arXiv subjects

Gorazd Cvetic

Publications and source records attributed to Gorazd Cvetic.

At least 55 records · Page 3Linked to original sources

arXiv2010

Simple analytic QCD model with perturbative QCD behavior at high momenta

Analytic QCD models are those where the QCD running coupling has the physically correct analytic behavior, i.e., no Landau singularities in the Euclidean regime. We present a simple analytic QCD model in which the discontinuity function of the running coupling at high momentum scales is the same as in perturbative QCD (just like in the analytic QCD model of Shirkov and Solovtsov), but at low scales it is replaced by a delta function which parametrizes the unknown behavior there. We require that the running coupling agree to a high degree with the perturbative coupling at high energies, which reduces the number of free parameters of the model from four to one. The remaining parameter is fixed by requiring the reproduction of the correct value of the semihadronic tau decay ratio.

hep-ph↗

arXiv2010

Analytic QCD coupling with no power terms in UV regime

We construct models of analytic QCD (i.e.,with the running coupling parameter free of Landau singularities) which address several problems encountered in previous analytic QCD models, among them their incompatibility with the ITEP-OPE philosophy (due to UV power terms) and too low values of the semihadronic tau decay ratio. The starting point of the approach is the construction of appropriate nonperturbative beta functions.

hep-ph↗

arXiv2010

An analytic Pade-motivated QCD coupling

We consider a modification of the Minimal Analytic (MA) coupling of Shirkov and Solovtsov. This modified MA (mMA) coupling reflects the desired analytic properties of the space-like observables. We show that an approximation by Dirac deltas of its discontinuity function $ρ$ is equivalent to a Padé (rational) approximation of the mMA coupling that keeps its analytic structure. We propose a modification to mMA that, as preliminary results indicate, could be an improvement in the evaluation of low-energy observables compared with other analytic couplings.

hep-ph↗

arXiv2009

Rational approximations in Analytic QCD

We consider the ``modified Minimal Analytic'' (mMA) coupling that involves an infrared cut to the standard MA coupling. The mMA coupling is a Stieltjes function and, as a consequence, the paradiagonal Pade approximants converge to the coupling in the entire $Q^2$-plane except on the time-like semiaxis below the cut. The equivalence between the narrow width approximation of the discontinuity function of the coupling, on the one hand, and this Pade (rational) approximation of the coupling, on the other hand, is shown. We approximate the analytic analogs of the higher powers of mMA coupling by rational functions in such a way that the singularity region is respected by the approximants.Several comparisons, for real and complex arguments $Q^2$, between the exact and approximate expressions are made and the speed of convergence is discussed. Motivated by the success of these approximants, an improvement of the mMA coupling is suggested, and possible uses in the reproduction of experimental data are discussed.

hep-ph↗

arXiv2008

Gluon self-interaction in the position space in Landau gauge

We propose a method to treat the three-gluon self-interaction vertex in the position space in D = 4 - 2e dimensions. As an example, we calculate a two-loop contribution to auxiliary Lcc vertex in the Landau gauge which contains the three-gluon vertex for SU(N) Yang-Mills theory. We represent the integral expression as a sum of separate contributions so that each of the contributions is a double finite integral or single integral (singular or finite) in the position space. In each double finite integral we use the freedom to shift exponents in powers in the denominator of integrands by some multiples of e, in order to perform at least one of the integrations by the uniqueness technique without corrupting the first term of the decomposition in e.

hep-th↗

arXiv2008

Analytic QCD - a short review

Analytic versions of QCD are those whose coupling alpha_s(Q^2) does not have the unphysical Landau singularities on the space-like axis (-q^2=Q^2 > 0). The coupling is analytic in the entire complex plane except the time-like axis (Q^2 < 0). Such couplings are thus suitable for application of perturbative methods down to energies of order GeV. We present a short review of the activity in the area which started with a seminal paper of Shirkov and Solovtsov ten years ago. Several models for analytic QCD coupling are presented. Strengths and weaknesses of some of these models are pointed out. Further, for such analytic couplings, constructions of the corresponding higher order analytic couplings (the analogs of the higher powers of the perturbative coupling) are outlined, and an approach based on the renormalization group considerations is singled out. Methods of evaluation of the leading-twist part of space-like observables in such analytic frameworks are described. Such methods are applicable also to the inclusive time-like observables. Two analytic models are outlined which respect the ITEP Operator Product Expansion philosophy, and thus allow for an evaluation of higher-twist contributions to observables.

hep-ph↗

arXiv2008

Further results for the two-loop Lcc vertex in the Landau gauge

In the previous paper hep-th/0604112 we calculated the first of the five planar two-loop diagrams for the Lcc vertex of the general non-Abelian Yang-Mills theory, the vertex which allows us in principle to obtain all other vertices via the Slavnov-Taylor identity. The integrand of this first diagram has a simple Lorentz structure. In this letter we present the result for the second diagram, whose integrand has a complicated Lorentz structure. The calculation is performed in the D-dimensional Euclidean position space. We initially perform one of the two integrations in the position space and then reduce the Lorentz structure to D-dimensional scalar single integrals. Some of the latter are then calculated by the uniqueness method, others by the Gegenbauer polynomial technique. The result is independent of the ultraviolet and the infrared scale. It is expressed in terms of the squares of spacetime intervals between points of the effective fields in the position space -- it includes simple powers of these intervals, as well as logarithms and polylogarithms thereof, with some of the latter appearing within the Davydychev integral J(1,1,1). Concerning the rest of diagrams, we present the result for the contributions correponding to third, fourth and fifth diagrams without giving the details of calculation. The full result for the Lcc correlator of the effective action at the planar two-loop level is written explicitly for maximally supersymmetric Yang-Mills theory.

hep-th↗

arXiv2007

Exponentially Modified QCD Coupling

We present a specific class of models for an infrared-finite analytic QCD coupling, such that at large space-like energy scales the coupling differs from the perturbative one by less than any inverse power of the energy scale. This condition is motivated by the ITEP Operator Product Expansion philosophy. Allowed by the ambiguity in the analytization of the perturbative coupling, the proposed class of couplings has three parameters. In the intermediate energy region, the proposed coupling has low loop-level and renormalization scheme dependence. The present modification of perturbative QCD must be considered as a phenomenological attempt, with the aim of enlarging the applicability range of the theory of the strong interactions at low energies.

hep-ph↗

arXiv2006

Towards the two-loop Lcc vertex in Landau gauge

We are interested in the structure of the Lcc vertex in the Yang-Mills theory, where c is the ghost field and L the corresponding BRST auxiliary field. This vertex can give us information on other vertices, and the possible conformal structure of the theory should be reflected in the structure of this vertex. There are five two-loop contributions to the Lcc vertex in the Yang-Mills theory. We present here calculation of the first of the five contributions. The calculation has been performed in the position space. One main feature of the result is that it does not depend on any scale, ultraviolet or infrared. The result is expressed in terms of logarithms and Davydychev integral J(1,1,1) that are functions of the ratios of the intervals between points of effective fields in the position space. To perform the calculation we apply Gegenbauer polynomial technique and uniqueness method.

hep-th↗

arXiv2006

Various versions of analytic QCD and skeleton-motivated evaluation of observables

We present skeleton-motivated evaluation of QCD observables. The approach can be applied in analytic versions of QCD in certain classes of renormalization schemes. We present two versions of analytic QCD which can be regarded as low-energy modifications of the ``minimal'' analytic QCD and which reproduce the measured value of the semihadronic tau decay ratio r{tau}. Further, we describe an approach of calculating the higher order analytic couplings Ak (k=2,3,...) on the basis of logarithmic derivatives of the analytic coupling A1(Q^2). This approach can be easily applied in any version of analytic QCD. We adjust the free parameters of the afore-mentioned two analytic models in such a way that the skeleton-motivated evaluation reproduces the correct known values of r{tau} and of the Bjorken polarized sum rule (BjPSR) db(Q^2) at a given point (e.g., at Q^2=2 GeV^2). We then evaluate the low-energy behavior of the Adler function dv(Q^2) and the BjPSR db(Q^2) in the afore-mentioned evaluation approach, in the three analytic versions of QCD. We compare with the results obtained in the ``minimal'' analytic QCD and with the evaluation approach of Milton et al. and Shirkov.

hep-ph↗

arXiv2006

Lepton flavor violation in muonium decay and muon colliders in models with heavy neutrinos

We study the lepton-flavor-violating reaction $μ^+ e^- \to e^+ e^-$ within two extensions of the standard model that include heavy neutrinos. The reaction is studied in the low energy limit in the form of muonium decay $M\to e^+ e^-$ and in the high energy regime of a muon collider. The two theoretical models we consider are: model I, a typical see-saw model that violates lepton flavor and number by inclusion of extra right handed neutrinos, and model II, a variant where lepton number is conserved and which includes extra right handed as well as left handed neutrinos, singlets under the gauge group. We find for muonium decay into $e^+e^-$ the extremely small result $Br(M\to e^+ e^-) < 10^{-19}$ in both scenarios. Alternatively, for $μ^+ e^-$ collisions up to $\sqrt{s}\sim 50$ GeV we find $σ(μ^+ e^- \to e^+ e^-)< 10^{-5}$ fb, while for energies above the $W^+ W^-$ threshold we find $σ(μ^+ e^- \to W^+ W^-)$ up to 1 fb.

hep-ph↗

arXiv2006

An approach for evaluation of observables in analytic versions of QCD

We present two variants of an approach for evaluation of observables in analytic QCD models. The approach is motivated by the skeleton expansion in a certain class of schemes. We then evaluate the Adler function at low energies in one variant of this approach, in various analytic QCD models for the coupling parameter, and compare with perturbative QCD predictions and the experimental results. We introduce two analytic QCD models for the coupling parameter which reproduce the measured value of the semihadronic tau decay ratio. Further, we evaluate the Bjorken polarized sum rule at low energies in both variants of the evaluation approach, using for the coupling parameter the analytic QCD model of Shirkov and Solovtsov, and compare with values obtained by the evaluation approach of Milton et al. and Shirkov.

hep-ph↗

arXiv2006

On the Effective Action of Dressed Mean Fields for N = 4 Super-Yang-Mills Theory

On the basis of the general considerations such as $R$-operation and Slavnov-Taylor identity we show that the effective action, being understood as Legendre transform of the logarithm of the path integral, possesses particular structure in ${\cal N} = 4$ supersymmetric Yang-Mills theory for kernels of the effective action expressed in terms of the dressed effective fields. These dressed effective fields have been introduced in our previous papers as actual variables of the effective action. The concept of dressed effective fields naturally appears in the framework of solution to Slavnov-Taylor identity. The particularity of the structure is independence of these kernels on the ultraviolet regularization scale $Λ$. These kernels are functions of mutual spacetime distances and of the gauge coupling. The fact that $β$ function in this theory vanishes is used significantly.

math-ph↗

arXiv2005

Effective action of dressed mean fields for N = 4 super-Yang-Mills theory

Based on general considerations such as $R$-operation and Slavnov-Taylor identity we show that the effective action, being understood as Legendre transform of the logarithm of the path integral, possesses particular structure in ${\cal N} =4$ supersymmetric Yang--Mills theory for kernels of the effective action expressed in terms of the dressed effective fields. These dressed effective fields have been introduced in our previous papers as actual variables of the effective action. The concept of dressed effective fields naturally appears in the framework of solution to Slavnov-Taylor identity. The particularity of the structure is the independence of these kernels on the ultraviolet regularization scale $Λ.$ These kernels are functions of mutual spacetime distances and of the gauge coupling. The fact that $β$ function in this theory is zero is used significantly.

hep-th↗

arXiv2005

Muonium-antimuonium conversion in models with heavy neutrinos

We study muonium-antimuonium conversion and mu+ e- to mu- e+ scattering within two different lepton-flavor-violating models with heavy neutrinos: model I is a typical seesaw that violates lepton number as well as flavor; model II has a neutrino mass texture where lepton number is conserved. We look for the largest possible amplitudes of these processes that are consistent with current bounds. We find that model I has very limited chance of providing an observable signal, except if a finely tuned condition in parameter space occurs. Model II, on the other hand, requires no fine tuning and could cause larger effects. However, the maximum amplitude provided by this model is still two orders of magnitude below the sensitivity of current experiments: one predicts an effective coupling G_MM up to 10^{-4}G_F for heavy neutrino masses near 10 TeV. We have also clarified some discrepancies in previous literature on this subject.

hep-ph↗

arXiv2004

Estimate of the three-loop contribution to the QCD static potential from renormalon cancellation

It had been known that the Borel transforms of the twice quark pole mass 2*mq and of the QCD q-barq static potential V(r) have leading infrared renormalons at b=1/2 such that they cancel in the sum. The renormalon residue of 2*mq had been determined with reasonably high precision from the known perturbative coefficients of the ratio mq/(bar mq), where (bar mq) is the barMS renormalon-free mass of the quark q. These values of the residues are used here to estimate the hitherto unknown part of the three-loop coefficient of the static potential V(r). Further, the method takes into account the fact that the ultrasoft energy regime contributions must be excluded from the analysis. In the b-barb quarkonium, aforementioned estimated part of the three-loop term turns out to give a contribution to the binding energy comparable to the nonpertubative contribution.

hep-ph↗

arXiv2003

Infrared renormalons and analyticity structure in pQCD

Relation between the infrared renormalons, the Borel resummation prescriptions, and the analyticity structure of Green functions in perturbative QCD (pQCD) is investigated. A specific recently suggested Borel resummation prescription resulted in the Principal Value and an additional power-suppressed correction that is consistent with the Operator Product Expansion. Arguments requiring the finiteness of the result for any power coefficient of the leading infrared renormalon, and the consistency in the case of the absence of that renormalon, require that this prescription be modified. The apparently most natural modification leads to the result represented by the Principal Value. The analytic structure of the amplitude in the complex coupling plane, obtained in this way, is consistent with that obtained in the literature by other methods.

hep-ph↗

arXiv2002

An approach to solve Slavnov-Taylor identities in nonsupersymmetric non-Abelian gauge theories

We present a way to solve Slavnov--Taylor identities in a general nonsupersymmetric theory. The solution can be parametrized by a limited number of functions of spacetime coordinates, so that all the effective fields are dressed by these functions via integral convolution. The solution restricts the ghost part of the effective action and gives predictions for the physical part of the effective action.

hep-ph↗