Tensor-polarized quark and antiquark distribution functions in a spin-one hadron

Abstract

To understand orbital-angular-momentum contributions is becoming crucial for clarifying nucleonspin issue in the parton level. Twist-two structure functions b1 and b2 for spin-one hadrons could probe orbital-angular-momentum effects, which reflect a different aspect from current studies for the spin-1/2 nucleon, since they should vanish if internal constituents are in the S state. These structure functions are related to tensor structure in spin-one hadrons. Studies of such tensor structure will open a new field of high-energy spin physics. The structure functions b1 and b2 are described by tensor-polarized quark and antiquark distributions δT q and δTq. Using HERMES data on the b1 structure function for the deuteron, we made an analysis of extracting the distributions δT q and δTq in a simple x-dependent functional form. Optimum distributions are proposed for the tensor-polarized valence and antiquark distribution functions from the analysis. A finite tensor polarization is obtained for antiquarks if we impose a constraint that the first moments of tensorpolarized valence-quark distributions vanish. It is interesting to investigate a physics mechanism to create a finite tensor-polarized antiquark distribution.PACS numbers: 13.60.Hb, 13.88.+eOrigin of nucleon spin has been investigated extensively after the EMC discovery that almost none of nucleon spin is carried by quarks [1]. Recent studies of polarized parton distribution functions (PDFs) are found in Ref. [2]. Although a gluon-spin contribution is not determined accurately, orbital angular momenta are likely to be the crucial quantities in explaining the nucleon spin. Such contributions have been investigated recently by generalized parton distribution functions in lepton scattering [3] and will be studied possibly at hadron facilities [4].There are other quantities which are sensitive to the orbital angular momenta. For example, there are twisttwo structure functions b 1 and b 2 in spin-one hadrons [5,6]. They could be related to the orbital angular momenta of internal constituents because they vanish if the constituents are in the S wave. Of course, they probe a different aspect of orbital-angular-momentum effects from the current ones for the nucleon because they are related to tensor-structure nature of spin-one hadrons. It is noteworthy that tensor structure is not understood at all in the parton level, which suggests that a new field of spin physics should be created by investigating the tensor-polarized structure functions.New polarized structure functions (b 1 , b 2 , b 3 , and b 4 ) were introduced in describing lepton deep inelastic scattering from a spin-one hadron [5][6][7]. A useful sum rule for the twist-two function b 1 was proposed in Ref. [8], and it is partially used in this work. In conventional hadron models, such tensor structure arises due to the D-state admixture [5,6,9], pions [10], and shadowing effects [11] if the target is the deuteron. However, the tensor structure would not be simply described by such conventional models at high...

Theoretical estimate on tensor-polarization asymmetry in proton-deuteron Drell-Yan process

“…The solid and dashed curves indicate theoretical results with finite tensor-polarized antiquark distributions (set-2, αq = 0) and without them (set-1, αq = 0), respectively. The open circle is the data at Q 2 < 1 GeV 2 , and it is not included in the fit analysis [18]. The uncertainties of the set-2 curve are shown by the bands with ∆χ 2 = 1 and 3.53. the solid and dotted curves, and the valence-quark distribution of the set-1 is shown by the dashed curves.…”

“…[18]. Since there is little information for the tensor-polarized PDFs at this stage, we need to introduce bold assumptions for extracting the distributions from the experimental data.…”

“…There is sum rule for b 1 based on the parton model [5,18] in the similar way to the Gottfried sum rule [19]:…”

“…In the analysis of Ref. [18], the scale is taken as the average Q 2 of the HERMES experiment (Q 2 0 = 2.5 GeV 2 ). The parameters a, b, c, and x 0 are determined by a χ 2 analysis of the HERMES data with the leadingorder expression for b 1 in Eq.…”

“…Its data indicated that b 1 has interesting oscillatory behavior as the function of x and that the magnitude of xb 1 is of the order of 10 −3 . Since b 1 is expressed by tensor-polarized parton distribution functions, possible quark and antiquark distributions (δ T q(x), δ Tq (x)) were extracted from the HERMES data [18]. The analysis suggested finite tensor-polarized antiquark distributions from the data at x < 0.1.…”