Heavy hadron production through pair annihilation in the ordinary and noncommutative SM

Different processes have been yet studied in the noncommutative standard model (NCSM) and various limits on the scale of noncommutative parameter have been determined. In the present work we, for the first time, investigate the production process of heavy hadrons through pair annihilation in the NCSM using Seiberg-Witten maps to the second-order of noncommutative parameter ${\Theta }^{\mu \nu }$. Having experimental data from Belle and OPAL Collaborations for inclusive production of B-mesons we will determine a low limit for the noncommutative scale ${\Lambda }_{NC}$. The effects of noncommutativity will be imposed both on the differential cross section at the parton level ($e^{+}{e}^{-}\to q\overline{q}$) and the fragmentation function of $q/\overline{q}\to B$ so that the limit ${\Lambda }_{NC}>1.10$ TeV is determined. Using analytical result for the pair annihilation cross section we will also predict the production rate of $B_c$ mesons in future electron-positron international linear collider (ILC).