Reply to “Comment on ‘Reevaluation of the parton distribution of strange quarks in the nucleon’”

A Comment on the recently published reevaluation of the polarization-averaged parton distribution of strange quarks in the nucleon using final data on the multiplicities of charged kaons in semi-inclusive deep-inelastic scattering (DIS) is reviewed. Important features of the comparison of one-dimensional projections of the multidimensional HERMES data are pointed out. A test of the leading-order extraction of $x_{\mathrm{B}}$ $S(x_{\mathrm{B}})$ using the difference between charged-kaon multiplicities is repeated. The results are consistent with leading-order predictions within the uncertainties in the input data, and do not invalidate the earlier extraction of $x_{\mathrm{B}}$ $S(x_{\mathrm{B}})$.

Figure 1

Comparison of the shapes of multiplicities corrected to $4\pi$ of charged kaons and pions in semi-inclusive DIS from a deuterium target, as a function of Bjorken $x_{\mathrm{B}}$. The kaon multiplicities are scaled to agree with those of pions in the range of $x_{\mathrm{B}}$ where both distributions flatten. Data are plotted at the average $x_{\mathrm{B}}$ of each individual $x_{\mathrm{B}}$ bin.

Figure 2

Born space in ($x_{\mathrm{B}}$, ${\mathrm{Q}}^2$) corresponding to the multiplicities reported in Ref. [2]. Kinematic regions covered by two data points with similar average kinematics, as discussed in the Comment [3], are superimposed (highlighted slices in either $x_{\mathrm{B}}$ or ${\mathrm{Q}}^2$). Note that the color coding is logarithmic, and that most of the events [$\mathcal{O}(70\%)$] in either of the two bins are in fact not shared.

Figure 3

Left: $K^{\prime }$ “multiplicities” corrected to $4\pi$ of charged kaons in semi-inclusive DIS from a deuterium target, as a function of $x_{\mathrm{B}}$, evaluated with Eq. (4) using MSTW08 (squares), CTEQ6 (upward triangles), NNPDF3.0 (downward triangles), and NNPDF2.3 (full circles) LO PDF sets. Also shown are the LO predictions [e.g., Eq. (5)] using DSS FFs (crosses) or using the high-$x_{\mathrm{B}}$ HERMES data to constrain the unfavored $\overline{u}$ and $\overline{d}$ to $K^{+}$ FFs (stars). For both the crosses and stars, $S\int \mathrm{d}z{D}_S^K$ from Ref. [1] and $Q$ from NNPDF3.0 were used. Note that uncertainties on PDFs or FFs—when available at all—were not propagated, but only total experimental uncertainties. Right: Equation (5) evaluated in the same way as the crosses to the left, but for a range of scaled DSS unfavored nonstrange kaon FFs (using scaling factors from 0 (bottom) to 4 (top) as in Fig. 2 (left) in the Comment [3]). As in the Comment [3], all points were evaluated at the average ${\mathrm{Q}}^2$ of each individual $x_{\mathrm{B}}$ bin.

Figure 4

The ${\mathrm{Q}}^2$ dependence of the DSS favored $u$ and $\overline{s}$ (scaled by a factor $1/7$) as well as the unfavored $\overline{u}$ to $K^{+}$ fragmentation functions. Note that for the DSS FF set $D_{\overline{u}}^{K^{+}}=D_{\overline{d}}^{K^{+}}$. Chosen ${\mathrm{Q}}^2$ values correspond to the average ${\mathrm{Q}}^2$ of the $x_{\mathrm{B}}$ bins in Figs. 3 and 5.

Figure 5

The scaled charge-difference multiplicities $\mathrm{d}{N}^{K^{\mathrm{diff}}}/\mathrm{d}{N}^{\mathrm{DIS}}·(5Q+2S)/[4(u_v+d_v)]$ of charged kaons in semi-inclusive DIS from a deuterium target, as a function of $x_{\mathrm{B}}$, evaluated using various LO PDF sets [MSTW08 (squares), CTEQ6 (upward triangles), NNPDF3.0 (downward triangles), and NNPDF2.3 (circles)], compared with the LO predictions based on solely DSS FFs (crosses) and DSS FFs combined with unfavored kaon FFs constrained using HERMES data at high $x_{\mathrm{B}}$ (stars). As in the Comment [3], all points were evaluated at the average ${\mathrm{Q}}^2$ of each individual $x_{\mathrm{B}}$ bin.