Fragmentation functions from semi-inclusive DIS pion production and implications for the polarized parton densities

TL;DR

The paper demonstrates that combining HERMES semi-inclusive DIS π^± data with the e^+e^- determined singlet fragmentation function D_Σ^{π^+} enables, for the first time, flavour-separated fragmentation functions D_u^{π^+}, D_d^{π^+}, and D_s^{π^+} in a LO framework. While D_u^{π^+} and D_d^{π^+} are tightly constrained, D_s^{π^+} remains uncertain due to the evolution of D_Σ^{π^+} down to SIDIS scales, dominated by gluon mixing. The study also shows that relying on purity functions to extract polarized parton densities can underestimate uncertainties, underscoring the need for joint, factorized analyses of FFs and PDFs to obtain robust polarized densities from SIDIS data. These results guide future improvements in FF determinations and in the extraction of polarized parton densities from SIDIS measurements.

Abstract

By combining recent HERMES data on semi-inclusive DIS $π^\pm$-production with the singlet fragmentation function $D_Σ^{π^+}$, which is well determined from $e^+e^-$ data, we are able to extract, for the first time, the flavoured fragmentation functions $D_u^{π^+}$, $D_d^{π^+}$ and $D_s^{π^+}$ without making any assumptions about favoured and unfavoured transitions. Whereas $D_u^{π^+}$ and $D_d^{π^+}$ are very well determined, the accuracy of $D_s^{π^+}$ is limited by the uncertainty in evolving $D_Σ^{π^+}$ from the $Z^0$ pole down to the SIDIS scale of a few $(GeV)^2$. We discuss how the precision on $D_s^{π^+}$ could be improved. Knowledge of the $D_{q=u,d,s}^{π^+}$ will permit the extraction of the polarized parton densities from future polarized SIDIS asymmetry measurements. We study the precision that can be expected in such an extraction.

Figures (7)

• Figure 1: The ratio of singlet fragmentation functions $D_{\Sigma}^{\pi^+}$ found in Kr (K) and KKP (KKP), at $Q^2 = 100\ {\rm GeV}^2$ (left) and at a typical SIDIS value $Q^2 = 2\ {\rm GeV}^2$ (right).
• Figure 2: The valence-type ($D_u^{\pi^+}$), sea-type ($D_d^{\pi^+}$) and strange-type ($D_s^{\pi^+}$) FF into charged pions extracted under the assumption of isospin-invariance from HERMES SIDIS measurements supplemented by the singlet FF of Kr (solid) and KKP (dashed), respectively. Details are given in the text. Switching between the LO $\leftrightarrow$ NLO parametrizations of KrKKP leads to similar variations in the FFs whereas the variation from employing different unpolarized PDFs is negligible.
• Figure 3: The extracted fragmentation functions with errors which combine the experimental errors from HERMES with a typical 20% uncertainty arising from the evolution of the singlet fragmentation function.
• Figure 4: A comparison of the extracted FFs $D_u^{\pi^+}$, $D_d^{\pi^+}$ (solid lines) at $\left< Q^2 \right> = 2.5\ {\rm GeV}^2$ as in Fig. \ref{['fig1']} to the LO-parametrization in Kr (dashed) where $(1-z) D_u^{\pi^+}(z) = D_d^{\pi^+}(z)$ at the input $Q_0^2$.
• Figure 5: Purity functions $P_{q/p}^{\pi^+}(x)$ extracted from HERMES data HERMES01 with 20% uncertainty from the evolution of the flavour-singlet $D_\Sigma^\pi$.