First Monte Carlo Global Analysis of Nucleon Transversity with Lattice QCD Constraints

We report on the first global QCD analysis of the quark transversity distributions in the nucleon from semi-inclusive deep-inelastic scattering (SIDIS), using a new Monte Carlo method based on nested sampling and constraints on the isovector tensor charge $g_T$ from lattice QCD. A simultaneous fit to the available SIDIS Collins asymmetry data is compatible with $g_T$ values extracted from a comprehensive reanalysis of existing lattice simulations, in contrast to previous analyses, which found significantly smaller $g_T$ values. The contributions to the nucleon tensor charge from $u$ and $d$ quarks are found to be $\delta u=0.3(2)$ and $\delta d=-0.7(2)$ at a scale $Q^2=2{\mathrm{GeV}}^2$.

Figure 1

A comparison of the full $\mathrm{SIDI}\mathrm{S}+\mathrm{lattice}$ fit with the ${\pi }^{+}$ (filled circles) and ${\pi }^{-}$ (open circles) Collins asymmetries $A_{UT}^{\sin ({\varphi }_h+{\varphi }_s)}$ from HERMES [47] and COMPASS [48, 49] data (in percent), as a function of $x$, $z$, and $P_{h\perp }$ (in GeV).

Figure 2

Transversity PDFs $h_1^{u,d}$ and favored $z{H}_{1(\text{fav})}^{\perp (1)}$ and unfavored $z{H}_{1(\text{unf})}^{\perp (1)}$ Collins FFs for the $\mathrm{SIDI}\mathrm{S}+\mathrm{lattice}$ fit (red and blue bands) at $Q^2=2{\mathrm{GeV}}^2$, compared with the SIDIS-only fit uncertainties (yellow bands). The range of direct experimental constraints is indicated by the horizontal dashed lines.

Figure 3

(a) A contour plot of $\delta u$ and $\delta d$ samples from the MC analysis, for the SIDIS only (blue) and $\mathrm{SIDIS}+\mathrm{lattice}$ (red) analysis. The expectation values and $1\sigma$ uncertainties for both fits are indicated by the respective error bars. (b) Normalized yields for the isovector tensor charge $g_T$, for the SIDIS-only (yellow histograms) and $\mathrm{SIDIS}+\mathrm{lattice}$ (red histograms) MC analyses.