Revisiting the bottom quark forward–backward asymmetry $$A_\mathrm{{FB}}$$ AFB in electron–positron collisions

• Main Authors: Sheng-Quan Wang, Rui-Qing Meng, Xing-Gang Wu, Long Chen, Jian-Ming Shen
• Format: Article
• Language: English
• Published: SpringerOpen 2020-07-01
• Series: European Physical Journal C: Particles and Fields
• Online Access: http://link.springer.com/article/10.1140/epjc/s10052-020-8234-x
• ISSN: 1434-6044; 1434-6052

Abstract The bottom quark forward–backward asymmetry $$A_\mathrm{{FB}}$$ AFB is a key observable in electron–positron collisions at the $$Z^{0}$$ Z0 peak. In this paper, we employ the Principle of Maximum Conformality (PMC) to fix the $$\alpha _s$$ αs -running behavior of the next-to-next-to-leading order QCD corrections to $$A_\mathrm{{FB}}$$ AFB . The resulting PMC scale for this $$A_\mathrm{{FB}}$$ AFB is an order of magnitude smaller than the conventional choice $$\mu _r=M_Z$$ μr=MZ . This scale has the physically reasonable behavior and reflects the virtuality of its QCD dynamics, which is independent to the choice of renormalization scale. Our analyses show that the effective momentum flow for the bottom quark forward–backward asymmetry should be $$\mu _r\ll M_Z$$ μr≪MZ other than the conventionally suggested $$\mu _r=M_Z$$ μr=MZ . Moreover, the convergence of perturbative QCD series for $$A_\mathrm{{FB}}$$ AFB is greatly improved using the PMC. Our prediction for the bare bottom quark forward–backward asymmetry is refined to be $$A^{0,b}_\mathrm{FB}=0.1004\pm 0.0016$$ AFB0,b=0.1004±0.0016 , which diminishes the well known tension between the experimental determination for this (pseudo) observable and the respective Standard Model fit to $$2.1\sigma $$ 2.1σ .