Hunting for an EMClike eect for antiquarks Massimiliano Alvioli12 1Consiglio Nazionale delle Ricerche

2025-05-06 0 0 868.97KB 22 页 10玖币

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Hunting for an EMC–like eﬀect for antiquarks

Massimiliano Alvioli1,2

1Consiglio Nazionale delle Ricerche,

Istituto di Ricerca per la Protezione Idrogeologica,

via Madonna Alta 126, I-06128, Perugia, Italy and

2Istituto Nazionale di Fisica Nucleare, Sezione di Perugia,

via Pascoli 23c, I-06123, Perugia, Italy

Mark Strikman3

3104 Davey Lab, The Pennsylvania State University, University Park, PA 16803, USA

(Dated: April 27, 2023)

Abstract

We argue that the Drell–Yan process in the xA≥0.15 kinematics recently studied at FNAL by

the E906/SeaQuest experiment may allow to observe an analogous of the EMC eﬀect for antiquarks.

The eﬀects of Fermi motion and energy loss are considered. The preliminary E906/SeaQuest data

are inconsistent with the growth of the σA/AσNratio expected in the Fermi motion scenario at

xA≥0.25. The pattern of the xAdependence of the ratio seems also inconsistent with a scenario

in which the dominant nuclear eﬀect is a suppression of the cross section due to the energy loss

experienced by a quark of the projectile proton involved in the Drell–Yan process. All together

the data suggest the possibility of a modiﬁcation of the antiquark parton distributions in nuclei,

with a pattern similar to the one observed in the EMC eﬀect. We argue that optimal kinematics

to look for an antiquark EMC–like eﬀect would be to measure the σDY

A/AσDY

Nratios for xA= 0.2

– 0.4 and xp≈constant.

arXiv:2210.12597v3 [hep-ph] 26 Apr 2023

I. INTRODUCTION

Forty years ago the European muon collaboration (EMC) [1] has found that the quark

parton distributions in nuclei at x≥0.4 are substantially diﬀerent from the expectations

from the impulse approximation, which includes Fermi motion eﬀects. For example, the

ratio of structure functions F2:

RA(x, Q2) = F2A(x, Q2)

Z F2p(x, Q2) + N F2n(x, Q2),(1)

for µA scattering is about 0.9 at x∼0.5 for A≥12, Q2≥few GeV2. This pattern (the

EMC eﬀect) is inconsistent with the expectations from models in which the conservation

of baryon, electric charge, and momentum distribution sum rules are implemented [2], and

non–nucleonic degrees of freedom are neglected; see also the discussion in section II.

Over the years a number of searches have been performed, looking for deviations of RA

from unity for diﬀerent parton densities outside the nuclear shadowing region x≤0.01.

No signiﬁcant deviations were observed for antiquarks in the region 0.05 ≤x≤0.15 (for

a review see [8]), in which they were expected in the pion models of the EMC eﬀect (see

discussion in Ref. [3]). Precision data from the new muon collaboration (NMC) [4] also

show a minuscular (∼3%) enhancement of the valence quarks in the same xrange and

A= 40. This enhancement appears to be mostly due to the conservation of the number of

valence quarks (the baryon sum rule). In the gluon channel, the momentum sum rule in

combination with the gluon shadowing data suggests an enhancement at x∼0.1 [3]. Also

the large hadron collider (LHC) forward dijet production data [5] are in a better agreement

with the models assuming the existence of an EMC–like eﬀect for gluons at x∼0.5 than

with models assuming that the nuclear gluon density is not modiﬁed for these values of x.

Still, studies of dijet production do not allow to measure directly an EMC eﬀect for gluons,

since in the x∼0.5 kinematics the gluon contribution is a small correction to the quark

contribution, which is known at large Q2and x= 0.5 due to large errors of the measurements

of F2A(x, Q2) in this kinematics.

Recently, a new series of measurements of the Drell–Yan (DY) process have been per-

formed by the E906/SeaQuest collaboration at Fermi Lab using an injector proton beam

of the energy 120 GeV [6, 7]. The data covered a wide range of xAand xpfor the target

antiquarks, up to xA= 0.45. The experiment also studied the A–dependence of the DY

cross section. Thus, in principle, these data allow to measure the antiquark ratio in a much

wider xrange than the data obtained at the Tevatron [8].

Muon pair production data from E906/SeaQuest show a substantial diﬀerence in up and

down antiquark distributions [9], with larger distributions for down than up antiquarks,

over a wide range of momenta. Global analyses of parton distribution functions now include

E906/SeaQuest data, which helped reducing signiﬁcantly the uncertainties of ¯

d/¯uat large x

[10]. The observation of a ﬂavor asymmetry for antiquarks may have consequences for the

existence of an EMC eﬀect for antiquarks.

Since the antiquark distributions in the nucleon drops very rapidly with increasing x, one

may expect that deviations from a Fermi motion model of nuclear eﬀects may show up at

smaller xthan for quarks, where a signiﬁcant eﬀect is observed only for x≥0.45; see Section

II. We stress that EMC–like eﬀects for antiquarks may be present in a number of diﬀerent

models.

For example, the QCD radiation model [11, 12] assumes that the size of a bound nucleon

is larger than that of a free nucleon, and the QCD evolution starts at values of Q2inversely

proportional to the radius of the bound nucleon. As a result, the model predicts a suppression

of quarks, antiquarks and gluons distributions at large x. Another model [3, 13] starts from

the observation that a bound nucleon in a small size conﬁguration interacts with smaller

attraction with the nearby nucleons due to color transparency, resulting in a reduction of

the probability of such conﬁgurations. To relate this eﬀect to the EMC eﬀect, the authors

argue that the conﬁgurations including a leading large–xparton with a small size. In the

case of valence quarks, this conjecture is supported by the analysis of the LHC and RHIC

pA and dA dijet production data [14, 15].

Overall, the observation of nuclear modiﬁcation of a second nuclear parton density would

provide a strong boost to the theoretical and experimental studies of non–nucleonic degrees

of freedom in nuclei.

Hence, in Section II, we explore what kinematics is optimal for distinguishing between

the Fermi motion eﬀect and possible eﬀects of non–nucleonic degrees of freedom in nuclei. In

section III we also compare the A–dependence of the DY process due to possible energy loss

experienced by quarks propagating through the nucleus and due to non–nucleonic degrees of

freedom, and ﬁnd them substantially diﬀerent. Moreover, we point out that in the kinematics

xp∼0.8, xA∼0.2 the energy loss eﬀect should be much larger than for xp∼0.2, xA∼0.4.

Thus, combined studies of the nuclear eﬀects in these kinematics would allow to look for an

EMC eﬀect for antiquarks in nuclei in a more constrained way.

II. FERMI MOTION EFFECT FOR ANTIQUARKS

To observe an EMC eﬀect for antiquarks one needs to ﬁnd the optimal x–range where

Fermi motion eﬀects are small as compared to potential eﬀects of the existence of non–

nucleonic degrees of freedom. Since parton densities represent the light cone projection of

the hadron wave function, we need to use light cone nuclear wave functions [2]. Similar to

the case of quark and gluon parton distribution functions, see e.g. [16], we introduce the

light cone single nucleon density matrix: ρN

A(α). Here α/A is the fraction of the momentum

of the fast nucleus, PA, carried by a nucleon, with 0 ≤α≤A. It can be interpreted as

the probability to ﬁnd a nucleon having longitudinal momentum αPA/A. Considering the

matrix element of the baryon current at t= 0, one ﬁnds:

ZρN

A(α)dα

α=A , (2)

while the sum rule

AZα ρN

A(α)dα

α= 1 (3)

follows from considering the energy–momentum tensor sum rule, basically from the condition

that the sum of the light cone fractions of Anucleons is equal to unity.

The eﬀect of Fermi motion can be written in terms of nuclear parton distributions in

complete analogy with the QCD evolution equations:

x pA(x) = ZρN

A(α)x

αpNx

αdα

α,(4)

where we do not write explicitly the dependence of the parton densities on Q2. Since the

spread of the momentum distribution over the light cone fraction αis pretty modest, we

can consider a Taylor series expansion using 1 −αas a small parameter. We obtain, after

applying the sum rules in Eqs. (2) and (3):

RA(x) = 1 + x2(x pN(x))00 + 2 x(x pN(x))0

x pN(x)

3mN

.(5)

In the last step of Eq.(5), we substituted Rdα

α(1 −α)2with its non–relativistic limit, TA/3,

where TAis the nucleon average kinetic energy. For a detailed discussion, see Ref. [3].

To see the pattern given by Eq. (5) we can use the parametrization:

x pN(x)∝(1 −x)n,(6)

where n≈3 for quarks and n≈7 for antiquarks; thus, we obtain:

RA(x) = 1 + x n [x(n+ 1) −2]

(1 −x)2

3mN

.(7)

It follows from Eq. (7) that the contribution of Fermi motion passes through zero at the

crossover point, xcr:

xcr =2

n+ 1 ,(8)

that is, xcr = 0.5 for n= 3 (quarks), and xcr = 0.25 for n= 7 (antiquarks). For x < xcr,

RAreaches the minimum at x= 1/n, where

RA1

n= 1 −n

n−1

3mN

.(9)

Assuming TA= 40 MeV, for illustration, (using TA=Rdkk2/(2mN)nA(k) we have TA

= 30.35 MeV for carbon, and TA= 36.75 MeV for iron, with the momentum distribution

adopted here), we ﬁnd that the deviation from unity of RAfor antiquarks expected from

the Fermi motion model to be of the order 1.5% for xA∼0.1.

Hence xA∼0.2 – 0.3 is the optimal x–range to suppress the contribution of Fermi motion

into RAfor antiquarks. We checked that Eq. (7) is a good approximation to the convolution

expression. For simplicity we considered a model in which, for k≤kF, the non–relativistic

momentum distribution, nA(k), is constant. For k > kFwe used the two–nucleon short

range correlation approximation with high momentum tail enhanced by a factor a2≈4 as

compared to the deuteron wave function. The value of nA(k) for k < kFwas determined

from normalization condition RnA(k)dk= 1. The resulting nA(k) is presented in Fig. 1.

Obviously one can use a more sophisticated model including the motion of the short range

correlations in a mean ﬁeld [17–20]; for a recent review see Ref. [21]. However, this seems

not necessary since these eﬀects constitute a small correction to an already small eﬀect. To

ensure that the momentum sum rule is fulﬁlled, we used the two–nucleon relation valid for

the deuteron for any value of k. Hence, for the two–nucleon short range contribution:

α= 1 + k3

√k2+mN

.(10)

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摘要：

HuntingforanEMC{likeeectforantiquarksMassimilianoAlvioli1;21ConsiglioNazionaledelleRicerche,IstitutodiRicercaperlaProtezioneIdrogeologica,viaMadonnaAlta126,I-06128,Perugia,Italyand2IstitutoNazionalediFisicaNucleare,SezionediPerugia,viaPascoli23c,I-06123,Perugia,ItalyMarkStrikman33104DaveyLab,ThePen...

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