Quantum properties of a non-Abelian gauge invariant action with a mass parameter

We continue the study of a local, gauge invariant Yang-Mills action containing a mass parameter, which we constructed in a previous paper starting from the nonlocal gauge invariant mass dimension two operator F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}. We return briefly to the renormalizability of the model, which can be proven to all orders of perturbation theory by embedding it in a more general model with a larger symmetry content. We point out the existence of a nilpotent BRST symmetry. Although our action contains extra (anti)commuting tensor fields and coupling constants, we prove that our model in the limit of vanishing mass is equivalent with ordinary massless Yang-Mills theories. The full theory is renormalized explicitly at two loops in the MSbar scheme and all the renormalization group functions are presented. We end with some comments on the potential relevance of this gauge model for the issue of a dynamical gluon mass generation.Comment: 17 pages. v2: version accepted for publication in Phys.Rev.

A nonperturbative model for the strong running coupling within potential approach

A nonperturbative model for the QCD invariant charge, which contains no low-energy unphysical singularities and possesses an elevated higher loop corrections stability, is developed in the framework of potential approach. The static quark-antiquark potential is constructed by making use of the proposed model for the strong running coupling. The obtained result coincides with the perturbative potential at small distances and agrees with relevant lattice simulation data in the nonperturbative physically-relevant region. The developed model yields a reasonable value of the QCD scale parameter, which is consistent with its previous estimations obtained within potential approach.Comment: 14 pages, 4 figure

Analogs of noninteger powers in general analytic QCD

In contrast to the coupling parameter in the usual perturbative QCD (pQCD), the coupling parameter in the analytic QCD models has cuts only on the negative semiaxis of the Q^2-plane (where q^2 = -Q^2 is the momentum squared), thus reflecting correctly the analytic structure of the spacelike observables. The Minimal Analytic model (MA, named also APT) of Shirkov and Solovtsov removes the nonphysical cut (at positive Q^2) of the usual pQCD coupling and keeps the pQCD cut discontinuity of the coupling at negative Q^2 unchanged. In order to evaluate in MA the physical QCD quantities whose perturbation expansion involves noninteger powers of the pQCD coupling, a specific method of construction of MA analogs of noninteger pQCD powers was developed by Bakulev, Mikhailov and Stefanis (BMS). We present a construction, applicable now in any analytic QCD model, of analytic analogs of noninteger pQCD powers; this method generalizes the BMS approach obtained in the framework of MA. We need to know only the discontinuity function of the analytic coupling (the analog of the pQCD coupling) along its cut in order to obtain the analytic analogs of the noninteger powers of the pQCD coupling, as well as their timelike (Minkowskian) counterparts. As an illustration, we apply the method to the evaluation of the width for the Higgs decay into b+(bar b) pair.Comment: 29 pages, 5 figures; sections II and III extended, appendix B is ne

The No-Hair Conjecture in 2D Dilaton Supergravity

We study two dimensional dilaton gravity and supergravity following hamiltonian methods. Firstly, we consider the structure of constraints of 2D dilaton gravity and then the 2D dilaton supergravity is obtained taking the squere root of the bosonic constraints. We integrate exactly the equations of motion in both cases and we show that the solutions of the equation of motion of 2D dilaton supergravity differs from the solutions of 2D dilaton gravity only by boundary conditions on the fermionic variables, i.e. the black holes of 2D dilaton supergravity theory are exactly the same black holes of 2D bosonic dilaton gravity modulo supersymmetry transformations. This result is the bidimensional analogue of the no-hair theorem for supergravity.Comment: Plain Tex, 19pp, IPNO-TH 93/2

Hamiltonian of Tensionless Strings with Tensor Central Charge Coordinates

A new class of twistor-like string models in four-dimensional space-time extended by the addition of six tensorial central charge (TCC) coordinates $z_{mn}$ is studied. The Hamiltonian of tensionless string in the extended space-time is derived and its symmetries are investigated. We establish that the string constraints reduce the number of independent TCC coordinates $z_{mn}$ to one real effective coordinate which composes an effective 5-dimensional target space together with the $x^{m}$ coordinates. We construct the P.B. algebra of the first class constraints and discover that it coincides with the P.B. algebra of tensionless strings. The Lorentz covariant antisymmetric Dirac $\hat{\mathbf C}$-matrix of the P.B. of the second class constraints is constructed and its algebraic structure is further presented.Comment: 18 pages, Latex, no figure

Two-loop three-gluon vertex in zero-momentum limit

The two-loop three-gluon vertex is calculated in an arbitrary covariant gauge, in the limit when one of the external momenta vanishes. The differential Ward-Slavnov-Taylor (WST) identity related to this limit is discussed, and the relevant results for the ghost-gluon vertex and two-point functions are obtained. Together with the differential WST identity, they provide another independent way for calculating the three-gluon vertex. The renormalization of the results obtained is also presented.Comment: 22 pages, LaTeX, including 4 figures, uses eps

On-shell two-loop three-gluon vertex

The two-loop three-gluon vertex is calculated in an arbitrary covariant gauge, in the limit when two of the gluons are on the mass shell. The corresponding two-loop results for the ghost-gluon vertex are also obtained. It is shown that the results are consistent with the Ward-Slavnov-Taylor identities.Comment: 34 pages, LaTeX, including 5 figures, uses eps

Two-loop Anomalous Dimensions of Heavy Baryon Currents in Heavy Quark Effective Theory

We present results on the two-loop anomalous dimensions of the heavy baryon HQET currents $J=(q^TC\Gamma\tau q)\Gamma'Q$ with arbitrary Dirac matrices $\Gamma$ and $\Gamma'$. From our general result we obtain the two-loop anomalous dimensions for currents with quantum numbers of the ground state heavy baryons $\Lambda_Q$, $\Sigma_Q$ and $\Sigma_Q^*$. As a by-product of our calculation and as an additional check we rederive the known two-loop anomalous dimensions of mesonic scalar, pseudoscalar, vector, axial vector and tensor currents $(J=\bar q\Gamma q)$ in massless QCD as well as in HQET.Comment: 21 pages, LaTeX, 2 figures are included in PostScript forma

On the Behavior of the Effective QCD Coupling alpha_tau(s) at Low Scales

The hadronic decays of the tau lepton can be used to determine the effective charge alpha_tau(m^2_tau') for a hypothetical tau-lepton with mass in the range 0 < m_tau' < m_tau. This definition provides a fundamental definition of the QCD coupling at low mass scales. We study the behavior of alpha_tau at low mass scales directly from first principles and without any renormalization-scheme dependence by looking at the experimental data from the OPAL Collaboration. The results are consistent with the freezing of the physical coupling at mass scales s = m^2_tau' of order 1 GeV^2 with a magnitude alpha_tau ~ 0.9 +/- 0.1.Comment: 15 pages, 4 figures, submitted to Physical Review D, added references, some text added, no results nor figures change