QCD perturbation theory in the temporal gauge

In this paper we present a non-trivial check of the consistency of the quantization of a gauge theory with fermions (QCD) in the temporal gauge. We use the approach based on the finite time Feynman propagation kernel, in which the Gauss law is imposed as a constraint on the states by means of a functional integration over all the time independent gauge transformations acting on the boundary values of the fields. We spell out in detail the “Feynman rules” when fermions are present and we compute, as an example, the gauge invariant correlation function $$\begin{gathered} G(t) = \left\langle {\bar \psi (0,t)(\gamma _5 \gamma _0 )\frac{{1 - \gamma _0 }}{2}P} \right. \hfill \\ \left. { \cdot \exp \left( {ig\int\limits_0^t {A_0 (0,t')dt'} } \right)(\gamma _5 \gamma _0 )^ + (0,0)} \right\rangle \hfill \\ \end{gathered} $$ up to orderg ², obtaining the expected result.     

Connection between perturbation theory and lattice QCD

The problems associated with comparing perturbation theory and lattice Monte Carlo techniques when applied to QCD matter at zero net baryon number are discussed. In particular, the importance of next-to-leading order corrections to optimising the magnitude of the leading corrections to the equation of state and screening lenghts is emphasised.     

Topological susceptibility in lattice QCD and perturbation theory

We consider the definition of topological susceptibility suggested by the anomaloys U_A(1) Ward identify in lattice QCD with Wilson fermions and show that, in the limit of zero renormalized quark mass, its perturbative expansion is zero to all orders. This definition is thus suitable for Monte Carlo simulations.     

Resummation in QCD fractional analytic perturbation theory

An analytic approach in the QCD perturbation theory that has its origin in studies by Jones, Solovtsov, and Shirkov is briefly summarized. Basic propositions of the fractional analytic perturbation theory (FAPT) are also briefly taken into account with a fixed number of quark flavors and allowing for heavy-quark thresholds in a global FAPT version. Summation of perturbative series in (F)APT is examined. Application of the developed global FAPT version to calculations of the width of Higgs boson decay H → b $ \bar b $ \bar b is described.     

Analytic perturbation theory in analyzing some QCD observables

This paper is devoted to the application of the recently devised ghost-free analytic perturbation theory (APT) for the analysis of some QCD observables. We start with a discussion of the main problem of the perturbative QCD, ghost singularities, and with a resume of its resolving within the APT. By a few examples in various energy and momentum transfer regions (with the flavor number f=3,4 and 5) we demonstrate the effect of the improved convergence of the APT modified perturbative QCD expansion. Our first observation is that in the APT analysis the three-loop contribution () is as a rule numerically inessential. This gives hope for a practical solution of the well-known problem of the asymptotic nature of the common QFT perturbation series. The second result is that the usual perturbative analysis of time-like events with the large term in the coefficient is not adequate at . In particular, this relates to decay. Then for the “high” () region it is shown that the common two-loop (NLO, NLLA) perturbation approximation widely used there (at ) for the analysis of shape/events data contains a systematic negative error at the 1–2 per cent level for the extracted values. Our physical conclusion is that the value averaged over the data appreciably differs, , from the currently accepted “world average” (=0.118). Received: 30 July 2001 / Published online: 5 November 2001     

Analytic perturbation theory for QCD practitioners and upsilon decay

Within ghost-free analytic perturbation theory (APT), devised in the last decade for low-energy QCD, simple approximations are proposed for three-loop analytic couplings and their effective powers, in both the spacelike (Euclidean) and timelike (Minkowskian) regions, accurate enough in a large range (1–100 GeV) of current physical interest. Effectiveness of the new model is illustrated by the example of γ(1S) decay, where a standard analysis gives α _s(M _γ) = 0.170 ± 0.004, which is inconsistent with the bulk of data on α _s. Instead, we obtain α _s ^mod (M _γ) = 0.185 ± 0.005, which corresponds to α _s ^mod (M _Z = 0.120 ± 0.002, which is close to the world-average value. The issue of scale uncertainty for γ decay is also discussed. Published in Russian in Yadernaya Fizika, 2007, Vol. 70, No. 4, pp. 808–806. The text was translated by the authors.     

Nonperturbative calculations in the framework of variational perturbation theory in QCD

Physics of Atomic Nuclei - We discuss applications of the method based on the variational perturbation theory to perform calculations down to the lowest energy scale. The variational series is...     

Global fractional analytic perturbation theory in QCD with selected applications

We give the generalization of Fractional Analytic Perturbation Theory (FAPT) for QCD observables, recently developed both for the Euclidean and Minkowski regions of the squared momentum transfer q ², which takes into account heavy-quark thresholds. The original analytic approach to QCD, initiated by Jones, Solovtsov, and Shirkov, is briefly summarized. We also shortly consider the basic aspects of FAPT, and then, concentrate on the accounting for the problem of heavy-quark thresholds and the construction of a global version of FAPT. We discuss what one should use as an analytic coupling in the timelike region q ² = s > 0 for the e ⁺ e ⁻ annihilation and the pion’s form factor, and consider applications to phenomenologically relevant processes (the factorizable part of the pion’s form factor and the Higgs boson decay into a b $ \bar b $ \bar b pair), as well as to the summation of perturbative series.     

Probing the convergence of perturbative series in baryon chiral perturbation theory

Using the examples of pion-nucleon scattering and the nucleon mass we analyze the convergence of perturbative series in the framework of baryon chiral perturbation theory. For both cases we sum up sets of an infinite number of diagrams by solving equations exactly and compare the solutions with the perturbative contributions.     

Effective Hamiltonains and degenerate perturbation theory calculations of the mass spectrum in lattice QCD

Hamiltonian quantum chromodynamics has been formulated on a discrete lattice, in an attempt to calculate the hadronspectrum using strong coupling expansions. Previous attempts have involved including an irrelevant four-fermion interaction term in the Hamiltonian. As well as making the quark content of the zeroth order states the same as that of the simple additive quark model, this term splits the infinite zeroth order degeneracies of the original Hamiltonian. In this paper we calculate the masses of low lying states in the absence of such a term, using an effective Hamiltonian method to solve the degeneracy problem. We discuss the problems of continuing our series to the continuum limit in the presence of level repulsion.     

Photon and dilepton production in the quark-gluon plasma: perturbation theory versus lattice QCD

This talk reviews the status of QCD calculations of photon and dilepton production rates in a quark-gluon plasma. Theses rates are known to order . Their calculations involve various resummations to account for well identified physical effects that are briefly described. Lattice calculations of the spectral functions give also access to the dilepton rates. Comparison with perturbative results points to inconsistencies in both approaches when the dilepton energy becomes small.Arrival of the final proofs: 16 June 2005PACS: 12.38.Mh, 13.85.Qk     

Soft photon production rate in resummed perturbation theory of high temperature QCD

We calculate the production rate of soft real photons from a hot quark-gluon plasma using Braaten-Pisarski's perturbative resummation method. To leading order in the QCD coupling constantg we find a logarithmically divergent result for photon energies of ordergT, whereT is the plasma temperature. This divergent behaviour is due to unscreened mass singularities in the effective hard thermal loop vertices in the case of a massless external photon.Laboratoire associé du Centre National de la Recherche Scientifique     

Consistency constraints on from QCD dispersion relations and chiral perturbation theory in decays

We use both old and new theoretical developments in QCD dispersion relation constraints on the scalar form factor in the decay to obtain constraints on the strange quark mass. The perturbative QCD side of the calculation incorporates up to four-loop corrections, while the hadronic side uses a recently developed parameterization constructed explicitly to satisfy the dispersive constraints. Using chiral perturbation theory ( PT) as a model for soon-to-be measured data, we find a series of lower bounds on increasing with the accuracy to which one believes PT to represent the full QCD result.     

QCD nuclear factor and moments of multiplicity distributions in higher orders of perturbation theory

Perturbative solutions to the gluodynamics equations withmodified integral kernel in the second and third orders of the perturbation theory (2NLO, i.e., next-to-next-to-leading order, and 3NLO, i.e., next-to-next-to-next-to-leading order approximations) were found. The effect of the nuclear factor N _S on the behavior of the ratio H _q of cumulant and factorial moments of multiplicity distributions was analyzed. Theoretical conclusions were compared to the results of simulation of p-Pb and Pb-Pb collisions of nuclei with energies of 200 and 546 GeV/nucleon.