Laplace method for the evolution of the fragmentation function of Bc mesons

In high-energy processes, the predominant mechanism for b¯c bound states is the production of a high-energy b¯ or c   quark, which fragments into the b¯c state. An approximate approach for the evolution of the fragmentation functions for the production of the S-wave states of BcBc and Bc⁎ is presented using Laplace transform technique in the leading order (LO) and next-to-leading order (NLO) analyses. The cross sections, as a function of the transverse momentum for the direct hadro-production b¯(c)→Bc and b¯(c)→Bc⁎ based on the nonrelativistic quantum chromodynamics (QCD) factorization, are determined and compared with the Large Hadron Collider (LHC) and Tevatron data at the 1S-wave state.