核子海动量依赖性：新证据与理论挑战

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本文主要探讨了核子（proton）内部的味结构——特别是u夸克（up quarks）与d夸克（down quarks）在深非弹性散射（Deep Inelastic Scattering, DIS）中的动量依赖性。在这个研究中，科学家们关注的是一个早期发现的现象，即在质子中u夸克和d夸克的分布存在显著差异，这违背了Gottfried和规则。Gottfried sum rule原本预测u和d两种轻子的海洋（sea quarks）在质子中的贡献应该相等，但实际上实验观测显示这一平衡在较小的动量分数x区间（0.02 < x < 0.35）内被打破。 Drell-Yan和半包容性DIS实验的数据揭示了d(x)-u(x)这个差值的部分动量依赖特性，其中d(x)减去u(x)可能在x约等于0.3时出现符号反转。这是一个重要的物理现象，因为理论模型在此之前未能充分解释这一反转行为。作者通过分析DIS数据，提供了独立证据支持在x=0.3处d(x)与u(x)的分布反转，这挑战了现有理论的理解。文章进一步深入研究了这一问题，将讨论的焦点置于介子云模型（Meson Cloud Model）以及基于晶格量子色动力学（Lattice Quantum Chromodynamics, LQCD）的计算框架。介子云模型考虑了质子内部可能存在各种介子态，这些介子由u和d夸克组成，可能影响它们在不同动量尺度下的分布。而LQCD作为第一性原理的计算方法，能够提供基于量子色动力学的精确计算结果，有助于揭示夸克分布的微观细节。这篇研究不仅验证了核子内部味结构的复杂性，而且还提出了一个有待进一步探索的物理现象，即在x=0.3附近的d(x)-u(x)符号反转，这可能对理解质子内部夸克动态、强相互作用以及粒子物理学的基本定律有着深远的影响。后续的工作将围绕这两个模型展开，以期更全面地揭示核子内部夸克分布的深层次规律。

Physics Letters B 736 (2014) 411–414

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

On the momentum dependence of the ﬂavor structure

the nucleon sea

Jen-Chieh Peng

, Wen-Chen Chang

, Hai-Yang Cheng

, Tie-Jiun Hou

, Keh-Fei Liu

Jian-Wei Qiu

d,e

Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

Institute of Physics, Academia Sinica, Taipei 11529, Taiwan

Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506, USA

Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA

C.N. Yang Institute for Theoretical Physics and Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794, USA

a r t i c l e i n f o a b s t r a c t

Article history:

Received

16 May 2014

Received

in revised form 1 July 2014

Accepted

28 July 2014

Available

online 1 August 2014

Editor:

D.F. Geesaman

Keywords:

Parton

distributions

Sea

quark

d(x) −

u(x)

Lattice QCD

Difference between the

u and

d sea quark distributions in the proton was ﬁrst observed in the violation

of the Gottfried sum rule in deep-inelastic scattering (DIS) experiments. The parton momentum fraction

x dependence of this difference has been measured over the region 0.02 < x < 0.35 from Drell–Yan and

semi-inclusive DIS experiments. The Drell–Yan data suggested a possible sign-change for

d(x) −

u(x) near

x ∼ 0.3, which has not yet been explained by existing theoretical models. We present an independent

evidence for the

d(x) −

u(x) sign-change at x ∼ 0.3from an analysis of the DIS data. We further discuss

the x-dependence of

d −

u in the context of meson cloud model and the lattice QCD formulation.

(http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP

It is now a well established fact that the

u and

d distribu-

tions

in the proton are strikingly different. The ﬁrst evidence for

this difference came from the observation of the violation of the

Gottfried sum rule [1] in a deep-inelastic scattering (DIS) ex-

periment

by the NMC Collaboration [2]. The Gottfried sum rule,

≡



) − F

)]/x

= 1/3, is obtained under the as-

sumption

of a symmetric

u and

d sea [1], where x

is the Bjorken

variable and is effectively equal to parton momentum fraction x

probed

in DIS using the leading order QCD factorization formal-

ism

of the structure function F

). The NMC measurement of

= 0.235 ± 0.026 implies that this assumption is invalid with an

x-integrated difference of



[

d(x) −

u(x)]dx = 0.148 ± 0.039.

The

NMC result was subsequently checked using two indepen-

dent

experimental techniques. From measurements of the Drell–

Yan

cross section ratios of [σ (p + d)]/[σ (p + p)], the NA51 [3] and

the Fermilab E866 [4] experiments measured

u as a function of x

over

the kinematic range of 0.015 < x < 0.35. As shown in Fig. 1,

the

u ratios clearly differ from unity. From a semi-inclusive DIS

measurement, the HERMES Collaboration also reported the obser-

vation [5] of

d(x) −

u(x) = 0, consistent with the Drell–Yan results.

The

d(x)/

u(x) data obtained from the Drell–Yan experiments

have provided stringent constraints for parameterizing the parton

distribution functions (PDFs). Fig. 1 compares the data measured

at Q

= 54 GeV

from Fermilab E866 with parameterizations of

several PDFs. The E866 data show the salient feature that

rises

linearly with x for x < 0.15 and then drops as x further in-

creases.

At the largest value of x (x = 0.315), the

u ratio falls

below unity, albeit with large experimental uncertainty. This in-

triguing

x-dependence of

u is reﬂected in recent PDFs including

CTEQ6 [6], CT10 [7], MSTW08 [8], and JR14 [9]. However, for the

CTEQ4M [10] PDF, which predated the E866 data, the

u ra-

tios

at large x are not well described by the parameterizations.

In particular,

d(x)/

u(x) remains greater than unity, or equivalently,

d(x) −

u(x) > 0, at all x. The parameterizations of the more re-

cent

PDFs are suﬃciently ﬂexible to accommodate a sign-change

for

d(x) −

u(x) at x ∼ 0.3, as suggested by the E866 data.

Many

theoretical models have been put forward to explain the

surprisingly large difference between

d(x) and

u(x). For reviews on

various

theoretical models, see Refs. [11–15]. While these models

can explain the enhancement of

d over

u involving various mecha-

nisms

such as meson cloud, chiral-quark, intrinsic sea, soliton, and

Pauli-blocking, none of them predicts that the

u ratio falls be-

low

unity at any value of x [14]. In order to understand the origin

of the sea-quark ﬂavor structure, it is important to improve the

http://dx.doi.org/10.1016/j.physletb.2014.07.050

0370-2693/

SCOAP

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