Parton-to-kaon fragmentation revisited

We revisit the global QCD analysis of parton-to-kaon fragmentation functions at next-to-leading-order accuracy using the latest experimental information on single-inclusive kaon production in electron-positron annihilation, lepton-nucleon deep-inelastic scattering, and proton-proton collisions. An excellent description of all data sets is achieved, and the remaining uncertainties in parton-to-kaon fragmentation functions are estimated and discussed based on the Hessian method. Extensive comparisons to the results from our previous global analysis are made.

Figure 1

The individual FFs for positively charged kaons $z{D}_i^{K^{+}}(z,Q^2)$ at $Q^2=10{\mathrm{GeV}}^2$ (solid lines) along with uncertainty estimates at 68% and 90% C.L. indicated by the inner and outer shaded bands, respectively. Also shown is a comparison to our previous DSS 07 global analysis [3] (dashed lines).

Figure 2

As in Fig. 1 but now at the scale $Q=M_Z$ where also the bottom-to-$K^{+}$ fragmentation function is nonzero. Also shown are the results of the recent JAM analysis [12] of SIA data.

Figure 3

Left: Comparison of our new NLO results (solid lines) and the previous DSS 07 fit [3] (dashed lines) with data sets for inclusive kaon production in SIA used in both fits; see Table 1. The inner and outer shaded bands correspond to new uncertainty estimates at 68% and 90% C.L., respectively. Right: “(Data-theory)/theory” for each of the data sets with respect to our new fit (symbols) and the DSS 07 analysis (dashed lines).

Figure 4

Left: Comparison of our new NLO results (solid line) with the new Belle data [20]; also shown is the result obtained with the DSS 07 fit [3] (dashed line). Right: Same as the left panel, but for the BABAR data [19]. Lower panels: (Data-theory)/theory for each of the data sets with respect to our new fit (symbols) and the DSS 07 analysis (dashed lines). The inner and outer shaded bands correspond to the new uncertainty estimates at 68% and 90% C.L., respectively. Data below $z=0.2$ are not included in the fit.

Figure 5

Comparison of our NLO results (solid lines) for charged kaon multiplicities in SIDIS in four different bins of $z$ with data from the Hermes Collaboration [21] for both proton and deuteron targets. The $z-Q^2$ and $z-x$ projection are shown in the left and right panels, respectively. The light shaded (yellow) bands correspond to uncertainty estimates at 90% C.L., the dark shaded (green) bands illustrate the PDF uncertainty also at 90% C.L. The results obtained with the DSS 07 set of FFs (dashed lines) are included as well. As indicated in the plot, different constant factors are added to the multiplicities to better distinguish the results for different ranges of $z$ in each panel.

Figure 6

Comparison of our NLO results for $K^{+}$ multiplicities in SIDIS (solid lines) with data from the Compass experiment [24] taken on a deuteron target for various bins in $x$ and $y$. As in Fig. 5, the light (yellow) and dark (green) shaded bands correspond to FF and PDF uncertainty estimates at 90% C.L., respectively. Also shown are the results obtained with our previous DSS 07 set of FFs (dashed lines). As indicated in the plot, different constant factors are added to the multiplicities $M_{\mu d}^{K^{+}}$ to more easily distinguish the results for different values of $y$ (i.e., $Q^2$) in the same bin of $x$.

Figure 7

Same as in Fig. 6 but now for the $K^{-}$ multiplicities $M_{\mu d}^{K^{-}}$.

Figure 8

Comparison of our NLO results for the $K^{+}$ (left) and $K^{-}$ (right) cross sections in $pp$ collisions at $\sqrt{S}=200\mathrm{GeV}$ and midrapidity with the Star data [26]. The inner and outer shaded bands correspond to uncertainty estimates at 68% and 90% C.L., respectively. Also shown are the results obtained with the DSS 07 set of kaon FFs (dashed lines). The lower panels show the corresponding results for (data-theory)/theory.

Figure 9

Same as in Fig. 8 but now for the $K^{-}/K^{+}$ cross section ratio.

Figure 10

Ratio of the charged kaon to charged pion cross section at $\sqrt{S}=2.76\mathrm{TeV}$ as measured by Alice [25] compared to our NLO results (solid line). The pion cross section is computed with the DSS 14 set [17]. The dashed line illustrates the result obtained with the old DSS 07 sets of FFs for both pions and kaons. The inner and outer shaded bands correspond to uncertainty estimates at 68% and 90% C.L., respectively.