Three-Loop Anomalous Dimension of the Heavy Quark Pair Production Current in Non-Relativistic QCD

The three-loop non-mixing contributions to the anomalous dimension of the leading order quark pair production current in non-relativistic QCD are computed. It is demonstrated that the renormalization procedure can only be carried out consistently if the dynamics of both soft and the ultrasoft degrees of freedom is present for all scales below the heavy quark mass, and if the soft and ultrasoft renormalization scales are always correlated.Comment: 19 pages, revtex, 5 postscript figures include

Electroweak Absorptive Parts in NRQCD Matching Conditions

Electroweak corrections associated with the instability of the top quark to the next-to-next-to-leading logarithmic (NNLL) total top pair threshold cross section in e+e- annihilation are determined. Our method is based on absorptive parts in electroweak matching conditions of the NRQCD operators and the optical theorem. The corrections lead to ultraviolet phase space divergences that have to be renormalized and lead to NLL mixing effects. Numerically, the corrections can amount to several percent and are comparable to the known NNLL QCD corrections.Comment: 17 pages, revtex4, 4 postscript figures included; minor changes in text and references, title modified in printed versio

Phase Space Matching and Finite Lifetime Effects for Top-Pair Production Close to Threshold

The top-pair $t\bar t$ production cross section close to threshold in $e^+e^-$ collisions is strongly affected by the small lifetime of the top quark. Since the cross section is defined through final states containing the top decay products, a consistent definition of the cross section depends on prescriptions how these final states are accounted for the cross section. Experimentally, these prescriptions are implemented for example through cuts on kinematic quantities such as the reconstructed top quark invariant masses. As long as these cuts do not reject final states that can arise from the decay of a top and an anti-top quark with a small off-shellness compatible with the nonrelativistic power-counting, they can be implemented through imaginary phase space matching conditions in NRQCD. The prescription-dependent cross section can then be determined from the optical theorem using the $e^+e^-$ forward scattering amplitude. We compute the phase space matching conditions associated to cuts on the top and anti-top invariant masses at next-to-next-to-leading logarithmic (NNLL) order and partially at next-to-next-to-next-to-leading logarithmic (N${}^3$LL) order in the nonrelativistic expansion and, together with finite lifetime and electroweak effects known from previous work, analyze their numerical impact on the $t\bar t$ cross section. We show that the phase space matching contributions are essential to make reliable NRQCD predictions, particularly for energies below the peak region, where the cross section is small. We find that irreducible background contributions associated to final states that do not come from top decays are strongly suppressed and can be neglected for the theoretical predictions.Comment: 62 pages, 21 figure

On Electroweak Matching Conditions for Top Pair Production at Threshold

We determine the real parts of electroweak matching conditions relevant for top quark pair production close to threshold in e+e- annihilation at next-to-next-to-leading logarithmic (NNLL) order. Numerically the corrections are comparable to the NNLL QCD corrections.Comment: 12 pages, revtex4, 1 postscript figure included; minor changes in text and references, version published in Phys. Rev.

Top quark mass definition and top quark pair production near threshold at the NLC

We suggest an infrared-insensitive quark mass, defined by subtracting the soft part of the quark self energy from the pole mass. We demonstrate the deep relation of this definition with the static quark-antiquark potential. At leading order in 1/m this mass coincides with the PS mass which is defined in a completely different manner. Going beyond static limit, the small normalization point introduces recoil corrections which are calculated here as well. Using this mass concept and other concepts for the quark mass we calculate the cross section of e+ e- -> t t-bar near threshold at NNLO accuracy adopting three alternative approaches, namely (1) fixing the pole mass, (2) fixing the PS mass, and (3) fixing the new mass which we call the PS-bar mass. We demonstrate that perturbative predictions for the cross section become much more stable if we use the PS or the PS-bar mass for the calculations. A careful analysis suggests that the top quark mass can be extracted from a threshold scan at NLC with an accuracy of about 100-200 MeV.Comment: published version, 21 pages in LaTeX including 11 PostScript figure

The Threshold t-tbar Cross Section at NNLL Order

The total cross section for top quark pair production close to threshold in e+e- annihilation is investigated. Details are given about the calculation at next-to-next-to-leading logarithmic order. The summation of logarithms leads to a convergent expansion for the normalization of the cross section, and small residual dependence on the subtraction parameter nu. A detailed analysis of the residual nu dependence is carried out. A conservative estimate for the remaining uncertainty in the normalization of the total cross section from QCD effects is $\lesssim \pm 3$. This makes precise extractions of the strong coupling and top width feasible, and further studies of electroweak effects mandatory.Comment: 33 pages, 11 figs, a program to produce the cross section will be available soo

Top Quark Pair Production close to Threshold: Top Mass, Width and Momentum Distribution

The complete NNLO QCD corrections to the total cross section $\sigma(e^+e^- \to Z*,\gamma*\to t\bar t)$ in the kinematic region close to the top-antitop threshold are calculated by solving the corresponding Schroedinger equations exactly in momentum space in a consistent momentum cutoff regularization scheme. The corrections coming from the same NNLO QCD effects to the top quark three-momentum distribution $d\sigma/d |\vec k_t|$ are determined. We discuss the origin of the large NNLO corrections to the peak position and the normalization of the total cross section observed in previous works and propose a new top mass definition, the 1S mass M_1S, which stabilizes the peak in the total cross section. If the influence of beamstrahlung and initial state radiation on the mass determination is small, a theoretical uncertainty on the 1S top mass measurement of 200 MeV from the total cross section at the linear collider seems possible. We discuss how well the 1S mass can be related to the $\bar{MS}$ mass. We propose a consistent way to implement the top quark width at NNLO by including electroweak effects into the NRQCD matching coefficients, which then can become complex.Comment: 53 pages, latex; minor changes, a number of typos correcte