Instanton contribution to the Sivers function

TL;DR

The paper addresses the nonperturbative origin of the Sivers function for valence quarks by employing the instanton model of the QCD vacuum in conjunction with MIT bag model quark wave functions. It demonstrates that instanton-induced chromomagnetic interactions generate spin-spin correlations that produce a flavour-dependent Sivers effect, yielding $f_{1T}^{\perp}$ with distinct u/d behavior and a sizable contribution not suppressed by $\alpha_s$. The results indicate a sizeable negative Sivers function for $u$ quarks and a near-cancellation with perturbative contributions for $d$ quarks, offering improved alignment with HERMES valence-region data for $u$. The work highlights the potential importance of nonperturbative QCD dynamics in transverse spin phenomena and motivates further refinement with more elaborate nucleon wave functions and diagrams.

Abstract

We study the Sivers function for valence u and d quarks in the proton within the instanton model for QCD vacuum, adopting the MIT bag model wave functions for quarks. Within approaches based on perturbative one-gluon final state interactions a non-zero value of the Sivers function is related to the presence of both S and P wave components in quark wave functions. We show that the instanton-induced chromomagnetic, nonperturbative interaction leads to very specific spin-spin correlations between the struck and spectator quarks, resulting in a non-trivial flavour dependence of the Sivers function. Comparison of the obtained Sivers functions with phenomenological parameterizations is discussed.

Figures (4)

• Figure 1: Perturbative (a) and instanton induced (b) contributions to the Sivers function. The symbol $I$ denotes the instanton.
• Figure 2: The instanton (thick lines) and the one-gluon (thin lines) contributions to the first moment of the $d$-quark (solid) and $u$-quark (dashed) Sivers function, vs. $x$.
• Figure 3: The instanton and one-gluon contributions to the Sivers function at $x$=0.3 vs. $k_\perp$(GeV$/c$). Notations are the same as in Fig. 2.
• Figure 4: The total contribution to the first moment of $d$ (solid line) and $u$ (dashed line) quark Sivers distributions as a function of $x$. The 1-$\sigma$ band for the parameterizations extracted by fitting the HERMES data (see first of Ref.s sidis) is also shown.