Strong QCD corrections of the wave function in S-wave quarkonium decays

The first non-leading QCD corrections to the coulombic wave function of an S-state in quarkonium have been computed. The result is presented for general principal quantum number n of the decaying state. The corrections increase with n; in most cases, they dominate by far the decay corrections in the simplest example, the leptonic decay of quarkonium.     

Strong radiative corrections to annihilations of quarkonia in QCD

The significance of the lowest-order QCD prediction for the annihilations of heavy quark-antiquark bound states is analyzed. The calculation of the leading strong radiative corrections to the hadronic versus electromagnetic annihilation rate ratio R of pseudoscalar quarkonium is presented. In terms of the coupling constant α_s, as defined in the minimal subtraction scheme, we find R = R⁽⁰⁾(1 + 22.14α_s/π). The physical significance of this result is discussed by comparing it with the calculation of the non-leading effects in α_s on the scaling violations in deep inelastic scattering. A bad convergence of the relative perturbative expansion is found, demanding for its safe application a value of the relevant momentum definitely higher than that of charmonium physics.     

Small QCD corrections in inclusive 0−+ quarkonium decay for the bound-state renormalization scheme

A consistent field theoretic computation of the first-order correction to the total decay of a non-relativistic heavy quarkonium state must consider contributions from the annihilation amplitude, with a typical scale of the order of the quark mass m, and from the bound-state wave function, where the typical scale is of the order of the Bohr momentum α_sm. Therefore, not only the latter smaller scale is the one to be taken for the total decay rate, but also a quite specific renormalization, the “bound-state renormalization scheme”, must be used for a computation of the total inclusive decay rate of 0^?+→hadrons. Due to important cancellations between large individual contributions, the net result turns out to be small, encouraging the use of pure perturbative QCD in such systems.     

Form factors of heavy mesons in QCD

We discuss logarithmic corrections to form factors of mesons built from heavy quarks. The reactions e⁺e^? → η_cγ and H → Jψγ are considered as an example. A novel feature as compared to the well-studied problem of the pion form factor is the existence of transitions between the quark-antiquark state $\text{c}\text{c}$ and the gluonic one. O(α_s) corrections are calculated exactly. An infinite series of the leading logarithmic terms (α_sln[Q²/m_c²])ⁿ is summed up with the help of the operator technique. Apart from ree results already known for quark operators, we use some new results referring to gluon operators and their mixing with those made from quarks. Two alternative derivations of the multiplicatively renormalizable operators are given. The first one reduces to a direct computation of the mixing matrix and its diagonalization, the second is based on conformal symmetry considerations.     

Gluonic corrections to the decay rate of heavy quarkonium states into lepton pairs

We calculate one-gluon corrections to the decay rate of heavy quarkonium states into lepton pairs. We find that the correction due to one-gluon exchange is not very significant for charmonium, and for practical purposes only the relativistic kinematical effects need to be taken into account. For theY family the gluonic corrections are, relatively, of greater importance.     

Mass corrections to the tau decay rate

In this note radiative corrections to the total hadronic decay rate of the τ-lepton are studied employing perturbative QCD and the operator product expansion. We calculate quadratic quark mass corrections to the decay rate rationR _τ to the order0(α _s ² m²) and find that they contribute appreciably to the Cabbibo supressed decay modes of the τ-lepton. We also discuss corrections of mass dimensionD=4, where we emphasize the need of a suitable choice of the renormalization scale of the quark and gluon condensates.     

Effective field theories for the heavy quarkonium

We briefly review how nonrelativistic effective field theories give us a definition of the QCD potentials and a coherent field-theory-derived quantum-mechanical scheme to calculate the properties of bound states made by two or more heavy quarks. In this framework heavy quarkonium properties depend only on the QCD parameters (quark masses and α _s ) and nonpotential corrections are systematically accounted for. The relation between the form of the nonperturbative potentials and the low-energy QCD dynamics is also discussed.     

Jet production in hadronic collisions to0(α s 3 )

We present the full0(α _s ³ ) QCD corrections to jet production within a small opening angle δ at large transverse momenta for all partonic subprocesses. Results for CERN and Tevatron colliders are given with particular emphasis on the sensitivity to renormalization and factorization mass scales.     

SUSY-QCD corrections to scalar quark pair production in e+e− annihilation

We calculate the supersymmetric O(α_s) QCD corrections to the cross section e⁺e⁻ → q̃_iq̃_j (i, j = 1,2) within the Minimal Supersymmetric Standard Model. We pay particular attention to the case of the left-right squark mixing and to the renormalization of the mixing angle. The corrections due to gluino exchange turn out to be smaller than those due to gluon exchange, but they can be significant at higher energies, even for a gluino mass of a few hundred GeV.     

Perturbative QCD calculation of jet cross sections in e+e− annihilation

We calculate the α_s² to three-jet cross sections in e⁺e^? annihilation in a scheme that uses regulator masses for the infrared and collinear divergences. Using various methods to define the three-jet region, we find that the corrections to the O(α_s) cross sections are large.     

Soft gluon corrections to large-pT direct photon and dilepton production

QCD O(α_s²) corrections to large-p_T real and virtual photon production from scattering in the quark-gluon channel are studied in the soft gluon limit. In this limit we carefully preserve the analytic structure of amplitudes in the small-momenta integration regions. The result is a rather large correction to the Born term which significantly improves the agreement with data on p + p → γ + X. The application of the approach to other processes is discussed and the dominant terms of the O(α_s²) correction to e⁺e^? → three jets are reproduced.     

Effective gauge theory and the effect of heavy quarks in Higgs boson decays

A general framework is given for evaluating the contributions of as yet undiscovered heavy quarks to the gluonic decay rate of the Weinberg-Salam type Higgs boson. Since the Yukawa coupling of the Higgs boson to a quark pair is proportional to the quark mass, loop graphs involving heavy quarks have a non-vanishing effect on the gluonic decay width of the Higgs boson. This effect of heavy quarks with massesM _j(j=t,...) much greater than the Higgs boson massm _H is calculated in an effective gauge theory. The effects of two different kinds of large logarithms, lnM _j ² /μ m _h ² /μ ² are separated and summed up by the renormalization group method. It is found that the higher order QCD corrections are large and that the gluonic contribution to the hadronic decay width is significant if there are more than three generations. The Higgs decay width can therefore be used to probe the number of generations of heavy quarks.     

Duality and radiative corrections to leptonic widths in heavy quark systems

We use a duality argument to estimate the gluonic radiative corrections of orders α_s and α_s² to the leptonic widths for heavy quark systems.     

The heavy quarkonium spectrum at order mαslnαs

We compute the complete leading-log terms of the next-to-next-to-next-to-leading-order corrections to potential NRQCD. As a by-product we obtain the leading logs at O(mα_s⁵) in the heavy quarkonium spectrum. These leading logs, when Λ_QCDmα_s², give the complete O(mα_s⁵lnα_s) corrections to the heavy quarkonium spectrum.     

Heavy quarkonium production in the regge limit of quantum chromodynamics

Heavy quarkonium \((c\bar c,b\bar b)\) hadronic production at Tevatron (run I and run II) and LHC energies is considered in the framework of nonrelativistic quantum chromodynamics in the leading order with respect to α _s and v using the quasi-multi-Regge kinematics approach. Fitting of p _T spectra of different S and P wave heavy quarkonium states at Tevatron (run I and run II) energies is carried out. The obtained set of octet nonperturbative matrix elements is used for prediction of heavy quarkonium production at LHC energies. The results obtained in the framework of quasi-multi-Regge kinematics are compared with predictions of the collinear parton model.     

Virtual very heavy top effects in LEP/SLC precision measurements

We estimate the O(α_s) strong interaction virtual corrections to the very heavy top (m_t = 200 GeV) virtual effects in several observable quantities to be measured in the near future in high precision experiments at LEP/SLC. In the cases of the measurements of M_w and of the longitudinal polarization asymmetry A_LR on Z₀ resonance we conclude that these corrections cannot be neglected, being of a size which is comparable with the effect coming from a possibly large Higgs mass, M_H≅1 TeV.     

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.     

Beyond leading order QCD perturbative corrections to the pion form factor

The order α_s²(Q²) corrections to the pion form factor, F_π(Q²), are calculated using perturbative quantum chromodynamics and dimensional regularization. In the $\text{MS}$ renormalization scheme these corrections are large. This means that reliable perturbative predictions cannot be made until momentum transfers, Q, of about 300–400 GeV are reached or unless one can sum the large perturbative terms to all orders. Attempts to reorganize the perturbation series so that the first term gives a better approximation of the complete sum indicate that at Q = 10 GeV the pion form factor may be about a factor of two larger than the leading order result.     

Gluonic contributions to the exclusive amplitudes

The contributions from gluonic wave functions to the amplitudes of meson production ine ⁺ e ^? annihilation, quarkonium decays and twophoton processes are calculated.     

B c-meson decays and lifetime within QCD sum rules

On the basis of three-point sum rules, the form factors for the semileptonic decays B _c ⁺ → B _s(B _s ^* )l ⁺ ν _l are calculated with allowance for α _s/v Coulomb corrections for the heavy quarkonium. Generalized relations associated with spin symmetry within the approach combining heavy-quark effective theory and nonrelativistic QCD are derived for form factors in the region of recoil momenta close to zero. The nonleptonic decays of the B _c meson are studied on the basis of the factorization hypothesis. By summing the main exclusive modes of c-quark decays and by using the results of a previous analysis of b-quark decays, the B _c-meson lifetime is estimated within QCD sumrules and within nonrelativistic QCD.