Fragmentation fraction <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ω</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math> and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ω</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:mi mathvariant="normal">Ω</mml:mi><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi></mml:mrow></mml:math> decay in the light-front formalism

Abstract

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

Topics & Concepts