Two-loop calculations for the propagators of gluonic currents. Erratum
This is an erratum to the paper published in Nucl. Phys. B198(1982)508.
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arXiv subjects
A. A. Pivovarov
Publications and source records attributed to A. A. Pivovarov.
Theoretical uncertainties for weak decays: higher dimension operators
A brief review of recent results on computing contributions of higher dimension operators to weak effective $ΔS=1,2$ hamiltonians for light quarks is presented.
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Infrared modified analysis for the $τ$ lepton width
We argue that accounting for higher order corrections in QCD by integrating a running coupling constant through an infrared region can be most easily done with making use of a scheme without the Landau pole. Within this approach the entire ambiguity of the answer is identical to that of the choice of renormalization scheme. The uncertainties for the $τ$ lepton width resulting from such a technique are discussed.
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Mixing of neutral B mesons and factorization
A brief review of checking the factorization hypothesis for matrix element of $B^0 - \bar B^0$ mixing within operator product expansion and QCD sum rules is given. Both perturbative and power corrections are considered.
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Renormalization schemes and renormalons
We describe some ways how higher order corrections can reveal themselves if integrated over the infrared region. We show that in different renormalization group (RG) schemes and for some observables one has no factorial divergences. We argue that for treating things in the infrared region it is preferable to start with a RG scheme without the infrared Landau pole in the running coupling constant. The uncertainties for the $τ$ lepton width resulting from accounting for higher order corrections are discussed.
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Bubble chain resummation and universality
We propose a parameterization for contributions of an infinite set of diagrams (bubble chains) into physical observables represented as integrals of running coupling constant over the finite region in momentum space. The perturbation theory part of contributions is rendered well-defined by the principal value prescrition for treating the Landau pole while the rest is connected to the gluon condensate in case of observables allowing the OPE analysis. The hypothesis of universality, i.e. the use of our parameterization for non-OPE cases, is discussed.
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A scalar gluonium contribution to $K\rightarrowππ$ decay
We study a new $K\rightarrowππ$ decay channel with gluons in intermediate state which is normally neglected within the factorization framework. Both short-distance and long-distance parts of the amplitude are calculated. The chiral Lagrangian approach is used for obtaining the long-distance contribution. The nonperturbative contribution gives an additional enhancement to $K\rightarrowππ$ decay amplitude with $ΔI=1/2$. A sizable violation of factorization in the $p^4$ order of chiral perturbation theory is found.
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Optimized perturbation theory for bound states: toy model and realistic problem
Within quantum mechanics model we study the problem of resummation of an asymptotic perturbation series for bound state parameters via optimization of the perturbative expansion. A possible application of the method to the positronium lifetime calculation is also briefly considered.
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COMPUTATION OF COEFFICIENT FUNCTIONS FOR AN EXPANSION OF PARAPOSITRONIUM DECAY WIDTH USING REDUCE
A kind of asymptotic expansion for calculation of the (para)positronium decay rate is formulated. The method is completely relativistic and gauge invariant. The expansion goes over the inverse square of relative momentum $k$ of two photons in Euclidean region and the actual width is determined at $k^2=-m^2$, $m$ being the electron mass.
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On a subtle point of sum rules calculations: toy model
We consider a two-point correlator in massless $ϕ^3$ model within the ladder approximation . The spectral density of the correlator is known explicitly and does not contain any resonances. Meanwhile making use of the standard sum rules technique with a simple "resonance + continuum" model of the spectrum allows to predict parameters of the "resonance" very accurately in the sense that all necessary criteria of stability are perfectly satisfied.
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Extended analysis of the "penguin" part of $K\toππ$ amplitude
We make an attempt to clarify the role of the annihilation or "penguin" mode in the description of the $K\rightarrowππ$ decay within the Standard Model. The attention is concentrated on new operators in the effective $ΔS=1$ Hamiltonian and the violation of factorization for mesonic matrix elements of the local four-quark operators. We propose a regular method to evaluate the mesonic matrix elements of $K\rightarrowππ$ transitions based on studying three-point correlators via {\it QCD} sum rules using the chiral effective theory as an underlying low-energy model for strong interaction. Matrix elements of the {\it QCD} penguin operator are calculated within this approach. The total "penguin" contribution is found to be relatively large that improves the theoretical description of the $ΔI=1/2$ rule in non-leptonic kaon decays.
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QSSR estimate of the $B_B$ parameter at next-to-leading order
We compute the leading $α_s$ corrections to the two-point correlator of the $O_{ΔB=2}$ operator which controls the $B^0 \bar B^0$ mixing. Using this result within the QCD spectral sum rules approach and some phenomenologically reasonable assumptions in the parametrization of the spectral function, we conclude that the vacuum saturation values $B_B\simeq B_{B^*}\simeq 1$ are satisfied within 15\%.
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