The Drell-Yan process offers access, complementary to deep inelastic scattering (DIS) to the transverse-momentum distributions of the quarks within a hadron. When neither the beam nor the target are polarized, the angular distributions of Drell-Yan scattering provide access to the h⊥1 , Boer-Mulders, distribution. With the addition of either a polarized beam or target, other transverse-momentum

distributions (TMDs) can be accessed, in particular the Sivers’ distribution, f⊥1'. Existing Boer-Mulders and planned Sivers’ Drell-Yan measurements of these distributions are discussed

Reimer, P. E.

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DOI 10.1393/ncc/i2012-11204-yColloquia: Transversity 2011IL NUOVO CIMENTO Vol. 35 C, N. 2 Marzo-Aprile 2012Probing transverse-momentum distributionswith the Drell-Yan processP. E. ReimerPhysics Division, Argonne National Laboratory - Argonne, IL 60439, USAricevuto il 20 Gennaio 2012; approvato il 30 Gennaio 2012pubblicato online il 26 Marzo 2012Summary. — The Drell-Yan process offers access, complementary to deep inelasticscattering (DIS) to the transverse-momentum distributions of the quarks within ahadron. When neither the beam nor the target are polarized, the angular distribu-tions of Drell-Yan scattering provide access to the h⊥1 , Boer-Mulders, distribution.With the addition of either a polarized beam or target, other transverse-momentumdistributions (TMDs) can be accessed, in particular the Sivers’ distribution, f⊥1 .Existing Boer-Mulders and planned Sivers’ Drell-Yan measurements of these distri-butions are discussed.PACS 14.20.Dh – Protons and neutrons.PACS 24.85.+p – Quarks, gluons, and QCD in nuclear reactions.PACS 13.88.+e – Polarization in interactions and scattering.PACS 13.85.Qk – Inclusive production with identified leptons, photons, or othernonhadronic particles.The Drell-Yan process to leading order in the strong coupling constant, αs, is theannihilation into a massive virtual photon of a quark in one hadron with an antiquark inanother. The virtual photon then decays into a lepton-antilepton pair (dilepton) that isdetected. This process was first observed by J. H. Christenson et al. [1,2] in 1970 at theBrookhaven National Laboratory using a 29GeV proton beam on a uranium target. Thefeatures of the observed cross-section were explained in the same year by S. D. Drell andT.-M. Yan [3,4] in terms of the (then very new) parton model. In addition to explainingthe drop in cross-section of over seven orders of magnitude as a function of the dilepton’sinvariant mass, the model of Drell and Yan predicted the observed angular distributionof 1 + cos2 θ.To leading order in αs the Drell-Yan cross-section can be expressed as(1)d2σdx1dx2=4πα2esx1x2∑q∈{u,d,s,... }e2q [q¯1(x1)q2(x2) + q1(x1)q¯2(x2)] ,c© Societa` Italiana di Fisica 225226 P. E. REIMERwhere x1(2) represent xBj, the fractional momentum carried by the interacting beam(target) quark; qi(xi) is the parton distribution of quark of flavor q; eq is the charge ofquark flavor q; s is the center-of-mass energy squared; αe ≈ 1/137 is the fine structureconstant; and the sum is over all quark flavors. Of course next-to-leading-order terms inαs can contribute up to half of the observed cross-section and cannot be neglected.One can make several interesting observations based on eq. (1). The annihilation of au-quark with a u¯-antiquark is enhanced by a factor of four relative to the d-d¯ annihilationbecause of the charge-squared weighting. For example, with a π− beam, containing avalence anti-up quark, on a proton target, such as at the COMPASS experiment [5]the cross-section is dominated by the annihilation of the pion’s anti-up quark with thetarget’s up quarks. Similarity, with an antiproton beam such as at GSI-FAIR [6], thecross-section is also dominated by the annihilation of a valence anti-up quark with avalence up quark. In addition, the spectrometer configuration is important. In a typicaldipole-based fixed-target spectrometer such as the E-906/SeaQuest spectrometer [7], theacceptance is decidedly skewed toward large Feynman-x (xF = x1 − x2). In a proton-proton or proton-neutron collision, this, when combined with the steeply falling sea quarkdistributions, produces a situation favoring the detection of events in which the quark islikely to come from the beam hadron and the antiquark from the sea of the target. Whencomparing current and proposed Drell-Yan experiments, it is important to remember thatthe different sensitivity can be very complementary.1. – Unpolarized Drell-Yan, the Lam-Tung relation and the Boer-MuldersdistributionThe Boer-Mulders distribution, denoted h⊥1 (xBj, kT , Q2), represents the transversepolarization of quarks within an unpolarized nucleus [8]. The Boer-Mulders distributionvanishes when integrated over the transverse momentum of the interacting parton, kT ,and is naively T -odd. The existence of such a distribution that was non-zero was initiallysuggested to explain both single spin asymmetries in pp↑ scattering [9] and a large cos 2φdependence observed in Drell-Yan scattering [10,11].While the dominant term in the Drell-Yan angular distribution is 1 + cos2 θ, a moregeneral expression was derived by John Collins and Davison Soper [12]:(2)dσdΩ∝ 1 + cos2 θ + μ sin 2θ cosφ + ν2sin2 θ cos 2φ.Then, in analogy to the Collin-Gross relation [13], Wu-Ki Tung and C. S. Lam deriveda relation between the coefficients λ and ν [14, 15]:(3) 1− λ = 2ν,known as the Lam-Tung relation. The Lam-Tung relation has been shown to be largelyunaffected by QCD corrections [15] and even resummation effects [16]. Despite its theo-retical robustness, however, angular distribution measurements from π−-tungsten Drell-Yan at CERN (NA10) [11,10] and Fermilab [17] show a violation of the Lam-Tung relationat large virtual photon transverse momentum, pT , with the size of the violation increas-ing as pT increases. From examination of the data, it is clear that this violation comesalmost entirely from the increase in the ν term of eq. (2), shown in fig. 1. In addition tothe Boer-Mulders h⊥1 distribution mentioned earlier, several other explanations have beenPROBING TRANSVERSE-MOMENTUM DISTRIBUTIONS WITH THE DRELL-YAN PROCESS 22700.10.20.30.40.50 1 2 3 4pT (GeV)νCERN NA10 πWFermilab E615 πW00.10.20.30.40.50 1 2 3 4pT (GeV)νFermilab E-866/NuSea ppFermilab E-866/NuSea pD-0.500.511.522.50 1 2 3 4pT (GeV)2ν-(1-λ)CERN NA10 πWFermilab E615 πW-0.500.511.522.50 1 2 3 4pT (GeV)2ν-(1-λ)Fermilab E-866/NuSea ppFermilab E-866/NuSea pDFig. 1. – The coefficient ν for the NA10 π−W [11,10] (top left) and for the E-866/NuSea pp [23]and pd [24] (top right) Drell-Yan scattering. Note that in the pion case, ν grows with increasingpT while in the proton-induced data, ν is relatively flat, with the exception of the highest pTpoint for the proton-proton dataset. The corresponding violation of the Lam-Tung relation isshown for π−W (bottom left) and pp and pd (bottom right) Drell-Yan scattering.proposed for these observations. These include QCD factorization breaking [18, 19] andcontributions from higher terms in the twist expansion [20-22]. Nuclear effects were alsoconsidered, but these were not seen in the NA10 data, although, with limited statisticalprecision.More recently, the Fermilab E-866/NuSea experiment observed no such violation ofthe Lam-Tung relation in proton-proton [23] and proton-deuterium [24] Drell-Yan. Whileon the surface, these two observations seem inconsistent, there is an important differencebetween pion- and proton-induced Drell-Yan. In the π− measurements there is a valenceanti-u quark in the π− making the dominate annihilation u¯u, and thus probing thevalence u-quark distributions in the target nucleon. In the proton-induced case, wherethe spectrometer acceptance dictates large xF , the valence quark comes predominantlyfrom the beam-proton and the antiquark comes from the target. This convolution couldbe indicating that the sea-quark h⊥1 (xBj, kT , Q2) is small, while at the same time, thepion data indicated that the valence distribution is large. It should be noted that whilethe data are consistent with the Boer-Mulders description, QCD effects are not ruledout [25]. More precise data for both pion- and proton-induced Drell-Yan at larger pT228 P. E. REIMERwould help to resolve these questions. The prospects of obtaining more data in both thepion- and proton-induced cases from the COMPASS [5] and SeaQuest [7] experimentsare discussed in sect. 3. Both the pion and the proton data are shown in fig. 1.2. – Polarized Drell-Yan and the Sivers’ distributionThe Sivers’ distribution, f⊥1 (xBj, kT , Q2), is also a naively T -odd distribution whichvanishes when integrated over kT . This distribution represents the asymmetry in theunpolarized quark distributions in transversely polarized nucleons [26, 27]. Initially, itwas argued that the Sivers’ distribution must be identically zero [28]. The fact thatthis distribution was non-zero was first proposed by D. W. Sivers [27, 26] to explain theasymmetries observed in single spin experiments [29]. One very interesting property ofthe Sivers’ distribution is that it is non-universal. More specifically, while the magnitudeis universal, the sign of the Sivers’ distribution is dependent on the process being usedto measure it [30]. That is(4) f⊥1∣∣SIDIS= − f⊥1∣∣Drell-Yan .This sign reversal is a fundamental prediction of the gauge structure of QCD.Recently, the Sivers’ distribution has been measured using semi-inclusive deep inelas-tic scattering (SIDIS) by both the HERMES [31] and by the COMPASS [32] collabo-rations. In the future, there are several planned SIDIS measurements which will takeplace at Thomas Jefferson National Accelerator Facility (JLab) [33-35]. It is importantto note that the measurement of individual kinematic points with either SIDIS or Drell-Yan is not sufficient to make this comparison if the points are not at exactly the samekinematics because of QCD evolution. Rather, as much of the function as possible mustbe measured in both SIDIS and Drell-Yan to allow for evolution to common kinematicsfor the comparison [36].3. – Anticipated Drell-Yan measurementsThere are several measurements at various stages of planning, construction and datacollection that will use the Drell-Yan process to explore the transverse structure of theproton. These include both polarized and unpolarized experiments. The Fermilab E-906/SeaQuest experiment expects to collect data in 2012-14 using a 120GeV unpolar-ized proton beam on proton, deuterium and nuclear targets [7, 37]. The primary goalsof this experiment are measurement of the longitudinal sea quarks distributions in theproton and their modification in a nuclear environment. In addition, the angular distri-butions measured in this experiment will also provide information on the Boer-Muldersdistribution as mentioned in sect. 1.At Brookhaven National Laboratory, the ANDY experiment [38] has completed thefirst stage of a three-stage program, completing in 2013 the Drell-Yan program usingpolarized protons in RHIC. The experimental goal is to measure the sign of f⊥1 at onekinematic point, 〈xF〉 = 0.2, M > 4GeV and pT < 2GeV. In addition, ANDY will be ademonstration of feasibility for the forward upgrades of STAR and PHENIX.The COMPASS experiment will measure Drell-Yan scattering with a π− beam ona polarized proton or deuterium targets to study the transversity distributions of thevalence distributions in the target nucleon [5]. For the proton target, this will result ina measurement of the Boer-Mulders’ distribution of the u-quarks. The initial phasePROBING TRANSVERSE-MOMENTUM DISTRIBUTIONS WITH THE DRELL-YAN PROCESS 229of this program will be completed in 2014 and will measure several points coveringroughly the same kinematics at their previous Sivers DIS measurements [39], providinga basis for comparison with these measurements. In addition, the angular distributions,averaged of target polarization, should provide better measurements of the Boer-Mulders’distribution and its behavior as a function of pT .There are two possible upgrades to the Fermilab E-906/SeaQuest experiment whichwould allow for singly or, when combined, even doubly polarized Drell-Yan measure-ments. A study has just been completed on the technical feasibility and cost of polar-izing the Fermilab Main Injector [40]. The estimated cost is very roughly US$4M. Thepolarized beam could then be extracted to the existing E-906/SeaQuest apparatus [37],giving access to the valence quarks in a polarized proton. This plan would allow for arelatively complete measurement over a broad range in xBj. As noted in the talk byWerner Vogelsang [36], to make a valid comparison of the relation of the Sivers’ DISand Drell-Yan distributions, it is necessary to know the distributions, rather than onlya few, kinematically isolated points, especially if there is a node in the distribution orif there are substantial differences between the Drell-Yan and DIS kinematics. At thesame time, it is possible to measure the Sivers’ function for the sea quarks by using apolarized target with the existing E-906/SeaQuest apparatus [41].4. – ConclusionsThe Drell-Yan process offers access, complementary to deep inelastic scattering (DIS)to the transverse-momentum distributions of the quarks within a hadron. When neitherthe beam nor the target are polarized, the angular distributions of Drell-Yan Scatteringprovide access to the h⊥1 , Boer-Mulders, distribution. The available data from pion- andproton-induced Drell-Yan scattering can be interpreted to say that the Boer-Muldersdistribution for sea quarks is small, while for the valence distributions it is somewhatlarger. This interpretation is clouded by the poor statistical precision of the data atlarge-x, but fortunately soon there should be more data available from COMPASS forpion-induced Drell-Yan and SeaQuest for proton-induced Drell-Yan. With the additionof either a polarized beam or target, other transverse-momentum distributions (TMDs)can be accessed, in particular the Sivers’ distribution, f⊥1 . While the Sivers’ distribu-tion has been measured in SIDIS, it has yet to be measured with Drell-Yan scattering. Afundamental prediction of the gauge nature of QCD is that this distribution will have op-posite sign when measured with Drell-Yan scattering: f⊥1 |SIDIS = −f⊥1 |Drell-Yan. Severalexperiments will soon be collecting Drell-Yan data to test this prediction.∗ ∗ ∗This work is supported in part by the U.S. Department of Energy, Office of NuclearPhysics, under Contract No. DE-AC02-06CH11357.REFERENCES[1] Christenson J. H., Hicks G. S., Lederman L. M., Limon P. J., Pope B. G. andZavattini E., Phys. Rev. Lett., 25 (1970) 1523.[2] Christenson J. H., Hicks G. S., Lederman L. M., Limon P. J., Pope B. G. andZavattini E., Phys. Rev. D, 8 (1973) 2016.[3] Drell S. D. and Yan T.-M., Phys. Rev. Lett., 25 (1970) 316.[4] Drell S. D. and Yan T.-M., Phys. Rev. Lett., 25 (1970) 902.230 P. E. REIMER[5] Denisov O., these proceedings.[6] Gutbrod H. H., Augustin I., Eickhoff H., Gross K.-D., Henning W. F., Kra¨merD. and Walter G. (Editors), FAIR Baseline Technical Report 2006.[7] Reimer P., Geesaman D. et al., Proposal for Drell-Yan measurements of nucleon andnuclear structure with the FNAL Main Injector, Proposal to the Fermilab PAC (2001).[8] Boer D. and Mulders P. J., Phys. 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Probing transverse-momentum distributions with the 

Drell-Yan process

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Probing transverse-momentum distributions with the Drell-Yan process

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