Semi-inclusive DIS Research Articles

Left–right asymmetry for pion and kaon production in the semi-inclusive deep-inelastic scattering process

We analyze the left-right asymmetry in the semi-inclusive deep inelastic scattering (SIDIS) process without introducing any weighting functions. With the current theoretical understanding, we find that the Sivers effect plays a key role in our analysis. We use the latest parametrization of the Sivers and fragmentation functions to reanalyze the $\pi^\pm$ production process and find that the results are sensitive to the parametrization. We also extend our calculation on the $K^{\pm}$ production, which can help us know more about the Sivers distribution of the sea quarks and the unfavored fragmentation processes. HERMES kinematics with a proton target, COMPASS kinematics with a proton, deuteron, and neutron target (the information on the neutron target can be effectively extracted from the $^3$He target), and JLab kinematics (both 6 GeV and 12 GeV) with a proton and neutron target are considered in our paper.

Experimental Studies of Hadronization and Parton Propagation in the Space-Time Domain

Over the past decade, new data have become available from DESY, Jefferson Lab, Fermilab, and RHIC that connect to parton propagation and hadron formation. Semi-inclusive DIS on nuclei, the Drell-Yan reaction, and heavy-ion collisions all bring different kinds of information on parton propagation within a medium, while the most direct information on hadron formation comes from the DIS data. Over the next decade one can hope to begin to understand these data within a unified picture. We briefly survey the most relevant data and the common elements of the physics picture, then highlight the new Jefferson Lab data from CLAS, and close with prospects for the future.

Update on transversity and Collins functions from SIDIS and [formula omitted] data

We present an update of a previous global analysis of the experimental data on azimuthal asymmetries in semi-inclusive deep inelastic scattering (SIDIS), from the HERMES and COMPASS Collaborations, and in e+ e- -> h1 h2 X processes, from the Belle Collaboration. Compared to the first extraction, a more precise determination of the Collins fragmentation function and the transversity distribution function for u and d quarks is obtained.

Partonic state and single transverse spin asymmetries in semi-inclusive DIS

Using partonic states we verify the transverse momentum dependent factorization for single transverse spin asymmetries in semi-inclusive DIS at leading but nontrivial order of αs. The factorization has been previously derived in a formal way by using diagram expansion at hadron level. We find with our partonic results that two relevant structure functions satisfy the factorization. Our results also satisfy the collinear factorization but with the perturbative coefficient different than that derived formally.

Transverse momentum broadening in semi-inclusive DIS on nuclei

Using a three stage model of hadron formation we calculate the change of the transverse momentum distribution of hadrons produced in semi-inclusive deep inelastic scattering (SIDIS) on nuclei. In the first stage after its interaction with the virtual photon, the struck quark propagates quasi free in the nuclear environment undergoing multiple collisions with nucleons. During this stage it can acquire transverse momentum. In the second stage a prehadron is formed which has a very small elastic cross section with the nucleons. In the third stage the prehadron turns into a hadron. For HERMES energies, prehadron elastic scatterings contribute little to p ⊥ -broadening. The acquired extra Δ p ⊥ 2 of hadrons can therefore be deduced entirely from the first stage of quasi free quark propagation with quark–nucleon collisions. We use this model to describe π-production on Ne, Kr, Xe and compare with the most recent HERMES data.

Sivers effect for pion and kaon production in semi-inclusive deep inelastic scattering

We study the Sivers effect in the transverse single spin asymmetries (SSA) for pion and kaon production in semi-inclusive deep inelastic scattering (SIDIS) processes. We perform a fit of \(\ensuremath A^{\sin(\phi_h-\phi_S)}_{UT}\) which, by including recent high-statistics experimental data for pion and kaon production from HERMES and COMPASS Collaborations, allows a new determination of the Sivers distribution functions for quarks and antiquarks with u , d and s flavours. Estimates for forthcoming SIDIS experiments at COMPASS and JLab are given.

The neutron transversity from semi-inclusive DIS off 3He

A calculation of nuclear effects in the extraction of neutron single spin asymmetries in semi-inclusive deep inelastic scattering off 3He is described. In the kinematics of forth-coming experiments at JLab, it is found that the nuclear effects arising within an Impulse Approximation approach are under control.

Hadron Production in Nuclear Deep Inelastic Scattering at HERMES

The influence of the cold nuclear medium on hadron production in semi-inclusive deep-inelastic scattering (SIDIS) was studied extensively by the Hermes experiment using a 27.6 GeV positron or electron beam. A series of measurements on deuterium, helium, neon, krypton and xenon targets has been performed in order to study quark propagation and hadronization. Hadron multiplicities on nucleus relative to those on deuteron, together with the first direct measurement of the hadron transverse momentum broadening in SIDIS, are presented.

Systematic phenomenological study of thecos2ϕasymmetry in unpolarized semi-inclusive DIS

We study the $\mathrm{cos}2\ensuremath{\phi}$ azimuthal asymmetry in unpolarized semi-inclusive DIS, taking into account both the perturbative contribution (gluon emission and splitting) and the nonperturbative effects arising from intrinsic transverse motion and transverse spin of quarks. In particular we explore the possibility to extract from $⟨\mathrm{cos}2\ensuremath{\phi}⟩$ some information about the Boer-Mulders function ${h}_{1}^{\ensuremath{\perp}}$, which represents a transverse-polarization asymmetry of quarks inside an unpolarized hadron. Predictions are presented for the HERMES, COMPASS and JLab kinematics, where $⟨\mathrm{cos}2\ensuremath{\phi}⟩$ is dominated by the kinematical higher-twist contribution, and turns to be of order of a few percent. We show that under reasonable assumptions a larger asymmetry in ${\ensuremath{\pi}}^{\ensuremath{-}}$ production, compared to ${\ensuremath{\pi}}^{+}$ production, would represent a signature of the Boer-Mulders effect.

Measurement of transversity signals in two hadron production at COMPASS

The quark structure of the nucleon at the twist two level can be completely described with three quark distribution functions: the spin averaged distribution function q(x), the helicity distribution Δq(x) and the transverse spin distribution ΔTq(x). This last function, referred to as transversity, is chiral-odd and can only be measured in combination with another chiral-odd function. COMPASS is a fixed target experiment at the CERN SPS M2 beamline. Its target (6LiD) can be both longitudinally and transversely polarized with respect to the polarized 160 GeV/c µ+-beam. In transverse configuration ΔTq(x) can be measured in semi-inclusive deep-inelastic scattering (SIDIS), requiring the detection of hadronic products. A rather new probe of the transverse spin distribution function ΔTq(x) is the measurement of two hadron production, introducing the chiral odd interference fragmentation function H1∢(z, Mh2). Results are presented for the years 2003–2004 including particle identification by using the information of the RICH detector. The analysis was performed using all positive/negative charged pairs and z-ordered pairs.

Left–right asymmetry in semi-inclusive deep inelastic scattering process

We analyze the left–right asymmetry of pion production in semi-inclusive deep inelastic scattering (SIDIS) process of unpolarized charged lepton on transversely polarized nucleon target. Unlike available treatments, in which some specific weighting functions are multiplied to separate theoretically motivated quantities, we do not introduce any weighting function following the analyzing method by the E704 experiment. The advantage is that this basic observable is free of any theoretical bias, although we can perform the calculation under the current theoretical framework. We present numerical calculations at both HERMES kinematics for the proton target and JLab kinematics for the neutron target. We find that with the current theoretical understanding, Sivers effect plays a key role in our analysis.

Transverse quark spin effects and the flavor dependence of the Boer-Mulders function

The naive time-reversal-odd (``$T$-odd'') parton distribution ${h}_{1}^{\ensuremath{\perp}}$, the so-called Boer-Mulders function, for both up ($u$) and down ($d$) quarks is considered in the diquark spectator model. While the results of different articles in the literature suggest that the signs of the Boer-Mulders function in semi-inclusive deep inelastic scattering (SIDIS) for both flavors $u$ and $d$ are the same and negative, a previous calculation in the diquark spectator model found that ${h}_{1}^{\ensuremath{\perp}(u)}$ and ${h}_{1}^{\ensuremath{\perp}(d)}$ have different signs. The flavor dependence is of significance for the analysis of the azimuthal $\mathrm{cos}(2\ensuremath{\phi})$ asymmetries in unpolarized SIDIS and Drell-Yan processes, as well as for the overall physical understanding of the distribution of transversely polarized quarks in unpolarized nucleons. We find substantial differences with previous work. In particular, we obtain half and first moments of the Boer-Mulders function that are negative over the full range in Bjorken $x$ for both the $u$ and $d$ quarks. In conjunction with the Collins function, we then predict the $\mathrm{cos}(2\ensuremath{\phi})$ azimuthal asymmetry for ${\ensuremath{\pi}}^{+}$ and ${\ensuremath{\pi}}^{\ensuremath{-}}$ in this framework. We also find that the Sivers $u$ and $d$ quarks are negative and positive, respectively. As a by-product of the formalism, we calculate the chiral-odd but ``$T$-even'' function ${h}_{1L}^{\ensuremath{\perp}}$, which allows us to present a prediction for the single-spin asymmetry ${A}_{UL}^{\mathrm{sin}(2\ensuremath{\phi})}$ for a longitudinally polarized target in SIDIS.

Collins asymmetry at hadron colliders

We study the Collins effect in the azimuthal asymmetricdistribution of hadrons inside a high energy jet in the single transversepolarized proton proton scattering. From the detailed analysis ofone-gluon and two-gluon exchange diagrams contributions, the Collinsfunction is found the same as that in the semi-inclusive deep inelasticscattering and e+e- annihilations. The eikonal propagators in thesediagrams do not contribute to the phase needed for the Collins-typesingle spin asymmetry, and the universality is derived as a result of theWard identity. We argue that this conclusion depends on the momentum flowof the exchanged gluon and the kinematic constraints in the fragmentationprocess, and is generic and model-independent.

Single spin asymmetries in inclusive hadron production from semiinclusive DIS to hadronic collisions: Universality and phenomenology

In a perturbative QCD approach, with inclusion of spin and transverse momentum effects, experimental data on azimuthal asymmetries observed in polarized semiinclusive deeply inelastic scattering and ${e}^{+}{e}^{\ensuremath{-}}$ annihilations can be used to determine the Sivers, transversity, and Collins soft functions. By using these functions, within the same scheme, we predict ${p}^{\ensuremath{\uparrow}}p\ensuremath{\rightarrow}h+X$ single spin asymmetries in remarkable agreement with high energy experimental data.

Transversity from two pion interference fragmentation

We present calculation on the azimuthal spin asymmetries for pion pair production in semi-inclusive deep inelastic scattering (SIDIS) process at both HERMES and COMPASS kinematics, with transversely polarized proton, deuteron, and neutron targets. We calculate the asymmetry by adopting a set of parametrization of the interference fragmentation functions and two different models for the transversity. We find that the result for the proton target is insensitive to the approaches of the transversity but more helpful to understand the interference fragmentation functions. However, for the neutron target, which can be obtained through using deuteron and $^{3}\mathrm{He}$ targets, we find different predictions for different approaches to the transversity. Thus probing the two pion interference fragmentation from the neutron can provide us more interesting information on the transversity.

The polarised valence quark distribution from semi-inclusive DIS

The semi-inclusive difference asymmetry Ah+−h− for hadrons of opposite charge has been measured by the COMPASS experiment at CERN. The data were collected in the years 2002–2004 using a 160 GeV polarised muon beam scattered off a large polarised 6LiD target in the kinematic range 0.006<x<0.7 and 1<Q2<100 (GeV/c)2. In leading order QCD (LO) the deuteron asymmetry Ah+−h− measures the valence quark polarisation and provides an evaluation of the first moment of Δuv+Δdv which is found to be equal to 0.40±0.07(stat.)±0.06(syst.) over the measured range of x at Q2=10 (GeV/c)2. When combined with the first moment of g1d previously measured on the same data, this result favours a non-symmetric polarisation of light quarks Δu¯=−Δd¯ at a confidence level of two standard deviations, in contrast to the often assumed symmetric scenario Δu¯=Δd¯=Δs¯=Δs.

An application of transverse momentum dependent evolution equations in QCD

The properties and behaviour of the solutions of the recently obtained kt-dependent QCD evolution equations are investigated. When used to reproduce transverse momentum spectra of hadrons in Semi-Inclusive DIS, an encouraging agreement with data is found. The present analysis also supports at the phenomenological level the factorization properties of the Semi-Inclusive DIS cross-sections in terms of kt-dependent distributions. Further improvements and possible developments of the proposed evolution equations are envisaged.

Transversity signals at COMPASS

COMPASS is a fixed target experiment at the CERN SPS, with a rich physics program focused on nucleon spin structure and on hadron spectroscopy. One of the main goals of the spin program is the measurement of the transverse spin distribution function ΔTq(x) in semi-inclusive DIS off transversely polarized nucleons. For this purpose approximately 20% of the running time in the years 2002 to 2004 with the longitudinally polarized muon beam of 160 GeV and with 6LiD polarized target was used to collect data with the target polarized transversely with respect to the beam direction. The 2002 data have been already analysed and published. We present here the preliminary results from the full statistics for the Collins and Sivers single hadron asymmetries and for the transverse spin asymmetry in hadron pair production.

THE QCD PARTON MODEL: A USEFUL APPROXIMATION

Approximate relations among transverse momentum dependent quark distribution functions are established in the framework of the QCD parton model. The validity of such results survives QCD evolution effects, owing to the Politzer theorem on equations of motion. Furthermore the model fixes an energy scale, involved in the parametrization of the correlator, which determines the Q2 dependence of the azimuthal asymmetries in inclusive reactions. Some of the present data — in particular the sin 2ϕ single spin asymmetry in semi-inclusive deep inelastic scattering (SIDIS) and the cos ϕ asymmetry in unpolarized SIDIS — support model predictions. Further measurements of SIDIS and Drell–Yan asymmetries are suggested, in particular the SIDIS double spin asymmetry, which allows to determine approximately the proton transversity.

Comparative analysis of the transversities and the longitudinally polarized distribution functions of the nucleon

A first empirical extraction of the transversity distributions for the u- and d-quarks has been done by Anselmino et al. based on the combined global analysis of the measured azimuthal asymmetries in semi-inclusive deep inelastic scatterings and those in e+e−→h1h2X processes. Although with large uncertainties, the determined transversity distributions already appear to reveal a remarkable qualitative difference with the corresponding longitudinally polarized distributions. We point out that this difference contains very important information on internal spin structure of the nucleon.