Phenomenology of the Flavor–Asymmetry in the Light–Quark Sea of the Nucleon

A phenomenological ansatz for the flavor–asymmetry of the light sea distributions of the nucleon, based on the Pauli exclusion principle, is proposed. This ansatz is compatible with the measured flavor–asymmetry of the unpolarized sea distributions, d̄ > ū, of the nucleon. A prediction for the corresponding polarized flavor–asymmetry is presented and shown to agree with predictions of (chiral quark–soliton) models which successfully reproduced the flavor–asymmetry of the unpolarized sea. The flavor–asymmetry of the light–quark sea in the nucleon has attracted a lot of attention and many attempts were undertaken to explain the origin and calculate its magnitude (e.g., Ref. [1] and references therein). In the present article we study this issue inspired by the suggestion [2] that this asymmetry is related to the Pauli exclusion principle (‘Pauli blocking’). Our proposed implementation of this idea is summarized by the phenomenological ansatz for the unpolarized and polarized antiquark distributions d̄(x,Q0)/ū(x,Q 2 0) = u(x,Q 2 0)/d(x,Q 2 0) (1) and ∆d̄(x,Q0)/∆ū(x,Q 2 0) = ∆u(x,Q 2 0)/∆d(x,Q 2 0) , (2) respectively, with Q0 being some low resolution scale, e.g., the one in [3, 4]. These are our basic relations for the flavor–asymmetries of the unpolarized and polarized light sea densities which imply that u > d determines ū < d̄, etc. This is in accordance with the suggestion of Feynman and Field [2] that, since there are more uthan d–quarks in the proton, uū pairs in the sea are suppressed more than dd̄ pairs by the exclusion principle. In Table I we present d̄(x,Q0)/ū(x,Q 2 0) calculated according to Eq. (1) from the (fitted) d, u input distributions of GRV98 [5], as compared to the actual fitted values of this ratio. The good agreement lends support to the phenomenological ansatz in Eq. (1) and thus also to the experimentally so far unknown polarized antiquark flavor–asymmetry implied by Eq. (2). The predictions for ∆d̄/∆ū according to Eq. (2) are shown in Table II utilizing the most recent LO ACC [6] distributions ∆u(x,Q0) and ∆d(x,Q 2 0) which compare favorably with the predictions of the chiral quark–soliton model [7] for ∆d̄/∆ū. The latter flavor–asymmetry for ∆ū and ∆d̄ can also be studied by replacing the common constraint ∆ū = ∆d̄ ≡ ∆q̄ by our present Eq. (2). Using the recent analysis of [6], for example, one obtains the LO results for ∆ū(x,Q0), ∆d̄(x,Q 2 0) and their difference presented in Figs. 1 and 2, respectively [8]. These predictions refer to an input scale 1 of Q0 = 1 GeV 2 [6]. At the somewhat lower dynamical input scales Q0 = 0.3 − 0.4 GeV [3, 4, 5], the maxima/minima of the curves shown in Figs. 1 and 2 move slightly to the right, i.e. to slightly larger values of x. Strictly speaking a more consistent study of the antiquark asymmetry should be done [9] within the framework of the ‘valence’ scenario [4] where ∆s(x,Q0) = ∆s̄(x,Q 2 0) = 0. This, however, is expected to modify the present results only marginally. The NLO analysis of the polarized antiquark asymmetry [9] affords a direct implementation of Eq. (2) in the fit procedure due to the enhanced sensitivity of the NLO calculation of g 1 (x,Q ) to the polarized gluon distribution which is affected by modifications of the polarized quark and antiquark distributions. Again, no qualitative changes of our present results are expected. It is interesting to note that our results for the flavor–asymmetry of the polarized sea distributions at Q0 = 1 GeV 2 in Figs. 1 and 2 are comparable to those obtained in chiral quark–soliton model calculations [7] which correctly reproduced the flavor–asymmetry of the unpolarized sea [10]! A further direct test of our phenomenological ansatz (2) must await the polarized version [11] of the Drell–Yan μμ pair production experiments [12] which provided the information on the flavor–asymmetry of the unpolarized sea distributions in Eq. (1). Finally it should be noted that the data select the solution of Eq. (2) which satisfies ∆q(x,Q0)∆q̄(x,Q 2 0) > 0 (3) where q = u, d. This can be understood as a consequence of the expected predominant (pseudo)scalar configuration of the quark–antiquark pairs in the nucleon sea. In fact, Eqs. (1) and (2) can be rewritten as u+ū+ + u−ū− = d+d̄+ + d−d̄− ≡ fp (4) u+ū− + u−ū+ = d+d̄− + d−d̄+ ≡ fa (5) where the common helicity densities are given by (−) q ± = ( (−) q ± ∆ (−) q )/2 and, for brevity, 2 we dropped the x–dependence everywhere. A predominant (pseudo)scalar configuration of the (qq̄) pairs in the nucleon sea implies, via Pauli–blocking, that the aligned quark– quark configurations q+(q+q̄−) and q−(q−q̄+) are suppressed relatively to the antialigned q+(q−q̄+) and q−(q+q̄−) ‘cloud’ configurations, i.e. fp > fa which yields the result in Eq. (3). We would like to thank M. Stratmann and W. Vogelsang for helpful discussions and comments. This work has been supported in part by the ‘Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie’, Bonn.