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Home > Physical Review D (APS) > Next-to-leading-order QCD corrections to the decay of <math><mi>Z</mi></math> boson into <math><msub><mi>χ</mi><mi>c</mi></msub><mo>(</mo><msub><mi>χ</mi><mi>b</mi></msub><mo>)</mo></math> |

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 $\Gamma (Z\to J/\psi +X){|}_{{\chi}_{c}-\text{feeddown}}=(0.28-2.4)\times {10}^{-5}$ and $\Gamma (Z\to \Upsilon (1S)+X){|}_{{\chi}_{b}-\text{feeddown}}=(0.15-0.49)\times {10}^{-6}$.

**Published in: ****Physical Review D 99 (2019)**
**Published by: **APS

**DOI: **10.1103/PhysRevD.99.094009

**arXiv: **1809.02426

**License: **CC-BY-4.0