Abstract
We determine the mass of the bottom quark from high moments of the bb¯ production cross section in e+e− annihilation, which are dominated by the threshold region. On the theory side next-to-next-to-next-to-leading order (NNNLO) calculations both for the resonances and the continuum cross section are used for the first time. We find mbPS(2 GeV)=4.532−0.039+0.013 GeV for the potential-subtracted mass and mbMS¯(mbMS¯)=4.193−0.035+0.022 GeV for the MS¯ bottom-quark mass.
Highlights
The bottom-quark mass is one of only a handful of fundamental QCD parameters, and its precise knowledge is of considerable interest by itself
In this work we present the first determination of the bottom-quark mass from large-n sum rules at next-to-next-to-next-to-leading order (NNNLO)
We have presented the first complete NNNLO determination of the bottom-quark mass from non-relativistic sum rules
Summary
The bottom-quark mass is one of only a handful of fundamental QCD parameters, and its precise knowledge is of considerable interest by itself. For small values of n it is most convenient to calculate moments directly from the derivatives of the polarisation function in conventional perturbation theory. At the same time the strong coupling constant αs is of the same order as the quark velocity For this reason terms scaling with powers of αs/v, which originate from Coulomb interaction, have to be summed to all orders. This is achieved in the effective theory of potential non-relativistic QCD (PNRQCD) [7]. Since we are aiming at high precision, we include the effects of the non-zero charm-quark mass The details of this computation are given in four appendices
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