Determination of Ds+ meson fragmentation functions through two different approaches

The hadronization mechanism is described by the fragmentation functions (FFs) which are universal and process-independent quantities. They can be generally determined theoretically or phenomenologically. In the phenomenological approach which is based on the data analysis, we present the FFs of ${D}_{s}^{+}$ both at leading-order (LO) and next-to-leading order (NLO) and, for the first time, at next-to-next-to-leading order in the minimal subtraction factorization scheme with five massless quarks. These functions are determined by fitting all available experimental data of inclusive single ${D}_{s}^{+}$-meson production in electron-positron annihilation, from the OPAL Collaboration at CERN LEP1. We shall also estimate the uncertainties in these FFs as well as in the corresponding observables. In the theoretical approach, we apply the perturbative FFs formalism based on the Suzuki's model and present our analytical results at LO and NLO perturbative QCD framework. For the first time, a comparison between both approaches will be presented in this work. We also apply our new FFs to generate theoretical predictions for the energy distribution of ${D}_{s}^{+}$ mesons produced through the decay of unpolarized top quarks, to be measured at the CERN LHC.