Precision QCD measurements at HERA

. A review of recent experimental results on perturbative QCD from the HERA experiments H1 and ZEUS is presented. All inclusive deep inelastic cross sections measured by the H1 and ZEUS collaborations in neutral and charged current unpolarised ep scattering are combined. They span six orders of magnitude in negative four-momentum-transfer squared, Q 2 , and in Bjorken x . This data set is used as the sole input to NLO and NNLO QCD analyses to determine new sets of parton distributions, HERAPDF2.0, with small experimental uncertainties and an estimate of model and parametrisation uncertainties. Also shown are new results on inclusive jet, dijet and trijet di ﬀ erential cross sections measured in neutral current deep inelastic scattering. The precision jet data is used to extract the strong coupling α s at NLO with small experimental errors.


Introduction
Deep-inelastic scattering (DIS) data provide high precision tests of perturbative quantum chromodynamics (QCD), and have led to a detailed and comprehensive understanding of proton structure.
The differential cross section for DIS ep scattering can be described in terms of proton structure functions F 2 , F L and xF 3 , which are related to parton distribution functions (PDFs). The structure functions depend on kinematic variables x and Q 2 only, whereas the cross section is additionally dependent on the inelasticity y related by y = Q 2 /sx. The reduced neutral current differential cross section for e + p scattering can be written as where Y ± = 1±(1−y) 2 and the fine structure constant is defined as α ≡ α(Q 2 = 0). As can be seen from the Eq. 1 the contribution of F L to the cross section is significant only at high y and the contribution of the xF 3 is significant only for high values of Q 2 . For the charged current (CC) processes the reduced differential cross section can be written in a form similar to Eq. 1 using the CC structure functions. At the electron-proton collider HERA (1992-2007) electrons and positrons of 27.6 GeV collided with protons of 920 GeV corresponding to an ep centre-of-mass energy of 319 GeV. The operation of HERA proceeded in two phases, HERA I (1992-2000) with an unpolarised and HERA II (2003-2007) with a longitudinally polarised lepton beam. At the end of the HERA data taking, special runs with reduced proton beam energies of 460 and 575 GeV were taken for dedicated F L measurement. The two ep interaction regions were instrumented with the multipurpose detectors of the H1 and ZEUS a e-mail: hayk.pirumov@desy.de experiments. The inclusive NC and CC ep DIS cross section data obtained by the H1 and ZEUS experiments are used to determine the proton structure functions and the partonic structure of the proton within the QCD framework.

NC e ± p cross section at high Bjorken x
Neutral current e ± p DIS double-differential cross sections as a function of x and Q 2 for Q 2 > 725 GeV 2 and up to x 1 [1]. An improved reconstruction method and increased amount of data allows to achieve a high precision of the measurement. The obtained cross sections show a good agreement with the predictions from the Standard Model (SM). The comparison of the measured e + p cross sections and SM expectations based on the HERAPDF 1.5 set of PDFs [2] is presented in Figure 1.  Figure 1. The double-differential cross section for NC e + p scattering at √ s = 318 GeV (dots) as a function of x and the double differential cross section integrated over x divided by the bin width and placed at the centre of the bin (triangles) for different values of Q 2 as shown, compared to the Standard Model expectations evaluated using HERAPDF1.5 PDFs (line). The error bars show the statistical and systematic uncertainties added in quadrature. For the bins with zero measured events, a 68% probability limit is given.

DIS cross section at different centre-of-mass energies and F L
The inclusive NC DIS cross sections for ep interactions are measured by the H1 experiment at two centre-of-mass energies of √ s = 225 and 251 GeV in the region 35 ≤ Q 2 ≥ 800 GeV 2 and up to the highest accessible inelasticity of y = 0.85 [3]. The data are used together with previous measurement at √ s = 318 GeV to simultaneously extract the F L and F 2 structure functions. The ratio R of the longitudinally to transversely polarised virtual photon cross section is consistent with being constant EPJ Web of Conferences 00024-p.2 over the kinematic range of the data and is determined to be 0.23 ± 0.04. The F L measurements are used to perform a gluon density extraction based on a NLO approximation which is found to have a reasonable agreement with the gluon determined from the scaling violations.
A new measurement of the reduced e + p cross sections up to large values of y is performed by the ZEUS expariment [4]. The analysed data is taken at different centre-of-mass energies, √ s = 318, 251 and 225 GeV, allowing for measurements at fixed x and Q 2 but different y values. This allows to decouple F 2 and F l , providing direct sensitivity to the gluon density. The measurement is performed in the kinematic region 0.13 ≤ y ≥ 0.75 and 5 ≤ Q 2 ≥ 110 GeV 2 . The ration R is also determined as a function of Q 2 together with an overall value of R = 0.105 +0.055 −0.037 . The   of kinematic reconstruction, the combination leads to a significantly reduced uncertainty. Figure 3 shows the averaged NC e + p reduced cross sections together with the input data from H1 and ZEUS for e + p scattering. The newly combined HERA I and II data are input to QCD analyses at NLO and NNLO, which determine preliminary versions of new sets of parton distributions, HERAPDF2.0(prel.) [8]. The QCD predictions for the structure functions are obtained by solving the DGLAP evolution equations. at NLO and NNLO in the MS scheme with the renormalisation and factorisation scales chosen to be Q 2 . The program QCDNUM [7] is used within the HERAFitter framework. The DGALP equations yield the PDFs at all values of Q 2 if they are provided as functions of Bjorken x at some input scale Q 2 0 . The light quark coefficient functions are calculated in QCDNUM, while the heavy quark coefficient functions are calculated in the general mass variable flavour scheme RTOPT [9,10]. Figure 4 shows summary plots of the HERAPDF2.0(prel.) at NLO and NNLO.

Multijet production at HERA and the strong coupling constant α s
Inclusive jet, dijet and trijet differential cross sections are measured in NC DIS for exchange boson virtualities 150 < Q 2 < 15000 GeV 2 using the H1 detector at HERA [11]. The data were taken in the years 2003 to 2007 and correspond to integrated luminosity of 351 pb −1 . Double differential jet cross sections are obtained using a regularised unfolding procedure to correct for detector effects. The measurement is done as a function of Q 2 and the transverse momentum of the jet P jet T , and as a function of Q 2 and the proton's longitudinal momentum fraction, ξ, carried by the parton participating in the hard interaction. In addition normalised double differential jet cross sections are measured as the ratio of the jet cross sections to the inclusive NC cross sections in the respective Q 2 bins of the jet measurements, which benefits from cancellation of systematic uncertainties correlated between the measurements. Figure 5 shows the measured cross sections as a function of Q 2 and P T .  The running of the α s , determined from the normalised cross section, is shown to be consistent with the expectation from the renormalisation group equation and with values of α s from other jet measurements. The comparison is shown in Figure 6.   QCD@Work 2014 00024-p.7