Completely automated computation of the heavy-fermion corrections to the three-loop matching coefficient of the vector current

We evaluate the corrections to the matching coefficient of the vector current between Quantum Chromodynamics (QCD) and Non-Relativistic QCD (NRQCD) to three-loop order containing a closed heavy-fermion loop. The result constitutes a building block both for the bottom- and top-quark system at threshold. Strong emphasis is put on our completely automated approach of the calculation including the generation of the Feynman diagrams, the identification of the topologies, the reduction to master integrals and the automated numerical computation of the latter.     

QCD sum rules with finite masses

The concept of QCD sum rules is extended to bound states composed of particles with finite mass such as scalar quarks or strange quarks. It turns out that mass corrections become important in this context. The number of relevant corrections is analyzed in a systematic discussion of the IR- and UV-divergencies, leading in general to a finite number of corrections. The results are demonstrated for a system of two massless quarks and two heavy scalar quarks.We wish to thank Dr. Lech Mankiewicz for very helpful discussions. This work was supported by DFG (G. Hess program).     

Calculation of the quark and gluon form factors to three loops in QCD

We describe the calculation of the three-loop QCD corrections to quark and gluon form factors. The relevant three-loop Feynman diagrams are evaluated and the resulting three-loop Feynman integrals are reduced to a small set of known master integrals by using integration-by-parts relations. Our calculation confirms the recent results by Baikov et al. for the three-loop form factors. In addition, we derive the subleading \( \mathcal{O}\left( \varepsilon \right) \) terms for the fermion-loop type contributions to the three-loop form factors which are required for the extraction of the fermionic contributions to the four-loop quark and gluon collinear anomalous dimensions. The finite parts of the form factors are used to determine the hard matching coefficients for the Drell-Yan process and inclusive Higgs-production in soft-collinear effective theory.     

Charm quark energy loss in QCD matter

The energy loss of heavy quarks in a quark-gluon plasma of finite size is studied within the light-cone path integral approach. A simple analytical formulation of the radiative energy loss of heavy quarks is derived. This provides a convenient way to quantitatively estimate the quark energy loss. Our results show that if the energy of a heavy quark is much larger than its mass, the radiative energy loss approaches the radiative energy loss of light quarks.     

Master integrals for massless three-loop form factors: One-loop and two-loop insertions

The three-loop form factors in massless QCD can be expressed as a linear combination of master integrals. Besides a number of master integrals which factorise into products of one-loop and two-loop integrals, one finds 16 genuine three-loop integrals. Of these, six have the form of a bubble insertion inside a one-loop or two-loop vertex integral. We compute all master integrals with these insertion topologies.     

Top quark production from black holes at the CERN LHC

LHC is expected to be a top quark factory. If the fundamental Planck scale is near a TeV, then we also expect the top quarks to be produced from black holes via Hawking radiation. In this Letter we calculate the cross sections for top quark production from black holes at the LHC and compare it with the direct top quark cross section via parton fusion processes at next-to-next-to-leading order (NNLO). We find that the top quark production from black holes can be larger or smaller than the pQCD predictions at NNLO depending upon the Planck mass and black hole mass. Hence the observation of very high rates for massive particle production (top quarks, Higgs or supersymmetry) at the LHC may be an useful signature for black hole production.     

Heavy-light current correlators at order \alpha_\mathrm{s}^2 in QCD and HQET

The non-diagonal correlators of vector and scalar currents are considered at three-loop order in QCD. The full mass dependence is computed in the case where one of the quarks is massless and the other one carries mass M. We exploit the decoupling relations between the full theory and the heavy quark effective theory (HQET) in order to obtain the logarithmic parts of the leading threshold terms. With the help of conformal mapping and Padé approximation numerical estimates for the non-logarithmic terms are extracted which in turn lead to a prediction of the correlator in HQET at order . As applications of the vector and scalar correlator we consider the single-top-quark production via the process and the decay rate of a charged Higgs boson into hadrons, respectively. In both cases the computed NLO corrections are shown to be numerically much less important than the leading ones. On the contrary, the NLO order QCD corrections to the HQET sum rule for the leptonic decay rate of a heavy-light meson proves to be comparable to the leading one. Received: 19 June 2001 / Published online: 10 August 2001     

Infrared Divergences of Three-Loop Vacuum Graghs of Gluon Field at Finite Temperature

The kinds of infrared divergent integrals in three-loop vacuum graghs of gluon field at finite temperature are pointed out and their regularization is discussed. All of the infrared divergences in three-loop vacuum graghs of gluon field are isolated.     

有限温度下胶子场三圈真空图中的红外发散

用热传播子的实时形式对有限温度下胶子场的三圈真空图进行了详细的计算，在维数正规化方案下把真空图中的红外发散全部孤立出来了.     

Gauge-invariant summation of All QCD virtual gluon exchanges

The interpretation of virtual gluons as ghosts in the non-linear gluonic structure of QCD permits the formulation and realization of a manifestly gauge-invariant and Lorentz covariant theory of interacting quarks/anti-quarks, for all values of coupling. The simplest example of quark/anti-quark scattering in a high-energy, quenched, eikonal model at large coupling is shown to be expressible as a set of finite, local integrals which may be evaluated numerically; and before evaluation, it is clear that the result will be dependent only on, and is damped by increasing momentum transfer, while displaying a physically-reasonable color dependence in a manner underlying the MIT Bag Model and an effective, asymptotic freedom. Similar but more complicated integrals will result from all possible gluonic-radiative corrections to this simplest eikonal model. Our results are compatible with an earlier, field-strength analysis of Reinhardt et al.     

Determination of the mass spectrum of the bound state in the framework of the relativistic hamiltonian approach

We propose one a variant of calculation of the energy spectrum of bound state systems with relativistic corrections. In the framework of quantum field theory, an expression that takes into account relativistic corrections to the mass of the bound state with a known nonrelativistic pair interaction potential is proposed on the basis of calculating the asymptotic behavior of correlation functions of the corresponding field currents with the necessary quantum numbers. Excluding the time variables allows one to determine nonperturbative corrections to the interaction potential. The following results have been obtained in the framework of this approach. The nonperturbative corrections arising due to the relativistic nature of a system to the interaction Hamiltonian are determined. The dependence of the constituent mass of bound-state forming particles on the free state mass and on the orbital and radial quantum numbers is analytically derived. The energy level shift of muonic hydrogen taking into account relativistic corrections is calculated. The energy spectrum of a wide class of potentials that describe the Coulomb bound state is analytically derived with relativistic corrections. The mass spectrum of the glueballs and the constituent masses of the gluons are analytically calculated taking into account spin-orbit, spin—spin, and tensor interactions. Our numerical results have shown very good agreement with the lattice data. Taking into account nonperturbative and nonlocality characters of interactions, the mass spectrum of the mesons consisting of light-light and light-heavy quarks with orbital and radial excitations is determined. Our results show that good agreement with the experimental data for the slope and the intercept of the Regge trajectory can be obtained only taking into account the nonperturbative and the nonlocal characters of interactions. The dependences of the constituent masses of constituent particles on the masses of a free state are certain. When quarks are light, then the difference between current and valent masses of quarks is greater than valent masses of quarks, and when quarks are heavy, then the difference between these masses is insignificant. One of the alternative variants of taking nonlocality into account has been suggested for the definition of properties of hadrons at large distances. The dependence of the constituent masses of constituent particles on the radius of confinement is determined.     

Results and techniques of multi-loop calculations

In this review some recent multi-loop results obtained in the framework of perturbative quantum chromodynamics (QCD) and quantum electrodynamics (QED) are discussed. After reviewing the most advanced techniques used for the computation of renormalization group functions, we consider the decoupling of heavy quarks. In particular, an effective method for the evaluation of the decoupling constants is presented and explicit results are given. Furthermore, the connection to observables involving a scalar Higgs boson is worked out in detail. An all-order low-energy theorem is derived which establishes a relation between the coefficient functions in the hadronic Higgs decay and the decoupling constants. We review the radiative corrections of a Higgs boson into gluons and quarks and present explicit results up to order α_s⁴ and α_s³, respectively. In this review special emphasis is put on the applications of asymptotic expansions. A method is described which combines expansion terms of different kinematical regions with the help of conformal mapping and Padé approximation. This method allows us to proceed beyond the present scope of exact multi-loop calculations. As far as physical processes are concerned, we review the computation of three-loop current correlators in QCD taking into account the full mass dependence. In particular, we concentrate on the evaluation of the total cross section for the production of hadrons in e⁺e⁻ annihilation. The knowledge of the complete mass dependence at order α_s² has triggered a bunch of theory-driven analyses of the hadronic contribution to the electromagnetic coupling evaluated at high energy scales. The status is summarized in this review. In a further application four-loop diagrams are considered which contribute to the order α² QED corrections to the μ decay. Its relevance for the determination of the Fermi constant G_F is discussed. Finally, the calculation of the three-loop relation between the $\text{MS}$ and on-shell quark mass definitions is presented and physical applications are given. To complete the presentation, some technical details are presented in the appendix, where also explicit analytical results are listed.     

Heavy quarks in the presence of higher derivative corrections from AdS/CFT

We use the gauge–string duality to study heavy quarks in the presence of higher derivative corrections. These corrections correspond to the finite-coupling corrections on the properties of heavy quarks in a hot plasma. In particular, we study the effects of these corrections on the energy loss and the dissociation length of a quark–antiquark pair. We show that the calculated energy loss of heavy quarks through the plasma increases. We also find in general that the dissociation length becomes shorter with the increase of coupling parameters of higher curvature terms.     

Finite temperature QCD corrections to lepton-pair formation in a quark-gluon plasma

We discuss theO(α _S ) corrections to lepton-pair production in a quark-gluon plasma in equilibrium, assuming the quarks are massless at zero temperature. The corrections are found to be very small in the domain of interest for ultrarelativistic heavy ions collisions. Interesting effects, however, appear at the annihilation threshold of the thermalized quarks where the correction factor has a (1/α _S ) behavior.     

Formation and decay of scalar Leptoquarks/Squarks in ep collisions

The cross sections for the formation of scalar resonances, leptoquarks or squarks, in electron/positron-proton collisions at HERA are presented, including next-to-leading order QCD corrections. Depending mildly on the mass of the resonances, the K-factors increase the production cross sections by up to 30% if the target quarks are valence quarks. The QCD corrections to the partial decay widths of leptoquarks/ squarks to leptons and quarks are small. The electron spectrum in the decays is nevertheless softened by perturbative gluon radiation at a level of 2 GeV for a leptoquark/ squark mass of 200 GeV.     

Measurement of the top quark charge at the atlas detector

We have investigated the possibility of reconstructing the top quark charge through measurement of its decay product charges at the ATLAS detector. Verification of the hypothesis about alternative interpretation of top-quark experimental data has been considered as well. The method of “semileptonic B-meson decay” was applied for reconstructing the b-jet charge. A statistical significance of more than 5σ can be achieved using this method after analyzing 1 fb⁻¹ of the t̄t-pairs data. The analysis was carried out with HERWIG and PYTHIA generators and using the GEANT4 detector simulation software package. The text was submitted by the authors in English.     

Interpretation of the NuTeV experiment

The NuTeV neutrino measurement of the Weinberg angle differs by 3 standard deviations from measurements at the Z pole. We review the status of various possibilities to explain this result, including contributions from physics outside the standard model; effects of radiative corrections; nuclear corrections to parton distributions; isospin-violating effects; and effects due to strange quarks.     

Potential of heavy quarks in the static limit of QCD

The potential of static quarks that is consistent both with the three-loop QCD running coupling constant, the two-loop perturbative matching of the \(\overline {MS} \) and V schemes being taken into account here, and with the regime of quark confinement at long distances is derived on the basis of the procedure and arguments proposed by Richardson, Buchmüller, and Tye. Applications of this approach are discussed for the masses of heavy quarks, for the mass spectra of heavy quarkonia, and for the leptonic widths of vector states.     

Neutral Higgs sector of the MSSM with explicit CP violation and non-holomorphic soft breaking

Using the effective potential method, we computed one-loop corrections to the mass matrix of neutral Higgs bosons of the Non-Holomorphic Supersymmetric Standard Model (NHSSM) with explicit CP violation, where the radiative corrections due to the quarks and squarks of the third generation were taken into account. We observed that the non-holomorphic trilinear couplings can compete with the holomorphic ones in CP violating issues for the mass and mixing of the neutral Higgs bosons.