Using a generalized parton model approach including spin and intrinsic parton motion effects, and assuming the validity of factorization for large p_T jet production in hadronic collisions, we study the azimuthal distribution around the jet axis of leading pions, produced in the jet fragmentation process. We identify the observable leading-twist azimuthal asymmetries for the unpolarized and single-polarized case related to both quark and gluon-originated jets. We account for all physically allowed combinations of the transverse momentum dependent (TMD) parton distribution and fragmentation functions, with special attention to the Sivers, Boer-Mulders, and transversity quark distributions, and to the Collins fragmentation function for quarks (and to the analogous functions for gluon partons).
We comment on theoretical aspects of the measurement of azimuthal asymmetries in semi-inclusive charged particle production, made recently by the ZEUS Collaboration at HERA. By taking the ratio of the two measured asymmetries, we find good agreement between the perturbative QCD prediction and the experimental data. To separate the perturbative and nonperturbative contributions to the asymmetries, we suggest that the azimuthal asymmetries of the transverse energy flow be measured as a function of a variable $q_T$ related to the pseudorapidity of the energy flow.
I review the phenomenology of unpolarized cross sections and azimuthal asymmetries in semi-inclusive deeply inelastic scattering (SIDIS). The general theoretical framework is presented and the validity of the Gaussian model is discussed. A brief account of the existing analyses is provided.
We discuss the possibilities of testing of perturbative quantum chromodynamics through azimuthal asymmetries in polarized ep in the context of future collider and fixed target facilities, such as Electron Ion Collider and TESLA-N.
The leading and sub-leading order results for pion electroproduction in polarized and unpolarized semi-inclusive deep-inelastic scattering, are considered putting emphasis on transverse momentum dependent effects appearing in azimuthal asymmetries. In particular the spin-dependent (single, double) and spin-independent asymmetries of the distributions in the azimuthal angle of the pion related to the lepton scattering plane are discussed.
We consider the leading order result for polarized leptoproduction, putting emphasis on transverse momentum dependent effects appearing in azimuthal asymmetries. Measurements of weighted cross sections enable extraction of the distribution of transversely polarized quarks. We focus on the distribution in a longitudinally polarized hadron and estimate the expected asymmetries in leptoproduction.
We present the complete azimuthal asymmetries at leading twist in terms of fragmentation functions in dihadron production semi-inclusive electron positron annihilation process. When the non-trivial $θ$ vacuum is taken into consideration, the parity symmetry of quantum chromodynamics is violated. As a consequence of the $local$ $\mathcal{P}$-odd effects, $\mathcal{P}$-odd fragmentation functions would contribute to the azimuthal asymmetries. Azimuthal asymmetry coming from two interference terms with opposite signs vanishes when sum over many events. This symmetry only survives on the event-by-…
The recent measurements of azimuthal single spin asymmetries by the HERMES collaboration at DESY may shed some light on presently unknown fragmentation and distribution functions. We present a study of such functions and give some estimates of weighted integrals directly related to those measurements.
Spin azimuthal asymmetries in pion electro-production in deep inelastic scattering off longitudinally polarized protons, measured by HERMES, are well reproduced theoretically with no adjustable parameters. Predictions for azimuthal asymmetries for a longitudinally polarized deuteron target are given. The z-dependence of the Collins fragmentation function is extracted. The first information on e(x) is extracted from CLAS A_LU asymmetry.
In this paper we study azimuthal asymmetries of the muon pair production in ultraperipheral heavy ion collisions within the joint impact parameter and transverse momentum dependent framework. The final state QED radiation effects are resummed to all orders in perturbation theory, where the complete muon mass corrections are also taken into account. We further make numerical estimations for azimuthal asymmetries in the different kinematic regions accessible at RHIC and LHC with the derived resummation formula. We find that the lepton mass effects can give sizable corrections to the asymmetries …
First information on the chirally odd twist-3 proton distribution function e(x) is extracted from the azimuthal asymmetry, A_{LU}, in the electro-production of pions from deeply inelastic scattering of longitudinally polarized electrons off unpolarized protons, which has been recently measured by CLAS collaboration. Furthermore parameter-free predictions are made for azimuthal asymmetries, A_{UL}, from scattering of an unpolarized beam on a polarized proton target for CLAS kinematics.
In this contribution TMD evolution of azimuthal asymmetries, in particular of the Sivers and double Collins asymmetries, is addressed. A comparison of the scale dependence is made between asymmetries described with TMD factorization at low transverse momentum and those described with collinear factorization at high transverse momentum. Finally, the advantages of Bessel weighting are discussed: convergence of transverse momentum integrals, suppression of large transverse momentum contributions, and well-defined lattice QCD evaluations of Bessel-weighted TMDs including proper gauge links.
The main properties of the leading-twist transverse momentum dependent parton distributions in a light-cone constituent quark model of the nucleon are reviewed, with focus on the role of the spin-spin and spin-orbit correlations of quarks. Results for azimuthal single spin asymmetries in semi-inclusive deep inelastic scattering are also discussed.
An attempt is made to understand the z-dependence of the azimuthal single spin asymmetries observed by the HERMES collaboration in terms of chiral models based on effective quark and Goldstone boson degrees of freedom. The effects of respectively neglecting and considering Gaussian intrinsic parton transverse momenta and the Sivers effect are explored. Predictions for the transverse target polarization experiment at HERMES are presented.
We calculate azimuthal asymmetries in back-to-back production of $J/ψ$ and a photon in electron-proton scattering process at the future electron-ion collider (EIC) using TMD factorization framework. We consider the cases where the proton is unpolarized or transversely polarized. For the formation of $J/ψ$, non-relativistic QCD (NRQCD) is used. We find that the cross-section gets contribution from only one color octet state, as a result, the azimuthal modulations become independent of the long-distance matrix elements (LDMEs), and thus can be used to probe, in particular the gluon TMDs which ar…
In these lectures I want to discuss how the structure functions in deep inelastic scattering relate to quark and gluon correlation functions. In particular we will consider the issue of intrinsic transverse momenta of quarks, which becomes important in processes like 1-particle inclusive leptoproduction. Some examples of cross sections and asymmetries, in particular in polarized scattering processes are discussed. We also discuss the operator structure for azimuthal asymmetries and their evolution.
Predictions are made for azimuthal asymmetries in pion and kaon production from SIDIS off a longitudinally polarized deuterium target for HERMES kinematics, based on information on the 'Collins fragmentation function' from DELPHI data and on predictions for the transversity distribution function from non-perturbative calculations in the chiral quark-soliton model. There are no free parameters in the approach, which has been already successfully applied to explain the azimuthal asymmetries from SIDIS off polarized proton targets observed by HERMES and SMC.
Predictions are made for single spin azimuthal asymmetries due to the Collins effect in pion production from semi-inclusive deeply inelastic scattering off transversely and longitudinally polarized targets for the HERMES and COMPASS experiments. The x-dependence of the asymmetries is evaluated using the parton distribution functions from the chiral quark-soliton model. The overall normalization of the predicted asymmetries is determined by the information on the Collins fragmentation function extracted from previous HERMES data on azimuthal asymmetries from a longitudinally polarized target. T…
We study several azimuthal asymmetries in semi-inclusive deep inelastic scattering and in Drell-Yan, interpreting them in the framework of the formalism of the quark correlator, with a particular reference to T-odd functions. The correlator contains an undetermined energy scale, which we fix on the basis of a simple and rather general argument. We find a different value than the one assumed in previous treatments of T-odd functions. This implies different predictions on the Q^2 dependence of the above mentioned asymmetries. Our result about the azimuthal asymmetry of unpolarized Drell-Yan agre…
We have presented the results for the single and double spin asymmetries in semi-inclusive deep inelastic scatterings for proton in a light front quark-diquark model. The asymmetries generated by the T-even TMDs are discussed here. The model predictions are found to agree with the available data. We also present our model predictions for the Collins asymmetry for the future electron-ion collider experiments.
It is shown that transverse momentum dependent azimuthal spin asymmetries suffer from suppression due to Sudakov factors, in the region where the transverse momentum is much smaller than the large energy scale Q^2. The size and Q^2 dependence of this suppression are studied numerically for two such asymmetries, both arising due to the Collins effect. General features are discussed of how the fall-off with Q^2 is affected by the nonperturbative Sudakov factor and by the transverse momentum weights and angular dependences that appear in different asymmetries. For a subset of asymmetries the asym…
We give a short overview of the phenomenology of azimuthal and transverse single spin asymmetries in (un)polarized high-energy hadronic collisions. We briefly summarize a transverse momentum dependent, generalized parton model approach to these polarization phenomena, and discuss some of its applications. Finally, open points and future developments will be outlined.
Using the recent experimental data on the left right asymmetry in fragmentation of transversely polarized quarks and the theoretical calculation of the proton transversity distribution in the effective chiral quark soliton model we explain the azimuthal asymmetries in semi-inclusive hadron production on longitudinal (HERMES) and transversely (SMC) polarized targets with no free parameters. On this basis we state that the proton transversity distribution could be successfully measured in future DIS experiments with longitudinally polarized target.
We point out the role of intrinsic transverse momentum of partons in the study of azimuthal asymmetries in deep-inelastic 1-particle inclusive leptoproduction. Leading asymmetries often appear in combination with spin asymmetries. This leads not only to transverse momentum dependence in the parton distribution functions, but also to functions beyond the ones known from inclusive deep-inelastic scattering (DIS). We use Lorentz invariance and the QCD equations of motion to study the evolution of functions that appear at leading (zeroth) order in a 1/Q expansion in azimuthal asymmetries. This inc…
We consider the leading and sub-leading twist $T$-odd and even contributions to the $\cos 2ϕ$ azimuthal asymmetry in unpolarized dilepton production in Drell-Yan Scattering. We estimate the contributions' effects at $500 {\rm GeV}$, $ 50 {\rm GeV}$, and $25 {\rm GeV}$ energies in the framework of the parton model using a quark diquark-spectator model of the nucleon to approximate the soft contributions.
One of the most interesting consequence of non-zero intrinsic transverse momentum of partons in the nucleon is the nontrivial azimuthal dependence of the cross section of hard scattering processes. Many of the observable asymmetries contain unknown functions which provide essential information on the quark and gluon structure. Several of them have been studied in the last few years; we discuss their qualitative and quantitative features in semi-inclusive DIS.
We review the information on the spin and orbital angular momentum structure of the nucleon encoded in the T-even transverse momentum dependent parton distributions within light-cone quark models. Model results for azimuthal spin asymmetries in semi-inclusive lepton-nucleon deep-inelastic scattering are discussed, showing a good agreement with available experimental data and providing predictions to be further tested by future CLAS, COMPASS and HERMES data.
I study hard collisions between unpolarized protons and antiprotons where a lepton-antilepton pair is detected in coincidence with a final proton-antiproton pair, and no more particles are produced, in the regime 10 GeV^2 << s << 1000 GeV^2, M > 4 GeV, q_T < 3 GeV/c. The present work is centered on azimuthal asymmetries. Because of momentum conservation, a Boer-Mulders term in the momentum distribution of a quark implies a balancing effect in the momentum distribution of some spectators. This produces azimuthal asymmetries of the final hadrons. To analyze this, I have organized a parton-level …
We use Lorentz invariance and the QCD equations of motion to study the evolution of functions that appear at leading (zeroth) order in a 1/Q expansion in azimuthal asymmetries. This includes the evolution equation of the Collins fragmentation function. The moments of these functions are matrix elements of known twist two and twist three operators. We present the evolution in the large N_c limit, restricted to the non-singlet case for the chiral-even functions.
New data on the Sivers azimuthal asymmetry measured in semi-inclusive deep-inelastic scattering processes have recently been released by the COMPASS Collaboration at CERN. Their increased precision and their particular binning, in terms of $Q^2$ as well as $x$, motivates a new extraction of the Sivers function, within the framework of a simple and transparent parametrization. Signals of TMD effects visible in the Sivers asymmetries are critically assessed. A thorough study of the uncertainties affecting the extracted Sivers function is presented, including the low-$x$ and large-$x$ regions.
We show that transverse and normal single-$tau$ polarization of $tau$ pairs produced at $e^+$ $e^-$ unpolarized collisions, at the $Z$ peak, are sensitive to weak (magnetic and electric) dipole moments of the $tau$. We also show how these components of the $τ$ polarization are accessible by measuring appropriate azimuthal asymmetries in the angular distribution of its decay products. Sensitivities of the order of $10^{-18}$ $e\cdot cm$, for the weak-electric dipole moment, and $10^{-4}$ ($10^{-3}$), for the real (imaginary) part of the weak-magnetic dipole moment of $τ$, may be achieved. Compa…
In this article we review the present understanding of azimuthal and single spin asymmetries for inclusive and semi-inclusive particle production in unpolarized and polarized hadronic collisions at high energy and moderately large transverse momentum. After summarizing the experimental information available, we discuss and compare the main theoretical approaches formulated in the framework of perturbative QCD. We then present in some detail a generalization of the parton model with inclusion of spin and intrinsic transverse momentum effects. In this context, we extensively discuss the phenomen…
We present a phenomenological analysis of the cos-phi and cos-2phi asymmetries in unpolarized semi-inclusive deep inelastic scattering, based on the recent multidimensional data released by the COMPASS and HERMES Collaborations. In the TMD framework, valid at relatively low transverse momenta, these asymmetries arise from intrinsic transverse momentum and transverse spin effects, and from their correlations. The role of the Cahn and Boer-Mulders effects in both azimuthal moments is explored up to order 1/Q. As the kinematics of the present experiments is dominated by the low-Q^2 region, higher…
The distribution of hadrons produced in deeply inelastic electron-proton collisions depends on the azimuthal angle between lepton scattering plane and hadron production plane in the photon-proton centre-of-mass frame. In addition to the well known up-down asymmetry induced by the azimuthal dependence of the Born level subprocess, there is also a non-vanishing left-right asymmetry, provided the incoming electron is polarized. This asymmetry is time-reversal-odd and induced by absorptive corrections to the Born level process. We investigate the numerical magnitude of azimuthal asymmetries in sem…
We study the azimuthal asymmetries for the distributions of leading pions inside a jet produced inclusively in high-energy proton-proton collisions within the framework of the transverse momentum dependent generalized parton model. We present results for the RHIC center-of-mass energies $\sqrt{s}$ = 200 and 500 GeV, mainly for forward jet rapidities, in particular for the two mechanisms which dominate such asymmetries: the Sivers and the Collins effects. We also briefly discuss the case of inclusive jet production and, adopting the so-called colour gauge invariant parton model, we propose a ph…
We consider transverse momentum dependent gluon distributions inside both unpolarized and transversely polarized protons and show how they can be probed by looking at azimuthal modulations in $e \, p \to e \, J/ψ\, \mathrm{jet} \, X$. We find that the contribution due to quark induced subprocesses is always suppressed in the considered kinematic regions, accessible in principle at a future Electron-Ion Collider. Our model-independent estimates of the maximal values of these asymmetries allowed by positivity bounds suggest the feasibility of their measurement. In addition, by adopting the McLer…
We present the systematical decomposition results of three-dimensional (3D) fragmentation functions (FFs) from parton correlators for spin-1 hadron. We choose one of the best process $e^+e^-\to VπX$ to study the 3D and tensor polarization dependent FFs. By making a general kinematic analysis we show that the cross section is expressed by 81 independent structure functions, and get the results of the azimuthal and spin asymmetries. We also present the parton model results for this process and express the results in terms of the 3D FFs. Based on this formalism, we also give the numerical results…
We demonstrate that the angular distribution of hadrons produced in semi-inclusive deep inelastic final states is related to the inclusive longitudinal structure function. This relation could provide a new method of accessing $F_L(x,Q^2)$ in deep inelastic scattering measurements.
Recently it has been argued that the transverse momentum dependent twist-2 Sivers distribution function does not vanish in QCD. Therefore both, the Collins and Sivers effects, should be considered in order to explain the azimuthal single spin asymmetries A(UL) in pion production in semi-inclusive deeply inelastic lepton scattering of a longitudinally polarized target. On the basis of presently available phenomenological information on the Sivers function we estimate that for those asymmetries A(UL) in the kinematic region of the HERMES experiments the Sivers effect can be neglected with respec…
We study the azimuthal asymmetries for quark pair production in proton-nucleus collisions using a hybrid approach in which the nucleus is treated in the Color Glass Condensate (CGC) framework while the Lipatov approximation is applied on the proton side. Our treatment goes beyond the large N_c limit. We particularly focus on the so-called correlation limit where the imbalance of the transverse momentum of the quark pair is much smaller than the out-going individual quark transverse momenta. In this kinematic region, a matching between the hybrid approach and a factorization in terms of transve…
We analyze the perturbative and parametric stability of the QCD predictions for the azimuthal asymmetries in heavy quark leptoproduction. At leading order, the $\cos ϕ$ asymmetry vanishes whereas the $\cos 2ϕ$ one is of leading twist and predicted to be about 15% at energies sufficiently above the production threshold. We calculate the NLO soft-gluon corrections to $ϕ$-dependent leptoproduction to the next-to-leading logarithmic accuracy. The soft-gluon approximation provides a good description of the available exact NLO results at $Q^{2}\lesssim m^{2}$. Our analysis shows that, contrary to th…
The Weizsaecker-Williams transverse momentum dependent (TMD) gluon distributions can be probed in the production of a hard dijet in semi-inclusive DIS. This process is sensitive not only to the conventional but also to the linearly polarized gluon distribution. The latter gives rise to an azimuthal dependence of the dijet cross section and therefore can be distinguished from the former. Feasibility study of a measurement of these TMDs through dijet production at a future electron-ion collider shows that the extraction of the distribution of linearly polarized gluons with a statistical accuracy…
The collective interactions of many partons in the first stage of the collisions is the usual accepted explanation of the sizable elliptical flow. The clustering of color sources provides a framework of partonic interactions. In this scheme, we show a reasonable agreement with RHIC data for pT<1.5 GeV/c in both the dependence of v2 transverse momentum and in the shape of the nuclear modified factor on the azimuthal angle for different centralities. We show the predictions at LHC energies for Pb-Pb. In the case of proton-proton collisions a sizable v2 is obtained at this energy.
We analyze the transverse momentum dependent distribution and fragmentation functions in space-like and time-like hard processes involving at least two hadrons, in particular 1-particle inclusive leptoproduction, the Drell-Yan process and two-particle inclusive hadron production in electron-positron annihilation. As is well-known, transverse momentum dependence allows for the appearance of unsuppressed single spin azimuthal asymmetries, such as Sivers and Collins asymmetries. Recently, Belitsky, Ji and Yuan obtained fully color gauge invariant expressions for the relevant matrix elements appea…
We calculate the azimuthal dependence of the heavy-quark-initiated ${\cal O}(α_{s})$ contributions to the lepton-nucleon deep inelastic scattering (DIS). It is shown that, contrary to the photon-gluon fusion (GF) component, the photon-quark scattering (QS) mechanism is practically $\cos2ϕ$-independent. We investigate the possibility to discriminate experimentally between the GF and QS contributions using their strongly different azimuthal distributions. Our analysis shows that the GF and QS predictions for the azimuthal $\cos2ϕ$ asymmetry are quantitatively well defined in the fixed flavor num…
We investigate the single-spin asymmetries in inclusive and exclusive processes of electron-proton scattering and electron-positron annihilation. In the decomposition of hadronic tensor, a Lorentz symmetric spin-dependent term is generally present. The existence of such a term implies single-spin asymmetries in these processes and these single-spin asymmetries for baryons can be understood in a unified manner. We argue that it is important to measure the single-spin asymmetries in both inclusive and exclusive processes for the $Λ$ production at the present B-factories. This will lead to the fi…
Using a generalized parton model approach including spin and intrinsic parton motion effects, and assuming the validity of factorization for large-pT jet production in hadronic collisions, we study the azimuthal distribution around the jet axis of leading unpolarized or (pseudo)scalar hadrons, namely pions, produced in the jet fragmentation process. We identify the observable leading-twist azimuthal asymmetries for the unpolarized and single-polarized case related to quark and gluon-originated jets. We account for all physically allowed combinations of the transverse momentum dependent (TMD) p…
We analyze single transverse-spin asymmetries for hadronic pion production at large transverse momenta using QCD factorization. In the large $x_F$ region, leading contributions to the asymmetries are naturally produced by twist-3 parton correlation functions that couple quark fields and gluon field strengths. With a simple model for these matrix elements, leading-order asymmetries calculated from QCD are consistent with data on pion production from Fermilab, and can be used to predict single-spin asymmetries at RHIC. We argue that our perturbative calculation for the asymmetries is relevant to…
We consider the azimuthal distribution of the final observed hadron in semi-inclusive deep-inelastic scattering and the lepton pair in the Drell-Yan process. In particular, we focus on the $\cos ϕ$ modulation of the unpolarized cross section and on its dependence upon transverse momentum. At low transverse momentum, for these observables we propose a factorized expression based on tree-level approach and conjecture that the same formula is valid in transverse-momentum dependent (TMD) factorization when written in terms of subtracted TMD parton distributions. Our formula correctly matches with …
Using the formalism obtained from collinear expansion, we calculate the differential cross section and azimuthal asymmetries in semi-inclusive deeply inelastic lepton-nucleon (nucleus) scattering process $e^-+N (A) \to e^-+q+X$ with both polarized beam and polarized target up to twist-3. We derive the azimuthal asymmetries in terms of twist-3 parton correlation functions. We simplify the results by using the QCD equation of motion that leads to a set of relationships between different twist-3 functions. We further study the nuclear dependence of azimuthal asymmetries and show that they have si…
In the TMD approach, the average transverse momentum of the unpolarised TMD PDFs and FFs is crucial not only to reproduce unpolarised cross sections and hadron multiplicities, but also for the understanding of azimuthal and spin asymmetries. Information on these transverse momenta is nowadays obtained mainly by fitting multiplicities data for SIDIS, where the intrinsic motion in the initial parton distributions and in the hadronisation process are strongly correlated and difficult to estimate separately without ambiguities. In this contribution we discuss the consequences of this correlation e…
We study nuclear dependences of azimuthal asymmetries in the Drell-Yan lepton pair production in nucleon-nucleus collisions with polarized nucleons.We use the "maximal two-gluon correlation approximation", so that we can relate the transverse momentum dependent quark distribution in a nucleus to that in a nucleon by a convolution with a Gaussian broadening.We use the Gaussian ansatz for the transverse momentum dependence of such quark distribution functions,and obtain the numerical results for the nuclear dependences.These results show that the averaged azimuthal asymmetries are suppressed.
We study single-spin asymmetries in semi-inclusive deep inelastic scattering with transversely polarized target. Based on the QCD factorization approach, we consider Sivers and Collins contributions to the asymmetries. We fit simple parameterizations for the Sivers and Collins functions to the recent HERMES data, and compare to results from COMPASS. Using the fitted parameterizations for the Sivers functions, we predict the single transverse spin asymmetries for various processes in $pp$ collisions at RHIC, including the Drell-Yan process and angular correlations in dijet and jet-plus-photon p…
We determine the distribution of linearly polarized gluons of a dense target at small $x$ by solving the B-JIMWLK rapidity evolution equations. From these solutions we estimate the amplitude of $\sim \cos 2ϕ$ azimuthal asymmetries in DIS dijet production at high energies. We find sizeable long-range in rapidity azimuthal asymmetries with a magnitude in the range of $v_2=\langle\cos 2ϕ\rangle \sim 10\%$.
In a perturbative QCD approach, with inclusion of spin and transverse momentum effects, experimental data on azimuthal asymmetries observed in polarized semi-inclusive deeply inelastic scattering and e+ e- annihilations can be used to determine the Sivers, transversity and Collins soft functions. By using these functions, within the same scheme, we predict p(transv. polarized) p -> h + X single spin asymmetries in remarkable agreement with RHIC experimental data.
We consider the single-spin azimuthal asymmetries recently measured at the HERMES experiment for charged pions produced in semi-inclusive deep inelastic scattering of leptons off longitudinally polarized protons. Guided by the experimental results and assuming a vanishing twist-2 transverse quark spin distribution in the longitudinally polarized nucleon, denoted as ``reduced twist-3 approximation'', a self-consistent description of the observed single-spin asymmetries is obtained. In addition, predictions are given for the z dependence of the single target-spin asymmetry.
In the resummation of collinear gluons emitted together with active partons from the hadrons in the Drell-Yan process (DY) effects of color entanglement become important when the transverse directions are taken into account. It is then no longer possible to write the cross section as the convolution of two soft correlators and a hard part. We show that the color entanglement introduces additional color factors that must be taken into account in the extraction of transverse momentum dependent parton distribution functions (TMD PDFs) from azimuthal asymmetries. Examples where such effects matter…
