Proton spin structure from lattice QCD.

A lattice QCD calculation of the proton matrix element of the flavor singlet axial-vector current is reported. Both the connected and disconnected contributions are calculated, for the latter employing the variant method of wall source without gauge fixing. From simulations in quenched QCD with the Wilson quark action on a 163 × 20 lattice at β = 5.7 (the lattice spacing a ≈ 0.14fm), we find ∆Σ = ∆u+∆d+∆s = +0.638(54) − 0.347(46) − 0.109(30) = +0.18(10) with the disconnected contribution to ∆u and ∆d equal to −0.119(44), which is reasonably consistent with the experiment. † Also at Institute for Advanced Study, Princeton, NJ 08540, U. S. A. 1 The flavor singlet axial-vector matrix element of proton has been widely discussed in recent years. The interest initially arose from the EMC data[1] for the spin-dependent proton structure function g1 which, taken together with earlier SLAC data[2], apparently indicated that the fraction of proton spin carried by quarks has a small value ∆Σ = ∆u+∆d+∆s = 0.12(17) and that the strange quark contribution is unexpectedly large and negative ∆s = −0.19(6)[1]. New experiments have since been performed with proton[3, 4], deuteron[4, 5] and neutron[6] targets. Combined reanalyses of these data using gA = ∆u−∆d = 1.2573(28) and g8 = ∆u+∆d− 2∆s = 0.601(38)[7], with the aid of three-loop perturbative QCD calculations for the structure functions[8], have recently been carried out[9, 10], reporting for the matrix elements renormalized at μ, ∆Σ = ∆u+∆d+∆s = { 0.83(3)− 0.43(3)− 0.10(3) = 0.31(7), μ = 10GeV[9] 0.832(15)− 0.425(15)− 0.097(18) = 0.31(4), μ = ∞[10]. (1) where the first analysis[9] employed the Bjorken sum rule to fix the value of the strong coupling constant αs while the world average for αs was used in the second analysis[10]. In this article we report[11] on a quenched lattice QCD calculation of the proton matrix elements of axial-vector current for u, d and s quarks including both connected and disconnected contributions. A serious technical obstacle in such a calculation has been a reliable estimate of the disconnected part, which we are now able to overcome with the variant of the method of wall sources[12]. An exploratory study employing a random Z(2) source was previously made in Ref. [13]. Majority of lattice QCD calculations to date, however, attempted to evaluate ∆Σ from the proton matrix element of topological charge density[14, 15, 16]. The use of quenched approximation is not valid in this approach due to the degeneracy of η and π[14]. It also turned out that data