Determination of light - flavor asymmetry in the Σ ± sea by the Drell - Yan process

We propose a flavor asymmetry in the light quark sea of Σ±, which can be measured in Drell-Yan experiments using charged hyperon beams on proton and deuteron targets. Such a measurement would help to reinforce the presence of pseudoscalar mesons in a quark model of baryons. Typeset using REVTEX 1 One of the surprises in the structure of the proton is that the sea appears to have a flavor asymmetry, an excess of d̄ compared to ū [1–3]. Although the experimental results could also imply an isospin asymmetry, this appears to be less likely, and we interpret them as an SU(2)Q flavor asymmetry in the sea [4]. The d̄ excess in the proton is expected to be reflected in an excess of ū in the neutron; isospin symmetry would be broken if this were not the case. The evidence for flavor asymmetry in the proton sea is based on analyses of deep inelastic muon scattering [1,2] and Drell-Yan processes [3]. One explanation that has been offered is that the excess of d̄ over ū is due to the Pauli exclusion principle [5,6]. A more likely explanation, in our view, is that offered by Thomas and colleagues [7–11], Henley and Miller [12], and others [13–20], namely that the presence of a pion cloud surrounding a proton favors d̄ over ū because of the excess positive charge of the meson cloud. It is interesting to apply these arguments to the strange baryons. Here we focus on the charged Σ±, composed primarily of uus or dds quarks. We argue that the Σ has an excess of d̄ and the Σ− has an excess of ū. The exclusion principle may also play a role here. Our arguments, however, are based on the pseudoscalar meson cloud picture. Thus a Σ(uus) will have components Λ(uds)π(ud̄), Σ(uds)π(ud̄), Σ(uus)π( 1 √ 2 [dd̄−uū]), or p(uud)K̄(d̄s); similarly a Σ−(dds) can be Λ0(uds)π−(dū), Σ0(uds)π−(dū), Σ−(dds)π0( 1 √ 2 [dd̄ − uū]), or n(udd)K−(ūs). Thus there is a clear favoring of d̄ for Σ and ū for Σ−. There are a number of ways this predicted excess can be tested. Probably, the most practical is in terms of the Drell-Yan cross sections for Σ±p and Σ±n (i.e. d), e.g., in the inclusive reactions Σ±p → l+l−X, where l± are muons or electrons and X is unmeasured. Beams of Σ± appear to be adequate for this purpose. We find that the ratio r̄Σ(x) ≡ ūΣ(x)/d̄Σ(x) for the Σ + depends on the known ratios rp(x) ≡ up(x)/dp(x) and r̄p(x) ≡ ūp(x)/d̄p(x) in the proton. The former is well-determined from DIS experiments, and the latter has recently been determined to be 0.51 ± 0.04 ± 0.05 (≈ 20 percent accuracy) at x ≈ 0.18. We expect this ratio to be even smaller for the Σ than the proton. We represent the composition of nucleons and sigma hyperons in terms of valence and sea quark momentum distributions q(x) and q̄(x). For clarity, the Q dependence of these 2 distributions is suppressed. We assume isospin reflection symmetry: up(x) = dn(x), ūp(x) = d̄n(x), uΣ+(x) = dΣ−(x), ūΣ+(x) = d̄Σ−(x), and sΣ+(x) = sΣ−(x). Drell-Yan cross-sections are proportional to the products q(x)q̄(x′), weighted by the product of the quark charges, and summed over contributions from beam and target. We neglect sea-quark sea-quark collisions, which would contribute below the likely level of accuracy of the experiment. In the following equations, q(x) represents valence quarks, q̄(x) represents sea quarks, and the subscript Σ refers to distribution functions for Σ. The valence quark normalizations are: ∫ u(x) dx = 2 and ∫ d(x) dx = 1. Consider the Drell-Yan process for Σp. If the experiment is carried out at y ≈ 0, then xp ≈ xΣ ≈ x, and σ(Σp) ≈ 8πα 2 9 √ τ K(x){ 9 [up(x)ūΣ(x) + uΣ(x)ūp(x)] + 1 9 [dp(x)d̄Σ(x) + sΣ(x)s̄p(x)]}. (1) Then by isospin symmetry σ(Σ−n) ≈ 8πα 2 9 √ τ K(x){ 9 [up(x)ūΣ(x) + uΣ(x)ūp(x) + sΣ(x)s̄p(x)] + 4 9 dp(x)d̄Σ(x)}. (2) We also find σ(Σn) ≈ 8πα 2 9 √ τ K(x){ 9 [dp(x)ūΣ(x) + uΣ(x)d̄p(x)] + 1 9 [up(x)d̄Σ(x) + sΣ(x)s̄p(x)]}, (3) and again by isospin symmetry σ(Σ−p) ≈ 8πα 2 9 √ τ K(x){ 9 [dp(x)ūΣ(x) + uΣ(x)d̄p(x) + sΣ(x)s̄p(x)] + 4 9 up(x)d̄Σ(x)}. (4) The factor K(x) accounts for higher-order QCD corrections, and will factor out in our analysis, since we take ratios of cross sections. We define a ratio R(x) determined from the Drell-Yan cross-sections so as to eliminate unknown ratios other than r̄Σ(x) and the recently measured r̄p(x): R(x) ≡ [σ(Σ +p)− σ(Σ−n)] + r̄p(x)[σ(Σp)− σ(Σn] [σ(Σ+p)− σ(Σn)] + 4[σ(Σ−p)− σ(Σ−n)] , (5) and use Equations 1-4 to write R(x) in terms of the ratios r̄Σ(x), rp(x) and r̄p(x): 3 R(x) = r̄Σ(x)[rp(x)− r̄p(x)]− [1− r̄p(x)rp(x)] 5[rp(x)− 1] . (6) Thus for rp(x) ≈ 2 and r̄p(x) ≈ 0.5, R(x) ≈ 0.3r̄Σ(x). If K(x) is known, d̄Σ(x) can be determined directly from the cross sections: d̄Σ(x) = 27 √ τ 40παK(x) [σ(Σ+p)− σ(Σn)] + 4[σ(Σ−p)− σ(Σ−n)] [up(x)− dp(x)] , (7) and sΣ(x) can be determined from the cross sections and s̄p(x): sΣ(x) = 27 √ τ 8παK(x) [σ(Σ+n)− 4σ(Σ−p)]− rp(x)[σ(Σp)− 4σ(Σ−n)] s̄p(x)[rp(x)− 1] . (8) Because of the higher mass of the strange quark, we expect sΣ(x) to peak at a larger x than dp(x). Quark models with a meson cloud predict the sea quark distributions q̄(x); they also predict that the difference D ≡ x[d̄p(x) − ūp(x)] peaks at x ≈ 0.1 [13–19]. On the basis of meson cloud models, the distributions of sea quarks in the Σ± may differ somewhat from those in the nucleon due to the presence of kaons; this may shift the maximum of D to somewhat smaller values of x. Nevertheless the region of 0 ≤ x ≤ 0.2 should be a good region for obtaining r̄Σ. We believe that the measurement of R should be possible to within ≈ 20% and this is sufficient to establish the preponderance of d̄ over ū in the Σ. As can be seen from Eq. (6), an error, e, in the measurement of R leads to an error of approximately 3e in r̄Σ. Together with the known value of r̄p ≈ 0.51, this measurement would help to reinforce the validity of the presence of pseudoscalar mesons in a quark model of baryons, especially if r̄Σ is found to be ≤ 0.5. This work has been supported in part by the U.S. Department of Energy, Contract # DOE/ER/4027-6-N96, and by the National Institute for Nuclear Theory. We wish to thank Jen-chieh Peng, Joel Moss, and other participants in the program INT-96-1, “Quark and Gluon Structure of Nucleons and Nuclei” for helpful discussions. We are undertaking a calculation of the Σ± sea quark distributions. 4