We study corrections suppressed by one power of the soft gluon energy to the resummation of threshold logarithms for the Drell-Yan cross section and for Deep Inelastic structure functions. While no general factorization theorem is known for these next-to-eikonal (NE) corrections, it is conjectured that at least a subset will exponentiate, along with the logarithms arising at leading power. Here we develop some general tools to study NE logarithms, and we construct an ansatz for threshold resummation that includes various sources of NE corrections, implementing in this context the improved collinear evolution recently proposed by Dokshitzer, Marchesini and Salam (DMS). We compare our ansatz to existing exact results at two and three loops, finding evidence for the exponentiation of leading NE logarithms and confirming the predictivity of DMS evolution.
We discuss power corrections associated with the infrared behavior of the perturbative running coupling in the eikonal approximation to Drell-Yan and other annihilation cross sections in hadron-hadron scattering. General properties of the eikonal approximation imply that only even powers of the energy scale are necessary.
We consider the diffractive Drell-Yan process in proton-(anti)proton collisions at high energies in the color dipole approach. The calculations are performed at forward rapidities of the leptonic pair. Effect of eikonalization of the universal "bare"dipole-target elastic amplitude in the saturation regime takes into account the principal part of the gap survival probability. We present predictions for the total and differential cross sections of the single diffractive lepton pair production at RHIC and LHC energies. We analyze implications of the QCD factorisation breakdown in the diffractive …
An alternative proof of factorization theorem for Drell-Yan process that works at operator level is given in the article. Final state interactions for such inclusive processes are proved to be cancel out at operator level according to the unitarity of time evolution operator. After this cancellation, one can always deform the integral path so that eikonal line approximation works while calculating the time evolution of electromagnetic currants. Decoupling of soft gluons from collinear jets is realized by defining new collinear fields that decouple from soft gluons. Cancelation of soft gluons i…
We consider the problem of soft gluon resummation for gauge theory amplitudes and cross sections, at next-to-eikonal order, using a Feynman diagram approach. At the amplitude level, we prove exponentiation for the set of factorizable contributions, and construct effective Feynman rules which can be used to compute next-to-eikonal emissions directly in the logarithm of the amplitude, finding agreement with earlier results obtained using path-integral methods. For cross sections, we also consider sub-eikonal corrections to the phase space for multiple soft-gluon emissions, which contribute to ne…
We perform a case study of the behavior of gluon radiation beyond the soft approximation, using as an example the Drell-Yan production cross section at NNLO. We draw a careful distinction between the eikonal expansion, which is in powers of the soft gluon energies, and the expansion in powers of the threshold variable $1 - z$, which involves important hard-collinear effects. Focusing on the contribution to the NNLO Drell-Yan K-factor arising from real-virtual interference, we use the method of regions to classify all relevant contributions up to next-to-leading power in the threshold expansion…
In the target rest frame and at high energies, Drell-Yan (DY) dilepton production looks like bremsstrahlung of massive photons, rather than parton annihilation. The projectile quark is decomposed into a series of Fock states. Configurations with fixed transverse separations are interaction eigenstates for pp scattering. The DY cross section can then be expressed in terms of the same color dipole cross section as DIS. This approach is especially suitable to describe nuclear effects, since it allows to apply Glauber multiple scattering theory. We go beyond the Glauber eikonal approximation by ta…
In the target rest frame and at high energies, Drell-Yan (DY) dilepton production looks like bremsstrahlung of massive photons, rather than parton annihilation. The projectile quark is decomposed into a series of Fock states. Configurations with fixed transverse separations in impact parameter space are interaction eigenstates for proton-proton (pp) scattering. The DY cross section can then be expressed in terms of the same color dipole cross section as DIS. We compare calculations in this dipole approach with E772 data and with next-to-leading order parton model calculations. This approach is…
We show that the resummation of large perturbative corrections in QCD leads to ambiguities in high energy cross sections that are suppressed by powers of large momentum scales. These ambiguities are caused by infrared renormalons, which are a general feature of resummed hard-scattering functions in perturbative QCD, even though these functions are infrared safe order-by-order in perturbation theory. As in the case of the operator product expansion, the contributions of infrared renormalons to coefficient functions may be absorbed into the definition of higher-dimensional operators, which induc…
I discuss recent progress in the calculation of two-loop QCD corrections in the eikonal approximation. I present specific results for the UV structure of the corrections.
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 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.
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 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.
We show that eikonal corrections imposed on diffraction dissociation processes calculated in the triple Regge limit, produce a radical change in the energy dependence of the predicted cross section. The induced correction is shown to be in general agreement with the new experimental data measured at the Tevatron.
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.
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.
Soft and Jet functions for SCET at four loops in QCD
The Institute of Mathematical Sciences（马哈拉施特拉数学科学研究所）；Homi Bhabha National Institute（霍米·巴巴国家研究所）；II. Institute for Theoretical Physics, Hamburg University（汉堡大学第二理论物理研究所）
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 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.
Using a subtraction method, we derive the formulae suitable for use in Monte-Carlo event generators to give the angular distribution for the gluon-quark induced NLO corrections in Drell-Yan lepton pair production. We also give the corresponding helicity density matrix for W and Z boson 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 calculate the hadron tensor related to the photon-induced Drell-Yan process, with incoming nucleon being transversally polarised. We predict the new single spin asymmetry which probes gluon poles and which is expressed in terms of photon (both chiral-odd and chiral-even) distribution amplitudes and chiral-odd nucleon function stemming from the nucleon transverse polarization.
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…
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 twist-four quark and gluon distributions in a transversely polarized nucleon are identified and relations among them are discussed by using QCD equations of motion. Their contribution, at the order of ${\cal O} \left( 1/Q^2 \right)$, to the Drell-Yan cross section in transversely polarized nucleon-nucleon collisions is calculated.
In this paper we calculate the O($α_s$) corrections to the $x_F$- and $y$-distributions of lepton pairs produced in collisions of longitudinally polarized hadrons. The numerical importance of these corrections is studied and consequences for the extraction of the polarized sea quark distributions from a measurement of the longitudinally polarized Drell-Yan cross section are discussed.
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.
Two twist-3 processes are discussed. We first present a simple estimate of the longitudinal-transverse spin asymmetry in the polarized Drell-Yan process. We next derive a cross section for the semi-inclusive production of a polarized spin-1/2 baryon in the DIS of an unpolarized electron off the polarized nucleon.
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.
The energy loss effect in nuclear matter is another nuclear effect apart from the nuclear effects on the parton distribution as in deep inelastic scattering process. The quark energy loss can be measured best by the nuclear dependence of the high energy nuclear Drell-Yan process. By means of three kinds of quark energy loss parameterizations given in literature and the nuclear parton distribution extracted only with lepton-nucleus deep inelastic scattering experimental data, measured Drell-Yan production cross sections are analyzed for 800GeV proton incident on a variety of nuclear targets fro…
We discuss the Drell-Yan dilepton production using the transverse momentum dependent parton distributions evolved with the Catani-Ciafaloni-Fiorani-Marchesini-Kwieciński (CCFM-K) equations in the single loop approximation. Such equations are obtained assuming angular ordering of emitted partons (coherence) for $x\sim 1$ and transverse momentum ordering for $x \ll 1$. This evolution scheme also contains the Collins-Soper-Sterman (CSS) soft gluon resummation. We make a comparison with a broad class of data on transverse momentum spectra of low mass Drell-Yan dileptons.
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 discuss the nuclear dependence of $ψ$ and $ψ'$ production in hadron-nucleus interactions as a function of longitudinal momentum fraction $x_F$. Nuclear effects such as final-state absorption, interactions with comovers, shadowing of parton distributions, energy loss, and intrinsic heavy-quark components are described separately and incorporated into the model which is then compared to the preliminary E866 data. The resulting nuclear dependence of Drell-Yan production at 800 GeV and proposed measurements of $ψ$, $ψ'$ and Drell-Yan production at 120 GeV are also calculated.
The Drell-Yan massive dilepton production in hadron-hadron collisions provides a unique tool, complementary to Deep Inelastic Scattering, for improving our understanding of hadronic substructure and in particular for testing parton distributions. We will consider measurements of the differential and double-differential Drell-Yan cross sections from FNAL Tevatron up to CERN LHC energies and they will be compared to the predictions of perturbative QCD calculations using most recent sets (CT14 and MMHT14) of parton distribution functions, as well as those provided by the statistical approach.
We present a derivation of the threshold resummation formula for the Drell-Yan rapidity distribution. Our argument is valid for all values of rapidity and to all orders in perturbative QCD and can be applied to all Drell-Yan processes in a universal way, i.e. both for the production of a virtual photon γ^{*} and the production of a vector boson W^{\pm}, Z^{0}. We show that for the fixed-target experiment E866/NuSea used in current parton fits, the NLL resummation corrections are comparable to NLO fixed-order corrections and are crucial to obtain agreement with the data.
The next-to-leading order and leading order analysis are performed on the differential cross section ratio from Drell-Yan process. It is found that the effect of next-to-leading order corrections can be negligible on the differential cross section ratios as a function of the quark momentum fraction in the beam proton and the target nuclei for the current Fermilab and future lower beam proton energy. The nuclear Drell-Yan reaction is an ideal tool to study the energy loss of the fast quark moving through cold nuclei. In the leading order analysis, the theoretical results with quark energy loss …
We calculate QCD corrections to transversely polarized Drell-Yan process at a measured $Q_T$ of the produced lepton pair in the dimensional regularization scheme. The $Q_T$ distribution is discussed resumming soft gluon effects relevant for small $Q_T$.
We estimate the power corrections (infrared renormalon contributions) to the coefficient functions for the differential Drell-Yan cross-section $d^2σ/dQ^2dy$, where $Q^2$ is the mass squared and $y$ the rapidity of the produced lepton pair. We employ the dispersive method based on the analysis of one-loop Feynman graphs containing a massive gluon.
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.
We study the theoretical predictions for the total inelastic $γγ$ cross-sections, with an emphasis on the eikonalised minijet model (EMM). In the context of the EMM, we discuss a new ansatz for the overlap function involving the photons. We discuss the dependence of the EMM predictions on various input parameters as well as predictions for \siggg from a simple extension of the Regge Pomeron Exchange model. We then compare both with the recent LEP data.
By means of two different parametrizations of quark energy loss and the nuclear parton distributions determined only with lepton-nuclear deep inelastic scattering experimental data, a leading order phenomenological analysis is performed on the nuclear Drell-Yan differential cross section ratios as a function of the quark momentum fraction in the beam proton and target nuclei for E772 experimental data. It is shown that there is the quark energy loss effect in nuclear Drell-Yan process apart from the nuclear effects on the parton distribution as in deep inelastic scattering. The uncertainties d…
We report recent results on the extraction of the rapidity evolution kernel for Sudakov processes from experimental measurements of Drell-Yan (DY) transverse momentum distributions. We discuss the role of high-precision Large Hadron Collider (LHC) data, and illustrate the interplay of this analysis with transverse momentum dependent and collinear parton density functions.
Radiative corrections to the neutral current Drell--Yan-like processes are considered. Complete one-loop electroweak corrections are calculated within the SANC system. Theoretical uncertainties are discussed. Numerical results are presented for typical conditions of LHC experiments.
The results of a recent calculation of the QCD corrections to the longitudinally polarized Drell-Yan process are summarized. In addition to the parity conserving double spin asymmetry which is already accessible in the Drell-Yan production of lepton pairs at fixed target energies, we consider parity violating single spin asymmetries appearing only in the production of massive vector bosons at polarized hadron colliders. The prospects for extracting polarized quark distributions from asymmetries in vector boson production at RHIC are briefly discussed.
We investigate the information which could be obtained from Drell-Yan processes with sufficiently intense beams of charged kaons on isoscalar targets. It is found that combinations of $K^+$ and $K^-$ Drell-Yan measurements on isoscalar nuclear targets would allow one to extract the kaon sea quark distributions. These cross sections are also sensitive to the strange valence quark distribution in the kaon, although one would need a significant increase over the presently available kaon fluxes in order to extract this quantity with sufficient accuracy.
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 Drell-Yan process is analyzed in soft-collinear effective theory near the end-point region. It is assumed that the relevant final-state hadron energy $Q(1-z)$ where $z$ is the momentum fraction transferred to the virtual photon is the typical hadronic scale $\simΛ$, thus no intermediate scale exists. It is shown that this setup successfully reproduces the full theory results. We also discuss the factorized soft Wilson lines for the Drell-Yan process.
New arguments are presented in favor of the infrared finite coupling approach to power corrections in the context of Sudakov resummation. The more regular infrared behavior of some peculiar combinations of Sudakov anomalous dimensions, free of Landau singularities at large Nf, is pointed out. A general conflict between the infrared finite coupling and infrared renormalon approaches to power corrections is explained, and a possible resolution is proposed, which makes use of the arbitrariness of the choice of constant terms in the Sudakov exponent. A simple ansatz for a `universal' non-perturbat…
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.
We study the polarized Drell-Yan processes from the collision of two spin-1/2 hadrons at order 1/Q based on the framework of transverse momentum dependent factorization.We give the complete twist-three results of total sixteen independent structure functions in terms of twist-two and twist-three transverse momentum dependent distribution functions.
We discuss the nuclear parton distribution functions on the basis of our recently developed semi-microscopic model, which takes into account a number of nuclear effects including Fermi motion and nuclear binding, nuclear meson-exchange currents and off-shell corrections to bound nucleon distributions as well as nuclear shadowing effect. We also discuss application to the nuclear Drell-Yan process and compare our predictions with data from the E772 and E866 experiments.
We evaluate the cross section for the pion induced Drell-Yan process in two different models of the pion light-front wave function, inspired by light-front holographic approaches. We obtain the valence quark distribution functions in those models, which after QCD evolution, are consistent with the experimental data from the E-0615 experiment at Fermilab. Supplemented by the parton distribution functions of the target nuclei, we obtain the cross section consistent with the experimental data for the $π^-$ Nucleus $\rightarrow {μ^+μ^-X}$ Drell-Yan process.
We consider deep-inelastic lepton scattering, Drell-Yan lepton pair and heavy quark production in the reference frame of the target. These reactions traditionally treated as hard have, however, a substantial leading twist soft contribution. One of the manifestations of such a soft component, nuclear shadowing, is overviewed.
We study the nuclear parton distribution functions on the basis of our recently developed semi-microscopic model, which takes into account a number of nuclear effects including nuclear shadowing, Fermi motion and nuclear binding, nuclear meson-exchange currents, and off-shell corrections to bound nucleon distributions. We discuss in detail the dependencies of nuclear effects on the type of parton distribution (nuclear sea vs valence), as well as on the parton flavor (isospin). We apply the resulting nuclear parton distributions to calculate ratios of cross sections for proton-induced Drell-Yan…
