Heavy-hadron production based on $k_t$-factorization with scale-dependent fragmentation functions

We present a comprehensive study of heavy-hadron production, including $D$ and $B$ mesons, heavy baryons, and the $B_c$ meson. Our calculations are based on the $k_t$-factorization and scale-dependent fragmentation functions, completing the program of implementing this formalism within a variable-flavor-number scheme, as initiated in Ref. Phys.Rev.D 104 (2021) 9. Special emphasis is placed on the gluon-to-heavy-hadron contribution, which improves the description of data at small transverse momenta. Finally, we explore and compare different factorization schemes. We achieve the non-trivial task of providing a reasonable description of all the data considered in this study with a factorization scheme fixed once and for all.