arXiv subjects
Publications and source records attributed to A. H. Hoang.
An introduction to the recent developments in perturbative heavy quarkonium physics is given. Covered are the effective theories NRQCD, pNRQCD and vNRQCD, the threshold expansion, the role of renormalons, and applications to bottom and top quark physics.
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.
Recent results for charm quark mass effects in perturbative bottom quark mass determinations from $Υ$ mesons are reviewed. The connection between the behavior of light quark mass corrections and the infrared sensitivity of some bottom quark mass definitions is examined in some detail.
The top quark cross section close to threshold in $e^+e^-$ annihilation is computed including the summation of logarithms of the velocity at next-to-next-to-leading-logarithmic order in QCD. The remaining theoretical uncertainty in the normalization of the total cross section is at the few percent level, an order of magnitude smaller than in previous next-to-next-to-leading order calculations. This uncertainty is smaller than the effects of a light standard model Higgs boson.
Recent developments for an effective theory for non-relativistic perturbative quark-antiquark systems are reviewed and some applications are discussed.
The effects of the finite charm quark mass on bottom quark mass determinations from $Υ$ sum rules are examined in detail. The charm quark mass effects are calculated at next-to-next-to-leading order in the non-relativistic power counting for the $Υ$ sum rules and at order $α_s^3$ for the determination of the bottom MSbar mass. For the bottom 1S mass, which is extracted from the $Υ$ sum rules directly, we obtain $M_b^{1S}=4.69\pm 0.03$ GeV with negligible correlation to the value of the strong coupling. For the bottom MSbar mass we obtain $\bar M_b(\bar M_b) = 4.17\pm 0.05$ GeV taking $α_s^{(n_l=5)}(M_Z)=0.118\pm 0.003$ as an input. Compared with an analysis where all quarks lighter than the bottom are treated as massless, we find that the finite charm mass shifts the bottom 1S mass, $M_b^{1S}$, by about -20 MeV and the MSbar mass, $\bar M_b(\bar M_b)$, by -30 to -35 MeV.
A detailed presentation is given of the analytic calculation of the single-photon annihilation contributions to the positronium ground state hyperfine splitting to order $m_eα^6$ in the framework of non-relativistic effective theories. The current status of the theoretical description of the positronium ground state hyperfine splitting is reviewed.
Using non-relativistic effective theories, new next-to-next-to-leading order (NNLO) QCD corrections to the total $t\bar t$ production cross section at the Linear Collider have been calculated recently. In this article the NNLO calculations of several groups are compared and the remaining uncertainties are discussed. The theoretical prospects for an accurate determination of top quark mass parameters are discussed in detail. An outlook on possible future improvements is given.
We study the shift in the $Υ$ mass due to a non-zero charm quark mass. This shift affects the value of the $\bar{\rm MS}$ $b$-quark mass extracted from the $Υ$ system by about -20 MeV, due to an incomplete cancellation of terms that are non-analytic in the charm quark mass. The precise size of the shift depends on unknown higher order corrections, and might have a considerable uncertainty if they are large.
A review on theoretical aspects of top quark physics at the Linear Collider is given with focus on the process $e^+e^-\to t\bar t$ and the presentations given at this conference.
Recent results from studies using half the perturbative mass of heavy quark-antiquark n=1, ${}^3S_1$ quarkonium as a new heavy quark mass definition for problems where the characteristic scale is smaller than or of the same order as the heavy quark mass are reviewed. In this new scheme, called the 1S mass scheme, the heavy quark mass can be determined very accurately, and many observables like inclusive B decays show nicely converging perturbative expansions. Updates on results using the 1S scheme due to new higher order calculations are presented.
The complete NNLO QCD corrections to the total cross section $σ(e^+e^- \to Z*,γ*\to t\bar t)$ 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 $dσ/d |\vec k_t|$ 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.
The bottom quark 1S mass, $M_b^{1S}$, is determined using sum rules which relate the masses and the electronic decay widths of the $Υ$ mesons to moments of the vacuum polarization function. The 1S mass is defined as half the perturbative mass of a fictitious ${}^3S_1$ bottom-antibottom quark bound state, and is free of the ambiguity of order $Λ_{QCD}$ which plagues the pole mass definition. Compared to an earlier analysis by the same author, which had been carried out in the pole mass scheme, the 1S mass scheme leads to a much better behaved perturbative series of the moments, smaller uncertainties in the mass extraction and to a reduced correlation of the mass and the strong coupling. We arrive at $M_b^{1S}=4.71\pm 0.03$ GeV taking $α_s(M_Z)=0.118\pm 0.004$ as an input. From that we determine the $\bar{MS}$ mass as $\bar m_b(\bar m_b) = 4.20 \pm 0.06$ GeV. The error in $\bar m_b(\bar m_b)$ can be reduced if the three-loop corrections to the relation of pole and $\bar{MS}$ mass are known and if the error in the strong coupling is decreased.
The pole mass of a heavy quark is ambiguous by an amount of order $Λ_{QCD}$. We show that the heavy-quark potential, $V(r)$, is similarly ambiguous, but that the total static energy, $2M_{pole}+V(r)$, is unambiguous when expressed in terms of a short-distance mass. This implies that the extraction of a short-distance mass from the quarkonium spectrum is free of an ambiguity of order $Λ_{QCD}$, in contrast with the pole mass.
We review the theoretical ideas and tools required to arrive at a next-to-next-to-leading order (NNLO) description of the heavy quark-antiquark production cross section in $e^+e^-$ annihilation for the case that the center of mass kinetic energy of the quarks is larger than $Λ_{QCD}$. In this case the NNLO cross section can be calculated with purely perturbative methods. We present details of the calculation and discuss two applications, the determination of the bottom quark mass from Upsilon sum rules and the top-antitop production cross section close to threshold in $e^+e^-$ annihilation.
Non-singlet ${\cal{O}}(α_s^2)$ corrections from light quarks are calculated analytically for the massive quark-antiquark pair production rates through the vector, axial-vector, scalar and pseudoscalar currents for all energies above the threshold. The results are presented in terms of the moments of the absorptive part of the vacuum polarization function of the light quarks which allows for an immediate determination of ${\cal{O}}(α_s^2)$ corrections coming from other types of light particles. The kinematic regime close to the threshold is examined.
The bottom quark pole mass $M_b$ is determined using a sum rule which relates the masses and the electronic decay widths of the $Υ$ 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. ${\cal{O}}(α_s^2, α_s v, v^2)$ 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 $α_s$, 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 $0.096 \le α_s(M_z) \le 0.124$ if experimental uncertainties are included at the 95% confidence level and if two-loop running for $α_s$ is employed. $M_b$ and $α_s$ have a sizeable positive correlation. For the running $\bar{MS}$ bottom quark mass this leads to 4.09 GeV $\le m_b(M_{Υ(1S)}/2)\le 4.32$ GeV. If $α_s$ 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 $\le m_b(M_{Υ(1S)}/2)\le 4.28$ GeV) for $0.114\lsim α_s(M_z)\le 0.122$. The discrepancies between the results of three previous analyses on the same subject by Voloshin, Jamin and Pich, and Kühn 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.
The complete next-to-next-to-leading order (i.e. $O(v^2)$, $O(v α_s)$ and $O(α_s^2)$) 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.