Deep Inelastic Scattering Cross Sections Research Articles

Measurement of partonic nuclear effects in deep-inelastic neutrino scattering using MINERvA

The MINERvA collaboration reports a novel study of neutrino-nucleus charged-current deep inelastic scattering (DIS) using the same neutrino beam incident on targets of polystyrene, graphite, iron, and lead. Results are presented as ratios of C, Fe, and Pb to CH. The ratios of total DIS cross sections as a function of neutrino energy and flux-integrated differential cross sections as a function of the Bjorken scaling variable x are presented in the neutrino-energy range of 5 - 50 GeV. Good agreement is found between the data and predicted ratios, based on charged-lepton nucleus scattering, at medium x and low neutrino energies. However, the data rate appears depleted in the vicinity of the nuclear shadowing region, x < 0.1. This apparent deficit, reflected in the DIS cross-section ratio at high neutrino energy , is consistent with previous MINERvA observations and with the predicted onset of nuclear shadowing with the the axial-vector current in neutrino scattering.

Combined Measurement of Inclusive ep Scattering Cross Sections at HERA

A combination is presented of all inclusive deep inelastic c ross sections previously published by the H1 and ZEUS collaborations at HERA for neutral and charged current e ± p scattering with zero beam polarisation. The data were taken at proton beam energies of 920, 820, 575 and 460 GeV and an electron beam energy of 27.5 GeV. The data correspond to an integrated luminosity of about 1 fb −1 and span six orders of magnitude in negative four-momentum-transfer squared, Q 2 , and Bjorken x. The correlations of the systematic uncertainties were eva luated and taken into account for the combination. An extraction of xF γZ 3 and results on electroweak unification and scaling violations are also presented. The h igh-precision deep inelastic scattering cross sections presented here form a coherent set and they ar e a major legacy of HERA.

Final Combined Deep Inelastic Scattering Cross Sections at HERA

The combination is presented of all inclusive deep inelastic scattering cross sections previously published by the H1 and ZEUS collaborations at HERA for neutral and charged current $ep$ scattering for zero beam polarisation. The data were taken at proton beam energies of 920, 820, 575 and 460 GeV and an electron beam energy of 27.5 GeV. The data correspond to an integrated luminosity of about 1 fb$^{-1}$ and span six orders of magnitude in negative four-momentum-transfer squared, $Q^2$, and Bjorken $x$. The correlations of the systematic uncertainties were evaluated and taken into account for the combination. The combined cross sections were input to QCD analyses at leading order, next-to-leading order and at next-to-next-to-leading order, providing a new set of parton distribution functions, called HERAPDF2.0. Additionally, the inclusion of jet-production cross sections made a simultaneous and precise determination of parton distributions and the strong coupling constant possible. Brief highlights of the results are presented.

SHiP: a new multipurpose beam-dump experiment at the SPS

SHiP is an experiment to look for very weakly interacting particles at a new to be constructed beam-dump facility at the CERN SPS. The SHiP Technical Proposal has been submitted to the CERN SPS Committee in April 2015. The 400 GeV/c proton beam extracted from the SPS will be dumped on a heavy target with the aim of integrat- ing 2× 10 20 proton on target in five years. A detector located downstream of the targe t, based on a long vacuum tank followed by a spectrometer and particle identifi cation de- tectors, will allow probing a variety of models with light long-lived exotic partic les and masses below a few GeV/c 2 . The main focus will be the physics of the so-called Hid- den Portals, i.e. search for Dark Photons, Light scalars and pseudo-scalars, and Heavy Neutral Leptons (HNL). The sensitivity to HNL will allow for the first time to pr obe, in the mass range between the kaon and the charm meson mass, a coupling range for which Baryogenesis and active neutrino masses could also be explained. Integrated in SHiP is an Emulsion Cloud Chamber, already used in the OPERA experiment, which will allow to study active neutrino cross-sections and angular distributions. In par ticular SHiP can distinguish betweeno? and ¯ o?, and their deep inelastic scattering cross sections will be measured with statistics three orders of magnitude larger than currently available.

Deep inelastic scattering cross sections from the gauge/string duality

Differential cross sections of deep inelastic scattering of charged leptons from hadrons are investigated by using the gauge/string duality. We consider vector mesons derived from different holographic dual models obtaining a general expression. We focus on the strongly coupled regime of dual gauge theories for different values of the Bjorken parameter. We find new predictions which are particularly interesting for differential scattering cross sections of polarized leptons scattered off polarized vector mesons. We also carry out a detailed comparison of the moments of the structure functions with lattice QCD results.

Rapidity divergences and deep inelastic scattering in the endpoint region

The deep inelastic scattering cross section in the endpoint region, $x \sim 1$, has been subjected to extensive analysis. We revisit this process, and show that in the endpoint individual factors in the factorized hadronic tensor have rapidity divergences. We regulate these divergences using a recently introduced rapidity regulator, and find that each factor requires a different scale to minimize large rapidity logarithms. Interestingly, in this case running in rapidity is non-perturbative. In addition, we give an operator definition of the parton distribution function in the endpoint region, and remark on the issues that should be considered in constructing this function.

A study on the interplay between perturbative QCD and CSS/TMD formalism in SIDIS processes

We study the Semi-Inclusive Deep Inelastic Scattering (SIDIS) cross section as a function of the transverse momentum, q T . In order to describe it over a wide region of q T , soft gluon resummation has to be performed. Here we will use the original Collins-Soper-Sterman (CSS) formalism; however, the same procedure would hold within the improved Transverse Momentum Dependent (TMD) framework. We study the matching between the region where fixed order perturbative QCD can successfully be applied and the region where soft gluon resummation is necessary. We find that the commonly used prescription of matching through the so-called Y-factor cannot be applied in the SIDIS kinematical configurations we examine. In particular, the non-perturbative component of the resummed cross section turns out to play a crucial role and should not be overlooked even at relatively high energies. Moreover, the perturbative expansion of the resummed cross section in the matching region is not as reliable as it is usually believed and its treatment requires special attention.

Dihadron Fragmentation Functions and Transversity

We present preliminary results for an updated extraction of the transversity parton distribution based on the analysis of pion-pair production in deep-inelastic scattering off transversely polarized targets in collinear factorization. Data for proton and deuteron targets by HERMES and COMPASS allow for a flavor separation of the valence components of transversity, while di-hadron fragmentation functions are taken from the semi-inclusive production of two pion pairs in back-to-back jets in $e^+ e^-$ annihilation. The latter data from Belle have been reanalyzed using the replica method and a more realistic estimate of the uncertainties on the chiral-odd interference fragmentation function has been obtained. After encoding this piece of information into the deep-inelastic scattering cross section, the transversity has been re-extracted by using the most recent and more precise COMPASS data for proton target. This picture represents the current most realistic estimate of the uncertainties on our knowledge of transversity. The preliminary results indicate that the valence up component seems smaller and with a narrower error band than in previous extraction.

Overview of recent results from the HERMES experiment

HERMES has taken a wealth of deep-inelastic scattering (DIS) data using the 27.6 GeV polarized lepton beam at HERA and various pure gas targets, both unpolarized and polarized, which opened the door to several unique results. Among them are the first evidences for the naive-T-odd Sivers and Collins effects but also the recent first measurements of azimuthal modulations in the unpolarized semi-inclusive DIS cross section for charged kaons and pions and of beam-helicity asymmetries in exclusive leptoproduction of real photons using recoil-proton detection. An overview of HERMES results is given with emphasis on the exploration of the three-dimensional structure of the nucleon.

Combination and QCD analysis of charm production cross section measurements in deep-inelastic ep scattering at HERA

Measurements of open charm production cross sections in deep-inelastic ep scattering at HERA from the H1 and ZEUS Collaborations are combined. Reduced cross sections \(\sigma_{\rm red}^{c\bar{c}}\) for charm production are obtained in the kinematic range of photon virtuality 2.5≤Q2≤2000 GeV2 and Bjorken scaling variable 3⋅10−5≤x≤5⋅10−2. The combination method accounts for the correlations of the systematic uncertainties among the different data sets. The combined charm data together with the combined inclusive deep-inelastic scattering cross sections from HERA are used as input for a detailed NLO QCD analysis to study the influence of different heavy flavour schemes on the parton distribution functions. The optimal values of the charm mass as a parameter in these different schemes are obtained. The implications on the NLO predictions for W± and Z production cross sections at the LHC are investigated. Using the fixed flavour number scheme, the running mass of the charm quark is determined.

Proton Structure Measurements from HERA to LHC

The inclusive ep neutral and charged current deep-inelastic scattering cross sections are measured in the H1 and ZEUS experiments at HERA, with an electron beam energy of 27.6 GeV and a nominal proton beam energy of 920 GeV and reduced proton beam energies of 575 and 460 GeV. The data span six orders of magnitude in negative four-momentum-transfer squared, Q2, and in Bjorken x. These data are used to determine the proton structure functions and to perform analyses in the QCD framework. The parton distribution functions of the proton, determined in QCD fits, are used for cross section calculations of various processes and for comparisons to data at the LHC.

Measurement of photon production in the very forward direction in deep-inelastic scattering at HERA

The production of photons at very small angles with respect to the proton beam direction is studied in deep-inelastic positron–proton scattering at HERA. The data are taken with the H1 detector in the years 2006 and 2007 and correspond to an integrated luminosity of 126 pb−1. The analysis covers the range of negative four momentum transfer squared at the positron vertex 6<Q 2<100 GeV2 and inelasticity 0.05<y<0.6. Cross sections are measured for the most energetic photon with pseudorapidity η>7.9 as a function of its transverse momentum $p_{T}^{\mathrm{lead}}$ and longitudinal momentum fraction of the incoming proton $x_{L}^{\mathrm{lead}}$ . In addition, the cross sections are studied as a function of the sum of the longitudinal momentum fraction $x_{L}^{\mathrm{sum}}$ of all photons in the pseudorapidity range η>7.9. The cross sections are normalised to the inclusive deep-inelastic scattering cross section and compared to the predictions of models of deep-inelastic scattering and models of the hadronic interactions of high energy cosmic rays.

Partonic transverse motion in unpolarized semi-inclusive deep inelastic scattering processes

We analyze the role of partonic transverse motion in unpolarized semi-inclusive deep inelastic scattering processes. Imposing appropriate kinematical conditions, we find some constraints which fix an upper limit to the range of allowed ${k}_{\ensuremath{\perp}}$ values. We show that, applying these additional requirements on the partonic kinematics, we obtain different results with respect to the usual phenomenological approach based on the Gaussian smearing with analytical integration over an unlimited range of ${k}_{\ensuremath{\perp}}$ values. These variations are particularly interesting for some observables, like the $⟨\mathrm{cos}{\ensuremath{\phi}}_{h}⟩$ azimuthal modulation of the unpolarized semi-inclusive deep inelastic scattering cross section or the average transverse momentum of the final, detected hadron.

Flavor-dependent azimuthal modulations in unpolarized SIDIS cross section at HERMES

The cos ϕh and cos 2ϕh azimuthal modulations of the unpolarized hadron Semi-Inclusive Deep Inelastic Scattering cross section are sensitive to the quark intrinsic transverse momentum and transverse spin. These modulations have been measured at HERMES in a fully differential way by means of a 4-dimensional unfolding procedure to correct for instrumental effects. Results have been extracted for hydrogen and deuterium targets and separately for positively and negatively charged pions and kaons, to access flavor-dependent information about the nucleon internal transverse degrees of freedom.

Short range correlations and the EMC effect

The magnitude of the EMC effect measured in electron deep inelastic scattering (DIS) is linearly related to the Short Range Correlation (SRC) scaling factor obtained from electron inclusive scattering. We speculate that the observed correlation is due to the fact that both the EMC effect and SRC are dominated by high momentum nucleons in the nucleus. The observed phenomenological relationship can be used to extract the ratio of the deuteron to the free pn-pair cross sections, the DIS cross section for a free neutron, F 2 n / F 2 p , the ratio of the free neutron to free proton structure functions, and the u/d ratio in a free proton.

Measurement of high-Q 2 charged current deep inelastic scattering cross sections with a longitudinally polarised positron beam at HERA

Measurements of the cross sections for charged current deep inelastic scattering in e+p collisions with a longitudinally polarised positron beam are presented. The measurements are based on a data sample with an integrated luminosity of 132 pb^-1 collected with the ZEUS detector at HERA at a centre-of-mass energy of 318 GeV. The total cross section is presented at positive and negative values of the longitudinal polarisation of the positron beams. The single-differential cross-sections ds/dQ^2, ds/dx and ds/dy are presented for Q^2 > 200 GeV^2. The reduced cross-section is presented in the kinematic range 200 < Q^2 < 60,000 GeV^2 and 0.006 < x < 0.562. The measurements agree well with the predictions of the Standard Model. The results are used to determine a lower limit on the mass of a hypothetical right-handed W boson.

Jet production in ep collisions at high Q 2 and determination of α s

The production of jets is studied in deep-inelastic e ± p scattering at large negative four momentum transfer squared 150<Q 2<15000 GeV2 using HERA data taken in 1999–2007, corresponding to an integrated luminosity of 395 pb−1. Inclusive jet, 2-jet and 3-jet cross sections, normalised to the neutral current deep-inelastic scattering cross sections, are measured as functions of Q 2, jet transverse momentum and proton momentum fraction. The measurements are well described by perturbative QCD calculations at next-to-leading order corrected for hadronisation effects. The strong coupling as determined from these measurements is $\alpha_{s}(M_{Z})=0.1168\pm0.0007\,\mathrm{(exp.)}{}^{+0.0046}_{-0.0030}\,\mathrm{(th.)}\pm 0.0016$ (PDF).

Measurement of the Structure of the Proton at HERA

A combination of the reduced e ± p cross section, previously measured by H1 and ZEUS, has been performed and leads to well constrained QCD fits of the parton densities in the proton. These results, as well as the high-Q 2 neutral current deep inelastic scattering cross sections are presented. First direct measurements of the longitudinal structure function F L are also reported.

Measurement of charged current deep inelastic scattering cross sections with a longitudinally polarised electron beam at HERA

Measurements of the cross sections for charged current deep inelastic scattering in e-p collisions with longitudinally polarised electron beams are presented. The measurements are based on a data sample with an integrated luminosity of 175 pb-1 collected with the ZEUS detector at HERA at a centre-of-mass energy of 318 GeV. The total cross section is given for positively and negatively polarised electron beams. The differential cross-sections dsigma/dQ2, dsigma/dx and dsigma/dy are presented for Q2>200 GeV2. The double-differential cross-section d2sigma/dxdQ2 is presented in the kinematic range 280<Q2<30000 GeV2 and 0.015<x<0.65. The measured cross sections are compared with the predictions of the Standard Model.

DIS on a large nucleus in AdS/CFT

We calculate the total cross section for deep inelastic scattering (DIS) on a nucleus at high energy for a strongly coupled = 4 super Yang-Mills theory using AdS/CFT correspondence. In analogy to the small coupling case we argue that at high energy the total DIS cross section is related to the expectation value of the Wilson loop formed by the quark-antiquark dipole. We model the nucleus by a metric of a shock wave in AdS5. We then calculate the expectation value of the Wilson loop by finding the extrema of the Nambu-Goto action for an open string attached to the quark and antiquark lines of the loop in the background of an AdS5 shock wave. We find three extrema of the Nambu-Goto action: the string coordinates at the extrema are complex-valued and are given by three different branches of the solution of a cubic equation. The physically meaningful solutions for the total DIS cross section are given either by the only branch with a purely imaginary string coordinate in the bulk or by a superposition of the two other branches. For both solutions we obtain the forward scattering amplitude N for the quark dipole-nucleus scattering. We study the onset of unitarity with increasing center-of-mass energy and transverse size of the dipole: we observe that for both solutions the saturation scale, while energy-dependent at lower energies, at very high energy becomes independent of energy/Bjorken-x. The saturation scale depends very strongly on the atomic number of the nucleus as Qs ~ A1/3.