} / (M^{2}_{0} + Q^{2}),
for fixed W (s_{L} contributions at small Q^{2}
lead to a small correction of s^{tot}).
A good description of the ZEUS BPC data measured in the range
0.1 < Q^{2} < 0.65 GeV^{2} is found with
M^{2}_{0} = 0.53 ±0.04 ±0.10 GeV^{2}.
Extrapolating to Q^{2} = 0 GeV^{2}, the corresponding
W^{2(\alphapom(0)1)} dependence
is given by the pomeron intercept value
\alphapom(0)_{BPC} = 1.145 ± 0.02(stat) ± 0.04(sys) (preliminary)
to be compared with the DonnachieLandshoff value \alphapom(0) = 1.08. In this Q^{2} range, the rise of the crosssection is therefore relatively modest. This behaviour is also seen in the lower Q^{2} points of Fig. 7(a). Here additional datsets are incorporated in fits to the F_{2} data of the form F_{2} = c·x^{leff} _{Q2}. The parameter l_{eff} @ \alphapom(0)  1 for x < 0.01 is then plotted as a function of Q^{2}. A relatively slow transition from l_{eff} @ 0.1 is observed with increasing Q^{2}. This rise of F_{2} with decreasing x is intimately coupled to the scaling violations via the gluon density (in leading order dF_{2}/dlog Q^{2} ~ xg(x) neglecting sea quark contributions). In Fig. 7(b), fits of the form F_{2} = a + b ·log(Q^{2})_{x} have been performed to the published HERA data and the preHERA prediction from the GRV94 PDFs. [7] For x \lsim 10^{4}, corresponding to < Q^{2} > \lsim 2 GeV^{2} there is a qualitative change in behaviour where the scaling violations stabilise and then decrease for lowerx values, a behaviour which is not reproduced by the GRV94 PDFs. [r]60mm
file=sg_mor.ps Low Q^{2} parton densities.
The question is whether this scaling violation behaviour and the slow onset of the rise of F_{2} with decreasing x can be simultaneously understood. A DGLAP NLO fit to the Q^{2} > 1 GeV^{2} data (not shown) describes the data, demonstrating that there is sufficient flexibility in such an approach to go down to relatively low Q^{2}. However, the relatively stable scaling violations observed around < Q^{2} > ~ 2 GeV^{2} in Fig. 7(b) yield a gluon contribution which is rapidly diminishing at smallx and which is significantly smaller than the sea quark contribution for small starting scales, as illustrated in Fig. 8: in this low Q^{2} region the sea appears to be driving the gluon at lowx. For larger Q^{2} values the gluon dominates the sea and we have an intuitively appealing picture where gluons radiate sea quarks. Whether such lowQ^{2} partons are universally valid could be tested using e.g. lowQ^{2} F_{2}^{c} data.
Forward Jet Production: [8] Why does F_{2} rise? In the DGLAP approach the x dependence is an input determined at a starting scale Q_{o}^{2} and evolved in Q^{2}. In the BFKL approach the xdependence has recently been calculated in NLO. The underlying dynamics may be tested using semiinclusive forward jet measurements in lowx events. Jets with E_{T}^{2} ~ Q^{2} and x_{jet} \gsim x, where x_{jet} is the momentum fraction of the jet relative to the incoming proton, are selected in order to enhance BFKLlike contributions where forward gluons may be emitted at relatively large E_{T}. In Fig. 9 the jets observed at detector level are shown as a function of E_{T}^{2}/Q^{2} compared to three Monte Carlo simulations: LEPTO 6.5 and HERWIG 5.9 are DGLAPbased models such that gluons emitted at successively larger x_{gluon} ~ x_{jet} have successively lower E_{T} whereas the colour dipole model ARIADNE 4.08 incorporates a BFKL feature that gluons are not strongly ordered.
Three regions are identified: I  E_{T}^{2} < Q^{2}/2, the "DGLAP" region, where all models approximately describe the data; II  Q^{2}/2 < E_{T}^{2} < 2Q^{2}, the "BFKL" region where the DGLAPbased models (LEPTO 6.5 and HERWIG 5.9) fall below the data; and, III  E_{T}^{2} > 2Q^{2}, where all models fail and we may need to describe the DIS data in terms of a virtual photon whose structure is being resolved by the highE_{T} jets. The crosssection is evaluated in region II as a function of x for x_{jet} > 0.036 and E_{T} > 5 GeV in Fig. 10. BFKL dynamics leads to an enhancement of the forward jet production crosssection proportional to (x_{jet}/x)^{\alphapom 1} over the O(aa_{S}^{2}) calculation.
As shown in Fig. 10(a) there is a significant difference between the O(aa_{S}^{2}) MEPJET calculation (represented by the shaded band which includes the uncertainty on the renormalisation scale) compared to the leadingorder BFKL prediction (full curve) at parton level. There are residual uncertainties in determining the hadrontoparton level corrections and therefore the measurement in Fig. 10(b) is presented at hadron level. The rise of F_{2} at small x is mirrored by the rise of the measured forward jet crosssection which is not described by the DGLAPbased models. A consistent description of the F_{2} and forwardjet data represents a considerable challenge to our understanding of QCD.
Fragmentation Functions: Recently published results on jet shapes have shown that the observed patterns of QCD radiation in highQ^{2} neutral current and charged current are similar to those observed in e^{+}e^{} experiments. [9]
At HERA we are able to study these properties as a function of Q^{2} in a single experiment and hence provide detailed information on quark fragmentation properties. [10] These properties can be studied in the semisoft limit by measuring the ln(1/x_{p}) distributions, where x_{p} = 2p/Q is the scaled momentum of charged hadrons in the current region of the Breit frame. The observed Gaussian distributions are then fitted within ±1 of the mean to yield the ln(1/x_{p})_{max} values as a function of Q given in Fig. 11(a). The precise data are consistent with data from e^{+}e^{} experiments establishing the universality of fragmentation over a large range of Q. An MLLA+LPHD fit (indicated by the full line) of the form ln(1/x_{p})_{max} = 1/2Y +c_{2}Ö(Y)c_{2}^{2}, where Y = lnQ/2L_{eff} and c_{2} = 0.52 for three active flavours in the cascading process, provides a reasonable description of the data with L_{eff} @ 245 MeV. The highstatistics data enables the region of high x_{p} to be studied. In Fig. 11(b) the fragmentation function data are presented for different x_{p} intervals as a function of Q^{2} (in various ranges of x). At high x_{p} and higher Q^{2} the fragmentation functions exhibit negative scaling violations, consistent with a dominant QCD Compton process (c.f. highx structure function data). The DIS data (full symbols) are observed to be reasonably consistent with e^{+}e^{} data (open symbols), but systematically lower at intermediate x_{p} values. Comparisons with NLO calculations where fragmentation functions extracted from e^{+}e^{} data are implemented can describe the DIS data (see Fig. 2 in [10]). However care needs to be taken to explicitly include strangequark fragmentation functions which are systematically softer than those of the up/down quarks. This is important since the production of strange quarks from the proton sea in DIS is suppressed (by a factor @ 0.2) compared to those from e^{+}e^{} annihilation. In order to compare with recent 1/Q^{2} powercorrection calculations, the fragmentation function data were also presented as function of x_{} = 2 p·q /Q^{2} = 2p_{Z}/Q, where the Z direction is defined by the virtualphoton proton axis.
Another approach to investigate the rôle of such power corrections is to sum over these momenta and measure the corresponding thrust distributions T_{Z} = 2 Sp_{Z}/ Sp. A series of event shape variables have been measured in the current region of the Breit frame where the power corrections, determined from renormalon calculations, are expected to be characterised by a universal [`(a_{o})] and to fall as 1/Q. In Fig. 12 the measurements using charged tracks in the current region of the Breit frame are displayed as < 1T_{Z} > versus Q. [11] The characteristic behaviour is in reasonable agreement with published H1 results given at slightly different x values. Other event shape variables are chosen which are relatively insensitive, in varying degrees, to soft gluon emission and collinear parton branchings in order to determine whether a universal [`(a_{o})] can be applied. As a first step, comparisons with NLO calculations illustrate the need for additional power correction terms (see Fig. 2 in [11]).
Vector meson t dependences: [13]
Diffraction is characterised
by a steeplyfalling dependence
of the crosssection as a function of t,
the momentum transferred at the proton vertex.
This characteristic falloff increases approximately linearly
with increasing W.
This ``shrinkage"
behaviour is built into the DonnachieLandshoff pomeron
a(t)_{r0} = (1.097±0.020) + (0.163±0.035)·t (preliminary)
a(t)_{J/y} = (1.175±0.026) + (0.015±0.065)·t (preliminary).
Higher Mass Vector Mesons: [14] Twenty years after the discovery of the U, the first observation of a signal in photoproduction is shown in Fig. 14(a) as a broad enhancement around 10 GeV in the dimuon mass spectrum. The insert in Fig. 14(a) indicates the J/y and y¢ resonances: the y¢/y production ratio is measured to be R = 0.16 ±0.02 ±0.04, where the largest contribution to the systematic uncertainty is on the y¢® m^{+}m^{} branching ratio. The result is in agreement with QCD calculations, determined by the wavefunction at the origin for the 1S and 2S states, of @ 0.17. The observation of the U leads to the measurement of the elastic crosssection for the unresolved U(1S), U(2S) and U(3S) states shown in Fig. 14(b). Here the relative rates or muon production from the U states is determined from CDF data and applied as a correction to the U(1S) calculation. Comparison with the leadingorder QCD calculations, where s_{diff} ~ xg(x)^{2} Ä[^(s)] , indicates that the measured crosssection is above these expectations.
Diffractive Structure Functions: [15] A new era for diffraction was opened by the observation of large rapidity gap events in DIS and their subsequent analysis in terms of a diffractive crosssection. The diffractive contribution is identified as a nonexponentially suppressed contribution at small masses, M_{X}, of the dissociating virtual photon system. In Fig. 15 the ratio of this diffractive contribution to the total virtual photon proton crosssection is given as a function of W for various M_{X} intervals.
An approximately constant ratio with W indicates a diffractive contribution which rises with a similar W dependence. This simple observation is contrary to the näive expectation where the diffractive contribution is identified with the forward part of the scattering amplitude and would therefore rise twice as quickly as the total crosssection as a function of W. The rise of the diffractive crosssection with W can be parameterised in terms of a power law, yielding \alphapom(0) = 1.16 ±0.01 ±0.02 (preliminary), after integration over t with a mean exponential slope, b = 7 GeV^{2} and assuming a¢ = 0.25 GeV^{2}. In order to understand the driving mechanism responsible for this rise, the crosssections at fixed M_{X} and W are plotted in terms of scaling variables. Integrating over \xpom, the momentum fraction of the pomeron within the proton, leads to the b dependence of F_{2}^{D(2)} (b,Q^{2}) ( º F_{2}^{\pom} specified at \xpom = 0.0042) shown in Fig. 16 where b is the momentum fraction of the struck quark within the pomeron. An approximately flat dependence on b is observed and an approximate scaling in Q^{2} emerges from analysis of the data. The decreasing fraction of events in each M_{X} interval with increasing Q^{2} observed in Fig. 15 can thus be seen as due to integrating over a decreasing b @ Q^{2}/(Q^{2}+M_{X}^{2}) region which is approximately flat in b.
Diffractive Event Shapes: [17] The measurements of the structure function of the pomeron constrain various models of diffraction. These models may be discriminated using event shape variables which are directly sensitive to the underlying partonic structure. Similarly, the data can be directly compared with e^{+}e^{} data where the underlying gluon Bremsstrahlung structure is well known. Tagging a leading proton in the LPS allows a wide range of M_{X} up to 25 GeV to be explored for \xpom < 0.03 and Q^{2} > 4 GeV^{2}.
Measurements of the mean thrust are presented as a function of M_{X} in Fig. 17. The LPS measurements are able to discriminate amongst various models which assign different partonic structures to the pomeron. The data exhibit reasonably similar values compared to e^{+}e^{} data for all values of M_{X} suggesting that additional gluon contributions from the pomeron are relatively small. They are also consistent, but systematically higher than, the H1 data obtained using the large rapidity gap method. Improved statistics, from existing data, will help to clarify whether the gluon contribution of the pomeron determined from the scaling violations of F_{2}^{D(2)} [15] is consistent with that extracted from event shape variables [17] and diffractive dijet photoproduction [16].
Leading Baryon Production: [18] Nondiffractive contributions play a rôle at higher values of \xpom. Measurements of forward proton production allow us to compare data with fragmentation models as well as models based on reggeon exchange. Preliminary results for the corrected rates of proton production in the range 0.60 < x_{L} º 1\xpom < 0.91 for DIS at low and higher Q^{2} (0.1 < Q^{2} < 0.8 GeV^{2} and Q^{2} > 4 GeV^{2}) are (13.0±0.5^{+0.7}_{0.8})% and (12.7±0.3±0.9)%, respectively. The measured rates are typically higher than the currently available fragmentation models by a factor of 1.5 to 2. Measurements of uncorrected forward neutron production rates have been compared to reggeon exchange models: the comparisons indicate that the internal structure of the exchanged reggeon falls like 1b at large b (a dependence similar to p (and higher) Regge exchanges), in contrast to the approximately flat behaviour with b noted earlier for diffractive exchange. The rates for neutron production are approximately the same for DIS, photoproduction and even protongas interactions although the W dependence of these crosssections is significantly different. This suggests that ``diquark" fragmentation is a universal process which is to a large extent independent of the type of interaction with the incident proton.
In Fig. 18(a), these events clearly stand out but no new NC outstanding events are observed in the 1997 data, corresponding to a further 26.5 pb^{1} of data. In Fig. 18(b), one charged current (CC) event is observed at very high Q^{2} @ 30,000 GeV^{2} from the 19941996 data as well as two further events from 1997 at Q^{2} @ 20,000 GeV^{2}. The number of events is higher than expectations but is consistent with the standard model. Attention has therefore focussed on measuring the crosssections at the highest accessible Q^{2} values. The theoretical uncertainty on the crosssections was determined from a ZEUS QCD fit to the structure function data on proton and deuteron targets from SLAC, BCDMS and NMC as well as the neutrino measurements from CCFR, taking into account the correlation amongst the systematic errors of each experiment. a_{S}(M^{2}_{Z}) was varied from 0.113 to 0.123 and a 50% uncertainty in the strange quark content was included. In addition, various published PDFs with different models for charm evolution were used as well as fits incorporating E706 prompt photon data and CDF jet data. The results yielded SM crosssection uncertainties of @ 68% on the NC crosssection and @ 612% on the CC crosssection at the highest accessible Q^{2} values. These crosssections therefore represent a benchmark for the standard model. The crosssections, discussed below, are corrected to the electroweak Born level and integrated over the complete y range.
Charged Current CrossSections: [19] Charged current events are identified by their missing transverse momentum (p_{T}) due to the escaping neutrino. The crosssection is sensitive to the valence dquark distribution in the proton:

M_{W} = 78.6 ^{+ 2.5}_{ 2.4}(stat.) ^{+3.3}_{ 3.0}(syst.) GeV (preliminary)
Photoproduction of Wbosons decaying semileptonically has been investigated by searching for events with a highp_{T} lepton and missing p_{T} with 46.6 pb^{1} of data. This is interesting in the context of the observed excess of highp_{T} muons with associated missing p_{T} observed by H1 [20]. In the ZEUS analysis four events are observed in the electron channel where 2.22±0.02 are expected from W production and 1.24±0.35 from various backgrounds. Similarly, zero events are observed in the muon channel where 0.46±0.02 are expected from W production and 0.84±0.23 from other sources. The ZEUS measurements enable 95%CL limits to be set on s(W) (p_{T}^{miss} > 20 GeV) of 2.5 pb and 2.0 pb in the electron and muon channels, respectively.
Neutral Current CrossSections: [21] HighQ^{2} neutral current events are easily identified from the highenergy scattered positron. The crosssection is particularly sensitive to the valence uquark distribution in the proton:

A wide range of new interactions would modify the NC crosssections in a way which can be parameterised by an effective fourfermion (eq® eq) coupling. Given a convention for the strength of the coupling (g^{2} = 4p), limits can be placed on the effective mass scale (L) of these contact interactions. Scalar and tensor terms are constrained by earlier experiments and atomic parity violation experiments provide strong constraints on various vector couplings: the relative size and sign of individual terms in the contact interaction amplitudes is therefore limited to 24 different combinations. These contact interactions all contain a term proportional to 1/L^{4} which enhances the crosssection as well as a SM interference term proportional to 1/L^{2} which can either enhance or suppress the crosssection at intermediate Q^{2}. No significant deviations are found and limits on the 24 models are set in the range of L @ 25 TeV. These limits are competitive with, and in some cases extend, those limits set from from hadronic crosssection measurements at LEP and DrellYan electron pair production at the Tevatron.
^{1} Alexander von Humboldt fellow (Hamburg II University), supported by DESY and PPARC.
^{2} This procedure neglects the possibility of additional contributions outside the measured region due, for example, to intrinsic charm.