Semi-inclusive Hadron Production Research Articles

Semi-Inclusive Deep-Inelastic Scattering at Next-to-Next-to-Leading Order in QCD.

Semi-inclusive hadron production processes in deep-inelastic lepton-nucleon scattering are important probes of the quark flavor structure of the nucleon and of the fragmentation dynamics of quarks into hadrons. We compute the full next-to-next-to-leading order QCD corrections to the coefficient functions for semi-inclusive deep-inelastic scattering in analytical form. The numerical impact of these corrections for precision physics is illustrated by a detailed comparison with data on single inclusive hadron spectra from the CERN COMPASS experiment.

Tests of the parametrizations of fragmentation functions using data on inclusive pion and kaon production in unpolarized pp collisions from the STAR collaboration and at the NICA project

The goal of this study is to check which, if any, of the published versions of the pion and kaon fragmentation functions (FFs) is compatible with the STAR data on semi-inclusive pion and kaon production in proton–proton collisions, and on the basis of this analysis to make reliable predictions for the [Formula: see text] spectra of the pions and kaons in inclusive pion and kaon production at the future NICA proton–proton collider. The calculations are carried out in next-to-leading order (NLO) of perturbative quantum chromodynamics (pQCD), using the well-tested CTEQ6 parton distributions. We consider the following pion and kaon FFs — DSEHS-14 [D. de Florian, R. Sassot, M. Epele, R. J. Hernández-Pinto and M. Stratmann, Phys. Rev. D 91, 014035 (2015), 1410.6027], DSEHS-17 [D. de Florian, M. Epele, R. J. Hernandez-Pinto, R. Sassot and M. Stratmann, Phys. Rev. D 95, 094019 (2017), 1702.06353], LSS-15 [E. Leader, A. V. Sidorov and D. B. Stamenov, Phys. Rev. D 93, 074026 (2016), 1506.06381], HKNS-07 [M. Hirai, S. Kumano, T. H. Nagai and K. Sudoh, Phys. Rev. D 75, 094009 (2007), hep-ph/0702250] and AKK-08 [S. Albino, B. A. Kniehl and G. Kramer, Nucl. Phys. B 803, 42 (2008), 0803.2768]. Our analysis shows that within the experimental errors all tested sets of FFs provide a good fit to STAR data at the c.m. energy [Formula: see text], and the best ones are both LSS-15 and DSEHS-14 for pions and DSEHS-17 for kaons. From comparison of the LO and NLO results it is clear that the latter fit data much better, specially in the region of small [Formula: see text]. The NLO cross-sections are also less scale-[Formula: see text] dependent, where [Formula: see text], than the LO ones. In order to make predictions for NICA energies, we compare the NLO pQCD results with the existing experimental BES STAR data on semi-inclusive hadron production in the most peripheral Au+Au collisions where the nuclear effects can be neglected. The comparison for lower energy scales, like at NICA, shows that a purely pQCD approach is inadequate and suggests the necessity to take into account also higher-order effects of initial-state soft-gluon radiation. Nevertheless, these data on the [Formula: see text] spectra of [Formula: see text], [Formula: see text] and also the ratios [Formula: see text] and [Formula: see text] seem to favor LSS-15 and DSEHS-14 FFs for pions and DSEHS-17 for kaons, similarly as at the energy scale [Formula: see text][Formula: see text]GeV.

Quark branching in QCD matter to any order in opacity beyond the soft gluon emission limit

Cold nuclear matter effects in reactions with nuclei at a future electron-ion collider (EIC) lead to a modification of semi-inclusive hadron production, jet cross sections, and jet substructure when compared to the vacuum. At leading order in the strong coupling, a jet produced at an EIC is initiated as an energetic quark, and the process of this quark splitting into a quark-gluon system underlies experimental observables. The spectrum of gluons associated with the branching of this quark jet is heavily modified by multiple scattering in a medium, allowing jet cross sections and jet substructure to be used as a probe of the medium's properties. We present a formalism that allows us to compute the gluon spectrum of a quark jet to an arbitrary order in opacity, the average number of scatterings in the medium. This calculation goes beyond the simplifying limit in which the gluon radiation is soft and can be interpreted as energy loss of the quark, and it significantly extends previous work which computes the full gluon spectrum only to first order in opacity. The theoretical framework demonstrated here applies equally well to light parton and heavy quark branching, and is easily generalizable to all in-medium splitting processes.

Nonperturbative functions for SIDIS and Drell–Yan processes

We update the well-known BLNY fit to the low transverse momentum Drell–Yan lepton pair productions in hadronic collisions, by considering the constraints from the semi-inclusive hadron production in deep inelastic scattering (SIDIS) from HERMES and COMPASS experiments. We follow the Collins–Soper–Sterman (CSS) formalism with the [Formula: see text]-prescription. A nonperturbative form factor associated with the transverse momentum dependent quark distributions is found in the analysis with a new functional form different from that of BLNY. This releases the tension between the BLNY fit to the Drell–Yan data with the SIDIS data from HERMES/COMPASS in the CSS resummation formalism.

Tensor polarization dependent fragmentation functions ande+e−→VπXat high energies

We present the systematic results for three dimensional fragmentation functions of spin one hadrons defined via quark-quark correlator. There are totally 72 such fragmentation functions, among them 18 are twist-2, 36 are twist-3 and 18 are twist-4. We also present the relationships between the twist-3 parts and those defined via quark-gluon-quark correlator obtained from the QCD equation of motion. We show that two particle semi-inclusive hadron production process $e^+e^-\to V\pi X$ at high energies is one of the best places to study the three-dimensional tensor polarization dependent fragmentation functions. We present the general kinematic analysis of this process and show that the cross section should be expressed in terms of 81 independent structure functions. After that we present parton model results for the hadronic tensor, the structure functions, the azimuthal and spin asymmetries in terms of these gauge invariant fragmentation functions at the leading order pQCD up to twist-3.

Extraction of quark transversity distribution and Collins fragmentation functions with QCD evolution

We study the transverse momentum dependent (TMD) evolution of the Collins azimuthal asymmetries in $e^+e^-$ annihilations and semi-inclusive hadron production in deep inelastic scattering (SIDIS) processes. All the relevant coefficients are calculated up to the next-to-leading logarithmic (NLL) order accuracy. By applying the TMD evolution at the approximate NLL order in the Collins-Soper-Sterman (CSS) formalism, we extract transversity distributions for $u$ and $d$ quarks and Collins fragmentation functions from current experimental data by a global analysis of the Collins asymmetries in back-to-back di-hadron productions in $e^+e^-$ annihilations measured by BELLE and BABAR Collaborations and SIDIS data from HERMES, COMPASS, and JLab HALL A experiments. The impact of the evolution effects and the relevant theoretical uncertainties are discussed. We further discuss the TMD interpretation for our results, and illustrate the unpolarized quark distribution, transversity distribution, unpolarized quark fragmentation and Collins fragmentation functions depending on the transverse momentum and the hard momentum scale. We make detailed predictions for future experiments and discuss their impact.

Higher Twist Effects in e+e− Annihilation at High Energies

In the two papers published recently,1, 2 we apply collinear expansion to both inclusive ([Formula: see text]) and semi-inclusive ([Formula: see text]) hadron production in [Formula: see text] annihilation to derive a formalism suitable for a systematic study of leading as well as higher twist contributions to fragmentation functions at the tree level. We carry out the calculations for hadrons with spin-0, spin-1/2 as well as spin-1. This proceeding is mainly a summary of these two papers.

Next-to-leading order transverse momentum-weighted Sivers asymmetry in semi-inclusive deep inelastic scattering: The role of the three-gluon correlator

We study the Sivers asymmetry in semi-inclusive hadron production in deep inelastic scattering. We concentrate on the contribution from the photon-gluon fusion channel at ${\cal O}(\alpha_{em}^2 \alpha_s)$, where three-gluon correlation functions play a major role within the twist-3 collinear factorization formalism. We establish the correspondence between such a formalism with three gluon correlation functions and the usual transverse momentum dependent (TMD) factorization formalism at moderate hadron transverse momenta. We derive the coefficient functions used in the usual TMD evolution formalism related to the quark Sivers function expansion in terms of the three-gluon correlation functions. We further perform the next-to-leading order calculation for the transverse-momentum-weighted spin-dependent differential cross section, and identify the off-diagonal contribution from the three-gluon correlation functions to the QCD collinear evolution of the twist-3 Qiu-Sterman function.

Nuclear geometry effect and transport coefficient in semi-inclusive lepton-production of hadrons off nuclei

Hadron production in semi-inclusive deep-inelastic scattering of leptons from nuclei is an ideal tool to determine and constrain the transport coefficient in cold nuclear matter. The leading-order computations for hadron multiplicity ratios are performed by means of the SW quenching weights and the analytic parameterizations of quenching weights based on BDMPS formalism. The theoretical results are compared to the HERMES positively charged pions production data with the quarks hadronization occurring outside the nucleus. With considering the nuclear geometry effect on hadron production, our predictions are in good agreement with the experimental measurements. The extracted transport parameter from the global fit is shown to be qˆ=0.74±0.03 GeV2/fm for the SW quenching weight without the finite energy corrections. As for the analytic parameterization of BDMPS quenching weight without the quark energy E dependence, the computed transport coefficient is qˆ=0.20±0.02 GeV2/fm. It is found that the nuclear geometry effect has a significant impact on the transport coefficient in cold nuclear matter. It is necessary to consider the detailed nuclear geometry in studying the semi-inclusive hadron production in deep inelastic scattering on nuclear targets.

Nucleon tensor charge from Collins azimuthal asymmetry measurements

We investigate the nucleon tensor charge from current experiments by a combined analysis of the Collins asymmetries in two hadron production in $e^+e^-$ annihilations and semi-inclusive hadron production in deep inelastic scattering processes. The transverse momentum dependent evolution is taken into account, for the first time, in the global fit of the Collins fragmentation functions and the quark transversity distributions at the approximate next-to-leading logarithmic order. We obtain the nucleon tensor charge contribution from up and down quarks as $\delta u=+0.30^{+0.12}_{-0.08}$ and $\delta d=-0.20_{-0.11}^{+0.28}$ at 90\% confidence level for momentum fraction $0.0065 \le x_B \le 0.35$ and $Q^2=$ 10 GeV$^2$.

Leading and higher twist contributions in semi-inclusivee+e−annihilation at high energies

By applying the collinear expansion to the semi-inclusive hadron production process $e^++e^-\to h+\bar q(jet)+X$ at high energies, we construct a theoretical framework where the leading and higher twist contributions at the leading perturbative QCD can be calculated systematically. With this framework, we calculate the contributions up to twist-3 for spin-0, spin-1/2 and spin-1 hadrons respectively. We present the results for the hadronic tensors, the differential cross sections, the azimuthal asymmetries, and the polarizations of the hadrons.

Recent HERMES results from inclusive and semi-inclusive hadron production

Hermes collected a wealth of data using the 27.6 GeV polarized Hera lepton beam and various pure, polarized and unpolarized, gaseous targets. This unique data set opens the door to various measurements sensi- tive to the multi-dimensional structure of the nucleon. Among them are two-hadron production in semi-inclusive deep-inelastic scattering on a transversely polarized target, providing access to different transverse-momentum- dependent distribution and fragmentation functions in a way complementary to single-hadron production. Also transverse-target single-spin asymmetries in inclusive electroproduction of charged pions and kaons have been recently extracted, complementing data from proton-proton collisions, where large, so far unexplained, asym- metries have been observed. From inclusive measurements on various nuclear targets, the Λ polarization is extracted, also here complementing measurements in proton-proton collisions.

Next-to-Leading Order QCD Factorization for Semi-Inclusive Deep Inelastic Scattering at Twist 4

Within the framework of a high-twist approach, we calculate the next-to-leading order (NLO) perturbative QCD corrections to the transverse momentum broadening in semi-inclusive hadron production in deeply inelastic e+A collisions, as well as lepton pair production in p+A collisions. With explicit calculations of both real and virtual contributions, we verify, for the first time, the factorization theorem at twist 4 in NLO for the nuclear-enhanced transverse momentum weighted differential cross section and demonstrate the universality of the associated twist-4 quark-gluon correlation function. We also identify the QCD evolution equation for the twist-4 quark-gluon correlation function in a large nucleus, which can be solved to determine the scale dependence of the jet transport parameter in the study of jet quenching.

TRANSVERSE MOMENTUM-WEIGHTED SIVERS ASYMMETRY IN SEMI-INCLUSIVE DEEP INELASTIC SCATTERING AT NEXT-TO-LEADING ORDER

We summarize the results of a recent study of next-to-leading order perturbative QCD corrections to the transverse momentum-weighted Sivers asymmetry in semi-inclusive hadron production in lepton-proton deep inelastic scattering. The corresponding differential cross section is evaluated as a convolution of a twist-three quark-gluon correlation function, often referred to as Qiu-Sterman function, the usual unpolarized fragmentation function, and a hard coefficient function. By studying the collinear divergence structure, we identify the evolution kernel for the Qiu-Sterman function. The hard coefficient function, which is finite and free of any divergence, is evaluated at one-loop order.

Transverse momentum dependent evolution: Matching semi-inclusive deep inelastic scattering processes to Drell-Yan andW/Zboson production

We examine the QCD evolution for the transverse momentum dependent observables in hard processes of semi-inclusive hadron production in deep inelastic scattering and Drell-Yan lepton pair production in $pp$ collisions, including the spin-average cross sections and Sivers single transverse spin asymmetries. We show that the evolution equations derived by a direct integral of the Collins-Soper-Sterman evolution kernel from low to high Q can describe well the transverse momentum distribution of the unpolarized cross sections in the Q^2 range from 2 to 100 GeV^2. In addition, the matching is established between our evolution and the Collins-Soper-Sterman resummation with b*-prescription and Konychev-Nodalsky parameterization of the non-perturbative form factors, which are formulated to describe the Drell-Yan lepton pair and W/Z boson production in hadronic collisions. With these results, we present the predictions for the Sivers single transverse spin asymmetries in Drell-Yan lepton pair production and $W^\pm$ boson production in polarized pp and $\pi^- p$ collisions for several proposed experiments. We emphasize that these experiments will not only provide crucial test of the sign change of the Sivers asymmetry, but also provide important opportunities to study the QCD evolution effects.

Energy evolution for the Sivers asymmetries in hard processes

We investigate the energy evolution of the azimuthal spin asymmetries in semi-inclusive hadron production in deep inelastic scattering (SIDIS) and Drell-Yan lepton pair production in pp collisions. The scale dependence is evaluated by applying an approximate solution to the Collins-Soper-Sterman (CSS) evolution equation at one-loop order which is adequate for moderate Q^2 variations. This describes well the unpolarized cross sections for SIDIS and Drell-Yan process in the $Q^2$ range of 2.4-100GeV^2. A combined analysis of the Sivers asymmetries in SIDIS from HERMES and COMPASS experiments, and the predictions for the Drell-Yan process at RHIC at \sqrt{S}=200GeV are presented. We further extend to the Collins asymmetries and find, for the first time, a consistent description for HERMES/COMPASS and BELLE experiments with the evolution effects. We emphasize an important test of the evolution effects by studying di-hadron azimuthal asymmetry in e^+e^- annihilation at moderate energy range, such as at BEPC at \sqrt{S}=4.6GeV.

Transverse momentum-weighted Sivers asymmetry in semi-inclusive deep inelastic scattering at next-to-leading order

We study the next-to-leading order perturbative QCD corrections to the transverse momentum-weighted Sivers asymmetry in semi-inclusive hadron production in lepton-proton deep inelastic scattering. The corresponding differential cross section is evaluated as a convolution of a twist-three quark-gluon correlation function, often referred to as Qiu-Sterman function, the usual unpolarized fragmentation function, and a hard coefficient function. By studying the collinear divergence structure, we identify the evolution kernel for the Qiu-Sterman function. The hard coefficient function, which is finite and free of any divergence, is evaluated at one-loop order.

QCD resummation for semi-inclusive hadron production processes

We investigate the resummation of large logarithmic perturbative corrections to hadron production in electron-positron annihilation and semi-inclusive deep-inelastic scattering. We find modest, but significant, enhancements of hadron multiplicities in the kinematic regimes accessible in present high-precision experiments. Our results are therefore relevant for the determination of hadron fragmentation functions from data for these processes.

Fully double-logarithm-resummed cross sections

We calculate the complete double logarithmic contribution to cross sections for semi-inclusive hadron production in the modified minimal-subtraction ( MS ¯ ) scheme by applying dimensional regularization to the double logarithm approximation. The full double logarithmic contribution to the coefficient functions for inclusive hadron production in e + e − annihilation is obtained in this scheme for the first time. Our result agrees with all fixed order results in the literature, which extend to next-to-next-to-leading order.

Semi-inclusive deep inelastic scattering at small-x

We study the semi-inclusive hadron production in deep inelastic scattering at small-x. A transverse-momentum-dependent factorization is found consistent with the results calculated in the small-x approaches, such as the color-dipole framework and the color glass condensate, in the appropriate kinematic region at the lowest order. The transverse-momentum-dependent quark distribution can be studied in this process as a probe for the small-x saturation physics. Especially, the ratio of quark distributions as a function of transverse momentum at different x demonstrates strong dependence on the saturation scale. The Q2 dependence of the same ratio is also studied by applying the Collins–Soper–Sterman resummation method.