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A. A. Vladimirov

Publications and source records attributed to A. A. Vladimirov.

At least 37 records · Page 2Linked to original sources
arXiv2014

TMD PDFs in the Laguerre polynomial basis

We suggest the modified matching procedure for TMD PDF to the integrated PDF aimed to increase the amount of perturbative information in the TMD PDF expression. The procedure consists in the selection and usage of the non-minimal operator basis, which restricts the expansion to desired general behavior. The implication of OPE allows to systematic account of the higher order corrections. In the case of TMD PDF we assume the Gaussian behavior, which suggests Laguerre polynomial basis as the best for the convergence of OPE. We present the leading and next-to-leading expression of TMD PDF in this basis. The obtained perturbative expression for the TMD PDF is valid in the wide region of $b_T$ (we estimate this region as $b_T\lesssim 2-3$ GeV$^{-1}$ depending on $x$).

hep-ph↗
arXiv2014

TMDs in Laguerre polynomial basis

We suggest modification of the standard approach to TMDs. The modification consists in the consideration of the small $b_T$ operator product expansion in the different operator basis. Instead of power expansion we suggest to use the Laguerre polynomial expansion. Within such a scheme the first term of OPE saturates TMDs in the wider range of $b_T$ in comparison to the power expansion that decreases the significance of non-perturbative factor at small $b_T$. The presented modification does not violate any TMD properties and can be used within any formulation of TMD factorization.

hep-ph↗
arXiv2014

Key features of the TMD soft-factor structure

We show that the geometry of the Wilson lines, entering the operator definition of the transverse-momentum dependent parton distributions and that of the soft factor, follows from the kinematics of the underlying physical process in conjunction with the gauge invariance of the QCD Lagrangian. We demonstrate our method in terms of concrete examples and determine the paths of the associated Wilson lines. The validation of the factorization theorem in our approach is postponed to future work.

hep-ph↗
arXiv2013

Chiral expansion of nucleon PDF at $x\sim m_π/M_N$

Based on the chiral perturbation theory, we investigate the low-energy dynamics of nucleon parton distributions. We show that in different regions of the momentum fraction $x$ the chiral expansion is significantly different. For nucleon parton distributions these regions are characterized by $x\sim1$, $x\sim m_π/M_N$ and $x\sim (m_π/M_N)^2$. We derive extended counting rules for each region and obtain model-independent results for the nucleon parton distributions down to $x\gtrsim m^2_π/M^2_N \approx 10^{-2}$.

hep-ph↗
arXiv2013

Causality constraints on TMD PDF

In this short note, we discuss constraints on the transverse momentum dependent factorization formulae coming from the causality properties for the hadronic tensor.

hep-ph↗
arXiv2013

Three-loop calculations in non-Abelian gauge theories

A detailed description of the method for analytical evaluation of the three-loop contributions to renormalization group functions is presented. This method is employed to calculate the charge renormalization function and anomalous dimensions for non-Abelian gauge theories with fermions in the three-loop approximation. A three-loop expression for the effective charge of QCD is given. Charge renormalization effects in the SU(4)-supersymmetric gauge model is shown to vanish at this level. A complete list of required formulas is given in Appendix. The above-mentioned results of three-loop calculations have been published by the present authors (with A.Yu., Zharkov and L.V., Avdeev) in 1980 in Physics Letters B. The present text, which treats the subject in more details and contains a lot of calculational techniques, has also been published in 1980 as the JINR Communication E2-80-483.

hep-ph↗
arXiv2012

Some remarks on integral parameters of Wiener process

We consider integrals $τ_ρ=\int_0^1ρξ^2\,dx$, where $ξ$ is Wiener process and $ρ$ is generalized function from some class of multipliers. In the case when multiplier $ρ$ belongs to the trace-class, it is shown that $τ_ρ$ has $χ^2$-distribution (or analogous). An example of multiplier $ρ$ not belonging to the trace-class is constructed.

math.SP↗
arXiv2012

Optical and dc conductivities of cuprates: Spin-fluctuation scattering in the t-J model

A microscopic theory of the electrical conductivity $σ(ω)$ within the t-J model is developed. An exact representation for $σ(ω)$ is obtained using the memory-function technique for the relaxation function in terms of the Hubbard operators, and the generalized Drude law is derived. The relaxation rate due to the decay of charge excitations into particle-hole pairs assisted by antiferromagnetic spin fluctuations is calculated in the mode-coupling approximation. Using results for the spectral function of spin excitations calculated previously, the relaxation rate and the optical and dc conductivities are calculated in a broad region of doping and temperatures. The reasonable agreement of the theory with experimental data for cuprates proves the important role of spin-fluctuation scattering in the charge dynamics.

cond-mat.str-el↗
arXiv2011

Spectral and oscillation properties for a linear pencil of fourth-order differential operators

The present paper deals with the spectral and the oscillation properties of a linear pencil $A-λB$. Here $A$ and $B$ are linear operators generated by the differential expressions $(py")"$ and $-y"+ cry$, respectively. In particular, it is shown that the negative eigenvalues of this problem are simple and the corresponding eigenfunctions $y_{-n}$ have $n-1$ zeros in $(0,1)$.

math.SP↗
arXiv2011

Chiral Inflation of the Pion Radius

We derive expression for the large b_perp asymptotic of the 3D parton distributions q(x,b_perp) in the pion. The asymptotic depends exclusively on the mass scales F_pi and m_pi. Therefore it provides us with a nice example of a strict non-perturbative result for the partonic structure of Nambu-Goldstone bosons in QCD. Analyzing the x-dependent pion transverse radius we reveal a new phenomenon of "chiral inflation"-- in the parametrically wide region of Bjorken x (m_pi^2/(4 pi F_pi)^2 << x << 1) the pion radius grows exponentially fast with the rapidity eta=ln(1/x). We show that the partons in this interval of Bjorken x contribute to famous logarithmic divergency of the pion radius. In other words, the partonic picture of the classical result of ChPT is provided. The phenomenon of the chiral inflation is at variance with the Gribov diffusion, because of long-range interaction of the Nambu-Goldstone bosons.

hep-ph↗
arXiv2011

On the Neumann problem for Sturm-Liouville equation with self-similar Cantor type weight

Sturm-Liouville problem with generalized derivative of self-similar Cantor type function as a weight is considered. Under Neumann and mixed boundary conditions the oscillating properties of the eigenfunctions are studied. The spectral asymptotics are made more precise then in previous papers. Namely, it is shown that for known asymptotics $N(λ)=λ^D\cdot [s(\lnλ)+o(1)]$ the function $s$ is a product of decreasing exponent and nondecreasing purely singular function (and hence it is not constant).

math.SP↗
arXiv2011

Dynamic spin susceptibility of superconducting cuprates: A microscopic theory of the magnetic resonance mode

A microscopic theory of the dynamic spin susceptibility (DSS) in the superconducting state within the t-J model is presented. It is based on an exact representation for the DSS obtained by applying the Mori-type projection technique for the relaxation function in terms of Hubbard operators. The static spin susceptibility is evaluated by a sum-rule-conserving generalized mean-field approximation, while the self-energy is calculated in the mode-coupling approximation. The spectrum of spin excitations is studied in the underdoped and optimally doped regions. The DSS reveals a resonance mode (RM) at the antiferromagnetic wave vector Q = π(1,1) at low temperatures due to a strong suppression of the damping of spin excitations. This is explained by an involvement of spin excitations in the decay process besides the particle-hole continuum usually considered in random-phase-type approximations. The spin gap in the spin-excitation spectrum at Q plays a dominant role in limiting the decay in comparison with the superconducting gap which results in the observation of the RM even above $T_c$ in the underdoped region. A good agreement with inelastic neutron-scattering experiments on the RM in YBCO compounds is found.

cond-mat.str-el↗
arXiv2010

Leading infrared logarithms for sigma-model with fields on arbitrary Riemann manifold

We derive non-linear recursion equation for the leading infrared logarithms (LL) in four dimensional sigma-model with fields on an arbitrary Riemann manifold. The derived equation allows one to compute leading infrared logarithms to essentially unlimited loop order in terms of geometric characteristics of the Riemann manifold. We reduce the solution of the SU(oo) principal chiral field in arbitrary number of dimensions in the LL approximation to the solution of very simple recursive equation. This result paves a way to the solution of the model in arbitrary number of dimensions at N-->oo

hep-th↗
arXiv2010

On separable nets in constructive topological spaces

A class of nets in constructive (in A.A.Markov's sense) topological space for which the convergence is equivalent to convergence of all subsequences, is described. B.A.Kushner's theorem about coincidence of strong and weak constructive variants of Riemann's integrability, is obtained as corollary.

math.LO↗