arXiv subjects

S. E. Derkachov

Publications and source records attributed to S. E. Derkachov.

45 records · Page 3Linked to original sources

arXiv1999

Baryon Distribution Amplitudes in QCD

We develop a new theoretical framework for the description of leading twist light-cone baryon distribution amplitudes which is based on integrability of the helicity $λ=3/2$ evolution equation to leading logarithmic accuracy. A physical interpretation is that one can identify a new `hidden' quantum number which distinguishes components in the $λ=3/2$ distribution amplitudes with different scale dependence. The solution of the corresponding evolution equation is reduced to a simple three-term recurrence relation. The exact analytic solution is found for the component with the lowest anomalous dimension for all moments $N$, and the WKB-type expansion is constructed for other levels, which becomes asymptotically exact at large $N$. Evolution equations for the $λ=1/2$ distribution amplitudes (e.g. for the nucleon) are studied as well. We find that the two lowest anomalous dimensions for the $λ=1/2$ operators (one for each parity) are separated from the rest of the spectrum by a finite `mass gap'. These special states can be interpreted as scalar diquarks.

hep-ph↗

arXiv1998

Integrability of three-particle evolution equations in QCD

We show that Brodsky-Lepage evolution equation for the leading twist spin 3/2 baryon distribution amplitude is completely integrable and reduces to the three-particle XXX_{s=-1} Heisenberg spin chain. Trajectories of the anomalous dimensions are identified and calculated using the 1/N expansion. Extending this result, we prove integrability of the evolution equations for twist 3 quark-gluon operators in the large N_c limit and derive explicit expressions for the corresponding integrals of motion.

hep-ph↗

arXiv1997

The simple scheme for the calculation of the anomalous dimensions of composite operators in the 1/N expansion

The simple method for the calculating of the anomalous dimensions of the composite operators up to 1/N^2 order is developed. We demonstrate the effectiveness of this approach by computing the critical exponents of the $(\otimes\vecΦ)^{s}$ and $\vecΦ\otimes(\otimes\vec\partial)^{n}\vecΦ$ operators in the 1/N^2 order in the nonlinear sigma model. The special simplifications due to the conformal invariance of the model are discussed.

hep-th↗

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↗

arXiv1993

On Calculation of 1/n Expansions of Critical Exponents in the Gross-Neveu Model with the Conformal Technique

A proof of critical conformal invariance of Green's functions for a quite wide class of models possessing critical scale invariance is given. A simple method for establishing critical conformal invariance of a composite operator, which has a certain critical dimension, is also presented. The method is illustrated with the example of the Gross--Neveu model and the exponents \et\ at order $1/n^3$, \Dl\ and $1/ν$ at order $1/n^2$ are calculated with the conformal bootstrap method.

hep-th↗