The b quark low-scale running mass from Upsilon sum rules

TL;DR

This work determines the bottom quark low-scale running mass m_kin by analyzing Upsilon sum rules at NNLO, arguing that the pole mass is infrared ambiguous and unreliable in this context. By adopting a kinetic mass defined at a low scale and carefully matching to full QCD, the authors demonstrate improved perturbative convergence of the spectral-density moments and extract m_kin(1 GeV)=4.56±0.06 GeV, translating to m̄(m̄)=4.20±0.10 GeV. The analysis also shows that pole-mass extractions from sum rules are problematic due to large higher-order corrections and strong scale dependence, reinforcing the utility of a low-scale mass scheme for threshold heavy-quark physics. As additional results, NNLO analytic expressions for the threshold e+e− → Q Q̄ cross section and for the energy levels/wave functions of 1S Q Q̄ states are provided, highlighting the broader applicability of the method to heavy-quark phenomenology.

Abstract

The b quark low-scale running mass m_kin is determined from an analysis of the Upsilon sum rules in the next-to-next-to-leading order (NNLO). It is demonstrated that using this mass one can significantly improve the convergence of the perturbation series for the spectral density moments. We obtain m_kin(1 GeV) = 4.56 \pm 0.06 GeV. Using this result we derive the value of the MS-bar mass m: m(m) = 4.20 \pm 0.1 GeV. Contrary to the low-scale running mass, the pole mass of the b quark cannot be reliably determined from the sum rules. As a byproduct of our study we find the NNLO analytical expression for the cross section e+e- --> Q\bar Q of the quark antiquark pair production in the threshold region, as well as the energy levels and the wave functions at the origin for the ^1S_3 bound states of Q\bar Q.