Precise calculation of transition frequencies of hydrogen and deuterium based on a least-squares analysis

We combine a limited number of accurately measured transition frequencies in hydrogen and deuterium, recent quantum electrodynamics (QED) calculations, and, as an essential additional ingredient, a generalized least-squares analysis, to obtain precise and optimal predictions for hydrogen and deuterium transition frequencies. Some of the predicted transition frequencies have relative uncertainties more than an order of magnitude smaller than that of the g-factor of the electron, which was previously the most accurate prediction of QED.Comment: 4 pages, RevTe

Top Quark Pair Production at Threshold: Complete Next-to-next-to-leading Order Relativistic Corrections

The complete next-to-next-to-leading order (i.e. $O(v^2)$, $O(v \alpha_s)$ and $O(\alpha_s^2)$) relativistic corrections to the total photon mediated $t\bar t$ production cross section at threshold are presented in the framework of nonrelativistic quantum chromodynamics. The results are obtained using semi-analytic methods and ``direct matching''. The size of the next-to-next-to-leading order relativistic corrections is found to be comparable to the size of the next-to-leading order ones.Comment: 9 pages, latex, two postscript figures include

Bottom Quark Mass from Upsilon Mesons

The bottom quark pole mass $M_b$ is determined using a sum rule which relates the masses and the electronic decay widths of the $\Upsilon$ mesons to large $n$ moments of the vacuum polarization function calculated from nonrelativistic quantum chromodynamics. The complete set of next-to-next-to-leading order (i.e. ${\cal{O}}(\alpha_s^2, \alpha_s v, v^2)$ where $v$ is the bottom quark c.m. velocity) corrections is calculated and leads to a considerable reduction of theoretical uncertainties compared to a pure next-to-leading order analysis. However, the theoretical uncertainties remain much larger than the experimental ones. For a two parameter fit for $M_b$, and the strong $\bar{{MS}}$ coupling $\alpha_s$, and using the scanning method to estimate theoretical uncertainties, the next-to-next-to-leading order analysis yields 4.74 GeV $\le M_b\le 4.87$ GeV and $0.096 \le \alpha_s(M_z) \le 0.124$ if experimental uncertainties are included at the 95% confidence level and if two-loop running for $\alpha_s$ is employed. $M_b$ and $\alpha_s$ have a sizeable positive correlation. For the running $\bar{{MS}}$ bottom quark mass this leads to 4.09 GeV $\le m_b(M_{\Upsilon(1S)}/2)\le 4.32$ GeV. If $\alpha_s$ is taken as an input, the result for the bottom quark pole mass reads 4.78 GeV $\le M_b\le 4.98$ GeV (4.08 GeV $\le m_b(M_{\Upsilon(1S)}/2)\le 4.28$ GeV) for 0.114\lsim \alpha_s(M_z)\le 0.122. The discrepancies between the results of three previous analyses on the same subject by Voloshin, Jamin and Pich, and K\"uhn et al. are clarified. A comprehensive review on the calculation of the heavy quark-antiquark pair production cross section through a vector current at next-to-next-to leading order in the nonrelativistic expansion is presented.Comment: 55 pages, latex, 13 postscript figures include