First Monte Carlo Global QCD Analysis of Pion Parton Distributions

We perform the first global QCD analysis of parton distribution functions (PDFs) in the pion, combining $\pi A$ Drell-Yan data with leading neutron electroproduction from HERA within a Monte Carlo approach based on nested sampling. Inclusion of the HERA data allows the pion PDFs to be determined down to much lower values of $x$, with relatively weak model dependence from uncertainties in the chiral splitting function. The combined analysis reveals that gluons carry a significantly higher pion momentum fraction, $\sim 30\%$, than that inferred from Drell-Yan data alone, with sea quarks carrying a somewhat smaller fraction, $\sim 15\%$, at the input scale. Within the same effective theory framework, the chiral splitting function and pion PDFs can be used to describe the $\overline{d}-\overline{u}$ asymmetry in the proton.

Figure 1

Cross sections computed with our fitted pion PDFs compared with DY $d^2\sigma /d\sqrt{\tau }d{x}_F$ data from E615 [5] (top left) and NA10 [4] (top right) [in units of nb] and with the LN structure function $F_2^{\mathrm{LN}(3)}$ from H1 [14] (bottom left) and LN to inclusive ratio $r$ from ZEUS [13] (bottom right). For display purposes, the E615, H1, and ZEUS data are scaled by a factor $3^i$ for clarity. The NA10 data are for ${\pi }^{-}$ beam energies of 194 GeV (green) and 286 GeV (blue).

Figure 2

Pion valence (green), sea quark (blue), and gluon (red, scaled by $1/10$) PDFs versus $x_{\pi }$ at $Q^2=10{\mathrm{GeV}}^2$ for the full $\mathrm{DY}+\mathrm{LN}$ (dark bands) and DY only (light bands) fits. The bands represent $1\sigma$ uncertainties, as defined in the standard Monte Carlo determination of the uncertainties [42] from the experimental errors. The model dependence of the fit is represented by the outer yellow bands.

Figure 3

(Top) Normalized yield for the average momentum fractions $⟨x_{\pi }⟩$ of the pion carried by valence quarks (green), sea quarks (blue), and gluons (red) at $Q^2=m_c^2$, for the full MC fit of $\mathrm{DY}+\mathrm{LN}$ data (dark shaded) and for DY-only (light shaded). (Bottom) Scale dependence of the momentum fractions for the full $\mathrm{DY}+\mathrm{LN}$ fit, compared with results from the SMRS (rectangular bands) [8] and GRS [10] (circles) parametrizations at $Q^2=5{\mathrm{GeV}}^2$ (offset for clarity).

Figure 4

$\overline{d}-\overline{u}$ asymmetry in the proton for various chiral splitting function models, with parameters from a combined fit to the $\pi A$ DY [4, 5], LN production [13, 14], and E866 [19] data (black circles) at $Q^2=54{\mathrm{GeV}}^2$. The kinematic coverage of the SeaQuest experiment [53] is indicated by the horizontal band.