Abstract
We compute the third-order correction to the heavy-quark current correlation function due to the emission and absorption of an ultrasoft gluon. Our result supplies a missing contribution to top-quark pair production near threshold and the determination of the bottom quark mass from QCD sum rules.
Highlights
In a previous paper [1] we described the calculation of the ultrasoft gluon contribution to the correlation function of heavy-quark vector currents, which constitutes one of the major missing pieces in perturbative calculations of quarkonium-like systems at the third order in non-relativistic perturbation theory
The ultrasoft contribution to G(E) refers to diagrams where one gluon has ultrasoft momentum k ∼ E ∼ mv2, while an infinite number of potential (Coulomb) gluons can be exchanged between the heavy quarks, promoting the heavy-quark propagators to the Green function of the Schrodinger operator including the colour Coulomb potential
The resulting scheme and scale dependence cancels with other NRQCD contributions to the correlation function, and matching coefficients, but there is a left-over dependence proportional to Γt due to the overall divergences discussed above, which cancels with electroweak corrections that are not yet known
Summary
In a previous paper [1] we described the calculation of the ultrasoft gluon contribution to the correlation function of heavy-quark vector currents, which constitutes one of the major missing pieces in perturbative calculations of quarkonium-like systems at the third order in non-relativistic perturbation theory. (8), (9) of [1]), the corresponding correction to the inclusive heavy-quark production cross section is computed as
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