ZEUS 1995 F ZEUS BPC95 ZEUS SVX95 ZEUS94 E665 H1 SVX95 ZEUSREGGE ZEUSQCD

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1 MEASUREMENT AND PHENOMENOLOGY OF THE PROTON STRUCTURE FUNCTION F FROM ZEUS AT HERA A. Quadt Department of Physics, Particle Physics, Keble Road, Oford OX 3RH, England quadt@mail.desy.de Measurements of the proton structure function F in the Q range :6? 7 GeV from ZEUS 995 shifted verte data and From the former and other ZEUS F data the slopes Q ' :5? GeV from 996 and 997 ZEUS data are presented. df =d ln Q at ed and df =d ln(=) at ed Q are derived. F data at Q below :9 GeV are described successfully by a combination of generalised vector meson dominance and Regge theory. Using a NLO QCD t the gluon density in the proton is etracted in the range 3?5 < < :7 from ZEUS 994 and 995 data. For Q GeV it is found that the qq sea distribution is still rising at small whereas the gluon distribution id strongly suppressed. It is shown that these observations may be understood from the behaviour of the F and df =d ln Q data themselves. Introduction Measurements of the low and medium Q a neutral current (NC) deep inelastic scattering (DIS) cross sections at HERA have revealed the rapid rise of the proton structure function F as Bjorken- decreases below?. At low Q down to : GeV ZEUS data allows study of the `transition region' as Q! in which perturbative QCD (pqcd) must break down. At high Q, NC DIS measurements are sensitive to details of the QCD evolution of parton densities, electroweak couplings and the propagator mass of the Z gauge boson. Furthermore, such measurements allow the searches for physics beyond the Standard Model, such as resonance searches or contact interactions. Phenomenology of F at low and low Q. Phenomenology of the low Q region The primary purpose is to use NLO DGLAP QCD on the one hand and the simplest non-perturbative models on the other to eplore the Q transition region and through probing their limitations to shed light on how the pqcd description of F breaks down. One way to understand the rise in F at low is advocated by Gluck, Reya and Vogt (GRV94) who argue that the starting scale for the evolution of the parton densities should be very low ( :3 GeV ) and at the starting scale the parton density functions should be non-singular. The observed rise in F, with a parameterisation valid above Q GeV, is then generated dynamically. On the other hand, at low one might epect that the standard NLO Q evolution given by the DGLAP equations breaks down because of the large ln(=) terms that are not included. Such terms are taken into account by the BFKL formalism, which in a the negative of the square of the four-momentum transfer between the positron and the proton leading order predicts a rising F at low. The rise comes from a singular gluon density, g, with in the range?:3 to -.5. Clearly accurate eperimental results on F at low and the implied value of are of great interest. At some low value of Q pqcd will break down and non-perturbative models must be used to describe the data. At low and large p centre-of-mass energy, W p Q =, the total p cross-section is given by p tot (W ; Q ) = T + L = 4 Q F (; Q ) () where T and L are the cross-sections for transversely and longitudinally polarised virtual photons respectively. Two non-perturbative approaches are considered, the generalised vector meson dominance model (GVMD) and a Regge-type two component Pomeron+Reggeon approach a la Donnachie and Landsho (DL) to give a good description of hadron-hadron and photoproduction total cross-section data.. Measurement of F with Shifted Verte Data The shifted verte data correspond to an integrated luminosity of 36 nb? taken in a special running period, in which the nominal interaction point was oset in the proton beam direction by +7 cm, away from the detecting calorimeter. Compared to the earlier shifted verte analysis, for the 995 data taking period the calorimeter modules above and below the beam were moved closer to the beam, thus etending the shifted verte Q range down to :6 GeV. The double dierential cross-section for single virtual-boson echange in DIS is given by d d dq = Y+ F Q 4? y F L? Y? F 3 ( + r )() ' (? y) + y F Q 4 ( + r ); (3) + R

2 F F F F ZEUS 995 Q =. GeV Q =.5 GeV Q =. GeV Q =.5 GeV Q =.3 GeV Q =.4 GeV Q =.5 GeV Q =.65 GeV Q =.9 GeV Q =.3 GeV Q =.9 GeV Q =.5 GeV Q = 3.5 GeV -5 - Q = 4.5 GeV -5 - Q = 6. GeV -5 - ZEUS BPC95 ZEUS SVX95 ZEUS94 E665 H SVX95 ZEUSREGGE ZEUSQCD Figure : Low Q F data for dierent Q bins together with the ZEUSDL style Regge model t to the ZEUS BPC95 data. At larger Q values the ZEUS NLO QCD t is also shown. where R is related to the longitudinal structure function F L by R = F L =(F? F L ) and r gives the radiative corrections to the Born cross-section, which in this kinematic region is at most %. The parity violating term F 3 arising from the Z echange is negligible in the Q range of this analysis. Further details about the data analysis can be found in ref.. Fig. shows the results for F as a function of in bins of Q between.65 and 6 GeV (ZEUS SVX95) together with ZEUS F measurements at very low Q = :? :65 GeV (ZEUS BPC95) and at larger Q those from the ZEUS94. There is good agreement between the dierent ZEUS data sets in the region of overlap. Also shown are data from the shifted verte measurements by H (H SVX95) and ed target data from E665. The steep increase of F at low observed in the higher Q bins softens at the lower Q values of this analysis. The curves shown will be discussed later in the tet..3 The low Q region We rst give an overview of the low Q region, Q < 5 GeV, taking ZEUS SVX95, BPC95 and ZEUS94 F data. Using Eq. we calculate p tot values from the F data. The DL model predicts that the cross-section rises slowly with energy / W, = P? :8 and this behaviour seems to be followed by the data at very low Q. Above Q = :65 GeV, the DL model predicts a shallower rise of the cross-section than the data ehibit. For Q values of around GeV and above, the GRV94 curves describe the qualitative behaviour of the data, namely the increasing rise of p tot with W, as Q increases. This suggests that the perturbative QCD calculations can account for a signicant fraction of the cross-section at the larger Q values. For the remainder of this section we concentrate on non-perturbative descriptions of the ZEUS BPC95 data. Since BPC95 data are binned in Q and y we rst rewrite the double dierential cross-section of Eq. 3 as d dydq =? ( T + L ) where L = Q 4 F L and T has been dened by Eq.. The virtual photon has u factor? and polarisation. Keeping only the continuum states in the GVMD at a ed W the longitudinal and transverse p cross-section are related to the corresponding photoproduction cross-section p by M L (W ; Q ) = Q ln M + Q? M M M + p (W Q ) T (W ; Q ) = M M p + Q (W ) (4) where the parameter is the ratio V p L =V p T for vector meson (V) proton scattering and M is the eective vector meson mass. Neither nor M are given by the model and they are either determined from a t to data or by other approaches. As we do not have much sensitivity to and it is small (. -.4) we set it here to zero. We thus have 9 parameters to be determined by tting the BPC data to the simplied GVMD epression F = Q M p M +Q 4 in 8 bins of W between 4 and 5 GeV. The t is reasonable and its quality might also be judged from the upper plot in Fig.. The value obtained for M is :53 :4(stat) :9(sys). The resulting etrapolated values of p are shown as a function of W in the lower plot of Fig., along with measurements from HERA and lower energy eperiments. The etrapolated BPC data lie somewhat above the direct measurements from HERA. They are also above the cross section prediction of the DL model. It should be clearly understood that the p data derived from the BPC95 data are not a measurement of the total photoproduction cross-section but the result of a physically motivated ansatz. The simple GVMD approach just described gives a concise account of the Q dependence of the BPC data but it says nothing about the energy dependence of p. To eplore this aspect of the data we turn to a two component Regge model tot(w p ) = A R (W ) R? + A P (W P? ) where P and R denote the Pomeron and Reggeon contributions. The Reggeon intercept R is ed to the value.5 which is compatible with the original DL value and by the re-evaluation of Cudell et al. With such an intercept

3 σ T +εσ L (µb) (scaled) σ tot γp (µb) ZEUS 995 W = 5 GeV ( 8) W = 33 GeV ( 7) W = GeV ( 6) W = 9 GeV ( 5) W = 73 GeV ( 4) W = 53 GeV ( 3) W = 34 GeV ( ) W = 4 GeV ( ) Reggeon+Pomeron Pomeron (BPC only) DL ZEUS BPC 995 (etrapolated) ZEUS, H γp low W γp Q (GeV ) W (GeV ) Figure : Upper plot: ZEUS BPC95 measurements of the total cross-section T + L in bins of W and the GVMD t to the data. Lower plot: p tot as a function of W. The ZEUS BPC95 points are those from the GVMD etrapolation of p. the Reggeon contribution is negligible at HERA energies. Fitting the etrapolated BPC95 data alone yields a value :4:(stat) for P. Fitting both terms to the real photoproduction data (with W > 3 GeV ) and BPC95 data yields P = : :(stat). Including in addition the two original measurements from HERA as well gives P = : :(stat). All these values of P are larger than the value of.8 used originally by DL, but we note that the best estimate of Cudell et al. is :964 +:5?:94, which within the errors is consistent with our result. The nal step in the analysis of the BPC data is to combine the GVMD tted Q dependence with the Regge model energy dependence p M tot = M + (A R (W ) R? + A P (W ) P? ): Q The parameters M and R are ed to their previous values of.53 and.5, respectively. The 3 remaining parameters are determined by tting to real photoproduction data and the original BPC data. The description of the low Q F data given by this DL style model is shown in Fig.. Data in the BPC region Q < :65 GeV is well described. At larger Q values the curves fall below the data. Also shown in Fig. for Q > 6 GeV are the results of a NLO QCD t (full line) as described in Sec F slopes: d ln F =d ln(=); df =d ln Q To quantify the behaviour of F as a function of Q and at low we calculate the two slopes d ln F =d ln(=); df =d ln Q from the ZEUS SVX95, BPC95 and ZEUS94 data sets. At a ed value of Q and at small the behaviour of F can be characterised by F /?, with taking rather dierent values in the Regge and BFKL approaches. eff is calculated from horizontal slices of ZEUS F data between the y = HERA kinematic limit and a ed cut of < :, here including E665 data. In a given Q bin h i is calculated from the mean value of ln(=) weighted by the statistical errors of the corresponding F values. The same procedure is applied to the theoretical curves shown for comparison. Figure 3 shows the measured values of eff as a function of Q. From the Regge approach one would epect eff : and independent of Q. Data for Q < GeV is consistent with this epectation. The linked points labelled DL are calculated from the Donnachie- Landsho t and as epected from the discussion of the previous section are somewhat below the data. For Q > GeV, eff increases slowly to around.3 at Q values of 4 GeV. Qualitatively the tendency of eff to increase with Q is described by a number of pqcd approaches. The linked points labelled GRV94 are calculated from the NLO QCD GRV94 t. Although the GRV94 prediction follows the trend of the data it tends to lie above the data, particularly in the Q range 3? GeV. λ eff ZEUS Q (GeV ) df /dlnq ZEUS Figure 3: Left plot: d ln F =d ln(=) as a function of Q calculated by tting ZEUS and E665 F data in bins of Q. Right plot: df =d ln Q as a function of calculated by tting ZEUS F data in bins of. Within the framework of pqcd, at small the behaviour of F is largely determined by the behaviour of the sea quarks F S, whereas the df =d ln Q is determined by the convolution of the splitting function P qg and the gluon density, df =d ln Q / s P qg g. In order to study the scaling violations of F in more detail the logarithmic slope df =d ln Q is derived from the data by tting F = a + b ln Q in bins of ed. The statistical and systematic errors are determined as described above. 3

4 The results for df =d ln Q as a function of are shown in Fig. 3. For values of down to 3?4, the slopes are increasing as decreases. At lower values of and Q, the slope decreases. Comparing the rapid increase in F at small with the behaviour of the df =d ln Q, one is tempted to the naive conclusion that the underlying behaviour of the sea quark and gluon momentum distributions must be dierent at small, with the sea dominant and the gluon tending to zero. The failure of DL is in line with the earlier discussion. GRV94 does not follow the trend of the data when it turns over..5 NLO QCD t to F data In perturbative QCD the scaling violations of the F structure function are caused by gluon bremsstrahlung from quarks and quark pair creation from gluons. In the low domain accessible at HERA the latter process dominates the scaling violations. A QCD analysis of F structure functions measured at HERA therefore allows one to etract the gluon momentum density in the proton down to low values of. In this section we present NLO QCD ts to the ZEUS 994 nominal verte data and the SVX95 data of this paper. We are not attempting to include all available information on parton densities, but concentrating on what ZEUS data and their errors allow us to conclude about the gluon density at low. To constrain the ts at high proton and deuteron F structure function data from NMC and BCDMS are included. The kinematic range covered in this analysis is 3?5 < < :7 and < Q < 5 GeV. The QCD predictions for the F structure functions are obtained by solving the DGLAP evolution equations at NLO. These equations yield the quark and gluon momentum distributions at all values of Q provided they are given at some input scale Q. In this analysis we adopt the so-called ed avour number scheme where only three light avours (u; d; s) contribute to the quark density in the proton. The corresponding structure functions F c and F b are calculated from the photon-gluon fusion process including massive NLO corrections. The input valence distributions are taken from the parton distribution set MRS(R). As for MRS(R) we assume that the strange quark distribution is a given fraction K s = : of the sea at the scale Q = GeV. The gluon normalisation is ed by the momentum sum rule. The input value for the strong coupling constant is set to s (MZ ) = :8 and the charm mass is taken to be m c = :5 GeV. In the QCD evolutions and the evaluation of the structure functions the renormalisation scale and mass factorisation scale are both set equal to Q. In the denition of the only statistical error are included and the relative normalisation of the data sets is ed at unity. The t yields a good description of the data as shown in Fig.. We have also checked that the gluon obtained from this t to scaling violations is in agreement with the recent ZEUS measurements of charm production and F c in deep inelastic scattering at HERA. Two types of systematic uncertainties have been considered in this analysis. `HERA standard errors' contain statistical error on the data, eperimental systematic uncertainties, relative normalisation of the dierent data sets and uncertainties on s, the strange quark content of the proton and the charm mass. `Parametrisation errors' contain uncertainties from a denition including statistical and eperimental systematic errors, variations of the starting scale Q and an alternative, more eible parametrisation of the gluon density using Chebyche polynomials. The rst type of errors amounts to 6% g=g at = 5?5, Q = 7 GeV, the second type yields 9:5% in g=g Q = GeV min Q = GeV g Σ ZEUS 995 NLO(MS) Q = 4 GeV min Q = GeV Q = 7 GeV Q = 7 GeV Q = GeV g Σ Q = GeV NLO(MS) Figure 4: The quark singlet momentum distribution, (shaded), and the gluon momentum distribution, g() (hatched), as a function of at ed values of Q =, 7 and GeV. The error bands correspond to the quadratic sum of all error sources considered for each parton density. The three plots of Fig. 4 show the distribution for and g as a function of for Q at, 7 and GeV. It can be seen that even at the smallest Q is rising at small whereas the gluon distribution has become almost at. These results give support to the naive conclusion of Sec..4, that the sea distribution dominates at low and Q. At Q = GeV the gluon distribution is poorly determined and can, within errors, be negative at low. 4

5 3 Measurement of the Proton Structure Function F from 996 and 997 data overlap with the ed target eperiments; in the overlap region reasonable agreement has been found. The F scaling violation from this analysis and the ed target data are also shown in Figure 5. For Q > GeV the increase in statistics allows a measurement of in smaller bins with respect to our previous measurement. Above Q = 8 GeV, the statistical error grows typically to 5-5% and dominates the total error. Overall our data are in agreement with our published data. where MZ is the mass of the Z and, Fwk and Fint are the contributions to F due to photon echange, Z echange and Z interference respectively. In this analysis we determined the structure function using 996 and 997 data with an integrated luminosity of 6:8 pb? and 7:4 pb?, respectively. The selection and kinematic reconstruction of NC DIS events is based on an observed positron and the hadronic nal state. For further details see ref.. Q=.5 Q=.7 ZEUS Preliminary Q= 3.5 ZEUS ZEUS 994 BCDMS, E665, NMC, SLAC ZEUS Preliminary Q= 35 Q= 45 Q= 6.5 Q= 4.5 Q= 8.5 Q= 7 Q= Q= Q= Q= Q= 5 Q= 5 Q= 8 Q= 7 Q=. Q= 35-5 Q= 9 Q= 5 Q= d = Y+ F (?? ) ( + ) (5) L 3 r d dq Q4 Here the F structure function contains contributions from virtual photon and Z echange Q4 int + F F wk (6) F = + (Q Q + MZ ) (Q + MZ ) 3. Kinematics in Deep Inelastic Scattering Recalling the double di erential NC cross-section (3), but now including the corrections ( L and 3 ) for FL and F3 yields Q= 65 Q= ZEUS Preliminary Q= 8 Q= Q= 5 Q= Q= 3 Q= 5 Q= 8 Q= Q=. 3. Results Monte Carlo samples are used to estimate the acceptance, migration, radiative corrections, electroweak corrections and background contributions. is then determined based on a bin-by-bin unfolding. The resulting statistical error, including the Monte Carlo statistics, ranges from % below Q = GeV to 5-6% at Q 8 GeV. The systematic uncertainties have been estimated by varying the selection cuts, e ciencies and reconstruction techniques and redetermining the cross section including background estimates. Potential error source such as possible detector misalignment, event verte reconstruction, calorimeter energy scale, positron identi cation efciency, background contributions and hadronic energy ow have been considered. The total systematic uncertainty amounts to 3-4% ecept at low and high y, where it grows to %. At the present preliminary state of the analysis we estimate an overall normalisation uncertainty of 3%. The resulting is shown as a function of for ed Q in Figure 5. Results from our previous analysis, and from ed target eperiments are also shown for comparison. At low Q the rise in F for! is measured with improved precision. The coverage in has also been etended to higher, yielding etended Figure 5: Top and bottom left plots: versus for ed Q. Bottom right plot: as a function of Q for ed. References. ZEUS Results on the Measurement and Phenomenology of F at Low and Low Q, DESY 98- (August 998) submitted to The European Physical Journal.. Measurement of the Proton Structure Function F in e+ p Collisions at HERA, Submitted paper to the XXIX International Conference on High Energy Physics, Vancouver, July 3-9,