We study the $\cos{ϕ_h}$ azimuthal asymmetry in double polarized semi-inclusive pion production by considering dynamical twist-3 effects. In particular, we evaluate the role of the transverse momentum dependent distributions $e_L(x, k_T^2)$ and $g_L^\perp(x, k_T^2)$ on the asymmetry. Using two different sets of spectator model results for these distributions, we predict the $\cos{ϕ_h}$ asymmetry of $π^+$, $π^-$, and $π^0$ at the kinematic configuration available at CLAS, HERMES and COMPASS. Our estimates show that the asymmetries are positive for all the pions and could be accessed by CLAS and HERMES. We also find that $g_L^\perp$ gives the dominant contribution to the $\cosϕ_h$ asymmetry, while the contribution of $e_L$ is almost negligible.
In this review a first comprehensive study of azimuthal asymmetries in semi-inclusive deep inelastic muoproduction of hadron pairs off longitudinally polarized protons at COMPASS is presented. The study is based on data taken in 2007 and 2011, obtained by impinging a high-energetic $μ^+$ beam of $160$ GeV/$\it{c}$, respectively $200$ GeV/$\it{c}$, momentum on a solid ammonia target. The discussion is focused on both leading and subleading longitudinal target-spin-dependent asymmetries arising in the di-hadron SIDIS cross section, addressing the role of spin-orbit couplings and quark-gluon corr…
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.
We present a study on the double longitudinal-spin asymmetry of dihadron production in semi-inclusive deep inelastic scattering, in which the total transverse momentum of the final-state hadron pairs is integrated out. In particular, we investigate the origin of the $\cosϕ_R$ azimuthal asymmetry for which we take into account the coupling of the helicity distribution $g_1$ and the twist-3 dihadron fragmentation function $\widetilde{D}^{\sphericalangle}$. We calculate the $s$-wave and $p$-wave interference term $\widetilde{D}^{\sphericalangle}_{ot}$ in a spectator model. We estimate the $\cosϕ_…
We study the single longitudinal-spin asymmetry of dihadron production in semi-inclusive deep inelastic scattering process. We consider the collinear picture in which the transverse momentum of the final-state hadron pair is integrated out, such that the $\sin ϕ_R$ azimuthal asymmetry arises from the coupling $h_L\, H_{1}^{\sphericalangle}$ as well as the coupling $g_1 \,\widetilde{G}^{\sphericalangle}$. We calculate the unknown twist-3 dihadron fragmentation function $\widetilde{G}^{\sphericalangle}$ using a spectator model which is successful in describing the dihadron production in the unpo…
In this paper we study the double longitudinal spin asymmetry of dihadron production in semi-inclusive deep inelastic scattering (SIDIS). We calculate a unknown twist-3 dihadron fragmentation function $\widetilde{D}^\sphericalangle$ within a spectator model which has been used successfully in describing the dihadron production in both the unpolarized and the single polarized processes. The collinear picture, in which the transverse momentum of the final state hadron pair is integrated out, has been considered. The $\cosϕ_R$ azimuthal asymmetry arises from the coupling $e_L H_1^\sphericalangle$…
We study the $\sin2ϕ_h$ azimuthal asymmetry of charged and neutral pion productions off the longitudinally polarized nucleon targets in semi-inclusive deeply inelastic scattering (SIDIS) process within the transverse momentum dependent~(TMD) factorization. The asymmetry is contributed by the convolution of the TMD distribution $h_{1L}^{\perp}$ and the Collins fragmentation function $H_{1}^\perp$. We adopt the Wandzura-Wilczek-type~(WW-type) approximation for $h_{1L}^{\perp}$ and two different parametrizations on the nonperturbative part of TMD evolution for $h_{1L}^{\perp}$ and $H_{1}^\perp$. …
One of the important objectives of the COMPASS experiment (CERN, SPS north area) is the exploration of transverse spin structure of nucleon via study of spin (in)dependent azimuthal asymmetries with semi-inclusive deep inelastic scattering (SIDIS) processes and recently also with Drell-Yan (DY) reactions. In the past twelve years series of measurements were made in COMPASS, using 160 GeV/c longitudinally polarized muon beam and polarized $^6LiD$ and $NH_3$ targets. Drell-Yan measurements with high energy (190 GeV/c) pion beam and transversely polarized $NH_3$ target started in 2014 with a pilo…
Preliminary results obtained by the COMPASS experiment for longitudinal-spin-dependent azimuthal asymmetries in single-hadron muoproduction off protons are presented for the first time. The analysis was carried out on the full data sample collected by COMPASS with longitudinally polarized proton ($NH_3$) target in 2007 and 2011 using 160~\gvc and 200~\gvc muon beams, correspondingly. Within QCD parton model approach extracted asymmetries are giving access to the specific convolutions of certain transverse-momentum-dependent \textit{twist-2} and \textit{higher twist} parton distribution functio…
One of the important objectives of the COMPASS experiment is the exploration of transverse spin structure of nucleon via spin (in)dependent azimuthal asymmetries in semi-inclusive deep inelastic scattering (SIDIS) of polarized leptons (and soon also Drell-Yan (DY) reactions with $π^-$) off transversely polarized target. For this purpose a series of measurements were made in COMPASS, using 160 GeV/c longitudinally polarized muon beam and polarized $^6LiD$ and $NH_3$ targets and are foreseen with 190 GeV/c $π^-$ beam on polarized $NH_3$. The experimental results obtained by COMPASS for azimuthal…
The exploration of the transverse spin structure of the nucleon by measuring spin (in)dependent azimuthal asymmetries in semi-inclusive DIS (SIDIS) and in Drell-Yan processes is one of the main objectives of the COMPASS experiment at CERN (SPS, M2 beamline). During the first phase of the experiment (2002-2011) a series of SIDIS measurements were performed, using a longitudinally polarized muon beam impinging on transversely polarized $^6$LiD or NH$_3$ targets. As a part of the COMPASS-II programme, in 2015 and 2018 the experiment performed Drell-Yan measurements with a $π^-$ beam interacting w…
COMPASS is a high-energy physics experiment operating at the SPS at CERN. Wide physics program of the experiment comprises study of hadron structure and spectroscopy with high energy muon and hadrons beams. As for the muon-program, one of the important objectives of the COMPASS experiment is the exploration of the transverse spin structure of the nucleon via spin (in)dependent azimuthal asymmetries in single-hadron production in deep inelastic scattering of polarized leptons off transversely polarized target. For this purpose a series of measurements were made in COMPASS, using 160 GeV/c longi…
Recently HERMES has observed an azimuthal asymmetry in electro-production of neutral pions in semi-inclusive deep-inelastic scattering of unpolarized positrons off longitudinally polarized protons. This asymmetry (like those observed in the production of charged pions) is well reproduced theoretically by using the non-perturbative calculation of the proton transversity distribution in the effective chiral quark-soliton model combined with experimental DELPHI-data on the new T-odd Collins fragmentation function. There are no free, adjustable parameters in the analysis. Using the $z$-dependence …
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…
Toward Precision Helicity PDFs from Global DIS and SIDIS Fits with Projected EIC Measurements
AGH University（AGH科技大学）；School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM)（基本科学研究所粒子与加速器学院）；Institut für Theoretische Physik, Universität Münster（明斯特大学理论物理研究所）；Istituto Nazionale di Fisica Nucleare, Gruppo collegato di Cosenza（意大利国家核物理研究所科森扎协作组）；Helmholtz-Institut für Strahlen-und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn（波恩大学斯特拉斯曼和核物理亥姆霍兹研究所及贝特理论物理中心）；Institute for Advanced Simulation (IAS-4), Forschungszentrum Jülich（于利希研究中心先进模拟研究所（IAS-4））；Peng Huanwu Collaborative Center for Research and Education, International Institute for Interdisciplinary and Frontiers, Beihang University（北京航空航天大学国际交叉前沿研究院彭桓武教研合作中心）
The flavor dependence of the naive time reversal odd (``T-odd'') parton distributions for $u$- and $d$-quarks are explored in the spectator model. The flavor dependence of $h_{1}^{\perp}$ is of significance for the analysis of the azimuthal $\cos(2ϕ)$ asymmetries in unpolarized SIDIS and DY-processes, as well as for the overall physical understanding of the distribution of transversely polarized quarks in unpolarized nucleons. As a by-product of the formalism, we calculate the chiral-odd but ``T-even'' function $h_{1L}^{\perp}$ which enables us to present a prediction for the single spin asymm…
The COMPASS Collaboration is measuring the asymmetries in the azimuthal distributions of positive and negative hadrons produced in Deep Inelastic Scattering (DIS) on unpolarized protons. The data have been collected in 2016 and 2017 with a 160 GeV/$c$ muon beam scattering off a liquid hydrogen target. The amplitudes of three modulations, $A_{UU}^{\cosϕ_h}$, $A_{UU}^{\cos 2ϕ_h}$ and $A_{LU}^{\sinϕ_h}$ are measured as function of the Bjorken variable $x$, of the fraction of virtual photon energy carried by the hadron $z$, and of the hadron transverse momentum with respect to the virtual photon $…
We present a phenomenological analysis of the $\cos 2 ϕ$ asymmetry recently measured by the COMPASS and HERMES collaborations in unpolarized semi-inclusive deep inelastic scattering. In the kinematical regimes explored by these experiments the asymmetry arises from transverse-spin and intrinsic transverse-momentum effects. We consider the leading-twist contribution, related to the so-called Boer-Mulders transverse-polarization distribution $h_1^{\perp}(x, k_T^2)$, and the twist-4 Cahn contribution, involving unpolarized transverse-momentum distribution functions. We show that a reasonably good…
The energy loss parameter $\hat q$ is one of the fundamental transport parameters of hadronic matter. Using the twist-4 collinear approach, we show that the $\cos ϕ$ azimuthal asymmetry in unpolarized semi-inclusive deeply inelastic scattering (SIDIS) off a large nucleus at intermediate transverse momentum is a sensitive observable for its determination. The effect is due to the suppression of the azimuthal asymmetry by final-state multiple scattering.
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 and semi-inclusive deep inelastic scattering of pions.
In 2016 and 2017 COMPASS has collected a considerable amount of deep inelastic scattering events with a 160 GeV/c muon beam and a liquid hydrogen target. An analysis of 4 % of these data has allowed to extract preliminary results on the amplitudes of three azimuthal modulations, $A_{UU}^{\cosϕ_h}$, $A_{UU}^{\cos2ϕ_h}$ and $A_{LU}^{\sinϕ_h}$. The first two are particularly important since they carry information on the intrinsic transverse momentum $\vec{k}_T$ of the quarks and on the correlations between the quark spin and $\vec{k}_T$, expressed by the Boer-Mulders TMD PDFs. They show strong ki…
We consider a rescattering mechanism to calculate a leading twist $T$-odd pion fragmentation function, a candidate for filtering the transversity properties of the nucleon. We evaluate the single spin azimuthal asymmetry for a transversely polarized target in semi-inclusive deep inelastic scattering (for HERMES kinematics) and the double $T$-odd $\cos2ϕ$ asymmetry in this framework.
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 Q^2 dependence of the azimuthal asymmetry in inclusive reactions. Some of the present data - the cos2ϕsymmetry in unpolarized Drell-Yan, the sin2ϕsingle spin asymmetry in semi-inclusive deep inelastic scattering (SIDIS) and…
We calculate the differential cross section for the unpolarized semi-inclusive deeply inelastic scattering (SIDIS) process $e^-+N \to e^-+q+X$ in leading order (LO) of perturbative QCD and up to twist-4 in power corrections and study in particular the azimuthal asymmetry $<cos2ϕ>$. The final results are expressed in terms of transverse momentum dependent (TMD) parton matrix elements of the target nucleon up to twist-4. %Under the maximal two-gluon correlation approximation, these TMD parton matrix elements in a nucleus %can be expressed terms of a Gaussian convolution of that in a nucleon with…
We analyse the role of partonic transverse motion in unpolarized Semi-Inclusive Deep Inelastic Scattering (SIDIS) processes. Imposing appropriate kinematical conditions, we find some constraints which fix an upper limit to the range of allowed k_perp values. We show that, applying these additional requirements on the partonic kinematics, we obtain different results with respect to the usual phenomenological approach based on the Gaussian smearing with analytical integration over an unlimited range of k_perp values. These variations are particularly interesting for some observables, like the < …
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 …
We revisit the effects of QCD instantons in semi-inclusive deep inelastic scattering (SIDIS). We show that large single spin asymmetry (SSA) effects can be induced in longitudinally and transversely polarized proton targets. The results are in agreement with most of the reported data for pion and kaon production. The same effects are found to be important in polarized proton on proton scattering for both charged and chargeless pion productions. The results agree with the reported data in a wide range of \sqrt{s} = 19.4-200 GeV. We predict the SSA for π^\pm production in p_\uparrow p in the col…
Polarized Semi-Inclusive Deep-Inelastic Scattering at $\mathcal O(α_s^3)$ in QCD
Shanghai Jiao Tong University（上海交通大学）；Fudan University（复旦大学）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；Shandong University（山东大学）
The naive time reversal odd (``T-odd'') parton distribution $h_{1}^{\perp}$, 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 DIS for both flavors $u$ and $d$ are the same and negative, a previous calculation in the diquark-spectator model found that $h_{1}^{\perp(u)}$ and $h_{1}^{\perp(d)}$ have different signs. The flavor dependence is of significance for the analysis of the azimuthal $\cos(2ϕ…
Hadron leptoproduction in Semi-Inclusive measurements of Deep-Inelastic Scattering (SIDIS) on unpolarised nucleons allows one to get information on the intrinsic transverse momentum of quarks in a nucleon and on the Boer-Mulders function through the measurement of azimuthal modulations in the cross section. These modulations were recently measured by the HERMES experiment at DESY on proton and deuteron targets, and by the COMPASS experiment using the CERN SPS muon beam and a $^6$LiD target. In both cases, the amplitudes of the $\cosϕ_h$ and $\cos 2ϕ_h$ modulations show strong kinematic depende…
We consider the transverse momentum spectrum and the $\cos 2ϕ$ azimuthal distribution of $J/ψ$ mesons produced in semi-inclusive, deep-inelastic electron-proton scattering, where the electron and the proton are unpolarized. At low transverse momentum, we propose factorized expressions in terms of transverse momentum dependent gluon distributions and shape functions. We show that our formulae, at the order $α_s,$ correctly match with the collinear factorization results at high transverse momentum. The latter are computed at the order $α_s^2$ in the framework of nonrelativistic QCD (NRQCD), with…
We consider the double-spin cos(phi) asymmetry for pion electroproduction in semi-inclusive deep inelastic scattering of longitudinally polarized leptons off longitudinally polarized protons. We estimate the size of the asymmetry in the approximation where all twist-3 interaction-dependent distribution and fragmentation functions are set to zero. In that approximation at HERMES kinematics a sizable negative cos(phi) double-spin asymmetry for pi+ electroproduction is predicted.
Within the framework of a generalized factorization, semi-inclusive deeply inelastic scattering (SIDIS) cross sections can be expressed as a series of products of collinear hard parts and transverse-momentum-dependent (TMD) parton distributions and correlations. The azimuthal asymmetry <cosϕ>$ of unpolarized SIDIS in the small transverse momentum region will depend on both twist-2 and 3 TMD quark distributions in target nucleons or nuclei. Nuclear broadening of these twist-2 and 3 quark distributions due to final-state multiple scattering in nuclei is investigated and the nuclear dependence of…
Within the LO QCD parton model of Semi Inclusive Deep Inelastic Scattering, $\ell N \to \ell h X$, with unintegrated quark distribution and fragmentation functions, we study the $\bfP_{hT}$ dependence of the double longitudinal-spin asymmetry $A_{LL}$. We include 1/Q kinematic corrections, which induce an azimuthal modulation of the asymmetry, analogous to the Cahn effect in unpolarized SIDIS. We show that a study of $A_{LL}$ and of the weighted DSA $A_{LL}^{\cosϕ_h}$ allows to extract the transverse momentum dependence of the unintegrated helicity distribution function $g_{1L}^q(x,k_\perp)$ […
In the spectator models of the nucleon with scalar and axial-vector diquarks, we show that the effect of Pauli coupling in photon-quark vertex to the parton distribution functions (PDFs) of nucleon and azimuthal asymmetry in the unpolarized semi-inclusive deep inelastic scattering (SIDIS). This anomalous coupling gives obvious contribution to unpolarized and polarized PDFs, and also leads to a $\cos 2ϕ_h$ azimuthal asymmetry proportional to the squared Pauli form factor, due to the helicity flip of the struck quark. After determining the model parameters by fitting PDFs to the global fits, thi…
Single hadron azimuthal asymmetries of positive and negative hadrons produced in muon semi-inclusive deep inelastic scattering off longitudinally polarised deuterons are determined using the 2006 COMPASS data and also combined all deuteron COMPASS data. For each hadron charge, the dependence of the azimuthal asymmetry on the hadron azimuthal angle $ϕ$ is obtained by means of a five-parameter fitting function that besides a $ϕ$-independent term includes four modulations predicted by theory: $\sinϕ$, $\sin 2 ϕ$, $\sin 3ϕ$ and $\cosϕ$. The amplitudes of the five terms have been extracted, first, …
Search for azimuthal asymmetries in semi-inclusive production of charged hadrons by 160 GeV muons on the longitudinally polarized deuterium target, has been performed using the 2002- 2004 COMPASS data. The observed asymmetries integrated over the kinematical variables do not depend on the azimuthal angle of produced hadrons and are consistent with the ratio $g_1^d(x)/f_1^d(x)$. The asymmetries are parameterized taking into account possible contributions from different parton distribution functions and parton fragmentation functions depending on the transverse spin of quarks.They can be modulat…
We show that initial-state interactions contribute to the $\cos 2 ϕ$ distribution in unpolarized Drell-Yan lepton pair production $p p$ and $ p \bar p \to \ell^+ \ell^- X$, without suppression. The asymmetry is expressed as a product of chiral-odd distributions $h_1^\perp(x_1,\bm{p}_\perp^2)\times \bar h_1^\perp(x_2,\bm{k}_\perp^2) $, where the quark-transversity function $h_1^\perp(x,\bm{p}_\perp^2)$ is the transverse momentum dependent, light-cone momentum distribution of transversely polarized quarks in an {\it unpolarized} proton. We compute this (naive) $T$-odd and chiral-odd distribution…
