The bottom $\bar{\rm MS}$ quark mass from sum rules at next-to-next-to-leading order

Abstract

We determine the bottom $\bar{\rm MS}$ quark mass $\bar{m}_b$ and the quark mass in the potential subtraction scheme from moments of the $b\bar{b}$ production cross section and from the mass of the Upsilon 1S state at next-to-next-to-leading order in a reorganized perturbative expansion that sums Coulomb exchange to all orders. We find $\bar{m}_b(\bar{m}_b)=(4.25\pm 0.08) $GeV and $m_{b,\rm PS}(2 {GeV})=(4.59\pm 0.08) $GeV for the potential-subtracted mass at the scale 2 GeV, adopting a conservative error estimate.

Figures (2)

• Figure 1: The value of $m_{b,\rm PS}(2\,\hbox{GeV})$ obtained from the 10th moment as a function of the renormalization scale in NLO and NNLO and for $\alpha_s(m_Z)=0.118$. The dark region specifies the variation due to the experimental error on the moment. The middle line marks the scale $\mu_n$, the two outer lines determine the scale variation from which the theoretical error is computed.
• Figure 2: The left-hand side (lhs, short-dashed line) and right-hand side (rhs, dash-dotted and solid lines) of (\ref{['truncated']}) as a function of the scale $\mu$ for $n=10$, $m_b=5\,$GeV (on-shell scheme, dash-dotted) and $m_{b,\rm PS}(2\,\hbox{GeV})=4.6\,$GeV (PS scheme, solid). The figure clearly shows the reduction of the scale dependence in the PS scheme for the predicted $\Upsilon({\rm 1S})$ mass. The scale dependence of the width (short-dashed line) is identical in the on-shell and PS schemes.