Transverse quark spin effects and the flavor dependence of the Boer-Mulders function

Abstract

The naive time-reversal-odd (``$T$-odd'') parton distribution ${h}_{1}^{\ensuremath{\perp}}$, the so-called Boer-Mulders function, for both up ($u$) and down ($d$) quarks is considered in the diquark spectator model. While the results of different articles in the literature suggest that the signs of the Boer-Mulders function in semi-inclusive deep inelastic scattering (SIDIS) for both flavors $u$ and $d$ are the same and negative, a previous calculation in the diquark spectator model found that ${h}_{1}^{\ensuremath{\perp}(u)}$ and ${h}_{1}^{\ensuremath{\perp}(d)}$ have different signs. The flavor dependence is of significance for the analysis of the azimuthal $\mathrm{cos}(2\ensuremath{\phi})$ asymmetries in unpolarized SIDIS and Drell-Yan processes, as well as for the overall physical understanding of the distribution of transversely polarized quarks in unpolarized nucleons. We find substantial differences with previous work. In particular, we obtain half and first moments of the Boer-Mulders function that are negative over the full range in Bjorken $x$ for both the $u$ and $d$ quarks. In conjunction with the Collins function, we then predict the $\mathrm{cos}(2\ensuremath{\phi})$ azimuthal asymmetry for ${\ensuremath{\pi}}^{+}$ and ${\ensuremath{\pi}}^{\ensuremath{-}}$ in this framework. We also find that the Sivers $u$ and $d$ quarks are negative and positive, respectively. As a by-product of the formalism, we calculate the chiral-odd but ``$T$-even'' function ${h}_{1L}^{\ensuremath{\perp}}$, which allows us to present a prediction for the single-spin asymmetry ${A}_{UL}^{\mathrm{sin}(2\ensuremath{\phi})}$ for a longitudinally polarized target in SIDIS.