arXiv subjects
Publications and source records attributed to A. H. Hoang.
For a proper theoretical description of the top quark pair production cross section at the First Muon Collider in the kinematic regime away from the threshold the complete mass and energy dependence has to be taken into account. Two-loop calculations for the photon mediated total cross section are reviewed.
It is shown how nonrelativistic QCD (NRQCD) can be used to determine next-to-next-to-leading order relativistic and short-distance contributions to the total $t\bar t$ production cross section in the threshold regime at lepton colliders. A recipe for the calculation of all such contributions for the total photon mediated production cross section is presented and a review of the already known Abelian next-to-next-to-leading results is given.
Recent analytical and numerical results for the three-loop polarization function allow to present a phenomenological analysis of the cross section for massive quark production in electron positron annihilation to order $α_s^2$. Numerical predictions based on fixed order perturbation theory are presented for charm and bottom production above 5 and 11.5 GeV, respectively. The contribution from these energy regions to $α(M_Z^2)$, the running QED coupling constant at scale M_Z, are given. The dominant terms close to threshold, i.e. in an expansion for small quark velocity $β$, are presented.
The single photon annihilation contributions for the positronium ground state hyperfine splitting are calculated analytically to order $m_eα^6$ using NRQED. Based on intuitive physical arguments the same result can also be determined by a trivial calculation using results from existing literature. Our result completes the hyperfine splitting calculation to order $m_eα^6$. We compare the theoretical prediction with the most recent experimental measurement.
It is demonstrated how perturbative O(alpha_s^2) relativistic corrections to the non-relativistic stable heavy quark-antiquark production cross section in e^+e^- annihilation based on a Coulombic QCD potential can be systematically calculated using the concept of effective field theories. The O(alpha_s^2) corrections from the relativistic energy-momentum relation, the relativistic phase space corrections and the O(alpha_s^2) corrections involving the group theoretical factors C_F^2 and C_F T are determined explicitly. For the case of $t\bar t$ production the sum of these corrections amounts to 3% - 7% over the whole threshold regime and is insensitive to variations in the top width. Perturbative O(alpha_s^2) corrections to the leptonic decay width of heavy quark-antiquark $^3S_1$ vector resonances are extracted.
Two-loop contributions to the electromagnetic form factors are calculated in the kinematic regime close to the fermion-antifermion threshold. The results are presented in an expansion in the velocity $β$ of the fermions in the c.m. frame up to next-to-next-to leading order in $β$. The existence of a new Coulomb singularity logarithmic in $β$, which is closely related to the $O(α^2\lnα)$ corrections known from positronium decays, is demonstrated. It is shown that due to this Coulomb singularity $O(α^2)$ relativistic corrections to the non-relativistic cross section of heavy fermion-antifermion pair production in $e^+e^-$ annihilation cannot be determined by means of conventional multi-loop perturbation theory.
The QED vacuum polarization function is calculated to O(alpha^2) (next-to-leading order) accuracy in the threshold regime by using the concept of effective field theories to resum diagrams with the instantaneous Coulomb exchange of longitudinally polarized photons. It is shown that the O(alpha^2) contributions are of order alpha^2 in size rather than alpha^2/Pi^2. The vacuum polarization contributions to the O(alpha^6) hyperfine splitting of the positronium ground state are recalculated and differences with an older calculation are pointed out. The results are used to determine O(C_F^2 alpha_s^2) (next-to-next-to-leading order) Darwin corrections to heavy quark-antiquark bound state l=0 wave functions at the origin and to the heavy quark-antiquark production cross section in e^+e^- collisions in the threshold region. The absolute value of the corrections amounts to 10%-20% and 17%-34% in the modulus squared of the ground state wave functions at the origin for the $b\bar b$ and $c\bar c$ systems, respectively. In the case of the $t\bar t$ production cross section in the threshold region the absolute value of the corrections is between 2% and 6% around the 1S peak and between 1% and 2% for higher energies. A critical comment on recent QCD sum rule calculations for the $Υ$ system is made.
Recent results on the entirely analytic calculation of second order corrections to massive quark pair production vertices induced by light quark flavours are reviewed. Based on the method presented in this talk the second order effects of the insertion of any massless one-loop vacuum polarization into the gluon line of the first order diagrams can be determined. The behaviour of the corrections at threshold for vector and axial-vector current induced massive quark production is discussed.
The cross-section for the production of $t\bar{t}$ pairs in $e^+e^-$-annihilation via a virtual photon is determined up to order $α_s^2$. For the cm-energies of interest the effect of the top mass may not be considered as a small parameter and the full mass dependence must be included.
Second order ${\cal O}(α_s^2)$ corrections to the heavy quark production cross-section due to massless quarks and coloured scalars are calculated for all energies above threshold. Based on the method introduced in this letter also the gauge non-invariant second order corrections due to the pure gluonic selfenergy insertion and a certain class of ${\cal{O}}(α_s^3)$ and ${\cal{O}}(α_s^4)$ corrections are determined. For the special choice of the gauge parameter, $ξ=4$, the leading threshold and high energy behaviour of the pure second order gluonic corrections to the cross-section are governed by the gluonic self energy insertion.
Recent analytic calculations on the rate for the production of a pair of massive fermions in $e^+ e^-$ annihilation plus real or virtual radiation of a pair of massless fermions are discussed. The contributions for real and virtual radiation are displayed separately. The asymptotic behaviour close to threshold is given in a compact form and an application to the angular distribution of massive quarks close to threshold is presented.
Predictions for the angular distribution of massive quarks and leptons are presented, including QCD and QED corrections. Recent results for the fermionic part of the two-loop corrections to the electromagnetic form factors are combined with the BLM scale fixing prescription. Two distinctly different scales arise as arguments of $α_s(μ^2)$ near threshold: the relative momentum of the quarks governing the soft gluon exchange responsible for the Coulomb potential, and a large momentum scale approximately equal to twice the quark mass for the corrections induced by transverse gluons. Numerical predictions for charmed, bottom, and top quarks are given. One obtains a direct determination of $α_V(Q^2)$, the coupling in the heavy quark potential, which can be compared with lattice gauge theory predictions. The corresponding QED results for $τ$ pair production allow for a measurement of the magnetic moment of the $τ$ and could be tested at a future $τ$-charm factory.
Secondary radiation of hadrons from a tau pair produced in electron positron collisions may constitute an important obstacle for precision measurements of the production cross section and of branching ratios. The rate for real and virtual radiation is calculated and various distributions are presented. For Z decays a comprehensive analysis is performed which incorporates real and virtual radiation of leptons. The corresponding results are also given for primary electron and muon pairs. Compact analytical formulae are presented for entirely leptonic configurations. Measurements of $Z$ partial decay rates which eliminate all hadron and lepton radiation are about 0.3\% to 0.4\% lower than totally inclusive measurements, a consequence of the ${\cal O}(α^2)$ negative virtual corrections which are enhanced by the third power of a large logarithm.
The rate for the production of a pair of massive fermions in $e^+ e^-$ annihilation plus real or virtual radiation of a pair of massless fermions is calculated analytically. The contributions for real and virtual radiation are displayed separately. The asymptotic behaviour close to threshold and for high energies is given in a compact form. These approximations provide arguments for the appropriate choice of the scale in the ${\cal O}(α)$ result, such that no large logarithms remain in the final answer.
The rate for the production of massive fermions radiated off a pair of massless fermions is calculated analytically. Combined with the analytic calculation of the corresponding virtual contribution one obtains the order $α^2$ correction to the cross section which is induced by the real and virtual radiation of a pair of massive fermions by massless fermions. Approximations valid for large and for small masses are derived and shown to agree with earlier calculations.
The rate for the final state radiation of hadrons in leptonic $Z$ decays is evaluated, using as input experimental data for $σ(e^+e^-\to hadrons)$ in the low energy region. Configurations with a lepton pair of large and a hadronic state of low invariant mass are dominant. A relative rate $Γ_{l\bar l had}/Γ_{l\bar l}=6.3\times 10^{-4}$ is calculated. This result is about twice the prediction based on a parton model calculation with a quark mass of $300$ MeV. The rate for secondary production of heavy quarks is calculated in the same formalism.