Fragmentation fraction $f_{{\Omega }_b}$ and the ${\Omega }_b\to \Omega J/\psi$ decay in the light-front formalism

Abstract

One has measured $f_{{\Omega }_b}\mathcal{B}({\Omega }_b^{-}\to {\Omega }^{-}J/\Psi )$ at the level of $10^{-6}$, where the fragmentation faction $f_{{\Omega }_b}$ is to evaluate the $b$-quark to ${\Omega }_b^{-}$ production rate. Using the ${\Omega }_b\to \Omega$ transition form factors calculated in the light-front quark model, we predict $\mathcal{B}({\Omega }_b^{-}\to {\Omega }^{-}J/\Psi )=(5.3_{-2.1-2.7}^{+3.3+3.8})\times 10^{-4}$. In particular, we extract $f_{{\Omega }_b}=(0.54_{-0.22-0.28-0.15}^{+0.34+0.39+0.21})\times 10^{-2}$, demonstrating that the $b$ to ${\Omega }_b$ productions are much more difficult than the $b$ to ${\Lambda }_b({\Xi }_b)$ ones. Since $f_{{\Omega }_b}$ has not been determined experimentally, $f_{{\Omega }_b}$ added to theoretical branching fractions can be compared to future measurements of the ${\Omega }_b$ decays.

Comments: 10 pages, 2 figures, 1 table, published version in PRD