arXiv subjects

V. I. Zakharov

Publications and source records attributed to V. I. Zakharov.

At least 127 records · Page 7Linked to original sources

arXiv1999

Short-distance tachyonic gluon mass and 1/Q^2 corrections

We consider the assumption that a tachyonic gluon mass imitates short-distance nonperturbative physics of QCD. The phenomenological implications include modifications of the QCD sum rules for correlators of currents with various quantum numbers. The new 1/Q^2 terms allow to resolve in a natural way old puzzles in the pion and scalar-gluonium channels. They lead to a slight reduction of the values of the running light quark masses from the (pseudo)scalar sum rules and of alpha_s(M_τ) from tau decay data. Further tests can be provided by precision measurements of the correlators on the lattice and by the e^+e^- --> hadrons data.

hep-ph↗

arXiv1999

Infrared Behaviour of the Gauge Boson Propagator in a Confining Theory

We study the gauge boson propagator in the dual Abelian Higgs theory which confines electric charges. The confinement is due to dual Abrikosov-Nielsen-Olesen strings. We show that the infrared double pole 1/(p^2)^2 in the propagator is absent due to the confinement phenomenon. Instead, specific angular singularities signal the eventual set in of the confinement. These angular singularities are a manifestation of the confining strings.

hep-ph↗

arXiv1998

Uncovereing thick and thin strings via renormalons

The talk is about the power corrections in QCD. Renormalons, both infrared and ultraviolet, provide with a kind of a kinematical framework to fix exponents of the leading power corrections to various observables. Any viable dynamical framework is to reproduce this pattern of the power corrections. In this mini-review, we emphasize that a simple dynamical framework satisfying this requirement may well be provided by the strings inherent to the Abelian Higgs model. This model comes naturally into consideration within the U(1) projection of QCD which makes explicit the dual-superconductor model of the confinement. At large distances (compared to $\LQ^{-1}$) there are Abrikosov-Nielsen-Olesen strings which develop a characteristic non-perturbative transverse size of order $\LQ^{-1}$ and match in this way the infrared renormalons. At short distances there are no ANO strings but there still exist dynamical manifestations of the stringy topological condition that (external) quarks are connected by a mathematically thin line along which the vacuum is trivial. These manifestations may match ultraviolet renormalons.

hep-ph↗

arXiv1998

QCD '98: status of the power corrections

We review status of the power corrections in QCD. The topics include shape variables, unconventional 1/Q^2 corrections, tachyonic gluon mass as a fit parameter to the 1/Q^2 corrections. The selection of the material is determined mostly by results presented at the Conference QCD'98 (Montpellier, July 1998). Some background comments are also included.

hep-ph↗

arXiv1998

Monopole-antimonopole interaction in Abelian Higgs model

We consider interaction of a probe monopole-antimonopole pair in the vacuum of the Abelian Higgs model. For simplicity, the mass of the Higgs particle is assumed to be much larger than the mass of the photon (London limit). In case of a massive photon the straightforward application of the Zwanziger formalism to accommodate both magnetic and electric charges is known to result in gauge dependence and infrared instabilities. We argue that the use of the string representation of the Abelian Higgs model allows to ameliorate both difficulties. In particular, we arrive at a well defined expression for the potential energy of the static monopole sources. We argue that the monopole-antimonopole interaction cannot be described by a massive photon exchange with a definite propagator having simple analytical properties.

hep-th↗

arXiv1998

Cancellation of $1/m_Q$ Corrections to the Inclusive Decay Width of a Heavy Quark

We consider the infrared sensitivity of the inclusive heavy quark decay width in perturbation theory. It is shown by explicit calculations to the second loop order (when the non-abelian nature of the QCD interactions first become apparent) that all infrared sensitive terms to logarithmic and linear accuracy cancel when the decay width is expressed in terms of the short distance mass. This in turn implies the absense of any non perturbative $1/m_Q$ power corrections to the decay width. The cancellation is shown algebraically at the level of the Feynman integrands without any use of an explicit infrared cutoff. This result is in accord with the implications of the KLN theorem.

hep-ph↗

arXiv1998

Renormalons as a Bridge between Perturbative and Nonperturbative Physics

In two lectures, we overview the renormalon and renormalon-related techniques and their phenomenological applications. We begin with a single renormalon chain which is a well defined and systematic way to specify the character of corrections in inverse powers of the total energy to observables directly in Minkowski space. Renormalons demonstrate also presence of nonperturbative contributions. We proceed then to multirenormalon chains and argue that they are in fact not suppressed compared to a single chain. On one hand, this phenomenon might be a mechanism for enhancement of power corrections. On the other hand, the derivation of relations between power corrections to various observables becomes a formidable task and asks for introduction of models. In the concluding, third part we consider dynamical models for nonperturbative effects, both in infrared and ultraviolet regions, inspired by renormalons.

hep-ph↗

arXiv1997

On Non Perturbative Corrections to the Potential for Heavy Quarks

We discuss non perturbative corrections to the Coulomb-like potential of heavy quarks at short distances. We consider both the standard framework provided by infrared renormalons and the assumption that confinement does not allow weak fields to penetrate the vacuum. In the former case the leading correction at short distances turns out to be quadratic in r for static quarks. In the latter case we find a potential which is proportional to r as r rightarrow 0. We point out that similar effects arise due to a new kind of non perturbative correction proportional to 1/Q^2, which is unaccounted for by the operator product expansion and which was recently discussed within a different framework. Phenomenological implications of the linear correction to the potential are briefly reviewed.

hep-ph↗

arXiv1997

The Physics of the Ultraviolet Renormalon

We review the physics of the ultraviolet renormalon. This mini-review is intended to be a sequel to the review by the same authors at the "QCD '96" conference last year (hep-ph/9610492).

hep-ph↗

arXiv1997

Renormalons and 1/Q^2 Corrections

We argue that the appearance of the Landau pole in the running coupling of QCD introduces 1/Q^2 power corrections in current correlation functions. These terms are not accounted for by the standard operator product expansion and is the price to be paid for the lack of a unique definition of the running coupling at the 1/Q^2 level. We review also possible phenomenological implications of the 1/Q^2 terms in an alternative language of the ultraviolet renormalon.

hep-ph↗

arXiv1997

The KLN Theorem and Soft Radiation in Gauge Theories: Abelian Case

We present a covariant formulation of the Kinoshita, Lee, Nauenberg (KLN) theorem for processes involving the radiation of soft particles. The role of the disconnected diagrams is explored and a rearrangement of the perturbation theory is performed such that the purely disconnected diagrams are factored out. The remaining effect of the disconnected diagrams results in a simple modification of the usual Feynman rules for the S-matrix elements. As an application, we show that when combined with the Low theorem, this leads to a proof of the absense of the $1/Q$ corrections to inclusive processes (like the Drell-Yan process). In this paper the abelian case is discussed to all orders in the coupling.

hep-ph↗

arXiv1997

Renormalon Variety in Deep Inelastic Scattering

We discuss the renormalon-based approach to power corrections in non-singlet deep inelastic scattering structure functions and compare it with the general operator product expansion. The renormalon technique and its variations relate the power corrections directly to infrared-sensitive parameters such as the position of the Landau pole Λ_{QCD} or the infinitesimal gluon mass λ. In terms of the standard OPE these techniques unify evaluations of the coefficient functions and of matrix elements. We argue that in case of deep inelastic scattering there is a proliferation of competeing infrared sensitive parameters. In particular we consider the gluon and quark masses, virtuality of quarks and Λ_{QCD} as possible infrared cut offs and compare the emerging results. In the standard renormalon technique where Λ_{QCD} is the infrared parameter, the argument of the running coupling is crucial to obtain the correct x dependance of the structure functions. Finally we discuss the limitations of the use of the renormalon based methods for determining of the x dependance of the power corrections.

hep-ph↗

arXiv1996

A Quick Look at Renormalons

We present a sketchy review of renormalon-based phenomenology. In particular, the leading, 1/Q corrections to various observables, KLN cancellations for power-suppressed corrections and the fixation of operator matrix elements are highlighted.

hep-ph↗

arXiv1996

Power Corrections and KLN Cancellations

We consider perturbative expansions in theories with an infrared cutoff $λ$. The infrared sensitive pieces are defined as terms nonanalytic in the infinitesimal $λ^2$ and powers of this cutoff characterize the strength of these infrared contributions. It is argued that the sum over the initial and final degenerate ( as $λ\to 0$) states which is required by the Kinoshita - Lee - Nauenberg theorem eliminates terms of order $λ^0$ and $λ^1$. However, the quadratic and higher order terms in general do not cancel. This is investigated in simple examples of KLN cancellations, of relevance to the inclusive decay rate of a heavy particle, at the one loop level.

hep-ph↗

arXiv1995

Power Corrections in QCD: A Matter of Energy Resolution

We consider power-like corrections in QCD which can be viewed as power surpressed infrared singularities. We argue that the presence of these singularities depends crucially on the energy resolution. In case of poor energy resolution, i.e., inclusive cross sections, there are constraints on infrared singularities expressed by the Kinoshita-Lee-Nauenberg (KLN) theorem. We rewrite the theorem in covariant notations and argue that the KLN theorem implies the extension of the Bloch-Nordsieck cancellation of logarithmic singularities to the case of linear corrections.

hep-ph↗

arXiv1995

Leading Power Corrections in QCD: From Renormalons to Phenomenology

We consider $1/Q$ corrections to hard processes in QCD where Q is a large mass scale, concentrating on shape variables in $e^{+}e^{-}$ annihilation. While the evidence for such corrections can be and has been established by means of the renormalon technique, theory can be confronted with experiment only after clarifying the properties of the corresponding non-perturbative contribution. We list predictions based on the universality of the $1/Q$ terms, and compare them with the existing data. We also identify the scale of the non-perturbative contributions in terms of jet masses.

hep-ph↗

arXiv1995

Ultraviolet-Renormalon Reexamined

We consider large-order perturbative expansions in QED and QCD. The coefficients of the expansions are known to be dominated by the so called ultraviolet (UV) renormalons which arise from inserting a chain of vacuum-polarization graphs into photonic (gluonic) lines. In large orders the contribution is associated with virtual momenta $k^2$ of order $Q^2e^n$ where $Q$ is external momentum, $e$ is the base of natural logs and $n$ is the order of perturbation theory considered. To evaluate the UV renormalon we develop formalism of operator product expansion (OPE) which utilizes the observation that $k^2\gg Q^2$. When applied to the simplest graphs the formalism reproduces the known results in a compact form. In more generality, the formalism reveals the fact that the class of the renormalon-type graphs is not well defined. In particular, graphs with extra vacuum-polarization chains are not suppressed. The reason is that while inclusion of extra chains lowers the power of $\ln k^2$ their contribution is enhanced by combinatorial factors.

hep-ph↗

arXiv1995

On the Universality of the Leading, $1/Q$ Power Corrections in QCD

We discuss $1/Q$ corrections to hard processes in QCD where $Q$ is a large mass parameter like the total energy in $e^+e^-$ annihilation. The main problem we address ourselves to is whether these corrections to different processes (concentrating for definiteness on the Thrust and the Drell-Yan cross section) can be related to each other in a reliable way so that the phenomenology of the $1/Q$ corrections can be developed. We derive first the relation valid to lowest order using both the renormalon and finite-gauge-boson mass techniques to check its independence on the infrared cut- off procedure. We then argue that the $1/Q$ corrections are due to soft gluons which factorize into a universal factor such that the lowest order relations are preserved in higher orders.

hep-ph↗