Two-loop QCD corrections to the heavy quark pair production cross section in e+e- annihilation near the threshold

We present the O(alpha_s) corrections to the cross section for the reaction e+e- --> gamma^* --> Q \bar Q in the energy region close to the threshold. We assume that the energy of the reaction is such that both the perturbative expansion in the strong coupling constant and expansion in the relative velocity of the heavy quarks can be used. We explicitly obtain terms O(alpha_s^2/beta^2, alpha_s^2/beta, alpha_s^2) in the relative correction to the threshold cross section. Using the ideas of asymptotic expansions, we demonstrate how an expansion of Feynman diagrams in the threshold region is constructed. From this analysis we obtain a matching relation between the vector current in full QCD and the quark-antiquark current in NRQCD at leading order in 1/m and the second order in the strong coupling constant.Comment: 9 pages, revte

Muonium Decay

Modifications of the mu+ lifetime in matter due to muonium (M = mu+ e-) formation and other medium effects are examined. Muonium and free mu+ decay spectra are found to differ at O(alpha m_e/m_mu) from Doppler broadening and O(alpha^2 m_e/m_mu) from the Coulomb bound state potential. However, both types of corrections are shown to cancel in the total decay rate due to Lorentz and gauge invariance respectively, leaving a very small time dilation lifetime difference, (tau_M - tau_mu+)/tau_mu+ = alpha^2 m_e^2/ 2m_mu^2 \simeq 6\times 10^-10, as the dominant bound state effect. It is argued that other medium effects on the stopped mu+ lifetime are similarly suppressed.Comment: 14 pages, revte

Gauge dependence and matching procedure of a nonrelativistic QED/QCD boundstate formalism

A nonrelativistic boundstate formalism used in contemporary calculations is investigated. It is known that the effective Hamiltonian of the boundstate system depends on the choice of gauge. We obtain the transformation charge Q of the Hamiltonian for an arbitrary infinitesimal change of gauge, by which gauge independence of the mass spectrum and gauge dependences of the boundstate wave functions are dictated. We give formal arguments based on the BRST symmetry supplemented by power countings of Coulomb singularities of diagrams. For illustration: (1)we calculate Q up to O(1/c), (2)we examine gauge dependences of diagrams for a decay of a qqbar boundstate up to O(1/c) and show that cumbersome gauge cancellations can be circumvented by directly calculating Q. As an application we point out that the present calculations of top quark momentum distribution in the ttbar threshold region are gauge dependent. We also show possibilities for incorrect calculations of physical quantities of boundstates when the on-shell matching procedure is employed. We give a proof of a justification for the use of the equation of motion to simplify the form of a local NRQCD Lagrangian. The formalism developed in this work will provide useful cross checks in computations involving NRQED/NRQCD boundstates.Comment: 30 pages, 15 figures (ver1); Presentations of Introduction and Conclusion were modified substantially, although none of our findings have been changed; Side remarks have been added in various parts of the paper. (ver2); Supplementary remarks and minor corrections (ver3

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

The Perturbative QCD Potential and the ttbar Threshold

We include the full second-order corrections to the static QCD potential in the analysis of the ttbar threshold cross section. There is an unexpectedly large difference between the QCD potential improved by the renormalization-group equation in momentum space and the potential improved by the renormalization-group equation in coordinate space. This difference remains even at a fairly short distance 1/r \simeq 100 GeV and its origin can be understood within perturbative QCD. We scrutinize the theoretical uncertainties of the QCD potential in relation to the ttbar threshold cross section. In particular there exists a theoretical uncertainty which limits our present theoretical accuracy of the ttbar threshold cross section at the peak to be not better than 6% within perturbative QCD.Comment: 16 pages, LaTeX. Improved version of hep-ph/9801419 for submission to a journa

Inclusive Decays of Heavy Quarkonium to Light Particles

We derive the imaginary part of the potential NRQCD Hamiltonian up to order 1/m^4, when the typical momentum transfer between the heavy quarks is of the order of Lambda_{QCD} or greater, and the binding energy E much smaller than Lambda_{QCD}. We use this result to calculate the inclusive decay widths into light hadrons, photons and lepton pairs, up to O(mv^3 x (Lambda_{QCD}^2/m^2,E/m)) and O(mv^5) times a short-distance coefficient, for S- and P-wave heavy quarkonium states, respectively. We achieve a large reduction in the number of unknown non-perturbative parameters and, therefore, we obtain new model-independent QCD predictions. All the NRQCD matrix elements relevant to that order are expressed in terms of the wave functions at the origin and six universal non-perturbative parameters. The wave-function dependence factorizes and drops out in the ratio of hadronic and electromagnetic decay widths. The universal non-perturbative parameters are expressed in terms of gluonic field-strength correlators, which may be fixed by experimental data or, alternatively, by lattice simulations. Our expressions are expected to hold for most of the charmonium and bottomonium states below threshold. The calculations and methodology are explained in detail so that the evaluation of higher order NRQCD matrix elements in this framework should be straightforward. An example is provided.Comment: 61 pages, 9 figures. Minor change

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

Calculations of binding energies and masses of heavy quarkonia using renormalon cancellation

We use various methods of Borel integration to calculate the binding ground energies and masses of b-bbar and t-tbar quarkonia. The methods take into account the leading infrared renormalon structure of the hard+soft part of the binding energies E(s), and of the corresponding quark pole masses m_q, where the contributions of these singularities in M(s) = 2 m_q + E(s) cancel. Beforehand, we carry out the separation of the binding energy into its hard+soft and ultrasoft parts. The resummation formalisms are applied to expansions of m_q and E(s) in terms of quantities which do not involve renormalon ambiguity, such as MSbar quark mass, and alpha_s. The renormalization scales are different in calculations of m_q, E(s) and E(us). The MSbar mass of b quark is extracted, and the binding energies of t-tbar and the peak (resonance) energies for (t+tbar) production are obtained.Comment: 23 pages, 8 double figures, revtex4; the version to appear in Phys.Rev.D; extended discussion between Eqs.(25) and (26); the paragraph between Eqs.(32) and (33) is new and explains the numerical dependence of the residue parameter on the factorization scale; several new references were added; acknowledgments were modified; the numerical results are unchange