Pion parton distribution function in the valence region

The parton distribution function of the pion in the valence region is extracted in a next-to-leading order analysis from Fermilab E-615 pionic Drell-Yan data. The effects of the parametrization of the pion's valence distributions are examined. Modern nucleon parton distributions and nuclear corrections were used and possible effects from higher twist contributions were considered in the analysis. In the next-to-leading order analysis, the high-x dependence of the pion structure function differs from that of the leading order analysis, but not enough to agree with the expectations of pQCD and Dyson-Schwinger calculations.

Figure 1

(Color online) The ratio of NLO to LO pionic Drell-Yan cross sections (K-factor) calculated using CTEQ5M proton PDF and the pion PDF from this work. One point is shown for each $(x_F,\sqrt{\tau })$ bin projected onto the $x_{\pi }$ axis. NLO terms are clearly important as $x\to 1$.

Figure 2

(Color online) Measured values of $d\sigma /{\mathit{dx}}_{F}d\sqrt{\tau }$ (points) reported by Conway et al. [1] along with the NLO fit to the data (curves).

Figure 3

(Color online) The valence pion PDF, $x{q}_{\pi }^v(x)$, for the preferred fit (solid) as well as those from Conway et al. [1] (dashed), SMRS [31] (dotted), and GRS [27] (dot-dashed) at a mass scale of $\langle M_{\gamma }\rangle {}^2=(5.2\hspace{1em}\mathrm{GeV}){}^2$ are shown. The present work shows evidence for greater curvature at high-x. The upper plot shows the entire x range of the data, while the lower plot emphasized the high-x region. For comparison, the small higher twist (γ) term has been removed.

Figure 4

(Color online) (a) The residuals, $R=({\sigma }^{\mathrm{meas}.}-{\sigma }^{\mathrm{calc}.})/{\delta }^{\mathrm{meas}.}$, for the preferred fit as a function of x. No bias is apparent as a function of x. (b) The residual distribution fit to a Gaussian with mean $\langle R\rangle$, of $0.14\pm 0.15$ and width, σ, of $1.09\pm 0.14$.