arXiv subjects

A. N. Manashov

Publications and source records attributed to A. N. Manashov.

79 records · Page 5Linked to original sources

arXiv1997

Four loop anomalous dimensions of gradient operators in phi^4 theory

We compute the anomalous dimensions of a set of composite operators which involve derivatives at four loops in MSbar in phi^4 theory as a function of the operator moment n. These operators are similar to the twist-2 operators which arise in QCD in the operator product expansion in deep inelastic scattering. By regarding their inverse Mellin transform as being equivalent to the DGLAP splitting functions we explore to what extent taking a restricted set of operator moments can give a good approximation to the exact four loop result.

hep-ph↗

arXiv1997

On the stability problem in the O(N) nonlinear sigma model

The stability problem for the O(N) nonlinear sigma model in the 2+εdimensions is considered. We present the results of the 1/N^{2} order calculations of the critical exponents (in the 2<d<4 dimensions) of the composite operators relevant for this problem. The arguments in the favor of the scenario with the conventional fixed point are given.

hep-th↗

arXiv1996

High-gradient operators in the N-vector model

It has been shown by several authors that a certain class of composite operators with many fields and gradients endangers the stability of nontrivial fixed points in 2+eps expansions for various models. This problem is so far unresolved. We investigate it in the N-vector model in an 1/N-expansion. By establishing an asymptotic naive addition law for anomalous dimensions we demonstrate that the first orders in the 2+eps expansion can lead to erroneous interpretations for high--gradient operators. While this makes us cautious against over--interpreting such expansions (either 2+eps or 1/N), the stability problem in the N-vector model persists also in first order in 1/N below three dimensions.

cond-mat.stat-mech↗

arXiv1996

Generic scaling relation in the scalar $ϕ^{4}$ model

The results of analysis of the one--loop spectrum of anomalous dimensions of composite operators in the scalar $ ϕ^{4} $ model are presented. We give the rigorous constructive proof of the hypothesis on the hierarchical structure of the spectrum of anomalous dimensions -- the naive sum of any two anomalous dimensions generates a limit point in the spectrum. Arguments in favor of the nonperturbative character of this result and the possible ways of a generalization to other field theories are briefly discussed.

hep-th↗

arXiv1995

The spectrum of the anomalous dimensions of the composite operators in the $ε$ - expansion in the scalar $ϕ^4$ - field theory

The spectrum of the anomalous dimensions of the composite operators (with arbitrary number of fields $n$ and derivatives $l$) in the scalar $ϕ^4$ - theory in the first order of the $ε$ -expansion is investigated. The exact solution for the operators with number of fields $\leq 4$ is presented. The behaviour of the anomalous dimensions in the large $l$ limit has been analyzed. It is given the qualitative description of the %structure of the spectrum for the arbitrary $n$.

hep-th↗

arXiv1995

Analysis of data on low energy piN-->pipiN reaction. I. Total cross sections

This is the first of a series of papers on a consistent model independent analysis of the complete experimental information on the reaction $πN \rightarrow ππN$ at pion momenta up to 500 MeV/c. The paper summarizes the theoretical approach and details of the computational procedure. The complete database on total cross sections in 5 $ππN$ channels is given together with a critical discussion of their model independent analysis.

hep-ph↗

arXiv1995

Contribution of the Sixth Order Effective Chiral Lagrangian to the $πK$ Scattering at Large $N_c$

Using the method of asymptotic sum rules we estimated the size of $O(m_s p_π^4)$ and $O(m_s^2 p_π^2)$ corrections to $πK$ scattering amplitude in large $N_c$ limit. These corrections arise from the sixth order effective chiral lagrangian (EChL). Our method enables us to estimate the corresponding terms of the sixth order EChL in leading order of $1/N_c$ expansion in model independent way. We found that the corrections numerically are suppressed in spite of naive expectation of 30--35\%. Our estimation gives the value of these corrections about 5--10\% .

hep-ph↗