Valentin I. Zakharov

On the universality of the leading, 1/Q power corrections in QCD

Abstract 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 certain event shape variables 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.

Bloch-Nordsieck cancellations beyond logarithms in heavy particle decays

We investigate the one-loop radiative corrections to the semileptonic decay of a charged particle at finite gauge boson mass. Extending the Bloch-Nordsieck cancellation of infrared logarithms, the subsequent non-analytic terms are also found to vanish after eliminating the pole mass in favor of a mass defined at short distances. This observation justifies the operator product expansion for inclusive decays of heavy mesons and implies that infrared effects associated with the summation of the radiative corrections are suppressed by at least three powers of the mass of the heavy decaying particle.

On non perturbative corrections to the potential for heavy quarks

Abstract 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→0. We point out that similar effects arise due to a new kind of non perturbative correction proportional to 1/Q2, 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.

Leading power corrections in QCD: from renormalons to phenomenology

We consider 1Q 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 1Q terms, and compare them with the existing data. We also identify the scale of the non-perturbative contributions in terms of jet masses.

Infrared effects in a de Sitter background.

We have estimated higher order quantum gravity corrections to de Sitter spacetime. Our results suggest that, while the classical spacetime metric may be distorted by the graviton self-interactions, the corrections are relatively weaker than previously thought, possibly growing like a power rather than exponentially in time.

Renormalons as a Bridge between Perturbative and Non-Perturbative 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.

Photonic chiral current and its anomaly in a gravitational field

Abstract The notion of chirality for an electromagnetic field which is conserved in interactions with gravitons is formulated. The corresponding chiral current is the one-particle-state analouge of the Pauli-Lubansky vector. The anomaly of this current in an external gravitational field is found. The results obtained are used for the calculation of the electromagnetic radiative correction to the fermionic chiral anomaly in a gravitational field.

Kinoshita-Lee-Nauenberg 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 absence of the 1/Q corrections to inclusive processes (such as the Drell-Yan process). In this paper the Abelian case is discussed to all orders in the coupling. {copyright} {ital 1997} {ital The American Physical Society}

Power corrections in QCD: A matter of energy resolution

We consider powerlike corrections in QCD which can be viewed as power suppressed infrared singularities. We argue that the presence of these singularities depends crucially on the energy resolution. In the 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. {copyright} {ital 1996 The American Physical Society.}

Current algebra and η → 3π, X → 2πη decays

Abstract Energy spectra of η → π + π − π 0 and X → ηπ + π − decays are calculated within the framework of current algebra and the hypothesis of partial conservation of axial current (PCAC). η → 3 π decay rates are obtained in the SU(3) limit.