Abstract
We consider the Lagrange density of non-relativistic Quantum Chromodynamics expanded up to order $1/m^2$, where $m$ is the heavy quark mass, and compute several matching coefficients up to two-loop order. Our results are building blocks for next-to-next-to-next-to-leading logarithmic and next-to-next-to-next-to-next-to-leading order corrections to the threshold production of top quark pairs and the decay of heavy quarkonia. We describe the techniques used for the calculation and provide analytic results for a general covariant gauge.
Highlights
Nonrelativistic quantum chromodynamics (NRQCD) [1] has proven to provide accurate predictions for systems of two heavy quarks, which move with a small relative velocity
These include predictions for top quark pair production [5],1 the decay of the Υð1SÞ meson [8], and energy levels of heavy quarkonia ground and excited states [9,10,11] together with phenomenological applications [12,13]
The remainder of the paper is organized as follows: we provide the relevant parts of the NRQCD Lagrange density and define the matching coefficients which we want to compute
Summary
Nonrelativistic quantum chromodynamics (NRQCD) [1] has proven to provide accurate predictions for systems of two heavy quarks, which move with a small relative velocity. Among them are decay rates and binding energies of quarkonia and the threshold production of top quark pairs in electron positron annihilation. For comprehensive compilations of results we refer to the review articles [2,3,4] and restrict ourselves here to recent next-to-next-to-next-toleading order (N3LO) results. These include predictions for top quark pair production [5],1 the decay of the Υð1SÞ meson [8], and energy levels of heavy quarkonia ground and excited states [9,10,11] together with phenomenological applications [12,13]. The dominant source of uncertainty in the determination of the charm and bottom quark masses from bound state energies originates from the renormalization scale dependence, due to unknown higher order corrections [11,12]
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