We study the $\cos 2 ϕ$ azimuthal asymmetry in unpolarized semi-inclusive DIS, taking into account both the perturbative contribution (gluon emission and splitting) and the non perturbative effects arising from intrinsic transverse motion and transverse spin of quarks. In particular we explore the possibility to extract from $<\cos 2 ϕ>$ some information about the Boer--Mulders function $h_1^{\perp}$, which represents a transverse--polarization asymmetry of quarks inside an unpolarized hadron. Predictions are presented for the HERMES, COMPASS and JLab kinematics, where $<\cos 2 ϕ>$ is dominated by the kinematical higher--twist contribution, and turns to be of order of few percent. We show that a larger asymmetry in $π^-$ production, compared to $π^+$ production, would represent a signature of the Boer--Mulders effect.
We present a recent calculation of the transverse momentum dependent gluon distributions inside unpolarised protons and show how the ratio of the linearly polarized and the unpolarized gluon distribution in the proton can be probed by looking at $Cos(2ϕ_h)$ asymmetry in $J/ψ$ production in unpolarized $ep$ collision. We use NRQCD for estimating $J/ψ$ production and include contributions both from color singlet and color octet states.
We calculate the $\cos2ϕ$ azimuthal asymmetry of the unpolarized $p\bar{p}$ Drell-Yan dilepton production process in the $Z$-resonance region at the Tevatron kinematic domain. Such an azimuthal asymmetry can provide additional information about a spin-related new parton distribution function, i.e., the Boer-Mulders function of the proton, compared to the $pp$ process. Therefore the available data of unpolarized proton-antiproton collision at Tevatron can contribute to our study on the spin structure of the nucleon.
We calculate the Sivers and $\cos2ϕ$ azimuthal asymmetries in $J/ψ$ production in polarized and unpolarized semi-inclusive $ep$ collision respectively, using the formalism based on transverse momentum dependent parton distributions (TMDs). Non-relativistic QCD based color octet model is employed for calculating the $J/ψ$ production rate. The Sivers asymmetry in this process directly probes the gluon Sivers function. The estimated Sivers asymmetry at $z=1$ is negative which is in good agreement with COMPASS data. We also investigate the effect of TMD evolution on the Sivers asymmetry. The $\cos…
We calculate the Boer-Mulders effect contribution to the $\cos2ϕ$ azimuthal asymmetry of unpolarized dilepton production near the $Z$-pole. Based on the tree-level expression in the transverse momentum dependent factorization framework, we show that the corresponding asymmetry near the $Z$-pole is negative, which is opposite to the asymmetry in the low $Q^2$ region, dominated by the production via a virtual photon. We calculate the asymmetry generated by the Boer-Mulders effect near the $Z$-pole at RHIC, with $\sqrt{s}=500$ GeV. We find that the magnitude of the asymmetry is several percent, a…
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…
We study the azimuthal $\cos φ$ and $\cos 2φ$ asymmetries in heavy-quark pair leptoproduction, $lN\rightarrow l^{\prime}Q\bar{Q}X$, as probes of linearly polarized gluons inside unpolarized proton, where the azimuth $φ$ is the angle between the lepton scattering plane $(l,l^{\prime})$ and the heavy quark production plane $(N,Q)$. First, we determine the maximal values for the $\cos φ$ and $\cos 2φ$ asymmetries allowed by the photon-gluon fusion with unpolarized gluons; these predictions are large, $(\sqrt{3}-1)/2$ and $1/3$, respectively. Then we calculate the contribution of the transverse-mo…
We extract the Boer-Mulders functions for the proton by combining the unpolarized pd and pp Drell-Yan data measured by the E866/NuSea Collaboration by the assumption that the $\cos 2ϕ$ asymmetry is from the Boer-Mulders function. Using the extracted Boer-Mulders functions, we present the predictions for the $\cos 2 ϕ$ asymmetries in future pp experiments at J-PARC and $p \bar{p}$ experiments at PANDA and PAX.
We present a calculation of the $cos (2 ϕ_h)$ asymmetry in $J/ψ$ production in electron-proton collision at the future electron-ion collider (EIC), a useful channel to probe the gluon TMDs. We calculate the asymmetry at next-to-leading order (NLO) in $α_s$ in the framework of generalized factorization. The dominating sub-process is $γ^* +g \rightarrow J/ψ+g$. The production of $J/ψ$ is calculated in the non-relativistic QCD(NRQCD) framework with the inclusion of both color singlet and color octet contributions. Numerical estimates of the $cos(2ϕ_h)$ asymmetry are given in the kinematical regio…
In recent papers [1,2], two new ways have been proposed to probe the linear polarization of gluons in unpolarized proton: using the azimuthal asymmetries and Callan-Gross ratio in heavy-quark pair leptoproduction, $lN\rightarrow l^{\prime}Q\bar{Q}X$. In this talk, we discuss in details the sensitivity of the QCD predictions for the azimuthal $\cos φ$ and $\cos 2φ$ asymmetries to the contribution of linearly polarized gluons inside unpolarized proton, where the azimuth $φ$ is the angle between the lepton scattering plane $(l,l^{\prime})$ and the heavy quark production plane $(N,Q)$. Our analysi…
Semi-inclusive $J/ψ$ production in electron-proton collisions is a promising process to study gluon transverse momentum distributions (TMDs) at the future Electron-Ion Collider. In this article, we improve on previous studies of the $\cos 2 ϕ$ azimuthal asymmetry that arises from the linear polarization of gluons inside unpolarized protons by including TMD evolution. We find that in the TMD regime the asymmetry grows monotonically with increasing transverse momentum of the outgoing $J/ψ$, in contrast to tree level calculations with Gaussian TMDs. Our predictions for the asymmetry at EIC can be…
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 kt values and lead to interesting results, particularly for some observables like the <cos phi_h> azimuthal modulation of the unpolarized SIDIS cross section and the average transverse momentum of the final, detected hadron.
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…
We calculate the two leading-twist transverse momentum dependent distribution functions of the pion meson, the unpolarized distribution $f_{1π}(x,\bm{k}^2_T)$ and the Boer-Mulders function $h_{1π}^\perp (x,\bm{k}^2_T)$, using the pion wave functions derived from a light-cone approach. The evolution effect of the first $\bm k_T$-moment of the pion Boer-Mulders function is studied by employing an approximate evolution kernel. Using the model resulting distributions, we predict the transverse momentum weighted $\cos2ϕ$ azimuthal asymmetry in the unpolarized $π^- p$ Drell-Yan process which can be …
We consider the azimuthal $\cos φ$ and $\cos 2φ$ distributions and the Callan-Gross ratio $R={\rm d}σ_L/{\rm d}σ_T$ in heavy-quark pair electroproduction, $lN\rightarrow l^{\prime}Q\bar{Q}X$, as probes of linearly polarized gluons in unpolarized nucleons. Our analysis shows that the azimuthal asymmetries and Callan-Gross ratio are predicted to be large and very sensitive to the contribution of the gluonic counterpart of the Boer-Mulders function, $h_{1}^{\perp g}$, describing the linear polarization of gluons inside unpolarized nucleon. In particular, the maximum values of the azimuthal distri…
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 a previous extraction of the quark Boer-Mulders distributions from semiinclusive deep inelastic scattering data, we fit the unpolarized Drell-Yan data on the $\cos 2 ϕ$ asymmetry, determining the antiquark Boer-Mulders distributions. A good agreement with the data is found in the region of low $q_T$, where the transverse-momentum factorization approach applies.
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 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 < …
Fixed-target unpolarized Drell-Yan experiments often feature an acceptance depending on the polar angle of the lepton tracks in the laboratory frame. Typically leptons are detected in a defined angular range, with a dead zone in the forward region. If the cutoffs imposed by the angular acceptance are independent of the azimuth, at first sight they do not appear dangerous for a measurement of the cos(2ϕ)-asymmetry, relevant because of its association with the violation of the Lam-Tung rule and with the Boer-Mulders function. On the contrary, direct simulations show that up to 10 percent asymmet…
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…
In this paper, we study the azimuthal asymmetry in the $J/ψ$ leptoproduction in unpolarized $ep$ collisions. There are two independent azimuthal asymmetry modulations, namely $\mathrm{cos}(ψ)$ and $\mathrm{cos}(2ψ)$, where $ψ$ is the azimuthal angle of the lepton scattering plane with respect to the hadron-interacting plane. We calculate the two modulations as functions of four kinematic variables, and find that they provide a very good laboratory to distinguish several models describing the heavy quarkonium production, including the color-singlet (CS) model, the nonrelativistic QCD (NRQCD) as…
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 investigate the theoretical framework of the $\cos 2ϕ$ azimuthal asymmetry contributed by the coupling of two Boer-Mulders functions in the dilepton production unpolarized $πp$ Drell-Yan process by applying the transverse momentum dependent factorization at leading order. We adopt the model calculation results of the unpolarized distribution function $f_1$ and Boer-Mulders function $h_1^\perp$ of pion meson from the light-cone wave functions. We take into account the transverse momentum evolution effects for both the distribution functions of pion and proton by adopting the existed extracti…
We perform a new extraction for unpolarized and polarized parton distribution functions considering a flavor decompositions for sea quarks and applying very recent deep inelastic scattering (DIS) and semi inclusive deep inelastic scattering (SIDIS) data in the fixed flavor number scheme (FFNS) framework. In the new symmetry breaking scenario the light quark and antiquark densities are extracted separately and new parametrization forms are determined for them. The heavy flavors contribution, including charm and bottom quarks, are also taken to be account for unpolarized distributions.
We present the study of accessing unpolarized and linearly polarized gluon TMDs in J/ψ and Υ(1S) production in unpolarized proton-proton collision at LHC, RHIC and AFTER energies. Non- relativistic QCD based color octet model (COM) is used for estimating quarkonium production rates within transverse momentum dependent factorization formalism. A comparison is drawn between the experimental data and the transverse momentum distribution of quarkonium obtained in COM and color evaporation model.
Recent data from semi-inclusive deep inelastic scattering collected by the HERMES collaboration allow for the first time to discuss how the transverse-momentum dependence of unpolarized distribution and fragmentation functions is affected by the flavor of the involved partons. A model built with flavor-dependent Gaussian transverse-momentum distributions fits data better than the same flavor-independent model. The current analysis is performed for totally unpolarized scattering of leptons off protons and deuterons, with detected pions in the final state. There are convincing indications of fla…
We present a detailed study of vector meson photoproduction in ultraperipheral heavy ion collisions (UPCs). Using the dipole model, we develop a framework for the joint impact parameter and transverse momentum dependent cross sections. We compute the unpolarized cross section and $\cos 2ϕ$ azimuthal angular correlation for $ρ^0$ photoproduction with $ϕ$ defined as the angle between the $ρ^0$'s transverse momentum and its decay product pion meson's transverse momentum. Our result on unpolarized coherent differential cross section gives excellent description to the STAR experimental data. A firs…
We present the extraction of unpolarized quark transverse momentum dependent parton distribution functions (TMDPDFs) and the non-perturbative part of TMD evolution kernel from the global analysis of Drell-Yan and $Z$-boson production data. The analysis is performed at the next-to-next-to-leading order (NNLO) in perturbative QCD, using the $ζ$-prescription. The estimation of the error-propagation from the experimental uncertainties to non-perturbative function is made by the replica method. The importance of the inclusion of the precise LHC data and its influence on the determination of non-per…
Transverse momentum dependent distribution and fragmentation functions of unpolarized quarks inside unpolarized protons are extracted, for the first time, through a simultaneous analysis of semi-inclusive deep-inelastic scattering, Drell-Yan and $Z$ boson hadroproduction processes. This study is performed at leading order in perturbative QCD, with energy scale evolution at the next-to-leading logarithmic accuracy. Moreover, some specific choices are made to deal with low scale evolution around 1 GeV$^2$. Since only data in the low transverse momentum region are considered, no matching to fixed…
We discuss the dependence on the flavor of the intrinsic transverse momentum in unpolarized transverse-momentum-dependent distribution functions (TMD PDFs) and fragmentation functions (TMD FFs) analyzing data of semi-inclusive deep-inelastic scattering (SIDIS) released by the HERMES collaboration. Adopting a flavor-dependent Gaussian model in the transverse momentum and neglecting QCD evolution, we find interesting evidences concerning the flavor dependence in TMD FFs, whereas the indications are weaker in TMD PDFs and deserve further investigations. Inclusions of new data sets of SIDIS, elect…
We study $ρ$ meson unpolarized generalized parton distributions based on a light-front constituent quark model where the quark-antiquark-meson vertex is constructed under the symmetric loop momentum convention. The form factors and some other low-energy observables of the $ρ$ meson are calculated. Moreover, the contributions to the form factors and generalized parton distributions from the valence and nonvalence regimes are discussed and analyzed in detail. In the forward limit, the usual structure functions are estimated as well. In addition, by evolving the moments of the obtained structure …
We investigate the heavy quark mass effects on the parton distribution functions in the unpolarized virtual photon up to the next-to-leading order in QCD. Our formalism is based on the QCD-improved parton model described by the DGLAP evolution equation as well as on the operator product expansion supplemented by the mass-independent renormalization group method. We evaluate the various components of the parton distributions inside the virtual photon with the massive quark effects, which are included through the initial condition for the heavy quark distributions, or equivalently from the matri…
