First Simultaneous Extraction of Spin-Dependent Parton Distributions and Fragmentation Functions from a Global QCD Analysis

We perform the first global QCD analysis of polarized inclusive and semi-inclusive deep-inelastic scattering and single-inclusive $e^{+}{e}^{-}$ annihilation data, simultaneously fitting the parton distribution and fragmentation functions using the iterative Monte Carlo method. Without imposing SU(3) symmetry relations, we find the strange polarization to be very small, consistent with zero for both inclusive and semi-inclusive data, which provides a resolution to the strange quark polarization puzzle. The combined analysis also allows the direct extraction from data of the isovector and octet axial charges, and is consistent with a small SU(2) flavor asymmetry in the polarized sea.

Figure 1

Spin-dependent PDFs with $1\sigma$ uncertainty bands from the JAM17 fit at the input scale $Q_0^2=1{\mathrm{GeV}}^2$. The full results (red solid curves) are compared with the JAM15 $\mathrm{\Delta }{q}^{+}$ PDFs [5] (blue dashed curves) and with the DSSV09 fit [10] for sea quark PDFs (green dotted curves). The $\mathrm{\Delta }{s}^{+}$ PDF is also compared with the JAM17 fit including the SU(3) constraint on the octet axial charge (black dot-dashed curve).

Figure 2

Semi-inclusive polarization asymmetries $A_{1p}^{{\pi }^{-}}$ from COMPASS [52] (left) and $A_{1d}^{K^{-}}$ from HERMES [50] (right) compared with the full JAM17 fit (red curves and band) and with the result assuming $\mathrm{\Delta }\overline{q}\equiv \mathrm{\Delta }\overline{u}=\mathrm{\Delta }\overline{d}=0$ (for $A_{1p}^{{\pi }^{-}}$) and the (negative) $\mathrm{\Delta }{s}^{+}$ from JAM15 [5] (for $A_{1d}^{K^{-}}$).

Figure 3

Fragmentation functions $z{D}_q^h$ to ${\pi }^{+}$ (left panel) and $K^{+}$ (right panel) for $u^{+}$ (blue), $\overline{u}$ (green), $s^{+}$ (red), and $s$ (grey) at $Q^2=5{\mathrm{GeV}}^2$ for the JAM17 analysis. Random samples of 50 posteriors are shown with the mean and variance, and compared with the $s^{+}\to K^{+}$ FFs from DSS [62] (dashed curve) and HKNS [63] (dotted curve).

Figure 4

Normalized yield of the lowest moments of the spin-dependent PDFs for the triplet ($a_3$), octet ($a_8$), and singlet ($\mathrm{\Delta }\mathrm{\Sigma }$) axial charges, and the flavor asymmetry $\mathrm{\Delta }\overline{u}-\mathrm{\Delta }\overline{d}$, with average values (red vertical lines) and $1\sigma$ deviations (pink bands) indicated at the input scale. For the scale invariant $a_3$ [$a_8$], the SU(2) [SU(3)] symmetric values are indicated (blue vertical bands), together with the flat prior distributions for $a_8$ without SU(3) (yellow histograms).