Inclusive Deep Inelastic Scattering Research Articles

Gluon-mediated inclusive Deep Inelastic Scattering from Regge to Bjorken kinematics

We revisit high energy factorization for gluon mediated inclusive Deep Inelastic Scattering (DIS) for which we propose a new semi-classical approach that accounts systematically for the longitudinal extent of the target in contrast with the shockwave limit. In this framework, based on a partial twist expansion, we derive a factorization formula that involves a new gauge invariant unintegrated gluon distribution which depends explicitly on the Feynman x variable. It is shown that both the Regge and Bjorken limits are recovered in this approach. We reproduce in particular the full one loop inclusive DIS cross-section in the leading twist approximation and the all-twist dipole factorization formula in the strict x = 0 limit. Although quantum evolution is not discussed explicitly in this work, we argue that the proper treatment of the x dependence of the gluon distribution encompasses the kinematic constraint that must be imposed on the phase-space of gluon fluctuations in the target to ensure stability of small-x evolution.

Extraction of the valence transversity distributions from SIDIS data

The transversity distribution for $u$ and $d$ quarks is usually extracted from data on spin asymmetries in Semi Inclusive Deep Inelastic Scattering (SIDIS): however, due to its chiral odd nature, it has to be coupled to another chiral odd function, typically the Collins or the di-hadron fragmentation function. A recent suggestion of considering SIDIS data involving ratios of spin asymmetries and avoiding a knowledge of the Collins function, is briefly discussed. New measurements, involving ratios of cross sections, are suggested. They would allow a direct extraction of the transversity ratio, $h_1^{d_V}/h_1^{u_V}$. Numerical estimates are given.

Combination and QCD Analysis of Charm and Beauty Production Cross-section Measurements in Deep Inelastic $ep$ Scattering at HERA

Measurements of open charm and beauty production cross sections in ep deep inelastic scattering (DIS) at HERA from the H1 and ZEUS collaborations are combined. Reduced cross sections are obtained in a restricted kinematic range. Perturbative QCD calculations are compared to the combined data. Next-to-leading order QCD analysis is performed using these data together with combined inclusive HERA DIS cross sections.

Impact of beauty and charm H1-ZEUS combined measurements on PDFs and determination of the strong coupling

In this QCD analysis, we investigate the impact of recent measurements of heavy-flavor charm and beauty cross sections data sets on the simultaneous determination of Parton Distribution Functions (PDFs) and the strong coupling, $\alpha_s(M^2_Z)$. We perform three different fits based on Variable-Flavour Number Scheme (VFNS) at the Leading Order (LO) and Next-to-Leading Order (NLO) and choose the full HERA run I and II combined data as a new measurement of inclusive Deep Inelastic Scattering (DIS) cross sections for our base data set. We show that including charm and beauty cross sections data reduces the uncertainty of gluon distribution and improves the fit quality up to 4.1\% from leading order to next-to-leading order and up to 1.7\% for only NLO without and with beauty and charm data contributions.

Accessing the nucleon transverse structure in inclusive deep inelastic scattering

We revisit the standard analysis of inclusive Deep Inelastic Scattering off nucleons taking into account the fact that on-shell quarks cannot be present in the final state, but they rather decay into hadrons – a process that can be described in terms of suitable “jet” correlators. As a consequence, a spin-flip term associated with the invariant mass of the produced hadrons is generated nonperturbatively and couples to the target's transversity distribution function. In inclusive cross sections, this provides an hitherto neglected and large contribution to the twist-3 part of the g2 structure function, that can explain the discrepancy between recent calculations and fits of this quantity. It also provides an extension of the Burkhardt–Cottingham sum rule, providing new information on the transversity function, as well as an extension of the Efremov–Teryaev–Leader sum rule, suggesting a novel way to measure the tensor charge of the proton.

Nuclear parton density functions from jet production in DIS at an EIC

We investigate the potential of inclusive-jet production in deep-inelastic scattering (DIS) at a future Electron-Ion Collider (EIC) to improve our current knowledge of nuclear parton density functions (PDFs). We demonstrate that the kinematic reach is extended similarly to inclusive DIS, but that the uncertainty of the nuclear PDFs, in particular of the gluon density at low Bjorken-x, is considerably reduced, by up to an order of magnitude compared to the present situation. Using an approximate next-to-next-to-leading order (aNNLO) calculation implemented in the program JetViP, we also make predictions for three different EIC designs and for four different light and heavy nuclei.

The Sivers asymmetry in Drell–Yan production at the J/Ψ peak at COMPASS

The abundant production of lepton pairs via J/Ψ creation at COMPASS, π±p↑→J/ΨX→ℓ+ℓ−X, allows a measurement of the transverse single spin asymmetry, ANJ/Ψ, generated by the Sivers effect. The crucial issue of the sign change of the Sivers function in Drell–Yan lepton pair production, with respect to Semi Inclusive Deep Inelastic Scattering processes, can be addressed in a different context. Assuming that the Sivers asymmetry is related to a universal and intrinsic property of the proton, predictions for the expected magnitude of ANJ/Ψ, which turns out to be large, are given. A comparison with the suggested measurement of this single spin asymmetry – an important quantity by itself – should give valuable information.

Diffractiveρandϕproduction at HERA using a holographic AdS/QCD light-front meson wave function

We use an anti-de Sitter/Quantum Chromodynamics (AdS/QCD) holographic light-front wavefunction for the $\rho$ and $\phi$ mesons, in conjunction with the Color Glass Condensate (CGC) dipole cross-section whose parameters are fitted to the most recent 2015 high precision HERA data on inclusive Deep Inelastic Scattering (DIS), in order to predict the cross-sections for diffractive $\rho$ and $\phi$ electroproduction. Our results suggest that the holographic meson light-front wavefunction is able to give a simultaneous description of the $\rho$ and $\phi$ production data provided we use a set of light quark masses with $m_{u,d}$ < $m_{s}$ ~ 0.14 GeV.

Extracting the kaon Collins function frome+e−hadron pair production data

The latest data released by the BaBar Collaboration on azimuthal correlations measured for pion-kaon and kaon-kaon pairs produced in $e^+e^-$ annihilations allow, for the first time, a direct extraction of the kaon Collins functions. These functions are then used to compute the kaon Collins asymmetries in Semi Inclusive Deep Inelastic Scattering processes, which result in good agreement with the measurements performed by the HERMES and COMPASS Collaborations.

Generalized threshold resummation in inclusive DIS and semi-inclusive electron-positron annihilation

We present analytic all-order results for the highest three threshold logarithms of the space-like and time-like off-diagonal splitting functions and the corresponding coefficient functions for inclusive deep-inelastic scattering (DIS) and semi-inclusive e^+ e^- annihilation. All these results, obtained through an order-by-order analysis of the structure of the corresponding unfactorized quantities in dimensional regularization, can be expressed in terms of the Bernoulli functions introduced by one of us and leading-logarithmic soft-gluon exponentials. The resulting numerical corrections are small for the splitting functions but large for the coefficient functions. In both cases more terms in the threshold expansion need to be determined in order to arrive at quantitatively reliable results.

Final-state interactions in deep-inelastic scattering from a tensor polarized deuteron target

Deep-inelastic scattering (DIS) from a tensor polarized deuteron is sensitive to possible non-nucleonic components of the deuteron wave function. To accurately estimate the size of the nucleonic contribution, final-state interactions (FSIs) need to be accounted for in calculations. We outline a model that, based on the diffractive nature of the effective hadron-nucleon interaction, uses the generalized eikonal approximation to model the FSIs in the resonance region, taking into account the proton-neutron component of the deuteron. The calculation uses a factorized model with a basis of three resonances with mass W < 2 GeV as the relevant set of effective hadron states entering the final-state interaction amplitude for inclusive DIS. We present results for the tensor asymmetry observable Azz for kinematics accessible in experiments at Jefferson Lab and Hermes. For inclusive DIS, sizeable effects are found when including FSIs for Bjorken x > 0.2, but the overall size of Azz remains small. For tagged spectator DIS, FSIs effects are largest at spectator momenta around 300 MeV and for forward spectator angles.

The Drell-Yan measurement at COMPASS-II

The Drell-Yan process can be used to access Transverse Momentum Dependent Parton Distribution Functions (TMD PDFs), such as the Sivers and the Boer-Mulders functions, as well as the transversity function providing complementary information to what is known from Semi Inclusive Deep Inelastic Scattering (SIDIS) data. The COMPASS experiment offers the possibility to study single polarized Drell-Yan processes (π− + p↑ → μμ + X), making use of its large acceptance spectrometer and its unique transversely polarised proton target. Moreover a fundamental test of the factorization theorem in the non-perturbative QCD can be performed, by verifying the sign change of the T-odd Boer-Mulders and Sivers functions depending if they are accessed via SIDIS or Drell-Yan process. As the start of the Drell-Yan program at COMPASS is approaching, foreseen in late 2014, the spectrometer has been updated to fulfill the needs of this measurement

Precision Tests of QCD at HERA

The study of inclusive deep inelastic scattering (DIS) and jet production processes in electron-proton scattering at HERA allows precision tests of QCD and to constrain the parton density functions (PDF) of the proton which are of particular importance for the measurements at the LHC. A selection of new measurements of structure functions and hadronic final state observables by the H1 and ZEUS collaborations is presented. Recent results on PDF fits (HERAPDF) using the inclusive DIS and jet data from both experiments are shown.

Inclusive Diffraction at HERA

Results are reported on measurements of diffractive cross sections in deep-inelastic scattering (DIS) and photoproduction at HERA. The cross sections are compared for processes with a leading proton in the final state and with a large gap in the rapidity distribution of the final state hadrons. The cross section dependences on the proton fractional longitudinal momentum loss x P and the squared four-momentum transfer at the proton vertex t are interpreted in terms of an effective pomeron trajectory and a sub-leading exchange. The hypothesis of proton vertex factorisation is tested. The longitudinal structure function is extracted from the diffractive cross sections measured at different proton beam energies. The cross sections of diffractive dijet production are compared with QCD predictions at next-to-leading order (NLO) based on parton distribution functions obtained from diffractive inclusive DIS data. Combined NLO QCD fits to the inclusive and dijet DIS data are performed to determine diffractive quark singlet and gluon densities with a better precision. The ratio of the diffractive dijet cross sections in photoproduction and DIS is compared with NLO QCD predictions to test QCD collinear factorisation.

Measurement of the diffractive longitudinal structure function $F_{L}^{D}$ at HERA

First measurements are presented of the diffractive cross section $\sigma_{ep \rightarrow eXY}$ at centre-of-mass energies $\sqrt{s}$ of 225 and 252 GeV, together with a precise new measurement at $\sqrt{s}$ of 319 GeV, using data taken with the H1 detector in the years 2006 and 2007. Together with previous H1 data at $\sqrt{s}$ of 301 GeV, the measurements are used to extract the diffractive longitudinal structure function F_L^D in the range of photon virtualities 4.0 <= Q^2 <= 44.0 GeV^2 and fractional proton longitudinal momentum loss 5 10^{-4} <= x_{IP} <= 3 10^{-3}. The measured F_L^D is compared with leading twist predictions based on diffractive parton densities extracted in NLO QCD fits to previous measurements of diffractive Deep-Inelastic Scattering and with a model which additionally includes a higher twist contribution derived from a colour dipole approach. The ratio of the diffractive cross section induced by longitudinally polarised photons to that for transversely polarised photons is extracted and compared with the analogous quantity for inclusive Deep-Inelastic Scattering.

Spin physics in polarised Drell-Yan processes at COMPASS

The Drell-Yan process can be used to access Transverse Momentum Dependent Parton Distribution Functions (TMD PDFs), such as Boer-Mulders function, Sivers function and Transversity functions, providing complementary informations to what is known from Semi Inclusive Deep Inelastic Scattering (SIDIS) data. The COMPASS experiment offers the possibility to extract TMD PDFs from Drell-Yan data, using its spectrometer and its unique transversely polarisable target.

Extraction of g1p, g1d and δg/g from HERMES data

HERMES collected deep-inelastic scattering (DIS) events of 27.6 GeV longitudinally polarised positrons off longitudinally polarised hydrogen and deuterium gas targets internal the HERA storage ring. Double-spin asymmetries A∥p,d of cross sections in inclusive DIS allow the precise extraction of spin structure functions of the proton g1p(x,Q2) and the deuteron g1d(x,Q2) in the kinematic range 0.0041 ≤ x ≤ 0.9 and 0.18 GeV ≤ Q2 ≤ 20GeV2. Furthermore, double-spin asymmetries of inclusive production of charged hadrons as a function of transverse momentum pt have been measured. For pt > 1 GeV the asymmetries are sensitive to the spin dependent gluon distribution function δg. Using a Leading Order Monte Carlo model to obtain information on the background asymmetry and background process kinematics, δg/g has been extracted.

Instanton-induced azimuthal spin asymmetry in deep inelastic scattering

It is by now well understood that spin asymmetry in deep inelastic scattering (DIS) can appear if two things are both present: (i) a chirality flip of the struck quark; (ii) a nonzero T-odd phase due to its final state interaction. So far (i) was attributed to a new structure/wave function of the nucleon and (ii) to some gluon exchanges. We propose a new mechanism utilizing strong vacuum fluctuations of the gluon field described semiclasically by instantons, and show that both (i) and (ii) are present. The magnitude of the effect is estimated using known parameters of the instanton ensemble in the QCD vacuum and known structure and fragmentation functions, without any new free parameters. The result agrees in sign and (roughly) in magnitude with the available data on single particle inclusive DIS. Furthermore, our predictions uniquely relate effects for longitudinally and transversely polarized targets.

Parametrization of nuclear parton distributions

Optimum nuclear parton distributions are obtained by analysing available experimental data on electron and muon deep inelastic scattering (DIS). The distributions are given at Q 2=1 GeV2 with a number of parameters, which are determined by a X 2 analysis of the data. Valencequark distributions are relatively well determined at medium x, but they are slightly dependent on the assumed parametrization form particularly at small x. Although antiquark distributions are shadowed at small x, their behavior is not obvious at medium x from the F 2 data. The gluon distributions could not be restricted well by the inclusive DIS data; however, the analysis tends to support the gluon shadowing at small x. We provide analytical expressions and computer subroutines for calculating the nuclear parton distributions, so that other researchers could use them for applications to other high-energy nuclear reactions.

Highlights from HERMES

A selection of recent results from the HERMES experiment is presented. The flavor decomposition of the nucleon spin is one of the highlights. Polarized semi-inclusive deep inelastic scattering (DIS) data are used to extract the polarization of the up, down and sea quarks separately and as a function of the scaling variable x. The polarization of the up (down) quarks is positive (negative) and its absolute value increases with x. The polarization of the sea quarks is compatible with zero. The first and second moments of the flavor spin distributions have been extracted and compared to predictions and to results from other experiments. A second semi-inclusive result from HERMES concerns the (unpolarized) flavor asymmetry of the light quark sea. The significant non-zero result shows an enhancement of down antiquarks compared to up antiquarks. This enhancement has not been naively expected in QCD but is consistent with the recent observation that the Gottfried sum rule is broken. HERMES discovered a new nuclear effect in DIS by comparing inclusive DIS cross sections of nitrogen, helium and deuterium. It was found that the ratio of the longitudinal to transverse photoabsorption cross section is very different for the different nuclei in certain kinematic areas. A natural explanation of this effect points to quark-gluon correlations in nuclear matter.