Tests of the parametrizations of Fragmentation Functions using data on inclusive pion and kaon production in unpolarized $pp$ collisions from the STAR collaboration and at the NICA project

The goal of this study is to check which, if any, of the published versions of the pion and kaon fragmentation functions is compatible with the STAR data on semi-inclusive pion and kaon production in proton-proton collisions, and on the basis of this analysis to make reliable predictions for the $p_T$ spectra of the pions and kaons in inclusive pion and kaon production at the future NICA proton-proton collider. The calculations are carried out in next-to-leading order of quantum chromodynamics, using the well tested CTEQ6 parton distributions. We consider the following pion and kaon fragmentation functions -- DSEHS-14~\cite{deFlorian:2014xna}, DSEHS-17~\cite{deFlorian:2017lwf}, LSS-15~\cite{Leader:2015hna}, HKNS-07~\cite{Hirai:2007cx} and AKK-08 \cite{Albino:2008fy}. Our analysis shows that within the experimental errors all tested sets of fragmentation functions provide a good fit to STAR data, and the best ones are LSS-15 for pions and DSEHS-17 for kaons. From comparison of the LO and NLO results it is clear that the latter fit data much better, specially in the region of small $p_T$. The NLO cross sections are also less scale-$Q^2$ dependent, where $p_T/2\leqslant Q \leqslant 2p_T$, than the LO ones. It seems that the NICA measurements will allow to discriminate among AKK and other fragmentation functions for charged pions and among HKNS and DSEHS for charged kaons. Unfortunately, due to the relatively large uncertainties, measurements of the difference cross sections, $\sigma^{h^+ - h^-}$, will not be able to distinguish between different FFs.