Abstract
In order to clarify the puzzling problems in double-charm production, relativistic corrections at order ${v}^{2}$ to the processes ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}+{\ensuremath{\eta}}_{c}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}+c\overline{c}$ at $B$ factories are studied in nonrelativistic quantum chromodynamics. The short-distance parts of production cross sections are calculated perturbatively, while the long-distance matrix elements are estimated from $J/\ensuremath{\psi}$ and ${\ensuremath{\eta}}_{c}$ decays up to errors of order ${v}^{4}$. Our results show that the relativistic correction to the exclusive process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}+{\ensuremath{\eta}}_{c}$ is significant, which, when combined together with the next-to-leading-order ${\ensuremath{\alpha}}_{s}$ corrections, could resolve the large discrepancy between theory and experiment; whereas for the inclusive process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}+c\overline{c}$ the relativistic correction is tiny and negligible. The physical reason for the above difference between exclusive and inclusive processes largely lies in the fact that in the exclusive process the relative momentum between quarks in charmonium substantially reduces the virtuality of the gluon that converts into a charm quark pair, but this is not the case for the inclusive process, in which the charm quark fragmentation $c\ensuremath{\rightarrow}J/\ensuremath{\psi}+c$ is significant, and QCD radiative corrections can be more essential.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.