---

Flavor Asymmetry of the Nucleon Sea:

arXiv:hep-ph/9210239v1 15 Oct 1992FERMILAB-PUB-92/264–TLBL-32987hep-ph@xxx/yymmnnFlavor Asymmetry of the Nucleon Sea:Consequences for Dilepton ProductionEstia J. Eichten∗Fermi National Accelerator Laboratory P.O. Box 500, Batavia, Illinois 60510Ian Hinchliffe†Lawrence Berkeley Laboratory Berkeley, California 94720Chris Quigg‡Fermi National Accelerator Laboratory P.O.

Box 500, Batavia, Illinois 60510Parton distributions derived from a chiral quark model that generates an excessof down quarks and antiquarks in the proton’s sea satisfactorily describe the mea-sured yields of muon pairs produced in proton-nucleus collisions.Comparison ofdilepton yields from hydrogen and deuterium targets promises greater sensitivity tothe predicted flavor asymmetry.Typeset Using REVTEX∗Internet address: eichten@fnal.fnal.gov.†Internet address: hinchliffe%theorm.hepnet@lbl.gov.‡Internet address: quigg@fnal.fnal.gov.1

In a recent article [1], we showed that the fluctuation of constituent quarks into quarksplus Goldstone bosons generates a flavor-asymmetry in the light-quark sea of the nucleonthat is a plausible origin for the violation of the Gottfried sum rule reported by the NewMuon Collaboration (NMC) at CERN [2]. Fermilab experiment E772 has now presentedmeasurements of the yields of massive muon pairs in collisions of 800-GeV/c protons withnuclear targets that are sensitive to the flavor content of the nucleon sea [3].

We show in thispaper that our picture of the Gottfried-sum-rule defect also accounts for the new dileptondata, and we make predictions for a more sensitive test using hydrogen and deuteriumtargets.Forward (Feynman-xF ∼> 0.1) production of massive dilepton pairs in high-energy colli-sions of protons with nuclear targets is dominated by the annihilation of a u-quark from thebeam with a ¯u-antiquark from the target, and so is sensitive to the distribution of antiquarksin the target nucleons. Charge symmetry relates the distribution of up-antiquarks in theneutron to the distribution of down-antiquarks in the proton,¯u(n)(x, Q2) = ¯d(p)(x, Q2),(1)where x is Bjorken’s scaling variable and Q2 labels the scale on which the parton distributionsare measured.

The yield per nucleon σA in proton collisions with nucleus A differs from theyield per nucleon σisoscalar in proton collisions with an isoscalar target by the factorRA(x) ≡σA(x)σisoscalar(x) ≈1 + (N −Z)A¯d(x) −¯u(x)¯d(x) + ¯u(x),(2)where A, Z, and N are the atomic weight, atomic number, and number of neutrons in thetarget, and the antiquark densities refer to the proton. The approximate equality followsupon neglect of d ¯d annihilations.

The deviation of RA(x) from unity measures the flavor-asymmetry of the light-quark sea.The possibility that the light-quark sea contains unequal numbers of up and down quarkshas been raised by the New Muon Collaboration’s determination [2] of the integralIG =Z 10 dx [F µp2 (x, Q2) −F µn2 (x, Q2)]x= 0.240 ± 0.016. (3)2

In the quark-parton model, the integral can be expressed asIG = 13 + 23Z 10 dxhu(x, Q2) −d(x, Q2)i. (4)The Gottfried sum rule [4], IG = 1/3, follows from the assumption that the sea is up-downsymmetric.

The observed defect implies a small excess,Z 10 dxhu(x, Q2) −d(x, Q2)i= −0.14 ± 0.024,(5)of down quarks in the sea.Because we expect IG to be essentially independent of Q2 [5], it is convenient to analyzethe flavor content of the sea at a momentum scale relevant to hadron structure, wherethe important degrees of freedom are constituent quarks, Goldstone bosons, and gluons.Consider a proton composed of three constituent quarks: uud. An excess of down quarks overup quarks in the sea arises naturally from the isospin-respecting fluctuation of the constituentquarks into quarks and pions, the lightest of the Goldstone bosons, viz.

u →(π+d, π0u) andd →(π0d, π−u). If a denotes the probability for a constituent up quark to turn into a downquark and a π+ (containing a u-quark and a ¯d-antiquark), the proton composition afterone iteration is (2 + 7a/4)u + (1 + 11a/4)d + (7a/4)u + (11a/4)d. The valence compositionremains uv = (u −u) = 2 and dv = (d −d) = 1, but the sea contains an excess of downquarks and antiquarks over up quarks and antiquarks.In Ref.

[1], we implemented this picture in the framework of the effective chiral quarkmodel formulated by Manohar and Georgi [6]. A straightforward calculation of the prob-ability for a constituent quark to fluctuate leads to IG = 0.278, encouragingly close to theexperimental value (3).

After adjusting the ultraviolet cutoffof the chiral quark model tobetter reproduce the observed Gottfried-sum-rule defect, we constructed parton distribu-tions based on the Eichten-Hinchliffe-Lane-Quigg (EHLQ) Set 1 distributions [7]. Thesenew distributions give a good account of the NMC measurements of the Gottfried integral,the difference F µp2−F µn2 , and the ratio F µn2 /F µp2 .

Details of the construction of the partondistributions and the comparison with data may be found in Ref. [1].

For present purposes,3

it is important to note that the flavor-asymmetric sea generated by chiral field theory, whichis concentrated at small values of x, is a small perturbation on the flavor-symmetric sea ofEHLQ Set 1 [7], x¯u(x) = x ¯d(x) = 0.182(1 −x)8.54.The production of massive muon pairs in proton-nucleus collisions offers another windowon the composition of the sea. Fermilab experiment E772 has compared yields from theisoscalar targets 2H and C with yields from a neutron-rich target, W. According to Eq.

(2), the ratio of yields per nucleon [8] is RW(x) ≈1 + 0.195( ¯d(x) −¯u(x))/( ¯d(x) + ¯u(x)).Because the measured ratio shown in Figure 1 is consistent with unity, the authors of Ref. [3] concluded that there is no evidence for a large flavor-asymmetry in the light-quark sea ofthe nucleon.

There is, however, no conflict between the dilepton results and the Gottfried-sum-rule defect observed by NMC.The chiral field theory calculation reviewed above leads with no readjustment of param-eters to the thick solid curve [9] shown in Figure 1. That prediction is entirely consistentwith the E772 data.

So, too, is the flavor-asymmetric fit (“D0”) made to deeply inelasticlepton scattering data by Martin, Roberts, and Stirling [10]. The effect on RW is smallbecause the ratio of ¯u(x)/ ¯d(x) is everywhere close to unity for both the chiral quark modeland the MRS(D0) fit.The data do discriminate against ad hoc modifications of the EHLQ structure functionsconsidered by Ellis and Stirling [11] and by us [1].

The dashed line in Figure 1 shows theprediction of the modified EHLQ structure functions with ¯u(x)/ ¯d(x) = (1 −x)5.4 that weexamined in Ref. [1].

This form magnifies the effect of a flavor asymmetry upon RW at largevalues of x, whereas the Gottfried integral is determined by the magnitude of the ( ¯d −¯u)excess, which is determined at small x. Even in the interval 0.04 < x < 0.15, however, thead hoc form predicts a larger asymmetry than is observed.Ellis and Stirling [11] proposed to examine the shape near xF = 0 of the differential crosssection m3dσ/dxFdm for the reaction pd →µ+µ−+ anything as a probe of the differencebetween the proton and neutron sea distributions.

We show in Figure 2 the Drell-Yan crosssection predicted using the structure functions obtained from the chiral quark model. The4

lowest-order calculation has been normalized to the large-xF data using a K-factor of 1.4. Itgives an excellent fit to the E772 data, without the suppression of the xF < 0 cross sectiongiven by the ad hoc parton distributions of Ellis and Stirling (cf.

Figure 2 of Ref. [3]).Direct comparison of the yield of dileptons from hydrogen and deuterium targets max-imizes the sensitivity of the ratio RA to a flavor asymmetry, because Rp ≈1 −( ¯d(x) −¯u(x))/( ¯d(x) + ¯u(x)).

A new experiment has been proposed using the E772 apparatus tomake this measurement [12]. The prediction of the chiral quark model, shown as the thicksolid curve in Figure 3, is slightly below unity because hydrogen is a (maximally) neutron-poor nucleus.

The effect of the flavor asymmetry in the nucleon sea is again small, as itis for the MRS(D0) structure functions plotted as the dotted curve. As expected, the adhoc modification of the EHLQ structure functions produces a very large effect.

Future ex-periments should be able to discriminate against this extreme possibility. Making the casefor or against the flavor-asymmetric sea predicted by the chiral quark model presents aconsiderable challenge to dilepton experiments.Dilepton production in hadron-nucleus collisions complements deeply inelastic leptonscattering as a probe of the composition of the light-quark sea of the nucleon.Leptonscattering is the more sensitive probe at small x, because the difference F µp2−F µn2is deter-mined by the difference ¯d(x)−¯u(x), whereas the Drell-Yan process has greater sensitivity atlarge x, where the parton densities are small, because it measures the fractional difference( ¯d(x) −¯u(x))/( ¯d(x) + ¯u(x)).

We find the chiral quark model mechanism compelling andwe look forward to new experimental tests of the small excess of ¯d over ¯u it implies at lowvalues of x.We thank Keith Ellis for supplying predictions for the MRS(D0) structure functions.Fermilab is operated by Universities Research Association, Inc., under contract DE-AC02-76CHO3000 with the United States Department of Energy. This work was supported atLBL by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics,Division of High Energy Physics of the U. S. Department of Energy under Contract DE-AC03-76SFO0098.5

REFERENCES1 E. J. Eichten, I. Hinchliffe, and C. Quigg, Phys. Rev.

D45, 2269 (1992).2 P. Amaudruz, et al. (New Muon Collaboration), Phys.

Rev. Lett.

66, 2712 (1991). Theresult is given for Q2 = 4 (GeV/c)2.3 P. L. McGaughey, et al.

(E772 Collaboration), Phys. Rev.

Lett. 69, 1726 (1992).4 K. Gottfried, Phys.

Rev. Lett.

18, 1174 (1967); J. D. Bjorken and E. A. Paschos, Phys.Rev. 185, 1975 (1969); J. Kuti and V. F. Weisskopf, Phys.

Rev. D4, 3418 (1971).5 D. A. Ross and C. T. Sachrajda, Nucl.

Phys. B149, 497 (1979); C. L´opez and F. J.Yndur´ain, Nucl.

Phys. B183, 157 (1981).6 A. Manohar and H. Georgi, Nucl.

Phys. B234, 189 (1984).7 E. J. Eichten, I. Hinchliffe, K. Lane, and C. Quigg, Rev.

Mod. Phys.

56, 579 (1984), 58,1065E (1986).8 We thank Joel Moss for confirming that the coefficient 0.183 (instead of 0.195) in Ref. [3]is a misprint.9 We have evolved the chiral quark model distributions to values of Q2 corresponding tothe E772 data points and evaluated the Drell-Yan cross section.

The thin solid line resultsfrom neglecting the effects of Q2-evolution and of d ¯d annihilations. Those effects are seento be are small.10 A. D. Martin, W. J. Stirling, and R. G. Roberts, “New Information on Parton Distribu-tions,” Preprint RAL-92-021 DTP/92/16 (unpublished).11 S. D. Ellis and W. J. Stirling, Phys.

Lett. B256, 258 (1991).12 G. T. Garvey, et al., “Measurement of ¯d(x)/¯u(x) in the Proton,” Fermilab proposal P866(unpublished).6

FIGURESFIG. 1.

The ratio RW ≡σW /σisoscalar of dilepton yields per nucleon from tungsten and isoscalartargets as a function of xtarget. The data are from Fermilab experiment E772, Ref.

[3]. Open circlesat small x are the ratio before correction for nuclear shadowing.

The thick solid curve is our pre-diction based on chiral field theory, using the full Drell-Yan cross section with parton distributionsevaluated at the dimuon mass. The thin solid curve is calculated using the parton distributionsfrom chiral field theory at fixed Q2 = 5 (GeV/c)2 in Eq.

(2). The dotted curve shows the predictionof the MRS(D0) parton distributions [10], using Eq.

(2). An ad hoc modification of the EHLQ Set 1structure functions (Ref.

[7]) yields the dashed curve (Drell-Yan cross section, parton distributionsevolved to Q2 = m2) and the dot-dashed curve (Eq. (2), fixed Q2 = 5 (GeV/c)2).FIG.

2.Differential cross section m3dσ/dxF dm as a function of xFfor the reactionpd →µ+µ−+ anything at 800 GeV from Fermilab experiment E772, Ref. [3].

The solid curveis our prediction based on chiral field theory for a dimuon mass m = 8.15 GeV/c2.FIG. 3.

The ratio Rp ≡σp/σd of dilepton yields per nucleon from hydrogen and deuteriumtargets as a function of xtarget. The thick solid curve is our prediction based on chiral field theory,using the full Drell-Yan cross section with parton distributions evaluated at the dimuon mass.The thin solid curve is calculated using the parton distributions from chiral field theory at fixedQ2 = 5 (GeV/c)2 in Eq.

(2). The dotted curve shows the prediction of the MRS(D0) partondistributions [10], using Eq.

(2). An ad hoc modification of the EHLQ Set 1 structure functions(Ref.

[7]) yields the dashed curve (Drell-Yan cross section, parton distributions evolved to Q2 = m2)and the dot-dashed curve (Eq. (2), fixed Q2 = 5 (GeV/c)2).7

---

출처: arXiv:9210.239 • 원문 보기