Next-to-leading-order QCD corrections to the decay of $Z$ boson into ${\chi }_{c}\left({\chi }_{b}\right)$

Sun, Zhan (Department of Physics, Guizhou Minzu University, Guiyang 550025, People’s Republic of China) ; Zhang, Hong-Fei (College of Big Data Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China)

10 May 2019

Abstract: Based on the framework of nonrelativistic quantum chromodynamics, we carry out next-to-leading-order (NLO) QCD corrections to the decay of $Z$ boson into ${\chi }_{c}$ and ${\chi }_{b}$, respectively. The branching ratio of $Z\to {\chi }_{c}\left({\chi }_{b}\right)+X$ is about ${10}^{-5}\left({10}^{-6}\right)$. For the color-singlet (CS) ${{}^{3}P}_{J}^{\left[1\right]}$ state, the heavy quark-antiquark pair associated process serves as the leading role. However the process of $Z\to Q\overline{Q}\left[{{}^{3}P}_{J}^{\left[1\right]}\right]+g+g$ can also provide non-negligible contributions, especially for the ${\chi }_{b}$ cases. In the case of the color-octet (CO) ${{}^{3}S}_{1}^{\left[8\right]}$ state, the single-gluon-fragmentation diagrams that first appear at the NLO level can significantly enhance the leading-order results. Consequently the CO contributions account for a large proportion of the total decay widths. Moreover, including the CO contributions will thoroughly change the CS predictions on the ratios of ${\Gamma }_{{\chi }_{c1}}/{\Gamma }_{{\chi }_{c0}}$, ${\Gamma }_{{\chi }_{c2}}/{\Gamma }_{{\chi }_{c0}}$, ${\Gamma }_{{\chi }_{b1}}/{\Gamma }_{{\chi }_{b0}}$, and ${\Gamma }_{{\chi }_{b2}}/{\Gamma }_{{\chi }_{b0}}$, which can be regarded as an outstanding probe to distinguish between the CO and CS mechanism. Summing over all the feeddown contributions from ${\chi }_{c}$ and ${\chi }_{b}$, respectively, we find $\Gamma \left(Z\to J/\psi +X\right){|}_{{\chi }_{c}-\text{feeddown}}=\left(0.28-2.4\right)×{10}^{-5}$ and $\Gamma \left(Z\to \Upsilon \left(1S\right)+X\right){|}_{{\chi }_{b}-\text{feeddown}}=\left(0.15-0.49\right)×{10}^{-6}$.

Published in: Physical Review D 99 (2019)