Studies of beauty hadron and non-prompt charm hadron production in pp collisions at $\sqrt{s}$=13 TeV within a transport model approach

In high-energy proton proton ($pp$) collisions at the LHC, non-prompt charm hadrons, originating from beauty hadron decays, provide a valuable probe for beauty quark dynamics, particularly at low transverse momentum where direct beauty measurements are challenging. We employ A Multi-Phase Transport Model (AMPT) of string melting version coupled with PYTHIA8 initial conditions to study the beauty hadron and non-prompt charm hadron productions in $pp$ collisions at $\sqrt{s} = 13$ TeV. In this work, the beauty quark mass during the generation stage has been increased to reproduce the measured $b\bar{b}$ cross section, and a beauty flavor specific coalescence parameter $r_{BM}^b$ is introduced to match LHCb measurements of beauty baryon to meson ratios. With these refinements, AMPT achieves a reasonable agreement with experimental data on beauty hadron yields and non-prompt charm hadron production from ALICE and LHCb. We present the transverse momentum and multiplicity dependence of non-prompt to prompt charm hadron ratios, providing new insights into the interplay between beauty quark production and hadronization process. We emphasize that the multiplicity dependence of the non-prompt to prompt charm hadron productions can be useful to constrain the flavor dependences of the coalescence dynamics. This work establishes a unified framework for future studies of heavy quark transport and collective flow behavior in small collision systems.