We report a measurement of the angular distributions of Drell-Yan dimuons
produced using an 800 GeV/c proton beam on a deuterium target. The muon angular
distributions in polar angle $\theta$ and azimuthal angle $\phi$ have been
measured over the kinematic range $4.5 < m_{\mu \mu} < 15$ GeV/c$^2$, $0 < p_T
< 4 $ GeV/c, and $0 < x_F < 0.8$. No significant cos$2\phi$ dependence is found
in these proton-induced Drell-Yan data, in contrast to the situation for
pion-induced Drell-Yan. The data are compared with expectations from models
which attribute the cos$2\phi$ distribution to a QCD vacuum effect or to the
presence of the transverse-momentum-dependent Boer-Mulders structure function
$h_1^\perp$. Constraints on the magnitude of the sea-quark $h_1^\perp$
structure functions are obtained.Comment: 4 pages, 3 figure

B. A. Mueller

B. K. Park

C. A. Gagliardi

C. N. Brown

D. D. Koetke

D. F. Geesaman

D. K. Wise

D. M. Kaplan

D. M. Lee

E. A. Hawker

G. Petitt

G. R. Young

G. T. Garvey

J. C. Peng

J. C. Webb

J. D. Bush

J. L. Willis

J. M. Moss

L. D. Isenhower

L. Y. Zhu

M. A. Vasiliev

M. E. Sadler

M. J. Leitch

M. L. Brooks

N. Makins

P. E. Reimer

P. L. McGaughey

P. M. Nord

P. W. Stankus

R. E. Tribble

R. S. Towell

S. A. Klinksiek

S. B. Kaufman

T. A. Carey

T. C. Awes

T. H. Chang

T. N. Thompson

V. Papavassiliou

W. E. Cooper

W. E. Sondheim

W. M. Lee

X. C. He

Z. Lu

Physical Review Letters

English

arXiv

Zhu, L. Y.

Peng, J. C.

Reimer, P. E.

Awes, T. C.

Brooks, M. L.

Brown, C. N.

Bush, J. D.

Carey, T. A.

Chang, T. H.

Cooper, W. E.

Gagliardi, C. A.

UNT (University of North Texas) Digital Library

arXiv:hep-ex/0609005 v1   6 Sep 2006Measurement of Angular Distributions of Drell-Yan Dimuons in p + d Interaction at800 GeV/cL.Y. Zhu,6 J.C. Peng,6, 7 P.E. Reimer,2, 7 T.C. Awes,10 M.L. Brooks,7 C.N. Brown,3 J.D. Bush,1 T.A. Carey,7T.H. Chang,9 W.E. Cooper,3 C.A. Gagliardi,11 G.T. Garvey,7 D.F. Geesaman,2 E.A. Hawker,11X.C. He,4 L.D. Isenhower,1 D.M. Kaplan,5 S.B. Kaufman,2 S.A. Klinksiek,8 D.D. Koetke,12 D.M. Lee,7W.M. Lee,3, 4 M.J. Leitch,7 N. Makins,2, 6 P.L. McGaughey,7 J.M. Moss,7 B.A. Mueller,2 P.M. Nord,12V. Papavassiliou,9 B.K. Park,7 G. Petitt,4 M.E. Sadler,1 W.E. Sondheim,7 P.W. Stankus,10 T.N. Thompson,7R.S. Towell,1 R.E. Tribble,11 M.A. Vasiliev,11 J.C. Webb,9 J.L. Willis,1 D.K. Wise,1 and G.R. Young10(FNAL E866/NuSea Collaboration)1Abilene Christian University, Abilene, TX 796992Physics Division, Argonne National Laboratory, Argonne, IL 604393Fermi National Accelerator Laboratory, Batavia, IL 605104Georgia State University, Atlanta, GA 303035Illinois Institute of Technology, Chicago, IL 606166University of Illinois at Urbana-Champaign, Urbana, IL 618017Los Alamos National Laboratory, Los Alamos, NM 875458University of New Mexico, Albuquerque, NM 871319New Mexico State University, Las Cruces, NM 8800310Oak Ridge National Laboratory, Oak Ridge, TN 3783111Texas A&M University, College Station, TX 7784312Valparaiso University, Valparaiso, IN 46383(Dated: September 6, 2006)We report a measurement of the angular distributions of Drell-Yan dimuons produced using an800 GeV/c proton beam on a deuterium target. The muon angular distributions in polar angleθ and azimuthal angle φ have been measured over the kinematic range 4.5 < mµµ < 15 GeV/c2,0 < pT < 4 GeV/c, and 0 < xF < 0.8. No significant cos2φ dependence is found in these proton-induced Drell-Yan data, in contrast to the situation for pion-induced Drell-Yan. The data arecompared with expectations from models which attribute the cos2φ distribution to a QCD vacuumeffect or to the presence of the transverse-momentum-dependent Boer-Mulders structure functionh⊥1 . Constraints on the magnitude of the sea-quark h⊥1 structure functions are obtained.PACS numbers: 13.85.Qk, 14.20.Dh, 24.85.+p, 13.88.+eThe Drell-Yan process [1], in which a charged leptonpair is produced in a high-energy hadron-hadron interac-tion via the qq¯ → l+l− process, has been a testing groundfor perturbative QCD and a unique tool for probing par-ton distributions of hadrons. The Drell-Yan productioncross sections can be well described by next-to-leadingorder QCD calculations [2]. This provides a firm theo-retical framework for using the Drell-Yan process to de-termine the antiquark content of nucleons and nuclei [3],as well as the quark distributions of pions, kaons, andantiprotons [4].Despite the success of perturbative QCD in describingthe Drell-Yan cross sections, it remains a challenge to un-derstand the angular distributions of the Drell-Yan pro-cess. Assuming dominance of the single-photon process,a general expression for the Drell-Yan angular distribu-tion is [5]dσdΩ∝ 1 + λ cos2 θ + µ sin 2θ cosφ+ν2sin2 θ cos 2φ, (1)where θ and φ denote the polar and azimuthal angle,respectively, of the l+ in the dilepton rest frame. Inthe “naive” Drell-Yan model, where the transverse mo-mentum of the quark is ignored and no gluon emissionis considered, λ = 1 and µ = ν = 0 are obtained.QCD effects [6] and non-zero intrinsic transverse mo-mentum of the quarks [7] can both lead to λ 6= 1 andµ, ν 6= 0. However, λ and ν should still satisfy the rela-tion 1 − λ = 2ν [5]. This so-called Lam-Tung relation,obtained as a consequence of the spin-1/2 nature of thequarks, is analogous to the Callan-Gross relation [8] inDeep-Inelastic Scattering. While QCD effects can signif-icantly modify the Callan-Gross relation, the Lam-Tungrelation is predicted to be largely unaffected by QCDcorrections [9].The first measurement of the Drell-Yan angular dis-tribution was performed by the NA10 Collaboration forpi− +W at 140, 194, and 286 GeV/c, with the higheststatistics at 194 GeV/c [10]. The cos 2φ angular depen-dences showed a sizable ν, increasing with dimuon trans-verse momentum (pT ) and reaching a value of ≈ 0.3 atpT = 2.5 GeV/c (see Fig. 1). The observed behavior of νcould not be described by perturbative QCD calculationswhich predict much smaller values of ν [6]. The FermilabE615 Collaboration subsequently performed a measure-FERMILAB-PUB-07-4342123NA10 pi-+W at 194 GeV/c E615 pi-+W at 252 GeV/cE866 p+d at 800 GeV/cλ-0.500.5µ-1-0.500.51ν-2020 0.5 1 1.5 2 2.5 3 3.5 4pT (GeV/c)2ν-(1-λ)FIG. 1: Parameters λ, µ, ν and 2ν − (1 − λ) vs. pT in theCollins-Soper frame. Solid circles are for E866 p + d at 800GeV/c, crosses are for NA10 pi− + W at 194 GeV/c, anddiamonds are E615 pi− +W at 252 GeV/c. The error barsinclude the statistical uncertainties only.ment of pi−+W Drell-Yan production at 252 GeV/c withbroad coverage in the decay angle θ [11]. The E615 re-sults showed that λ deviates from 1 at large values of xpi(the Bjorken-x of the incident pions), and both µ and νhave large non-zero values. Furthermore, the E615 datashowed that the Lam-Tung relation, 2ν = 1−λ, is clearlyviolated. (See Fig. 1.)The NA10 and E615 results on the Drell-Yan angu-lar distributions strongly suggest that new effects be-yond conventional perturbative QCD are present. Sev-eral attempts have been made to interprete these data.Brandenburg, Nachtmann and Mirke suggested that afactorization-breaking QCD vacuum may lead to a corre-lation between the transverse spin of the antiquark in thepion and that of the quark in the nucleon [12]. This wouldresult in a non-zero cos 2φ angular dependence consistentwith the data. As pointed out by Boer et al., a possiblesource for a factorization-breaking QCD vacuum is helic-ity flip in the instanton model [13]. Several authors havealso considered higher-twist effects from quark-antiquarkbinding in pions [14, 15], motivated by earlier work ofBerger and Brodsky [16]. This model predicts behaviorof µ and ν in qualitative agreement with the data. How-ever, the model is strictly applicable only in the xpi → 1region while the NA10 and E615 data exhibit nonpertur-bative effects over a much broader kinematic region.More recently, Boer pointed out [17] that the cos 2φ an-gular dependences observed in NA10 and E615 could bedue to the kT -dependent parton distribution function h⊥1 .This so-called Boer-Mulders function [18] is an exam-ple of a novel type of kT -dependent parton distributionfunction, and it characterizes the correlation of a quark’stransverse spin and its transverse momentum, kT , in anunpolarized nucleon. It has an interesting property of be-ing a time-reversal odd object and owes its existence tothe presence of initial/final state interactions [19]. TheBoer-Mulders function is the analog of the Collins frag-mentation function [20], which describes the correlationbetween the transverse spin of a quark and the trans-verse momentum of the particle into which it hadronizes.Model calculations for the nucleon (pion) Boer-Muldersfunctions have been carried out [21, 22, 23, 24] in theframework of quark-diquark (quark-spectator-antiquark)model, and can successfully describe the ν behavior ob-served in NA10 [24].To shed additional light on the origins of the NA10 andE615 Drell-Yan angular distributions, we have analyzedp+ d Drell-Yan angular distribution data at 800 GeV/cfrom Fermilab E866. There are several physics motiva-tions for this study. First, there has been no report on theazimuthal angular distributions for proton-induced Drell-Yan – all measurements so far have been for polar angulardistributions [3, 25]. Second, proton-induced Drell-Yandata provide a stringent test of theoretical models. Forexample, the cos 2φ dependence is expected to be muchreduced in proton-induced Drell-Yan if the underlyingmechanism involves the Boer-Mulders functions. Thisis due to the expectation that the Boer-Mulders func-tions are small for the sea-quarks. However, if the QCDvacuum effect [12] is the origin of the cos 2φ angular de-pendence, then the azimuthal behavior of proton-inducedDrell-Yan should be similar to that of pion-induced Drell-Yan. Third, the validity of the Lam-Tung relation hasnever been tested for proton-induced Drell-Yan, and thepresent study provides a first test.The Fermilab E866 experiment was performed usingthe upgraded Meson-East magnetic pair spectrometer.Details of the experimental setup have been describedelsewhere [26]. An 800 GeV/c primary proton beam withup to 2× 1012 protons per beam spill was incident uponone of three identical 50.8 cm long cylindrical stainlesssteel target flasks containing either liquid hydrogen, liq-uid deuterium or vacuum. A copper beam dump locatedinside the second dipole magnet (SM12) absorbed pro-tons that passed through the target. Downstream of thebeam dump was an absorber wall that completely filledthe aperture of the magnet. This absorber wall removedhadrons produced in the target and the beam dump.3TABLE I: Mean values of the λ, µ, ν parameters and the quan-tity 2ν − (1− λ) for three Drell-Yan measurements. The pTdependence of these quantities is shown in Fig. 1.p+ d pi− +W pi− +W800 GeV/c 194 GeV/c 252 GeV/c(E866) (NA10) (E615)〈λ〉 1.07 ± 0.07 0.83 ± 0.04 1.17 ± 0.06〈µ〉 0.003 ± 0.013 0.008 ± 0.010 0.09 ± 0.02〈ν〉 0.027 ± 0.010 0.091 ± 0.009 0.169 ± 0.019〈2ν − (1− λ)〉 0.12 ± 0.07 0.01 ± 0.04 0.51 ± 0.07Several settings of the currents in the three dipole mag-nets (SM0, SM12, SM3) were used in order to optimizeacceptance for different dimuon mass regions. Data col-lected with the “low mass” and “high mass” settings [26]on liquid deuterium and empty targets were used in thisanalysis. The detector system consisted of four track-ing stations and a momentum analyzing magnet (SM3).Tracks reconstructed by the drift chambers were extrapo-lated to the target using the momentum determined fromthe bend angle in SM3. The target position was used torefine the parameters of each muon track.From the momenta of the µ+ and µ−, kinematic vari-ables of the dimuons (xF ,mµµ, pT ) were readily recon-structed. The muon angles θ and φ in the Collins-Soperframe [27] were also calculated. To remove the quarko-nium background, only events with 4.5 < mµµ < 9GeV/c2 or mµµ > 10.7 GeV/c2 were analyzed. A totalof 118,000 p+ d Drell-Yan events covering the decay an-gular range −0.5 < cos θ < 0.5 and −pi < φ < pi remain.Detailed Monte-Carlo simulations for the experiment us-ing the MRST98 parton distribution functions [28] forNLO Drell-Yan cross sections have shown good agree-ments with the data for a variety of measured quantities.Figure 1 shows the angular distribution parametersλ, µ, and ν vs. pT . To extract these parameters, theDrell-Yan data were grouped into 5 bins in cos θ and 8bins in φ for each pT bin. A least-squares fit to the datausing Eq. 1 to describe the angular distribution was per-formed. Only statistical errors are shown in Fig. 1. Theprimary contributions to the systematic errors are theuncertainties of the incident beam angles on target. Theanalysis has been performed allowing the beam angles tovary within their ranges of uncertainty. From this study,we found that the systematic errors are comparable to thestatistical errors for each individual pT bin. However, thepT averaged values 〈λ〉, 〈µ〉, and 〈ν〉, are dominatd by thestatistical errors.For comparison with the p + d Drell-Yan data, theNA10 pi−+W data at 194 GeV/c and the E615 pi−+Wdata at 252 GeV/c are also shown in Fig. 1. To test thevalidity of the Lam-Tung relation, also shown in Fig. 100.20.40.60.810 0.5 1 1.5 2 2.5 3 3.5 4pT (GeV/c)νpi- + W at 194 GeV/cpi- + W at 252 GeV/cp + d at 800 GeV/cFIG. 2: Parameter ν vs. pT in the Collins-Soper frame forthree Drell-Yan measurements. Fits to the data using Eq. 3and MC = 2.4 GeV/c2 are also shown.is the quantity, 2ν − (1 − λ), for all three experiments.For p + d at 800 GeV/c, Fig. 1 shows that λ is consis-tent with 1, in agreement with previous studies [3, 25],while µ and ν deviate only slightly from zero. This is incontrast to the pion-induced Drell-Yan results, in whichmuch larger values of ν are found. Table I lists the meanvalues of λ, µ, ν and 2ν − (1 − λ) for these three experi-ments. Again, the qualitatively different behavior of theazimuthal angular distributions for p+ d versus pi− +Wis evident. It is also interesting to note that while E615clearly establishes the violation of the Lam-Tung rela-tion, the NA10 and the p+ d data are largely consistentwith the Lam-Tung relation.In an attempt to extract information on the magnitudeof the h⊥1 function from the NA10 data, Boer [17] as-sumed that h⊥1 is proportional to the spin-averaged par-ton distribution function f1:h⊥1 (x, k2T ) = CHαTpiMCMHk2T +M2Ce−αT k2T f1(x), (2)where kT is the quark transverse momentum, MH is themass of the hadron H (pion or nucleon), and MC andCH are constant fitting parameters. A Gaussian trans-verse momentum dependence of e−αTk2T with αT = 1(GeV/c)−2 was assumed. The cos 2φ dependence thenresults from the convolution of the pion h⊥1 /f1 term withthe nucleon h⊥1 /f1 term, and the parameter ν is given asν = 16κ1p2TM2C(p2T + 4M2C)2, (3)where κ1 = CH1CH2/2, and H1, H2 denote the two inter-acting hadrons. As shown in Fig. 2, a good descriptionof the NA10 data is obtained with κ1 = 0.47± 0.14 andMC = 2.4 ± 0.5 GeV/c2. A fit to the E615 ν data at252 GeV/c using MC = 2.4 GeV/c2, also shown in Fig.4-0.1-0.0500.050.15 7.5 10 12.5 15mµµ (GeV/c2)ν-0.1-0.0500.050.10 0.2 0.4 0.6 0.8xFν-0.1-0.0500.050.10.2 0.4 0.6 0.8x1ν-0.1-0.0500.050.10.05 0.1 0.15 0.2x2νFIG. 3: Parameter ν vs. mµµ, xF , x1, and x2 in the Collins-Soper frame for p+d at 800 GeV/c. The error bars correspondto the statistical uncertainties only.2, gives κ1 = 0.93 ± 0.10. These large values of κ1 sug-gest sizable h⊥1 functions for the valence antiquarks inthe pion and for the valence quarks in the nucleon.A fit to the E866 p + d data using Eq. 3 yields κ1 =0.11 ± 0.04 for MC = 2.4 GeV/c2, as shown in Fig. 2.As noted earlier, proton-induced Drell-Yan involves a va-lence quark annihilating with a sea quark. A comparisonof the values of κ1 from proton-induced Drell-Yan withthose from pion-induced Drell-Yan suggests that the ra-tio h⊥1 /f1 for the nucleon sea quarks is substantially be-low that for valence quarks. More specifically, the valueof CH for the sea is approximately a factor 4–8 smallerthan that for valence quarks.The Drell-Yan angular distributions have also been an-alyzed for other kinematic variables. Figure 3 shows thevalues of ν for p+d vs.mµµ, xF , x1, and x2, where x1 andx2 are the Bjorken-x for the beam and target partons,respectively. Again, for each bin the data were dividedinto 5 bins in cos θ and 8 bins in φ in order to extractthe angular distribution parameters. Figure 3 shows nosignificant dependence on these kinematic variables.In summary, we report a measurement of the angu-lar distributions of Drell-Yan dimuons for p + d at 800GeV/c. The pronounced cos 2φ azimuthal angular de-pendence observed previously in pion-induced Drell-Yanis not observed in the p + d reaction. The Lam-Tungrelation, found to be strongly violated in the E615 pion-induced Drell-Yan, remains largely valid for p+ d Drell-Yan. These results put constraints on theoretical mod-els that predict large cos 2φ dependence originating fromQCD vacuum effects. They also suggest that the Boer-Mulders functions h⊥1 for sea quarks are significantlysmaller than those for valence quarks.This work was supported in part by the U.S. Depart-ment of Energy and the National Science Foundation.[1] S.D. Drell and T.M. Yan, Phys. Rev. Lett. 25, 316(1970); Ann. Phys. (NY) 66, 578 (1971).[2] W.J. Stirling and M.R. Whalley, J. Phys. G19, D1(1993).[3] P.L. McGaughey, J.M. Moss, and J.C. Peng, Annu. Rev.Nucl. Part. Sci. 49, 217 (1999).[4] I.R. Kenyon, Rep. Prog. Phys. 45, 1261 (1982); K.Freudenreich, Int. J. Mod. Phys. A5, 3643 (1990).[5] C.S. Lam and W.K. Tung, Phys. Rev. D18, 2447 (1978).[6] P. Chiappetta and M. LeBellac, Z. Phys. C32, 521(1986).[7] J. Cleymans and M. Kuroda, Phys. Lett. B105, 68(1981).[8] C.G. Callan and D. J. Gross, Phys. Rev. Lett. 22, 156(1969).[9] C.S. Lam and W.K. Tung, Phys. Rev. D21, 2712 (1980).[10] NA10 Collaboration, S. Falciano et al., Z. Phys.C31, 513(1986); M. Guanziroli et al., Z. Phys. C37, 545 (1988).[11] E615 Collaboration, J.S. Conway et al., Phys. Rev. D39,92 (1989); J.G. Heinrich et al., Phys. Rev. D44, 1909(1991).[12] A. Brandenburg, O. Nachtmann, and E. Mirkes, Z. Phys.C60, 697 (1993).[13] D. Boer, A. Brandenburg, O. Nachtmann, and A. Uter-mann, Eur. Phys. J. C40, 55 (2005).[14] A. Brandenburg, S.J. Brodsky, V.V. Khoze, and D.Mu¨ller, Phys. Rev. Lett. 73, 939 (1994).[15] K.J. Eskola, P. Hoyer, M. Va¨ntinnen, and R. Vogt, Phys.Lett. B333, 526 (1994).[16] E.L. Berger and S.J. Brodsky, Phys. Rev. Lett. 42, 940(1979).[17] D. Boer, Phys. Rev. D60, 014012 (1999).[18] D. Boer and P.J. Mulders, Phys. Rev. D57, 5780 (1998).[19] S.J. Brodsky, D.S. Hwang, and I. Schmidt, Phys. Lett.B530, 99 (2002).[20] J.C. Collins, Nucl. Phys. B396, 161 (1993).[21] L.P. Gamberg, G.R. Goldstein, and K.A. Oganessyan,Phys. Rev. D67, 071504(R) (2003).[22] D. Boer, S.J. Brodsky, and D.S. Hwang, Phys. Rev. D67,054003 (2003).[23] A. Bacchetta, A. Scha¨fer, and J.-J. Yang, Phys. Lett.B578, 109 (2004).[24] Z. Lu and B.-Q. Ma, Phys. Lett. B615, 200 (2005).[25] Fermilab E866 Collaboration, C.N. Brown et al., Phys.Rev. Lett. 86, 2529 (2001); T.H. Chang et al., Phys. Rev.Lett. 91, 211801 (2003).[26] Fermilab E866 Collaboration, E.H. Hawker et al., Phys.Rev. Lett. 80, 3715 (1998); J.C. Peng et al., Phys. Rev.D58, 092004 (1998); R.S. Towell et al., Phys. Rev. D64,052002 (2001).[27] J.C. Collins and D.E. Soper, Phys. Rev. D16, 2219(1977).[28] A.D. Martin, R.G. Roberts, W.J. Stirling, and R.S.Thorne, Eur. Phys. J. C4, 463 (1998).

Measurement of Angular Distributions of Drell-Yan Dimuons in p + d Interaction at 800-GeV/c

Crossref

Measurement of Angular Distributions of Drell-Yan Dimuons in
                    
                      p

Garvey, G. T.

Geesaman, D. F.

Hawker, E. A.

He, X. C.

Isenhower, L. D.

Kaplan, D. M.

Kaufman, S. B.

Klinksiek, S. A.

Koetke, D. D.

Lee, D. M.

Lee, W. M.

Leitch, M. J.

Makins, N.

McGaughey, P. L.

Moss, J. M.

Mueller, B. A.

Nord, P. M.

Papavassiliou, V.

Park, B. K.

Petitt, G.

Sadler, M. E.

Sondheim, W. E.

Stankus, P. W.

Thompson, T. N.

Towell, R. S.

Tribble, R. E.

Vasiliev, M. A.

Webb, J. C.

Willis, J. L.

Wise, D. K.

Young, G. R.

Texas A&M University

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Measurement of Angular Distributions of Drell-Yan Dimuons in p + d Interaction at
800 GeV/c
L.Y. Zhu,6 J.C. Peng,6, 7 P.E. Reimer,2, 7 T.C. Awes,10 M.L. Brooks,7 C.N. Brown,3 J.D. Bush,1 T.A. Carey,7
T.H. Chang,9 W.E. Cooper,3 C.A. Gagliardi,11 G.T. Garvey,7 D.F. Geesaman,2 E.A. Hawker,11
X.C. He,4 L.D. Isenhower,1 D.M. Kaplan,5 S.B. Kaufman,2 S.A. Klinksiek,8 D.D. Koetke,12 D.M. Lee,7
W.M. Lee,3, 4 M.J. Leitch,7 N. Makins,2, 6 P.L. McGaughey,7 J.M. Moss,7 B.A. Mueller,2 P.M. Nord,12
V. Papavassiliou,9 B.K. Park,7 G. Petitt,4 M.E. Sadler,1 W.E. Sondheim,7 P.W. Stankus,10 T.N. Thompson,7
R.S. Towell,1 R.E. Tribble,11 M.A. Vasiliev,11 J.C. Webb,9 J.L. Willis,1 D.K. Wise,1 and G.R. Young10
(FNAL E866/NuSea Collaboration)
1Abilene Christian University, Abilene, TX 79699
2Physics Division, Argonne National Laboratory, Argonne, IL 60439
3Fermi National Accelerator Laboratory, Batavia, IL 60510
4Georgia State University, Atlanta, GA 30303
5Illinois Institute of Technology, Chicago, IL 60616
6University of Illinois at Urbana-Champaign, Urbana, IL 61801
7Los Alamos National Laboratory, Los Alamos, NM 87545
8University of New Mexico, Albuquerque, NM 87131
9New Mexico State University, Las Cruces, NM 88003
10Oak Ridge National Laboratory, Oak Ridge, TN 37831
11Texas A&M University, College Station, TX 77843
12Valparaiso University, Valparaiso, IN 46383
(Dated: July 25, 2018)
We report a measurement of the angular distributions of Drell-Yan dimuons produced using an
800 GeV/c proton beam on a deuterium target. The muon angular distributions in polar angle
θ and azimuthal angle φ have been measured over the kinematic range 4.5 < mµµ < 15 GeV/c
2,
0 < pT < 4 GeV/c, and 0 < xF < 0.8. No significant cos2φ dependence is found in these proton-
induced Drell-Yan data, in contrast to the situation for pion-induced Drell-Yan. The data are
compared with expectations from models which attribute the cos2φ distribution to a QCD vacuum
effect or to the presence of the transverse-momentum-dependent Boer-Mulders structure function
h⊥1 . Constraints on the magnitude of the sea-quark h
⊥
1 structure functions are obtained.
PACS numbers: 13.85.Qk, 14.20.Dh, 24.85.+p, 13.88.+e
The Drell-Yan process [1], in which a charged lepton
pair is produced in a high-energy hadron-hadron interac-
tion via the qq¯ → l+l− process, has been a testing ground
for perturbative QCD and a unique tool for probing par-
ton distributions of hadrons. The Drell-Yan production
cross sections can be well described by next-to-leading
order QCD calculations [2]. This provides a firm theo-
retical framework for using the Drell-Yan process to de-
termine the antiquark content of nucleons and nuclei [3],
as well as the quark distributions of pions, kaons, and
antiprotons [4].
Despite the success of perturbative QCD in describing
the Drell-Yan cross sections, it remains a challenge to un-
derstand the angular distributions of the Drell-Yan pro-
cess. Assuming dominance of the single-photon process,
a general expression for the Drell-Yan angular distribu-
tion is [5]
dσ
dΩ
∝ 1 + λ cos2 θ + µ sin 2θ cosφ+
ν
2
sin2 θ cos 2φ, (1)
where θ and φ denote the polar and azimuthal angle,
respectively, of the l+ in the dilepton rest frame. In
the “naive” Drell-Yan model, where the transverse mo-
mentum of the quark is ignored and no gluon emission
is considered, λ = 1 and µ = ν = 0 are obtained.
QCD effects [6] and non-zero intrinsic transverse mo-
mentum of the quarks [7] can both lead to λ 6= 1 and
µ, ν 6= 0. However, λ and ν should still satisfy the rela-
tion 1 − λ = 2ν [5]. This so-called Lam-Tung relation,
obtained as a consequence of the spin-1/2 nature of the
quarks, is analogous to the Callan-Gross relation [8] in
Deep-Inelastic Scattering. While QCD effects can signif-
icantly modify the Callan-Gross relation, the Lam-Tung
relation is predicted to be largely unaffected by QCD
corrections [9].
The first measurement of the Drell-Yan angular dis-
tribution was performed by the NA10 Collaboration for
pi− +W at 140, 194, and 286 GeV/c, with the highest
statistics at 194 GeV/c [10]. The cos 2φ angular depen-
dences showed a sizable ν, increasing with dimuon trans-
verse momentum (pT ) and reaching a value of ≈ 0.3 at
pT = 2.5 GeV/c (see Fig. 1). The observed behavior of ν
could not be described by perturbative QCD calculations
which predict much smaller values of ν [6]. The Fermilab
E615 Collaboration subsequently performed a measure-
21
2
3
NA10 pi-+W at 194 GeV/c E615 pi-+W at 252 GeV/c
E866 p+d at 800 GeV/c
λ
-0.5
0
0.5
µ
-1
-0.5
0
0.5
1
ν
-2
0
2
0 0.5 1 1.5 2 2.5 3 3.5 4
pT (GeV/c)
2ν
-
(1-
λ)
FIG. 1: Parameters λ, µ, ν and 2ν − (1 − λ) vs. pT in the
Collins-Soper frame. Solid circles are for E866 p + d at 800
GeV/c, crosses are for NA10 pi− + W at 194 GeV/c, and
diamonds are E615 pi− +W at 252 GeV/c. The error bars
include the statistical uncertainties only.
ment of pi−+W Drell-Yan production at 252 GeV/c with
broad coverage in the decay angle θ [11]. The E615 re-
sults showed that λ deviates from 1 at large values of xpi
(the Bjorken-x of the incident pions), and both µ and ν
have large non-zero values. Furthermore, the E615 data
showed that the Lam-Tung relation, 2ν = 1−λ, is clearly
violated. (See Fig. 1.)
The NA10 and E615 results on the Drell-Yan angu-
lar distributions strongly suggest that new effects be-
yond conventional perturbative QCD are present. Sev-
eral attempts have been made to interprete these data.
Brandenburg, Nachtmann and Mirke suggested that a
factorization-breaking QCD vacuum may lead to a corre-
lation between the transverse spin of the antiquark in the
pion and that of the quark in the nucleon [12]. This would
result in a non-zero cos 2φ angular dependence consistent
with the data. As pointed out by Boer et al., a possible
source for a factorization-breaking QCD vacuum is helic-
ity flip in the instanton model [13]. Several authors have
also considered higher-twist effects from quark-antiquark
binding in pions [14, 15], motivated by earlier work of
Berger and Brodsky [16]. This model predicts behavior
of µ and ν in qualitative agreement with the data. How-
ever, the model is strictly applicable only in the xpi → 1
region while the NA10 and E615 data exhibit nonpertur-
bative effects over a much broader kinematic region.
More recently, Boer pointed out [17] that the cos 2φ an-
gular dependences observed in NA10 and E615 could be
due to the kT -dependent parton distribution function h
⊥
1 .
This so-called Boer-Mulders function [18] is an exam-
ple of a novel type of kT -dependent parton distribution
function, and it characterizes the correlation of a quark’s
transverse spin and its transverse momentum, kT , in an
unpolarized nucleon. It has an interesting property of be-
ing a time-reversal odd object and owes its existence to
the presence of initial/final state interactions [19]. The
Boer-Mulders function is the analog of the Collins frag-
mentation function [20], which describes the correlation
between the transverse spin of a quark and the trans-
verse momentum of the particle into which it hadronizes.
Model calculations for the nucleon (pion) Boer-Mulders
functions have been carried out [21, 22, 23, 24] in the
framework of quark-diquark (quark-spectator-antiquark)
model, and can successfully describe the ν behavior ob-
served in NA10 [24].
To shed additional light on the origins of the NA10 and
E615 Drell-Yan angular distributions, we have analyzed
p+ d Drell-Yan angular distribution data at 800 GeV/c
from Fermilab E866. There are several physics motiva-
tions for this study. First, there has been no report on the
azimuthal angular distributions for proton-induced Drell-
Yan – all measurements so far have been for polar angular
distributions [3, 25]. Second, proton-induced Drell-Yan
data provide a stringent test of theoretical models. For
example, the cos 2φ dependence is expected to be much
reduced in proton-induced Drell-Yan if the underlying
mechanism involves the Boer-Mulders functions. This
is due to the expectation that the Boer-Mulders func-
tions are small for the sea-quarks. However, if the QCD
vacuum effect [12] is the origin of the cos 2φ angular de-
pendence, then the azimuthal behavior of proton-induced
Drell-Yan should be similar to that of pion-induced Drell-
Yan. Third, the validity of the Lam-Tung relation has
never been tested for proton-induced Drell-Yan, and the
present study provides a first test.
The Fermilab E866 experiment was performed using
the upgraded Meson-East magnetic pair spectrometer.
Details of the experimental setup have been described
elsewhere [26]. An 800 GeV/c primary proton beam with
up to 2× 1012 protons per beam spill was incident upon
one of three identical 50.8 cm long cylindrical stainless
steel target flasks containing either liquid hydrogen, liq-
uid deuterium or vacuum. A copper beam dump located
inside the second dipole magnet (SM12) absorbed pro-
tons that passed through the target. Downstream of the
beam dump was an absorber wall that completely filled
the aperture of the magnet. This absorber wall removed
hadrons produced in the target and the beam dump.
3TABLE I: Mean values of the λ, µ, ν parameters and the quan-
tity 2ν − (1− λ) for three Drell-Yan measurements. The pT
dependence of these quantities is shown in Fig. 1.
p+ d pi− +W pi− +W
800 GeV/c 194 GeV/c 252 GeV/c
(E866) (NA10) (E615)
〈λ〉 1.07 ± 0.07 0.83 ± 0.04 1.17 ± 0.06
〈µ〉 0.003 ± 0.013 0.008 ± 0.010 0.09 ± 0.02
〈ν〉 0.027 ± 0.010 0.091 ± 0.009 0.169 ± 0.019
〈2ν − (1− λ)〉 0.12 ± 0.07 0.01 ± 0.04 0.51 ± 0.07
Several settings of the currents in the three dipole mag-
nets (SM0, SM12, SM3) were used in order to optimize
acceptance for different dimuon mass regions. Data col-
lected with the “low mass” and “high mass” settings [26]
on liquid deuterium and empty targets were used in this
analysis. The detector system consisted of four track-
ing stations and a momentum analyzing magnet (SM3).
Tracks reconstructed by the drift chambers were extrapo-
lated to the target using the momentum determined from
the bend angle in SM3. The target position was used to
refine the parameters of each muon track.
From the momenta of the µ+ and µ−, kinematic vari-
ables of the dimuons (xF ,mµµ, pT ) were readily recon-
structed. The muon angles θ and φ in the Collins-Soper
frame [27] were also calculated. To remove the quarko-
nium background, only events with 4.5 < mµµ < 9
GeV/c2 or mµµ > 10.7 GeV/c
2 were analyzed. A total
of 118,000 p+ d Drell-Yan events covering the decay an-
gular range −0.5 < cos θ < 0.5 and −pi < φ < pi remain.
Detailed Monte-Carlo simulations for the experiment us-
ing the MRST98 parton distribution functions [28] for
NLO Drell-Yan cross sections have shown good agree-
ments with the data for a variety of measured quantities.
Figure 1 shows the angular distribution parameters
λ, µ, and ν vs. pT . To extract these parameters, the
Drell-Yan data were grouped into 5 bins in cos θ and 8
bins in φ for each pT bin. A least-squares fit to the data
using Eq. 1 to describe the angular distribution was per-
formed. Only statistical errors are shown in Fig. 1. The
primary contributions to the systematic errors are the
uncertainties of the incident beam angles on target. The
analysis has been performed allowing the beam angles to
vary within their ranges of uncertainty. From this study,
we found that the systematic errors are comparable to the
statistical errors for each individual pT bin. However, the
pT averaged values 〈λ〉, 〈µ〉, and 〈ν〉, are dominatd by the
statistical errors.
For comparison with the p + d Drell-Yan data, the
NA10 pi−+W data at 194 GeV/c and the E615 pi−+W
data at 252 GeV/c are also shown in Fig. 1. To test the
validity of the Lam-Tung relation, also shown in Fig. 1
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 3 3.5 4
pT (GeV/c)
ν
pi- + W at 194 GeV/c
pi- + W at 252 GeV/c
p + d at 800 GeV/c
FIG. 2: Parameter ν vs. pT in the Collins-Soper frame for
three Drell-Yan measurements. Fits to the data using Eq. 3
and MC = 2.4 GeV/c
2 are also shown.
is the quantity, 2ν − (1 − λ), for all three experiments.
For p + d at 800 GeV/c, Fig. 1 shows that λ is consis-
tent with 1, in agreement with previous studies [3, 25],
while µ and ν deviate only slightly from zero. This is in
contrast to the pion-induced Drell-Yan results, in which
much larger values of ν are found. Table I lists the mean
values of λ, µ, ν and 2ν − (1 − λ) for these three experi-
ments. Again, the qualitatively different behavior of the
azimuthal angular distributions for p+ d versus pi− +W
is evident. It is also interesting to note that while E615
clearly establishes the violation of the Lam-Tung rela-
tion, the NA10 and the p+ d data are largely consistent
with the Lam-Tung relation.
In an attempt to extract information on the magnitude
of the h⊥1 function from the NA10 data, Boer [17] as-
sumed that h⊥1 is proportional to the spin-averaged par-
ton distribution function f1:
h⊥1 (x, k
2
T ) = CH
αT
pi
MCMH
k2T +M
2
C
e−αT k
2
T f1(x), (2)
where kT is the quark transverse momentum, MH is the
mass of the hadron H (pion or nucleon), and MC and
CH are constant fitting parameters. A Gaussian trans-
verse momentum dependence of e−αTk
2
T with αT = 1
(GeV/c)−2 was assumed. The cos 2φ dependence then
results from the convolution of the pion h⊥1 /f1 term with
the nucleon h⊥1 /f1 term, and the parameter ν is given as
ν = 16κ1
p2TM
2
C
(p2T + 4M
2
C)
2
, (3)
where κ1 = CH1CH2/2, and H1, H2 denote the two inter-
acting hadrons. As shown in Fig. 2, a good description
of the NA10 data is obtained with κ1 = 0.47± 0.14 and
MC = 2.4 ± 0.5 GeV/c
2. A fit to the E615 ν data at
252 GeV/c using MC = 2.4 GeV/c
2, also shown in Fig.
4-0.1
-0.05
0
0.05
0.1
5 7.5 10 12.5 15
mµµ (GeV/c2)
ν
-0.1
-0.05
0
0.05
0.1
0 0.2 0.4 0.6 0.8
xF
ν
-0.1
-0.05
0
0.05
0.1
0.2 0.4 0.6 0.8
x1
ν
-0.1
-0.05
0
0.05
0.1
0.05 0.1 0.15 0.2
x2
ν
FIG. 3: Parameter ν vs. mµµ, xF , x1, and x2 in the Collins-
Soper frame for p+d at 800 GeV/c. The error bars correspond
to the statistical uncertainties only.
2, gives κ1 = 0.93 ± 0.10. These large values of κ1 sug-
gest sizable h⊥1 functions for the valence antiquarks in
the pion and for the valence quarks in the nucleon.
A fit to the E866 p + d data using Eq. 3 yields κ1 =
0.11 ± 0.04 for MC = 2.4 GeV/c
2, as shown in Fig. 2.
As noted earlier, proton-induced Drell-Yan involves a va-
lence quark annihilating with a sea quark. A comparison
of the values of κ1 from proton-induced Drell-Yan with
those from pion-induced Drell-Yan suggests that the ra-
tio h⊥1 /f1 for the nucleon sea quarks is substantially be-
low that for valence quarks. More specifically, the value
of CH for the sea is approximately a factor 4–8 smaller
than that for valence quarks.
The Drell-Yan angular distributions have also been an-
alyzed for other kinematic variables. Figure 3 shows the
values of ν for p+d vs.mµµ, xF , x1, and x2, where x1 and
x2 are the Bjorken-x for the beam and target partons,
respectively. Again, for each bin the data were divided
into 5 bins in cos θ and 8 bins in φ in order to extract
the angular distribution parameters. Figure 3 shows no
significant dependence on these kinematic variables.
In summary, we report a measurement of the angu-
lar distributions of Drell-Yan dimuons for p + d at 800
GeV/c. The pronounced cos 2φ azimuthal angular de-
pendence observed previously in pion-induced Drell-Yan
is not observed in the p + d reaction. The Lam-Tung
relation, found to be strongly violated in the E615 pion-
induced Drell-Yan, remains largely valid for p+ d Drell-
Yan. These results put constraints on theoretical mod-
els that predict large cos 2φ dependence originating from
QCD vacuum effects. They also suggest that the Boer-
Mulders functions h⊥1 for sea quarks are significantly
smaller than those for valence quarks.
This work was supported in part by the U.S. Depart-
ment of Energy and the National Science Foundation.
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Measurement of Angular Distributions of Drell-Yan Dimuons in p + d Interactions at 800 GeV / c

OAKTrust Digital Repository (Texas A&M Univ)

arXiv:0811.4589v2  [nucl-ex]  17 Apr 2009Measurement of Angular Distributions of Drell-Yan Dimuons in p+ p Interactions at800 GeV/cL.Y. Zhu,5, 7 J.C. Peng,7, 8 P.E. Reimer,2, 8 T.C. Awes,11 M.L. Brooks,8 C.N. Brown,3 J.D. Bush,1T.A. Carey,8 T.H. Chang,10 W.E. Cooper,3 C.A. Gagliardi,12 G.T. Garvey,8 D.F. Geesaman,2 E.A. Hawker,12X.C. He,4 L.D. Isenhower,1 D.M. Kaplan,6 S.B. Kaufman,2 S.A. Klinksiek,9 D.D. Koetke,13 D.M. Lee,8W.M. Lee,3, 4 M.J. Leitch,8 N. Makins,2, 7 P.L. McGaughey,8 J.M. Moss,8 B.A. Mueller,2 P.M. Nord,13V. Papavassiliou,10 B.K. Park,8 G. Petitt,4 M.E. Sadler,1 W.E. Sondheim,8 P.W. Stankus,11 T.N. Thompson,8R.S. Towell,1 R.E. Tribble,12 M.A. Vasiliev,12 J.C. Webb,10 J.L. Willis,1 D.K. Wise,1 and G.R. Young11(FNAL E866/NuSea Collaboration)1Abilene Christian University, Abilene, TX 796992Physics Division, Argonne National Laboratory, Argonne, IL 604393Fermi National Accelerator Laboratory, Batavia, IL 605104Georgia State University, Atlanta, GA 303035Hampton University, Hampton, VA 231876Illinois Institute of Technology, Chicago, IL 606167University of Illinois at Urbana-Champaign, Urbana, IL 618018Los Alamos National Laboratory, Los Alamos, NM 875459University of New Mexico, Albuquerque, NM 8713110New Mexico State University, Las Cruces, NM 8800311Oak Ridge National Laboratory, Oak Ridge, TN 3783112Texas A&M University, College Station, TX 7784313Valparaiso University, Valparaiso, IN 46383(Dated: August 6, 2018)We report a measurement of the angular distributions of Drell-Yan dimuons produced using an 800GeV/c proton beam on a hydrogen target. The polar and azimuthal angular distribution parametershave been extracted over the kinematic range 4.5 < mµµ < 15 GeV/c2 (excluding the Υ resonanceregion), 0 < pT < 4 GeV/c, and 0 < xF < 0.8. The p+ p angular distributions are similar to thoseof p+d, and both data sets are compared with models which attribute the cos 2φ distribution eitherto the presence of the transverse-momentum-dependent Boer-Mulders structure function h⊥1 or toQCD effects. The data indicate the need to include QCD effects before reliable information on theBoer-Mulders function can be extracted. The validity of the Lam-Tung relation in p+ p Drell-Yanis also tested.PACS numbers: 13.85.Qk, 14.20.Dh, 24.85.+p, 13.88.+eThe study of the transverse momentum dependent(TMD) parton distribution functions of the nucleon hasreceived much attention in recent years as it providesnew perspectives on the hadron structure and QCD [1].One of these TMD distribution functions, first consid-ered by Sivers [2], represents the correlation betweenthe quark’s transverse momentum, k⊥, and the trans-verse spin of the nucleon, S⊥. This so-called Sivers func-tion, f⊥1T (x, k2⊥), where x is the fraction of proton’s mo-mentum carried by the quark, is time-reversal odd (T-odd) and can arise from initial- or final-state interac-tions [3]. More generally, the requirement of gauge in-variance of parton distributions was shown to providenontrivial phases leading to the existence of T-odd distri-bution functions [4, 5]. Recent measurements of the semi-inclusive deep-inelastic scattering (SIDIS) by the HER-MES [6] and COMPASS [7] collaborations have shownclear evidence for the presence of the T-odd Sivers func-tions. These data also allow the first determination [8]of the magnitude and flavor structure of the Sivers func-tions.Another T-odd distribution function is the Boer-Mulders function, h⊥1 (x, k2⊥), which signifies the corre-lation between k⊥ and the quark transverse spin, s⊥, inan unpolarized nucleon [9]. The Boer-Mulders function isthe chiral-odd analog of the Sivers function and also owesits existence to the presence of initial/final state interac-tions [10]. While the Sivers function is beginning to bequantitatively determined from the SIDIS experiments,very little is known about the Boer-Mulders function sofar.Several model calculations have been carried out forthe Boer-Mulders functions. In the quark-diquark model,it was shown that the Boer-Mulders functions are identi-cal to the Sivers functions when only the scalar diquarkconfiguration is considered [10, 11]. More recently, cal-culations taking into account both the scalar and theaxial-vector diquark configurations found significant dif-ferences in flavor dependence between the Sivers andBoer-Mulders functions [12]. In particular, the u andd valence quark Boer-Mulders functions are predicted tobe both negative, while the Sivers function is negative2for the u and positive for the d valence quarks. Othercalculations using the MIT bag model [13], the relativis-tic constituent quark model [14], the large-Nc model [15],and lattice QCD [16] also predict negative signs for theu and d valence Boer-Mulders functions. Burkardt re-cently pointed out [17] that the negative signs for theBoer-Mulders functions are expected for both nucleonsand pions. The model predictions for the same signs ofthe u and d Boer-Mulders functions remain to be testedexperimentally. Furthermore, the striking prediction [4]that the T-odd Boer-Mulders functions in the SIDIS pro-cess will change their signs for the Drell-Yan process alsoawaits experimental confirmation.The Boer-Mulders functions can be extracted [18] fromthe azimuthal angular distributions in the unpolarizedDrell-Yan process, h1h2 → l+l−x. The general expres-sion for the Drell-Yan angular distribution is [19]dσdΩ∝ 1 + λ cos2 θ + µ sin 2θ cosφ+ν2sin2 θ cos 2φ, (1)where θ and φ are the polar and azimuthal decay an-gle of the l+ in the dilepton rest frame. Boer showedthat the cos 2φ term is proportional to the convolution ofthe quark and antiquark Boer-Mulders functions in theprojectile and target [18]. This can be understood bynoting that the Drell-Yan cross section depends on thetransverse spins of the annihilating quark and antiquark.Therefore, a correlation between the transverse spin andthe transverse momentum of the quark, as representedby the Boer-Mulders function, would lead to a preferredtransverse momentum direction.Pronounced cos 2φ dependences were indeed observedin the NA10 [20] and E615 [21] pion-induced Drell-Yanexperiments, and attributed to the Boer-Mulders func-tion. The first measurement of the cos 2φ dependenceof the proton-induced Drell-Yan process was recently re-ported for p + d interactions at 800 GeV/c [22]. Incontrast to pion-induced Drell-Yan, significantly smaller(but non-zero) cos2φ azimuthal angular dependence wasobserved in the p + d reaction. While the pion-inducedDrell-Yan process is dominated by annihilation between avalence antiquark in the pion and a valence quark in thenucleon, the proton-induced Drell-Yan process involvesa valence quark in the proton annihilating with a seaantiquark in the nucleon. Therefore, the p + d resultsuggests [22] that the Boer-Mulders functions for sea an-tiquarks are significantly smaller than those for valencequarks.A recent analysis [23] indicated that the E866 p + ddata are consistent with the u and d Boer-Mulders func-tions having the same signs, as predicted by various mod-els. However, the p + d data alone cannot provide anunambiguous determination of the flavor dependence ofthe Boer-Mulders functions. Moreover, it was recentlypointed out [24, 25] that QCD processes would lead toa sizeable cos 2φ effect which has not been taken into012p+p p+dλ-0.200.2µ-0.200.2ν-1-0.500.510 0.5 1 1.5 2 2.5 3 3.5 4pT (GeV/c)2ν-(1-λ)FIG. 1: Parameters λ, µ, ν and 2ν − (1 − λ) vs. pT in theCollins-Soper frame. Solid squares (open circles) are for E866p + p (p + d) at 800 GeV/c. The vertical error bars includethe statistical uncertainties only.account in the extractions [18, 23, 26] of Boer-Muldersfunctions from the Drell-Yan data. In this paper we re-port the Drell-Yan angular distributions of the p+p reac-tion at 800 GeV/c, which provides further constraints onthe flavor dependence of the Boer-Mulders functions [26].We also compare the cos 2φ dependences of p+p and p+ddata with the prediction of QCD.The Fermilab E866 experiment was performed us-ing the upgraded Meson-East magnetic pair spectrom-eter [27]. An 800 GeV/c primary proton beam with upto 2×1012 protons per 20 s beam spill was incident uponone of three identical 50.8 cm long target flasks contain-ing either liquid hydrogen, liquid deuterium or vacuum.A copper beam dump located inside the second dipolemagnet (SM12) absorbed protons that passed throughthe target. Downstream of the beam dump was an ab-sorber wall that removed hadrons produced in the targetand the beam dump.Several settings of the currents in the three dipole mag-nets (SM0, SM12, SM3) were used in order to optimizeacceptance for different dimuon mass regions. Data col-lected with the “low mass” and “high mass” settings [27]on liquid hydrogen and empty targets were used in thisanalysis. The detector system consisted of four track-3TABLE I: Mean values of the λ, µ, ν parameters and the quan-tity 2ν − (1− λ) for the p+ p, p+ d, and pi− +W Drell-Yanmeasurements.p+ p p+ d pi− +W800 GeV/c 800 GeV/c 194 GeV/c(E866) (E866) (NA10)〈λ〉 0.85 ± 0.10 1.07 ± 0.07 0.83± 0.04〈µ〉 −0.026 ± 0.019 0.003 ± 0.013 0.008 ± 0.010〈ν〉 0.040 ± 0.015 0.027 ± 0.010 0.091 ± 0.009〈2ν − (1− λ)〉 −0.07 ± 0.10 0.12 ± 0.07 0.01± 0.04ing stations and a momentum analyzing magnet (SM3).Tracks reconstructed by the drift chambers were extrapo-lated to the target using the momentum determined fromthe bend angle in SM3. The target position was used torefine the parameters of each muon track.From the momenta of the µ+ and µ−, kinematic vari-ables of the dimuons (xF ,mµµ, and pT , where xF is thefraction of the c.m. momentum carried by dimuon ofmass mµµ, and pT is the dimuon transverse momen-tum) were readily reconstructed. The muon angles θand φ in the Collins-Soper frame [28] were also calcu-lated. To eliminate the J/Ψ and Υ resonance back-ground, dimuon events with mµµ < 4.5 GeV/c2 and 9.0GeV/c2 < mµµ < 10.7 GeV/c2 were rejected in the anal-ysis. A total of ≈54,000 p + p Drell-Yan events cov-ering the decay angular range −0.5 < cos θ < 0.5 and−pi < φ < pi remain. Detailed Monte Carlo simulationsof the experiment using the MRST98 parton distribu-tion functions [29] for NLO Drell-Yan cross sections haveshown good agreement with the data for a variety of mea-sured quantities.Figure 1 shows the angular distribution parametersλ, µ, and ν vs. pT . To extract these parameters, theDrell-Yan data were grouped into 5 bins in cos θ and 8bins in φ for each pT bin. A least-squares fit to the datausing Eq. 1 to describe the angular distribution was per-formed. The extracted values of λ, µ, ν are insensitive totheir values used in the Monte Carlo simulation. Onlystatistical errors are shown in Fig. 1. The primary contri-butions to the systematic errors are the uncertainties ofthe incident beam angles on target. Analysis performedby allowing the beam angles to vary within their rangesof uncertainty has shown that the systematic errors aresmall compared to the statistical errors. The E866 p+ dDrell-Yan data are also shown in Fig. 1 for comparisonwith the E866 p+ p data. The p+ d data contain a totalof ≈118,000 events covering an identical cos θ range. ThepT -averaged values of 〈λ〉, 〈µ〉, and 〈ν〉 for p + p, p + d,and the NA10 pi− + W data [20] are listed in Table I.Within statistics, the angular distributions of p + p areconsistent with those of p+ d. Also shown in Fig. 1 andTable I is the quantity 2ν − (1− λ), which should vanishif the Lam-Tung relation is valid. While QCD effects canlead to λ 6= 1 and µ, ν 6= 0, Lam and Tung showed [30]that the relation 1−λ = 2ν is largely unaffected by QCDcorrections. Table I shows that while 〈λ〉 deviates from1 and 〈ν〉 is nonzero for the E866 p + p and the NA10pi−+W Drell-Yan data, the Lam-Tung relation is indeedquite well satisfied within statistical uncertainty for allpT . This differs from the observation of a significant vio-lation of the Lam-Tung relation at large pT by the E615collaboration in the pi−+W reaction at 252 GeV/c [21].Figure 2 shows the parameter ν vs. pT for the p + pand p + d Drell-Yan data. The solid curves are calcula-tions [23, 26] for p+ p and p+ d using parametrizationsof the Boer-Mulders functions deduced from a fit to thep + d Drell-Yan data. The predicted larger values of νfor p + p compared to p + d in the region of pT ∼ 1.5GeV/c are not observed (the predicted p + p/p + d ra-tio, R, for 0.5 < pT < 2.0 GeV/c, is ∼ 2, while thedata give R = 1.0± 0.5). Furthermore, the shape of thepredicted pT dependence differs from that of the data,resulting in a reduced χ2 value of 3.2 for 5 degrees offreedom (probability of 0.7%). This strongly suggeststhat there could be other mechanisms contributing to thecos 2φ azimuthal angular dependence at large pT . In re-cent papers [24, 25], the QCD contribution to the cos 2φazimuthal angular dependence is given asν =Q2⊥/Q21 + 32Q2⊥/Q2, (2)where Q⊥ is the dimuon transverse momentum. The pre-dicted QCD contribution, the same for p+p and p+d dueto the identical kinematic coverage for the two reactions,is shown as the dot-dashed curve in Fig. 2. A compar-ison between the QCD prediction with the data gives areduced χ2 of 1.0 for 5 degrees of freedom (probabilityof 42%) for p+ p and a reduced χ2 of 1.9 (probability of9%) for p + d. From Fig. 2 it is evident that the QCDcontribution is expected to become more important athigh pT while the Boer-Mulders functions contribute pri-marily at lower pT . An analysis combining both effectsis required in order to extract reliably the Boer-Muldersfunctions from the p+p and p+d data. It is worth notingthat the pi− +W Drell-Yan data [20, 21] also show largevalues of ν at large pT , consistent with the presence ofQCD effects.The p + p Drell-Yan angular distributions have alsobeen analyzed for other kinematic variables. Figure 3shows the values of ν vs. mµµ, xF , x1, and x2, where x1and x2 are the Bjorken-x for the beam and target par-tons, respectively. Again, for each bin the data weredivided into 5 bins in cos θ and 8 bins in φ in order to ex-tract the angular distribution parameters. The p+d dataare also shown for comparison. Figure 3 shows that themagnitude of ν for p+ p is consistent with that for p+ dfor most of the kinematic regimes. These data provide4-0.1-0.0500.050.10.150.20.250.30 0.5 1 1.5 2 2.5 3 3.5 4pT (GeV/c)νp + d at 800 GeV/cp + p at 800 GeV/cFIG. 2: (color online). Parameter ν vs. pT in the Collins-Soper frame for the p+ p and p+ d Drell-Yan data. The solidand dotted curves are calculations [23] for p + p and p + d,respectively, using parametrizations based on a fit to the p+ddata. The dot-dashed curve is the contribution from the QCDprocess (Eq. 2).-0.25-0.12500.1250.255 7.5 10 12.5 15mµµ (GeV/c2)ν-0.25-0.12500.1250.250 0.2 0.4 0.6 0.8xFν-0.25-0.12500.1250.250.2 0.4 0.6 0.8x1ν-0.25-0.12500.1250.250.05 0.1 0.15 0.2x2νFIG. 3: Parameter ν vs. mµµ, xF , x1, and x2 in the Collins-Soper frame for p+ p (solid squares) and p+ d (open circles)at 800 GeV/c. The vertical error bars correspond to the sta-tistical uncertainties only.further input for future extraction of the Boer-Muldersfunctions.In summary, we report a measurement of the angu-lar distributions of Drell-Yan dimuons for p + p at 800GeV/c. The pronounced cos 2φ azimuthal angular de-pendence observed previously in pion-induced Drell-Yanis not observed in the p + p reaction. The Lam-Tungrelation remains valid for the p+ p Drell-Yan data. Theoverall magnitude of the cos 2φ dependence for p + p isconsistent with, but slightly larger than that of p + d.The data suggest the presence of higher-order QCD cor-rections at high pT , and it is important to take this con-tribution into account before reliable extraction of theBoer-Mulders functions could be obtained.We acknowledge helpful discussion with Bo-Qiang Ma,Bing Zhang, Matthias Burkardt, Feng Yuan, Werner Vo-gelsang, and Jianwei Qiu. This work was supported inpart by the U.S. Department of Energy and the NationalScience Foundation.[1] V. Barone, A. Drago, and P. G. Ratcliffe, Phys. Rep.359, 1 (2002).[2] D. Sivers, Phys. Rev. D 41, 83 (1990).[3] S.J. Brodsky, D.S. Hwang, and I. Schmidt, Phys. Lett. B530, 99 (2002).[4] J.C. Collins, Phys. Lett. B 536, 43 (2002).[5] X. Ji and F. Yuan, Phys. Lett. B 543, 66 (2002).[6] HERMES Collaboration, A. Airapetian et al., Phys.Rev. Lett. 94, 012002 (2005); M. Diefenthaler, arXiv:0706.2242.[7] COMPASS Collaboration, V. Yu. Alexakhin et al., Phys.Rev. Lett. 94, 202002 (2005); M. Alekseev et al., arXiv:0802.2160.[8] W. Vogelsang and F. Yuan, Phys. Rev. D 72, 054028(2005); M. Anselmino et al., Phys. Rev. D 72, 094007(2005); M. Anselmino et al., arXiv:0807.0166.[9] D. Boer and P.J. Mulders, Phys. Rev. D 57, 5780 (1998).[10] D. Boer, S.J. Brodsky, and D.S. Hwang, Phys. Rev. D67, 054003 (2003).[11] L.P. Gamberg, G.R. Goldstein, and K.A. Oganessyan,Phys. Rev. D 67, 071504(R) (2003); A. Bacchetta, A.Scha¨fer, and J.-J. Yang, Phys. Lett. B 578, 109 (2004).[12] L.P. Gamberg, G.R. Goldstein, and M. Schlegel, Phys.Rev. D 77, 094016 (2008).[13] F. Yuan, Phys. Lett. B 575, 45 (2003).[14] B. Pasquini, M. Pincetti, and S. Boffi, Phys. Rev. D 76,034020 (2007).[15] P.V. Pobylitsa, hep-ph/0301236.[16] M. Go¨ckeler et al., Phys. Rev. Lett. 98, 222001 (2007).[17] M. Burkardt and B. Hannafious, Phys. Lett. B 658, 130(2008).[18] D. Boer, Phys. Rev. D 60, 014012 (1999).[19] C.S. Lam and W.K. Tung, Phys. Rev. D 18, 2447 (1978).[20] NA10 Collaboration, S. Falciano et al., Z. Phys. C 31,513 (1986); M. Guanziroli et al., Z. Phys. C 37, 545(1988).[21] E615 Collaboration, J.S. Conway et al., Phys. Rev. D 39,92 (1989).[22] E866 Collaboration, L.Y. Zhu et al., Phys. Rev. Lett. 99,082301 (2007).[23] B. Zhang, Z. Lu, B.-Q. Ma, and I. Schmidt, Phys. Rev.D 77, 054011 (2008).[24] D. Boer and W. Vogelsang, Phys. Rev. D 74, 014004(2006).[25] E.L. Berger, J.-W. Qiu, and R.A. Rodriguez-Pedraza,5Phys. Lett. B 656, 74 (2007); Phys. Rev. D 76, 074006(2007).[26] B. Zhang, Z. Lu, B.-Q. Ma, and I. Schmidt, arXiv:0807.0503.[27] E866 Collaboration, E.H. Hawker et al., Phys. Rev. Lett.80, 3715 (1998); J.C. Peng et al., Phys. Rev. D 58,092004 (1998); R.S. Towell et al., Phys. Rev. D 64,052002 (2001).[28] J.C. Collins and D.E. Soper, Phys. Rev. D 16, 2219(1977).[29] A.D. Martin, R.G. Roberts, W.J. Stirling, and R.S.Thorne, Eur. Phys. J. C 4, 463 (1998).[30] C.S. Lam and W.K. Tung, Phys. Rev. D 21, 2712 (1980).

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Measurement of Angular Distributions of Drell-Yan Dimuons in p + d
  Interaction at 800 GeV/c

Measurement of Angular Distributions of Drell-Yan Dimuons in p + d Interaction at 800 GeV/c

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