Polarized proton-deuteron Drell-Yan processes and parton distributions

We show in general that there are 108 structure functions in the proton-deuteron Drell-Yan processes. However, there exist only 22 finite ones after integrating the cross section over the virtual-photon transverse momentum or after taking the limit Q_T → 0. There are 11 new structure functions in comparison with the ones of the proton-proton reactions, and they are related to the tensor structure of the deuteron. Parton-model analyses indicate an important tensor structure function V_T^UQo, which can be measured by a quadrupole spin asymmetry. The Drell-Yan process has an advantage over lepton reactions in finding tensor polarized antiquark distributions. We hope that our studies will be realized in the next-generation RHIC-Spin project and other ones.     

Nuclear parton distribution functions and energy-loss effect in the Drell-Yan reaction off nuclei

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 two typical kinds of quark energy-loss parametrization and the different sets of nuclear parton distribution functions, we present an analysis of the E866 experiments on the nuclear dependence of Drell-Yan lepton pair production resulting from the bombardment of Be, Fe and W targets by 800 GeV protons at Fermilab. It is found that the quark energy loss in cold nuclei is strongly dependent on the used nuclear parton distribution functions. The further prospects of using relatively low energy protons incident on nuclear targets are presented by combining the quark energy-loss rate determined from a fit to the E866 nuclear-dependent ratios versus x ₁, with the nuclear parton distribution functions given from lA deep inelastic scattering (DIS) data. The experimental study of the relatively low energy nuclear Drell-Yan process can give valuable insight in the energy loss of the fast quark propagating through cold nuclei and help to pin down nuclear parton distribution functions.Received: 8 September 2004, Revised: 18 October 2004, Published online: 11 January 2005PACS: 24.85. + p, 13.85.Qk, 25.40.-h, 25.75.Nq     

Partonic energy loss and the Drell-Yan process

We examine the current status of the extraction of the rate of partonic energy loss in nuclei from A-dependent data. The advantages and difficulties of using the Drell-Yan process to measure the energy loss of a parton traversing a cold nuclear medium are discussed. The prospects of using relatively low energy proton beams for a definitive measurement of partonic energy loss are presented.     

What can Drell-Yan data tell us about the EMC effect and nucleon parton distributions?

We show that knowledge of thex ₁ andx ₂ dependence of the ratio of Drell-Yan cross-sections measured on heavy nuclei and deuterium can give us information about the origin of the EMC effect. Conversely, we show that an understanding of the EMC effect, together with (non-ratio) Drell-Yan data, can provide us with a way of discriminating between candidates for nucleon parton distributions.     

Evidence for multiple parton interactions from the observation of multi-muon events in Drell-Yan experiments

We calculate the production of two lepton pairs via the Drell-Yan mechanism. To establish the existence of multiple parton interactions in a single hadron collision, lepton pair production is superior to jet production from the theoretical, phenomenological and experimental points of view. The calculated rate agrees with the previously unexplained four-muon events observed in πp and pp interactions. Our results lend support to a recent analysis of ISR four-jet events and we discuss some implications of this study.     

Colour effects in Drell-Yan process

We examine the predictions of gauge theories with colour excitation for the processpp →μ ⁺ μ ⁻ X. Relative to the predictions of quark parton model (with three colours) we find enhancements as large as a factor 3 – 4 for the cross-sectionM ³ d ² σ/dMdy|_y=0 in the region 0·03 ≲M/√s ≲ 0·2 at √s=62 GeV,M being the invariant mass andy the rapidity of the muon pair. We study the sensitivity of this result to the colour gluon mass and the underlying parametrisation of the quark and gluon distribution functions.     

Spectator interactions and theK-factor in the Drell-Yan process

The precise value of theO(α _s perturbative QCD correction to the Drell-Yan cross-section seems to depend on the calculational procedure. We show how this ambiguity is removed when proper account is taken of the additional interactions involving spectator quarks. Explicit calculations in the scalar quark model reveal that the important contributions come from values of the gluon momentum that are very soft.

     

Drell-Yan nuclear modification due to nuclear effects of nPDFs and initial-state parton energy loss

By globally analyzing nuclear Drell-Yan data including all incident energies,the nuclear effects of nuclear parton distribution functions(nPDFs)and initial-state parton energy loss are investigated.Based on the Landau-Pomeranchuk-Migdal(LPM)regime,the calculations are carried out by means of analytic parametrizations of quenching weights derived from the Baier-Dokshitzer-Mueller-Peigné-Schiff(BDMPS)formalism and using the new EPPS16 nPDFs.It is found that the results are in good agreement with the data and the role of the energy loss effect in the suppression of Drell-Yan ratios is prominent,especially for low-mass Drell-Yan measurements.Thenuclear effects of nPDFs become more obvious with increasing nuclear mass number A,the same as the energy loss effect.By a global fit,the transport coefficient extracted is q=0.26±0.04 GeV²/fm.In addition,to avoid diminishing the QCD NLO correction to the data form of Drell-Yan ratios,separate calculations of the Compton differentialcross section ratios RFe(W)/C(xF)at 120 GeV are performed,which provides a feasible way to better distinguish the gluon energy loss in Compton scattering.It is found that the role of the initial-state gluon energy loss in the suppression of Compton scattering ratios is not very important and disappears with the increase of xF.     

Spin effects and factorization in the Drell-Yan process

We discuss the idea that the nontrivial vacuum structure in QCD may induce transverse momentum and spin correlations of the initial state partons in Drell-Yan type reactions, i.e. in hadron-hadron collisions with production of a vector bosonV=γ ^*,Z,W ^±. Transverse momentum correlations are found to have practically no effect on observable quantities, but spin correlations have drastic consequences for the polarization density matrices of theV-bosons. We therefore propose measurements of theV polarization as a good test for the basic factorization hypothesis which, so far, has been assumed to be valid in numerous applications of the naive and QCD-improved parton model. We compare our ansatz for a spin correlation violating factorization with data from the NA 10 collaboration onγ ^* production inπ ^? N scattering. We find that the data give an indication of spin correlations of the partons in the initial state to be present.     

Higher-twist effects in QCD,deep inelastic scattering,and the Drell-Yan process

Inclusion of specific effects associated with constituent binding in hadronic wave functions is shown to lead to important non-scaling, nonfactorizing 1/Q ² contributions to cross sections for semi-inclusive deep-inelastic scattering, the Drell-Yan process, and other hard scattering reactions. These 1/Q ² higher-twist terms are predicted to be dominant in well defined kinematic regions such as largex and/or largez. The provide angular distributions typical of longitudinally polarized virtual photons andW's, including sin² θ terms in meson induced Drell-Yan processes and ine ⁺ e ^?→πX, as well as unusual (1?y) terms in deep-inelastic scattering. Calculations are also presented of the quark structure functions of the pionq _π(x, Q ²) and for the quark to pion fragmentation functionD _π(z, Q ²). Predictions are made for the azimuthal angle dependence of the cross sections for \(\pi N \to \mu {\text{ }}\bar \mu X\) andlN→l′πX.     

Mesonic and binding contributions to the nuclear Drell-Yan process

We have evaluated the Drell-Yan cross section in nuclei paying special attention to the meson cloud contribution from pions and ϱ-mesons, for which an accurate calculation using the meson nuclear spectral functions is used. Similarly, the nucleonic contribution is evaluated in terms of a relativistic nucleon spectral function. Fair agreement with experiment is found for different nuclei and the results show a sizeable contribution from the renormalized meson cloud. In order to reproduce the experiment a novel element is introduced, consisting of a gradual energy loss of the incoming proton in its pass through the nucleus which produces a strong A dependence at x₁ large.     

Factorization for one-loop corrections in the Drell-Yan process

We study all the one-loop corrections to the Drell-Yan process in QCD, including gluon exchanges involving spectator partons. Our method demonstrates weak factorization at measured dimuon Q^T, and is suitable for generalization to higher orders.     

Remarks on optimized predictions for the Drell-Yan process

We discuss the optimization of the Drell-Yan pair production cross section calculated atO(α _s ) and compare it with theO(α _s ² ) results of van Neerven et al. It is shown that the optimized predictions do agree analytically with the latter calculation near the phase space boundary. They also provide a good numerical approximation wherever the stability equations have a solution.     

Cancellation of Sudakov effects in the Drell-Yan process

We show, by a direct examination of Feynman graphs, that lowest-order Sudakov effects factorize from Glauber-region gluons in quark-hadron scattering. We then find that the Sudakov double logarithms cancel. This result is consistent with order-by-order factorization in perturbation theory for the Drell-Yan process.     

A phenomenological study of theK-factor for the Drell-Yan process

We calculate within the framework of QCD perturbation theory, the 0(α _s ) corrections to the Drell-Yan process using various beam particles and parton distributions. We attempt to extract those features of these corrections which are least sensitive to the forms of the ill-determined parameters like the quark or gluon distributions. We emphasize the necessity to exponentiate certain π² terms in order to accommodate the available data in the relevant kinematical range.     

Large perturbative corrections to the Drell-Yan process in QCD

The total cross section $\text{d}\text{σ}\text{d}\text{Q}{}^2$ for the production of a muon pair of invariant mass Q²via the Drell-Yan mechanism and the Feynman x_F differential cross section $\text{d}{}^2\text{σ}\text{d}\text{Q}{}^2\text{d}\text{x}{}_{\mathrm{<mtext>F</mtext>}}$ are calculated in QCD retaining all terms up to order α_s(Q². The calculations are performed using dimensional regularisation of the intermediary infrared and collinear singularities, but we present our results in a form independent of such details. The corrections to both these cross sections coming from radiative corrections to the lowest-order $\text{q}\text{q}$ annihilation diagram are found to be large at present values of Q² and S when the cross section is expressed in terms of parton densities derived from leptonproduction, for all Drell-Yan processes of practical interest. Numerical calculations are presented which show, for any reasonable parametrisation of the parton densities, that the neglect of higher-order terms in α_s(Q²) is not justifiable. The quark-gluon diagrams on the other hand give small corrections in this order and are only important for PP scattering.     

Infrared properties of two-loop,initial state spectator interactions in the Drell-Yan process

We use the light-cone axial gauge of proper-time ordered perturbation theory and study the soft-IR properties of the two-loop virtuals' diagrams considered by Bodwin, Brodsky and Lepage for ππ → μ⁺μ^- + X. It is shown that although the systematic summation over all possible spectator interactions removes the outside soft-IR divergences in the non-overlapping ladder Glauber diagrams, unphysical inside soft-IR divergences persist. So, in the light-cone axial gauge the on-shell Glauber region is not a gauge invariant concept which can be physically isolated from radiative corrections which non-trivially involve other diagrammatic regions. Due to gauge invariance it can be potentially misleading in eikonal phenomenologies based on perturbative QCD to assume an ad hoc inside soft-IR cutoff in analyzing possible non-abelian effects in multiple scatterings involving spectators.