The information about the fragmentation process is used to describe the dynamics of hard processes at the different parts of experimental high energy physics. The information about probability of production of a final state hadron from a parton of a specific type plays a key role in those studies. The fragmentation processes are difficult to simulate, but the information about them could be obtained by analyzing the socalled fragmentation fractions, which can be evaluated using the relations between differential production cross sections. Electronpositron, electronproton and protonproton interactions are used for these purposes.
Until now, only the fragmentation fractions of charm hadrons such as: $D^{0}$, $D^{+}$, $D_s^+$, $\Lambda_c^{+}$, $\Xi_c^{+}$ have been measured with a high accuracy. However, there are no studies of the ratios of the differential cross sections for the production of excited states from the $\Xi_c^{+}$ family such as: $\Xi_c(2645)^{0}$, $\Xi_c(2815)^{+}$ and the corresponding antiparticles. The main interest is the universality of fragmentation fractions, that is their dependence on the kinematics of the charm hadrons. The LHCb experiment has already discovered a nonuniversality of the fragmentation fractions for $b$hadrons has already been discovered [1]. In the charmed hadron sector, there are theoretical predictions [2] indicating the nonuniversality of the fragmentation fractions. In addition, in the work [3] the ALICE collaboration also indicates a possible violation of nonuniversality in the hadronization process.
The main goal of the ongoing study is to obtain the relations of the differential cross sections for the production of excited charmed baryons: $\Xi_c(2645)^{0}$ and $\Xi_c(2815)^{+}$ with respect to their ground state. The relations of the differential production cross sections, with correction on branching ratios, are supposed to be equal to the relation of the fragmentation functions of the corresponding hadrons. The protonproton collisions dataset obtained by the LHCb experiment at the $\sqrt{s}$ = 7 and 8 TeV during RunI campaign is used. The decays candidates are selected by the following decay channels:
$\Xi_c^+$ → $pK^\pi^+$; $\Xi_c$(2645)$^{0}$ → $\Xi_c^+\pi^$; $\Xi_c$(2815)$^+$ → $\Xi_c$(2645)$^0\pi^+$.
The rapidity as well as the transverse momentum dependencies of the cross section are studied.

LHCb Coll. Measurement of b hadron production fractions in 7 TeV pp collisions. Phys. Rev., D85, 2012.

B.A. Kniehl, G. Kramer, I. Schienbein, and H. Spiesberger, $\Lambda_c^{+}$ production in pp collisions with a new fragmentation function, Phys. Rev. D 101, 114021 (2020).

ALICE Collaboration, Charmquark fragmentation fractions and production cross section at 4 midrapidity in pp collisions at the LHC, Phys. Rev. D 105, L011103 (2022).