Transversity Distribution Research Articles

Testing the universality of the Collins function in pion-jet production at RHIC

By adopting a generalised parton model approach at leading order in QCD, including spin and intrinsic parton motion effects, we study the Collins azimuthal asymmetries for pions within a large-pT jet produced at mid-rapidity in polarised hadronic collisions. Using available information on the quark transversity distributions and the pion Collins functions, as extracted from semi-inclusive deeply inelastic scattering and e+e−→h1h2X processes, we compute estimates for the Collins asymmetries in kinematical configurations presently investigated at RHIC by the STAR Collaboration. Collins-like asymmetries, involving linearly polarised gluons, are also considered. Our predictions, compared against available preliminary data, show a very good agreement, even if some discrepancies, to be further scrutinized both theoretically and experimentally, appear in the transverse momentum dependence of the Collins asymmetry. These results are in favour of the predicted universality of the Collins function and of a mild, if any, evolution with the hard scale of the asymmetries.

Transverse single-spin asymmetries in ℓp↑→hX within a TMD approach: Role of quasireal photon exchange

We present an updated study of transverse single-spin asymmetries for the inclusive large-$P_T$ processes $\ell \, p^\uparrow \to h\, X$ and $\ell\, p^\uparrow \to {\rm jet}\,X$, within a transverse momentum-dependent approach, including the contribution of quasireal (Weizs\"acker-Williams) photons. In the spirit of a unified transverse momentum-dependent scheme, predictions are obtained adopting the Sivers and transversity distributions and the Collins fragmentation functions as extracted from fits to the azimuthal asymmetries measured in semi-inclusive deep inelastic scattering and $e^+e^-$ annihilation processes. The description of the available data is extremely good, showing a clear general improvement with respect to the previous leading-order analysis. Predictions for unpolarized cross sections and single-spin asymmetries for ongoing and future experiments are also given.

Unveiling the nucleon tensor charge at Jefferson Lab: A study of the SoLID case

Future experiments at the Jefferson Lab 12 GeV upgrade, in particular, the Solenoidal Large Intensity Device (SoLID), aim at a very precise data set in the region where the partonic structure of the nucleon is dominated by the valence quarks. One of the main goals is to constrain the quark transversity distributions. We apply recent theoretical advances of the global QCD extraction of the transversity distributions to study the impact of future experimental data from the SoLID experiments. Especially, we develop a simple strategy based on the Hessian matrix analysis that allows one to estimate the uncertainties of the transversity quark distributions and their tensor charges extracted from SoLID data simulation. We find that the SoLID measurements with the proton and the effective neutron targets can improve the precision of the u- and d-quark transversity distributions up to one order of magnitude in the range 0.05 < x < 0.6.

Light front quark-diquark model for the nucleons

We present a quark-diquark model for the nucleons where the light front wave functions are constructed from the soft-wall AdS/QCD prediction. The model is consistent with quark counting rule and Drell-Yan-West relation. The model reproduces the scale evolution of unpolarized PDF of proton for a wide range of energy scale. Helicity and transversity distributions for the proton predicted in this model agree with phenomenological fits. The axial and tensor charges are also shown to agree with the experimental data. The model can be used to evaluate distributions like GPDS, TMDs etc. and their scale evolutions.

Double-spin asymmetryALTcosϕSin semi-inclusive DIS at CLAS12 and EIC within the collinear framework

We study the longitudinal-transverse double-spin asymmetry with a $\cos\phi_S$ modulation in semi-inclusive deep inelastic scattering for charged and neutral pions production. We consider the particular case in which the transverse momentum of the final state hadron is integrated out. The corresponding asymmetry may be contributed by two parts: one is the convolution of the twist-3 distribution function $g_{T}(x)$ and the unpolarized fragmentation function $D_1(z)$, the other is related to the coupling of the transversity distribution function $h_1(x)$ and the collinear twist-3 fragmentation function $\tilde{E}(z)$. We take into account both contributions to predict the $\cos\phi_S$ asymmetry at the kinematics of CLAS12 and a future Electron Ion Collider. We find that the asymmetry of pion production at CLAS12 is sizable, and $\tilde{E}(z)$ can play an important role in the asymmetry in the large-$z$ region.

Di-hadron fragmentation and mapping of the nucleon structure

The fragmentation of a colored parton directly into a pair of colorless hadrons is a non-perturbative mechanism that offers important insights into the nucleon structure. Di-hadron fragmentation functions can be extracted from semi-inclusive electron-positron annihilation data. They also appear in observables describing the semi-inclusive production of two hadrons in deep-inelastic scattering of leptons off nucleons or in hadron-hadron collisions. When a target nucleon is transversely polarized, a specific chiral-odd di-hadron fragmentation function can be used as the analyzer of the net density of transversely polarized quarks in a transversely polarized nucleon, the so-called transversity distribution. The latter can be extracted through suitable single-spin asymmetries in the framework of collinear factorization, thus in a much simpler framework with respect to the traditional one in single-hadron fragmentation. At subleading twist, the same chiral-odd di-hadron fragmentation function provides the cleanest access to the poorly known twist-3 parton distribution $e(x)$, which is intimately related to the mechanism of dynamical chiral symmetry breaking in QCD. When sensitive to details of transverse momentum dynamics of partons, the di-hadron fragmentation functions for a longitudinally polarized quark can be connected to the longitudinal jet handedness to explore possible effects due to $CP-$violation of the QCD vacuum. In this review, we outline the formalism of di-hadron fragmentation functions, we discuss different observables where they appear and we present measurements and future worldwide plans.

Predicting thesinϕStransverse single-spin asymmetry of pion production at an electron ion collider

We study the transverse single-spin asymmetry with a $\sin\phi_S$ modulation in semi-inclusive deep inelastic scattering. Particularly, we consider the case in which the transverse momentum of the final state hadron is integrated out. Thus, the asymmetry is merely contributed by the coupling of the transversity distribution function $h_1(x)$ and the twist-3 collinear fragmentation function $\tilde{H}(z)$. Using the available parametrization of $h_1(x)$ from SIDIS data and the recent extracted result for $\tilde{H}(z)$, we predict the $\sin\phi_S$ asymmetry for charged and neutral pion production at an Electron Ion Collider. We find that the asymmetry is sizable and could be measured. We also study the impact of the leading-order QCD evolution effect and find that it affects the $\sin\phi_S$ asymmetry at EIC considerably.

Overview of the COMPASS Experimental Programme on TMDs and GPDs

The investigation of the recently introduced transverse momentum dependent (TMD) parton distribution functions (PDFs) and generalized parton distributions (GPDs) is an important part of the programme of the COMPASS experiment at CERN. A variety of Semi-inclusive deeply inelastic scattering (SIDIS) measurements on transversely polarized proton and deuteron targets from the 2002–2010 data have allowed to obtain a wealth of results on the transversity distribution and on the TMD PDFs. Further SIDIS measurements are planned in 2016 and 2017 on a pure hydrogen target. In a complementary approach, the first ever Drell–Yan measurement on a transversely polarized proton target is the objective of the 2015 run, still ongoing at the time of this conference, to address the fundamental issue of the change of sign of the Sivers function when measured in the Drell–Yan process as compared to that measured in SIDIS. GPDs are also being investigated. Measurements of the exclusive muon-production of vector mesons, in particular the \(\rho ^0\) and the \(\omega \), on transversely polarized proton targets have provided information on the GPD E. Preliminary results from a test run on deeply virtual compton scattering of 160 GeV muons on a liquid hydrogen target are also given, as well as plans for a two-year long run in 2016 and 2017 with a suitably modified spectrometer.

Measurement of Azimuthal Asymmetries in Inclusive Charged Dipion Production in e^{+}e^{-} Annihilations at sqrt[s]=3.65 GeV.

We present a measurement of the azimuthal asymmetries of two charged pions in the inclusive process e^{+}e^{-}→ππX, based on a data set of 62 pb^{-1} at the center-of-mass energy of 3.65GeV collected with the BESIII detector. These asymmetries can be attributed to the Collins fragmentation function. We observe a nonzero asymmetry, which increases with increasing pion momentum. As our energy scale is close to that of the existing semi-inclusive deep inelastic scattering experimental data, the measured asymmetries are important inputs for the global analysis of extracting the quark transversity distribution inside the nucleon and are valuable to explore the energy evolution of the spin-dependent fragmentation function.

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.

Twist-3 contributions in semi-inclusive DIS with transversely polarized target

Abstract We study semi-inclusive DIS with a transversely polarized target in the approach of collinear factorization. The effects related to the transverse polarization are at twist-3. We derive the complete result of twist-3 contributions to the relevant hadronic tensor at leading order of α s , and construct correspondingly experimental observables. Measuring these observables will help to extract the twist-2 transversity distribution, twist-3 distributions and twist-3 fragmentation functions of the produced unpolarized hadron. A detailed comparison with the approach of transverse-momentum-dependent factorization is made.

Sivers, Boer-Mulders and transversity distributions in the difference cross sections in SIDIS

A major experimental program is presently underway to determine the Sivers, Boer-Mulders and transversity distributions, vital for understanding the internal structure of the nucleon. To this end we consider the Sivers, Boer-Mulders and transversity azimuthal asymmetries of the difference cross sections of hadrons with opposite charges in SIDIS reactions with unpolarized and transversely polarized target l + N → l' + h + X, h = π±, K±, h±. We show that on deuteron target these asymmetries are particularly simple and determine the sum of the valence-quark Qv = uv + dv transverse momentum dependent distributions without any contributions from the strange or other sea-quark functions.At present, data on these asymmetries are presented for the integrated asymmetries i.e. the xB- and zh-dependent asymmetries. If data are available in small bins in Q2, so that Q2-dependence can be neglected, these expressions simplify dramatically leading to remarkably simple and powerful tests of the simplifying assumptions used in extracting these functions from the data.

Extraction of Transversity from COMPASS and Belle Data

The valence transversity distributions of the u- and the d-quarks have been extracted point-by-point from single-hadron production and dihadron production data measured in semi-inclusive deep inelastic scattering and in [Formula: see text] annihilation. The transversity distributions are found to be compatible with each other and with previous analyses.

Opportunities with Polarized Hadron Beams

Spin physics at future hadron facilities provide unique opportunities for the study of QCD well beyond those available at existing facilities. Opportunities with polarized protons in the Fermilab Main Injector are discussed that encompass polarized Drell-Yan scattering of unprecedented precision and also enable measurements of transversity, helicty and other transverse momentum dependent distributions. Forthcoming measurements at COMPASS-II that aim to test fundamental predictions of non-perturbative QCD, and complementary studies at RHIC-Spin that address, among others, open puzzles such as the sharing of the nucleon spin among its constituents are also discussed.

Azimuthal Single-Spin Asymmetries of Charged Pions in Jets in s = 200 GeV p↑p Collisions at STAR

Single spin asymmetry measurements ([Formula: see text]) of the azimuthal distribution of charged pions inside jets produced in transversely polarized proton collisions are sensitive to the transversity distribution and the Collins fragmentation function. The STAR Detector at the Relativistic Heavy Ion Collider is well suited for these types of measurements as it is capable of full jet reconstruction and charged pion identification in the mid-rapidity region ([Formula: see text][Formula: see text][Formula: see text][Formula: see text]). We report here the first observation of Collins [Formula: see text] asymmetries in [Formula: see text] GeV [Formula: see text] collisions.

Work on the Interplay Among h+, h− and Hadron Pair Transverse Spin Asymmetries in SIDIS

In the fragmentation of a transversely polarized quark a left-right asymmetry, the Collins asymmetry, is expected for each hadron produced in the process [Formula: see text]. Similarly, an asymmetry is also expected for the hadron pair, the dihadron asymmetry. Both asymmetries have been measured to be different from zero on transversely polarised proton targets and have allowed for first extractions of the transversity distributions. From the high statistics COMPASS data we have further investigated these asymmetries getting strong indications that the two mechanisms are driven by a common physical process.

Measurement of Collins asymmetry at BESIII

In this talk, I present the recent measurement of the Collins fragmentation function based on a set of 62 pb-1 e+e- annihilation data at √s = 3.65 GeV collected with the BESIII detector at the BEPCII storage rings. In this work, the azimuthal asymmetries of two charged pions in the inclusive process e+e- → ππX are explored. These asymmetries can be attributed to the Collins fragmentation function, which describes the behavior of a hadron produced from a transversely polarized quark. The corresponding four-momentum transfer of the virtual photon, Q2, is close to the energy scale of the existing semi-inclusive DIS experimental data. We observe a nonzero asymmetry, which increases with increasing pion momentum and also indicates a larger spin-dependent Collins effect than at higher energy scale. The dependence of the asymmetry on the transverse momentum of hadrons to the reference axis is also investigated. The measured asymmetries are important inputs for the global analysis of extracting the quark transversity distribution inside the nucleon, and are valuable to explore the energy evolution of the spin-dependent fragmentation function.

High Precision Measurement of Transversity Using Di-hadron Correlations in p↑+p Collisions at sNN = 500 GeV

The transversity distribution, which describes transversely polarized quarks in a transversely polarized nucleon, is a fundamental component of the current picture of the spin structure of the nucleon, and is only loosely constrained by existing semi-inclusive deep inelastic scattering data. The di-hadron interference fragmentation function (IFF), which describes the fragmentation of transversely polarized quarks, is expected to give rise to spin-dependent di-hadron correlations in p[Formula: see text]+p collisions. Significant di-hadron correlations have recently been measured at RHIC in p[Formula: see text]+p collisions at [Formula: see text] = 200 GeV at mid-rapidity. In 2011, STAR collected p[Formula: see text]+p data at [Formula: see text] = 500 GeV, allowing STAR to extend these di-hadron asymmetries into a previously unexplored kinematic region. The status of the charge-ordered pion pair asymmetry measurement from [Formula: see text] = 500 GeV p[Formula: see text]+p collisions will be presented.

Collins functions for pions from SIDIS and newe+e−data: A first glance at their transverse momentum dependence

New data from Belle and BaBar Collaborations on azimuthal asymmetries, measured in e+e- annihilations into pion pairs at Q^2=112 GeV^2, allow to take the first, direct glance at the transverse momentum dependence of the Collins functions, in addition to their z dependence. These data, together with available Semi-Inclusive Deep Inelastic Scattering (SIDIS) data on the Collins asymmetry, are simultaneously analysed in the framework of the generalised parton model assuming two alternative Q^2 evolution schemes and exploiting two different parameterisations for the Collins functions. The corresponding results for the transversity distributions are presented. Analogous data, newly released by the BESIII Collaboration, on e+e- annihilations into pion pairs at the lower Q^2 of 13 GeV^2, offer the possibility to explore the sensitivity of these azimuthal correlations on transverse momentum dependent evolution effects.

Interplay among transversity induced asymmetries in hadron leptoproduction

In the fragmentation of a transversely polarized quark several left–right asymmetries are possible for the hadrons in the jet. When only one unpolarized hadron is selected, it exhibits an azimuthal modulation known as the Collins effect. When a pair of oppositely charged hadrons is observed, three asymmetries can be considered, a di-hadron asymmetry and two single hadron asymmetries. In lepton deep inelastic scattering on transversely polarized nucleons all these asymmetries are coupled with the transversity distribution. From the high statistics COMPASS data on oppositely charged hadron-pair production we have investigated for the first time the dependence of these three asymmetries on the difference of the azimuthal angles of the two hadrons. The similarity of transversity induced single and di-hadron asymmetries is discussed. A new analysis of the data allows quantitative relationships to be established among them, providing for the first time strong experimental indication that the underlying fragmentation mechanisms are all driven by a common physical process.