The Drell-Yan hadronic tensor for electromagnetic (EM) current is calculated in the Sudakov region $s\gg Q^2\gg q_\perp^2$ with ${1\over Q^2}$ accuracy, first at the tree level and then with the double-log accuracy. It is demonstrated that in the leading order in $N_c$ the higher-twist quark-quark-gluon TMDs reduce to leading-twist TMDs due to QCD equation of motion. The resulting tensor for unpolarized hadrons is EM gauge-invariant and depends on two leading-twist TMDs: $f_1$ responsible for total DY cross section, and Boer-Mulders function $h_1^\perp$. The order-of-magnitude estimates of angular distributions for DY process seem to agree with LHC results at corresponding kinematics.
We extract the pion transverse momentum dependent (TMD) parton distribution by fitting the pion-induced Drell-Yan process within the framework of TMD factorization. The analysis is done at the next-to-next-to-leading order (NNLO) with proton TMD distribution and non-perturbative TMD evolution extracted earlier in the global fit. We observe the significant difference in the normalization of transverse momentum differential cross-section measured by E615 experiment and the theory prediction.
Calculations of Drell-Yan (DY) production at next-to-leading (NLO) order have been combined with Transverse Momentum Dependent (TMD) distributions obtained with the Parton Branching (PB). The predictions show a remarkable agreement with DY measurement from E605 experiment, consistent with previous results we obtained for R209, PHENIX, CMS and ATLAS experiments. We also present predictions for Z+jet measurements showing the importance of TMD parton shower contributions to the jet multiplicity. We show that PB-TMD parton density and the corresponding PB-TMD parton shower can be combined with lea…
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 consider the transverse momentum dependent (TMD) quark densities of the proton which are very important ingredients for unpolarized Drell-Yan (DY) lepton pair production. We calculate the TMD sea quark density as a convolution of the Catani-Ciafaloni-Fiorani-Marchesini (CCFM)-evolved gluon distribution and the TMD gluon-to-quark splitting function. Based on the ${\cal O}(α^2)$ production amplitude $q^* + \bar q^* \to Z/γ^* \to l^+ + l^-$, calculated by taking into account the effective $q^*\bar q^* Z/γ^*$ - vertex, we analyze the distributions on the dilepton invariant mass, transverse mome…
We use the TMD quark densities of the proton to investigate unpolarized Drell-Yan lepton pair production in proton-proton collisions at the LHC energies. We investigate the case where the gluon-to-quark splitting occurs at the last evolution step and calculate the TMD sea quark density as a convolution of the CCFM-evolved gluon distribution and the TMD gluon-to-quark splitting function which contains all single logarithmic small-x corrections to the sea quark evolution for any order of perturbation theory. Based on the O(alpha) production amplitude of quark-antiquark annihilation calculated ac…
We present new results of our studies of soft-gluon angular ordering effects on the evolution of both collinear and transverse momentum dependent (TMD) parton distribution functions, and discuss their implications for precision predictions of Drell-Yan transverse momentum spectra at the LHC. Our method is based on the parton branching (PB) approach. We compare this with the implementation of angular ordering in the Kimber-Martin-Ryskin-Watt (KMRW) approach and with the Collins-Soper-Sterman (CSS) approach. We illustrate numerically the effects of different ordering scenarios ($p_{\bot}$, angul…
We map the distribution of unpolarized quarks inside a unpolarized pion as a function of the quark's transverse momentum, encoded in unpolarized Transverse Momentum Distributions (TMDs). We extract the pion TMDs from available data of unpolarized pion-nucleus Drell-Yan processes, where the cross section is differential in the lepton-pair transverse momentum. In the cross section, pion TMDs are convoluted with nucleon TMDs that we consistently take from our previous studies. We obtain a fairly good agreement with data. We present also predictions for pion-nucleus scattering that is being measur…
We consider semi-inclusive deep inelastic scattering (SIDIS) and Drell-Yan events within transverse momentum dependent (TMD) factorization. Based on the simultaneous fit of multiple data points, we extract the unpolarized TMD distributions and the non-perturbative evolution kernel. The high quality of the fit confirms a complete universality of TMD non-perturbative distributions. The extraction is supplemented by phenomenological analyses of various parts of the TMD factorization, such as sensitivity to non-perturbative parameterizations, perturbative orders, collinear distributions, correlati…
The Drell-Yan process is studied in the framework of TMD factorization in the Sudakov region $s\gg Q^2\gg q_\perp^2$ corresponding to recent LHC experiments with $Q^2$ of order of mass of Z-boson and transverse momentum of DY pair $\sim$ few tens GeV. The DY hadronic tensors are expressed in terms of quark and quark-gluon TMDs with ${1\over Q^2}$ and ${1\over N_c^2}$ accuracy. It is demonstrated that in the leading order in $N_c$ the higher-twist quark-quark-gluon TMDs reduce to leading-twist TMDs due to QCD equation of motion. The resulting hadronic tensors depend on two leading-twist TMDs: $…
We present an extraction of unpolarized partonic transverse momentum distributions (TMDs) from a simultaneous fit of available data measured in semi-inclusive deep-inelastic scattering, Drell-Yan and Z-boson production. To connect data at different scales, we use TMD evolution at next-to-leading logarithmic accuracy. The analysis is restricted to the low-transverse-momentum region, with no matching to fixed-order calculations at high transverse momentum. We introduce specific choices to deal with TMD evolution at low scales, of the order of 1 GeV$^2$. This could be considered as a first attemp…
We discuss our recent study of the impact of collinear PDFs and their uncertainties on the determination of transverse momentum dependent (TMD) distributions and the description of Drell-Yan (DY) production measurements at low transverse momenta. Using QCD factorization and evolution in transverse coordinate b space, this study takes into account for the first time flavor-dependent non-perturbative b-profiles. It illustrates that collinear PDF uncertainties and non-perturbative TMD flavor dependence are both essential to obtain reliable TMD determinations.
This article presents the review of the current understanding on the pion-nucleon Drell-Yan process from the point of view of the TMD factorization. Using the evolution formalism for the unpolarized and polarized TMD distributions developed recently, we provide the theoretical expression of the relevant physical observables, namely, the unpolarized cross section, the Sivers asymmetry, and the $\cos2ϕ$ asymmetry contributed by the double Boer-Mulders effects. The corresponding phenomenology, particularly at the kinematical configuration of the COMPASS $πN$ Drell-Yan facility, is displayed numer…
The theoretical description of Drell-Yan (DY) transverse momentum spectra over wide kinematic regions in energy, mass and transverse momentum requires not only fixed-order perturbative QCD calculations but also soft-gluon QCD resummations to all orders of perturbation theory. The latter are traditionally accomplished either by Parton Showers (PS) with Monte Carlo event generators or by (different versions of) analytical procedures. In this work we focus on issues involved in the matching of the fixed-order calculation and resummation, especially in the moderate to low mass and $p_{\bot}$ regio…
We examine the QCD evolution for the transverse momentum dependent observables in hard processes of semi-inclusive hadron production in deep inelastic scattering and Drell-Yan lepton pair production in $pp$ collisions, including the spin-average cross sections and Sivers single transverse spin asymmetries. We show that the evolution equations derived by a direct integral of the Collins-Soper-Sterman evolution kernel from low to high Q can describe well the transverse momentum distribution of the unpolarized cross sections in the Q^2 range from 2 to 100 GeV^2. In addition, the matching is estab…
The description of the Drell-Yan (DY) transverse momentum spectrum requires matching of fixed order QCD calculations with soft gluon resummation up to all orders in the QCD coupling. It has been noticed in the literature that a consistent description of DY data in a wide kinematic regime from fixed-target to LHC energies is problematic. In this talk the predictions for transverse momentum spectrum of DY data coming from experiments in very different kinematic ranges (NuSea, R209, Phenix, LHC 8 TeV and 13 TeV center-of-mass energies $\sqrt{s}$) are calculated by applying transverse momentum dep…
Generalized transverse momentum dependent parton distributions (GTMDs) are the most general parton correlation functions of hadrons. By considering the exclusive double Drell-Yan process it is shown for the first time how quark GTMDs can be measured. Specific GTMDs can be addressed by means of polarization observables.
We study the transverse momentum spectrum of dilepton produced in the unpolarized $π^- N$ Drell-Yan process, using transverse momentum dependent factorization up to next-to-logarithmic order of QCD. We extract the nonperturbative Sudakov form factor for the pion in the evolution formalism of the unpolarized TMD distribution function, by fitting the experimental data collected by the E615 Collaboration at Fermilab. With the extracted Sudakov factor, we calculate the normalized differential cross section with respect to transverse momentum of the dimuon and compare it with the recent measurement…
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…
We analyse polarised Drell-Yan process using the factorisation method and derive operator definitions for polarised parton distribution functions. We demonstrate that a factorisation analogous to that in the unpolarised Drell-Yan case holds in this process. We study the leading order gluonic contribution to the first moment of polarised Drell-Yan function and show that it is consistent with results obtained from polarised deep inelastic scattering.
Several properties of high energy hadronic collisions are illustrated by comparing DIS and the Drell-Yan process within a scalar QED model. Diffraction and transverse momentum broadening within the target system are found to be non-universal. Here these effects are simply due to the Coulomb phase shift in the Drell-Yan production amplitude.
We calculate the one-loop QCD correction for inclusive jet cross section and Drell-Yan process in a general low-energy effective Lagrangian for composite quarks and leptons.
We study angular distributions of Drell-Yan leptons in the proton-proton collisions invoking the hypothesis of quark Reggeization in t-channel exchanges at high energy.
The longitudinally polarized Drell-Yan process is one of most powerful tools to probe the structure of hadrons. By means of the recent formalism of the polarized proton-deuteron(pd) Drell-Yan, we calculate the ratio of the proton-deuteron Drell-Yan cross section to the proton-proton(pp) one $Δσ_{pd}/2Δσ_{pp}$in the polarized case.The theoretical results can be compared with future experimental data to confirm the nuclear effect due to the six-quark cluster in deuteron .
Dimensional continuation is applied to resummed expressions for the DIS and Drell-Yan partonic cross sections, to regularize the Landau pole. Simple analytic expression are obtained, encoding information about nonperturbative power--suppressed effects.
We briefly discuss the collinear factorization formula for the associated production of one particle and a Drell-Yan pair in hadronic collisions. We outline possible applications of the results to three different research areas.
Next-to-leading order electroweak and QCD radiative corrections to the Drell-Yan process with high dimuon masses for experiments CMS LHC at CERN have been studied in fully differential form. The FORTRAN code READY for numerical analysis of Drell-Yan observables has been presented. The radiative corrections are found to become significant for CMS LHC experiment setup.
We extract the Boer-Mulders functions of valence and sea quarks in the proton from unpolarized $p+D$ Drell-Yan data measured by the FNAL E866 Collaboration. Using these Boer-Mulders functions, we calculate the $\cos 2 ϕ$ asymmetries in unpolarized $pp$ Drell-Yan processes, both for the FNAL E866/NuSea and the BNL Relativistic Heavy Ion Collider (RHIC) experiments. We also estimate the $\cos 2 ϕ$ asymmetries in the unpolarized $p\bar{p}$ Drell-Yan processes at GSI.
In this work we directly fit the QCD dimensional transmutation parameter, ${Λ_{\overline {MS} }}$, to experimental data of Drell-Yan (DY) observables. For this purpose we first obtain the evolution of transverse momentum dependent parton distribution functions (TMDPDFs) up to the NNLO approximation based on Collins-Sopper-Sterman formalism. As is expecting the TMDPDFs are appearing at larger values of transvers momentum by increasing the energy scales and also the order of approximation. Then we calculate the cross section related to the TMDPDFs in the DY process. As a consequence of fitting t…
Production of a forward Drell-Yan lepton pair accompanied by a jet separated by a large rapidity interval is proposed to study the BFKL evolution at the LHC. Several observables to be measured are presented including the azimuthal angle dependence of the lepton pair which allows to determine Drell-Yan structure functions.
We present the analytic computation of leading high-energy logarithms of the inclusive Drell-Yan and vector boson production cross-section. We also study the phenomenological relevance of the high-energy corrections for Drell-Yan processes at the LHC. We find that the resummation corrects the NNLO result by no more than a few percent, for values of the invariant mass of the lepton pair below 100 GeV.
The transverse-momentum ($Q_T$) distribution of low-mass Drell-Yan pairs is calculated in QCD perturbation theory with all-order resummation of $α_s (α_s \ln(Q^2_T/Q^2))^n$ type terms. We demonstrate that the rapidity distribution of low-mass Drell-Yan pairs at large-enough transverse momentum is an advantageous source of constraints on the gluon distribution and its nuclear dependence. We argue that low-mass Drell-Yan pairs in the forward region provide a good and clean probe of small-$x$ gluons at collider energies.
The transverse momentum distribution of low-mass Drell-Yan pairs is calculated in QCD perturbation theory with all-order resummation. We argue that at LHC energies the results should be reliable for the entire transverse momentum range. We demonstrate that the transverse momentum distribution of low-mass Drell-Yan pairs is an advantageous source of constraints on the gluon distribution and its nuclear dependence.
Forward Drell-Yan process at the LHC probes the proton structure at very small Bjorken-$x$ and moderate hard scales. In this kinematical domain higher twist effects may be significant and introduce sizeable corrections to the standard leading twist description. We study the forward Drell-Yan process beyond the leading twist approximation within the color dipole model framework that incorporates multiple scattering effects. We derive the Mellin representation of the forward Drell-Yan impact factors for fully differential cross-sections. These results combined with the color dipole cross-section…
The Helicity Structure Functions in the Drell-Yan process are discussed in a framework of Parton Reggeization Approach, which includes the transverse momentum of initial-state partons in a way compatible with QED gauge-invariance. Relationships with conventional Transverse Momentum Dependent Parton Model formalism are clarified.
The unitarity corrections effects encoded in the Glauber-Mueller approach are taken into account to calculate the differential cross sections in the Drell-Yan process in the rest frame. A detailed study of the Drell-Yan process in terms of the $γ^{*}q$ transverse separation and the color dipole size, as well as the effective dipole cross section is performed and compared with the available small $x$ data. Estimates for the Drell-Yan cross section at RHIC energies are presented and discussed.
We present prospects and requirements for the study at HERA of hard photon processes which generate high $p_T$ photons in the final state, and processes which generate Drell-Yan lepton pairs.
We study the power corrections to the cross-section of Drell-Yan production within the Wilson line approach and apply the methods of QCD asymptotic dynamics to identify the leading renormalon contribution.
On the basis of a fit to the Sivers effect in deep-inelastic scattering, we make predictions for single-spin asymmetries in the Drell-Yan process at RHIC.
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.
We set tight constraints on the energy loss of hard quarks in nuclear matter from NA3 Drell-Yan measurements. Our estimate then allows for the description of HERMES preliminary deep inelastic scattering data on hadron production.
We calculate the transverse momentum distribution of low-mass Drell-Yan pairs in QCD perturbation theory with all-order resummation. We demonstrate that the transverse momentum distribution of low-mass Drell-Yan pairs is an advantageous source of constraints on the gluon distribution and its nuclear dependence. With the reduction in background, we argue that low-mass Drell-Yan pairs in the forward region provide a good and clean probe of small-x gluons at RHIC and LHC.
We present a simple approach to combine NNLO QCD calculations and parton showers, based on the UNLOPS technique. We apply the method to the computation of Drell-Yan lepton-pair production at the Large Hadron Collider. We comment on possible improvements and intrinsic uncertainties.
We briefly discuss the collinear factorization formula for the associated production of one particle and a Drell-Yan pair in hadronic collisions. We outline possible applications of the results to three different research areas.
We review the current status and future prospect for probing the transverse momentum dependent (TMD) parton distributions using the Drell-Yan process. We focus on the Boer-Mulders and Sivers functions, which are expected to undergo a sign-change from semi-inclusive deep-inelastic scattering (SIDIS) to Drell-Yan process. The constraints of existing Drell-Yan and SIDIS experiments on the signs of these functions are discussed. Future Drell-Yan measurements for the TMDs are also presented.
Based on a recent work on the quantum chromodynamic (QCD) factorization for semi-inclusive deep-inelastic scattering (DIS), we present a set of factorization formulas for the spin-dependent DIS and Drell-Yan cross sections at low transverse momentum.
We study the renormalization of the Wilson loop with a path corresponding to the Drell-Yan lepton pair production in two-loop approximation of perturbation theory. We establish the renormalization group equation in next-to-leading order and find a process specific anomalous dimension Gamma_DY in the corresponding approximation.
We calculate the gauge invariant Drell-Yan-like hadron tensors. In connection with new COMPASS results, we propose the single spin asymmetry which probes gluon poles together with chiral-odd and time-odd functions. The relevant pion production as a particular case of Drell-Yan-like process has been discussed. For the meson-induced Drell-Yan process, we model an analog of the twist three distribution function, which is a collinear function in inclusive channel, by means of two non-collinear distribution amplitudes which are associated with exclusive channel. This modelling demonstrates the fund…
Recently, a reconsideration of Drell-Yan cross sections at moderate energies and masses has suggested the possibility of relevant enhancements of the cross sections in some kinematical regions. If confirmed, these predictions could largely affect the planning of Drell-Yan experiments aimed at transverse spin measurements after 2010. More in general, the problem is present of a precision measurement of the $τ$ dependence of Drell-Yan cross sections. Here we discuss the feasibility of such a measurement within short time at the COMPASS apparatus, and its relevance for the PANDA experiment.
The results of a recent calculation of the QCD corrections to the polarized Drell-Yan process are summarized. Some implications for the production of vector bosons at RHIC are discussed.
We revisit the transverse single spin asymmetry in the angular distribution of a Drell-Yan dilepton pair. We study this asymmetry by using twist-3 collinear factorization, and we obtain the same result both in covariant gauge and in the light-cone gauge. Moreover, we have checked the electromagnetic gauge invariance of our calculation. Our final expression for the asymmetry differs from all the previous results given in the literature. The overall sign of this asymmetry is as important as the sign of the Sivers asymmetry in Drell-Yan.
Drell Yan production is a sensitive probe of new physics and as such has been calculated to high order in both the electroweak and QCD sectors of the Standard Model, allowing for precision comparisons between theory and data. Here we extend these calculations to the Standard Model Effective field theory (SMEFT) and present the NLO QCD and electroweak contributions to the neutral Drell Yan process that are linear in the Wilson coefficients of the SMEFT theory.
