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A. V. Kotikov

Publications and source records attributed to A. V. Kotikov.

At least 73 records · Page 4Linked to original sources
arXiv2018

Field theoretic renormalization study of interaction corrections to the universal ac conductivity of graphene

The two-loop interaction correction coefficient to the universal ac conductivity of disorder-free intrinsic graphene is computed with the help of a field theoretic renormalization study using the BPHZ prescription. Non-standard Ward identities imply that divergent subgraphs (related to Fermi velocity renormalization) contribute to the renormalized optical conductivity. Proceeding either via density-density or via current-current correlation functions, a single well-defined value is obtained: $\mathcal{C}= (19-6π)/12) = 0.01$ in agreement with the result first obtained by Mishchenko and which is compatible with experimental uncertainties.

cond-mat.mes-hall↗
arXiv2018

Multi-loop techniques for massless Feynman diagram calculations

We review several multi-loop techniques for analytical massless Feynman diagram calculations in relativistic quantum field theories: integration by parts, the method of uniqueness, functional equations and the Gegenbauer polynomial technique. A brief, historically oriented, overview of some of the results obtained over the decades for the massless 2-loop propagator-type diagram is given. Concrete examples of up to $5$-loop diagram calculations are also provided.

hep-th↗
arXiv2018

Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultra-relativistic limit of Dirac liquids

The field theoretic renormalization study of reduced quantum electrodynamics (QED) is performed up to two loops. In the condensed matter context, reduced QED constitutes a very natural effective relativistic field theory describing (planar) Dirac liquids, e.g., graphene and graphene-like materials, the surface states of some topological insulators and possibly half-filled fractional quantum Hall systems. From the field theory point of view, the model involves an effective (reduced) gauge field propagating with a fractional power of the d'Alembertian in marked contrast with usual QEDs. The use of the BPHZ prescription allows for a simple and clear understanding of the structure of the model. In particular, in relation with the ultra-relativistic limit of graphene, we straightforwardly recover the results for both the interaction correction to the optical conductivity: $\mathcal{C}^*=(92-9π^2)/(18π)$ and the anomalous dimension of the fermion field: $γ_ψ(\barα,ξ) = 2 \barα\,(1-3ξ)/3 -16\,\left( ζ_2 N_F + 4/27 \right)\, \barα^2 + O(\barα^3)$, where $\barα = e^2/(4π)^2$ and $ξ$ is the gauge-fixing parameter.

hep-th↗
arXiv2017

Bjorken sum rule in QCD with analytic coupling

We present details of study of the Bjorken polarized sum rule carried out recently in [1] within the range of energies where the data were collected by JLAB collaboration, 0.05 GeV2 < Q2 < 3 GeV2. Three approaches to QCD with analytic (holomorphic) coupling are considered: Analytic Perturbation Theory (APT), Two-delta analytic QCD, and Three-delta lattice-motivated analytic QCD in the three-loop and four-loop MiniMOM schemes. The new frameworks with respective couplings give results which agree well with the experimental data for 0.5 GeV2 < Q2 < 3GeV2 already when only one higher-twist term is taken into account.

hep-ph↗
arXiv2017

Gottfried sum rule in QCD NS analysis of DIS fixed target data

Deep inelastic scattering data on $F_2$ structure function obtained in the fixed-target experiments were analysed in the valence quark approximation with a next-to-next-to-leading-order accuracy. Parton distribution functions are parametrized by using information from the Gottfried sum rule. The strong coupling constant is found to be $α_s(M_Z^2) = 0.1180 \pm 0.0020~\mbox(total\,exp.error)$, which coincides very well with the average world value $α_s^{\rm PDG}(M_Z^2) = 0.1181 \pm 0.0013$ updated recently in a PDG report. The result for the second moment of the difference in $u$ and $d$ quark distributions $<\!\!x\!\!>_{u-d}=0.187 \pm 0.021$ is seen to be well compatible with the latest LATTICE result $<\!\!x\!\!>_{u-d}^{\rm LATTICE}=0.208 \pm 0.024$

hep-ph↗
arXiv2017

Application of the rescaling model at small Bjorken $x$ values

The Bessel-inspired behavior of parton densities at small Bjorken $x$ values, obtained in the case of the flat initial conditions for DGLAP evolution equations, is used along with "frozen" and analytic modifications of the strong coupling constant to study the so-called EMC effect. Among other results, this approach allowed predicting small $x$ behavior of the gluon density in nuclei.

hep-ph↗
arXiv2017

New results for a two-loop massless propagator-type Feynman diagram

We consider the two-loop massless propagator-type Feynman diagram with an arbitrary (non-integer) index on the central line. We analytically prove the equality of the two well-known results existing in the literature which express this diagram in terms of ${}_3F_2$-hypergeometric functions of argument $-1$ and $1$, respectively. We also derive new representations for this diagram which may be of importance in practical calculations.

hep-th↗
arXiv2016

Critical behaviour of reduced QED$_{4,3}$ and dynamical fermion gap generation in graphene

The dynamical generation of a fermion gap in graphene is studied at the infra-red Lorentz-invariant fixed point where the system is described by an effective relativistic-like field theory: reduced QED$_{4,3}$ with $N$ four component fermions ($N=2$ for graphene), where photons are $(3+1)$-dimensional and mediate a fully retarded interaction among $(2+1)$-dimensional fermions. A correspondence between reduced QED$_{4,3}$ and QED$_3$ allows us to derive an exact gap equation for QED$_{4,3}$ up to next-to-leading order. Our results show that a dynamical gap is generated for $α> α_c$ where $1.03 < α_c < 1.08$ in the case $N=2$ or for $N < N_c$ where $N_c$ is such that $α_c \to \infty$ and takes the values $3.24 < N_c < 3.36$. The striking feature of these results is that they are in good agreement with values found in models with instantaneous Coulomb interaction. At the fixed point: $α= 1/137 \ll α_c$, and the system is therefore in the semi-metallic regime in accordance with experiments.

hep-th↗
arXiv2016

Critical behaviour of ($2+1$)-dimensional QED: $1/N_f$-corrections in an arbitrary non-local gauge

Dynamical chiral symmetry breaking (D$χ$SB) is studied within ($2+1$)-dimensional QED with $N$ four-component fermions. The leading and next-to-leading orders of the $1/N$ expansion are computed exactly. The analysis is carried out in an arbitrary non-local gauge. Resumming the wave-function renormalization constant at the level of the gap equation yields a strong suppression of the gauge dependence of the critical fermion flavour number, $N_c(ξ)$ where $ξ$ is the gauge fixing parameter, which is such that D$χ$SB takes place for $N<N_c(ξ)$. Neglecting the weak gauge-dependent terms yields $N_c = 2.8469$ while, in the general case, it is found that: $N_c(1) = 3.0084$ in the Feynman gauge, $N_c(0) = 3.0844$ in the Landau gauge and $N_c(2/3)= 3.0377$ in the $ξ=2/3$ gauge where the leading order fermion wave function is finite. These results suggest that D$χ$SB should take place for integer values $N \leq 3$.

hep-th↗
arXiv2016

Critical behaviour of ($2+1$)-dimensional QED: 1/N_f-corrections in the Landau gauge

The dynamical generation of a fermion mass is studied within ($2+1$)-dimensional QED with $N$ four-component fermions in the leading and next-to-leading orders of the 1/N expansion. The analysis is carried out in the Landau gauge which is supposed to insure the gauge independence of the critical fermion flavour number, N_c. It is found that the dynamical fermion mass appears for N<N_c where N_c=3.29, that is only about $1\%$ larger than its value at leading order.

hep-th↗
arXiv2016

The method of uniqueness and the optical conductivity of graphene: new application of a powerful technique for multi-loop calculations

We review the method of uniqueness which is a powerful technique for multi-loop calculations in higher dimensional theories with conformal symmetry. We use the method in momentum space and show that it allows a very transparent evaluation of a two-loop massless propagator Feynman diagram with a non-integer index on the central line. The result is applied to the computation of the optical conductivity of graphene at the infra-red Lorentz invariant fixed point. The effect of counter-terms is analysed. A brief comparison with the non-relativistic case is included.

hep-th↗
arXiv2015

Improved nonsinglet QCD analysis of the fixed-target DIS data

Deep inelastic scattering data on $F_2$ structure function obtained by BCDMS, SLAC and NMC collaborations in fixed-target experiments were analyzed in the non-singlet approximation with next-to-next-to-leading-order accuracy. The strong coupling constant is found to be $α_s(M_Z^2) = 0.1157 \pm 0.0022 (total\,\,\,exp.error) + \biggl\{\begin{array}{l} +0.0028 \\ -0.0016 \end{array} (theor)$, which is seen to be well compatible with the average world value. Results obtained in the present paper by carrying out fits similar to those done in our earlier study, with the exception for systematic errors in BCDMS data taken into account in a different way, confirm those which were derived in that same paper.

hep-ph↗
arXiv2015

Pomeron in the N=4 SYM

We review the result for the BFKL Pomeron intercept at N=4 Supersymmetric Yang-Mills model in the form of the inverse coupling expansion $j_0=2-2λ^{-1/2}-λ^{-1} + 1/4 \, λ^{-3/2} + 2(3ζ_3+1) \, λ^{-2} +(18ζ_3+361/64) \, λ^{-5/2} + (39ζ_3+447/32) \, λ^{-3} + O(λ^{-7/2})$ which has been calculated in [1]-[5] with the use of the AdS/CFT correspondence.

hep-th↗
arXiv2014

Average gluon and quark jet multiplicities

We show the results in [1,2] for computing the QCD contributions to the scale evolution of average gluon and quark jet multiplicities. The new results came due a recent progress in timelike small-x resummation obtained in the MSbar factorization scheme. They depend on two nonperturbative parameters with clear and simple physical interpretations. A global fit of these two quantities to all available experimental data sets demonstrates by its goodness how our results solve a longstandig problem of QCD. Including all the available theoretical input within our approach, alphas(Mz)=0.1199 +- 0.0026 has been obtained in the MSbar scheme in an approximation equivalent to next-to-next-to-leading order enhanced by the resummations of ln x terms through the NNLL level and of ln Q2 terms by the renormalization group. This result is in excellent agreement with the present world average.

hep-ph↗