Search

It is shown the analysis [1] for QED in 2+1 dimensions with N four-component fermions in the leading and next-to-leading orders of the 1/N expansion. As it was demonstrated in [1] the range of the admissible values N, where the dynamical fermion mass exist, decreases strongly with the increasing of the gauge charge. So, in Landau gauge the dynamical chiral symmetry breaking appears for N<3.78, that is very close to the results of the leading order and in Feynman gauge dynamical mass is completely absent., Comment: 5 pages, presented on the 6th International Workshop on Critical Point and Onset of Deconfinement, 23 - 29 August 2010, Dubna, Russia

We study the heavy-quark contributions to the proton structure function F2(x,Q2) at next-to-leading order using compact formulas at small values of Bjorken's x variable. The formulas provide a good agreement with the modern HERA data for F2c(x,Q2)., Comment: 8 pages, 1 figure, presented on the XIV International Conference on Symmetry Methods in Physics (SYMPHYS-XIV), Tsakhkadzor, Armenia, August 16 - 22, 2010

We give a brief review of our recent QCD analysis carried out over the deep inelastic scattering data on F2 structure function and in the non-singlet approximation to the accuracy up to next-to-next-to-leading-order. Specifically, analysis was performed over high statistics deep inelastic scattering data provided by BCDMS, SLAC, NMC and BFP collaborations. For the coupling constant the following value alpha_s(M_Z^2) = 0.1167 \pm 0.0022 was found., Comment: 11 pp, 2 figs, contribution to the Proceedings of XLIV PNPI Winter School held in Roschino (Russia) on 9-14 March, 2010

Deep inelastic scattering data on the F_2 structure function provided by the BCDMS, SLAC and NMC collaborations are analyzed in the non-singlet approximation with the analytic and "frozen" modifications of the strong coupling constant featuring no unphysical singularity (the Landau pole). Improvement of agreement between theory and experiment, with respect to the case of the standard perturbative definition of alpha_s considered recently, is observed and the behavior of the higher twist terms in the next-to-next-to-leading-order is found to be confirming earlier studies on the subject., Comment: 22 pp, 8 figs

We present results for the universal anomalous dimension \gamma_{uni}(j) of Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills theory in the first four orders of perturbation theory., Comment: 21 pages; to be published in "Subtleties in Quantum Field Theories (Lev Lipatov Festschrift)", D. Diakonov, ed., Gatchina, 2010

New type of parametrization for parton distribution functions, based on an exact their Q^2-evolution at large and small x values, is constructed for valence quarks. It preserves exactly the low x and large x asymptotics of the solution of the DGLAP equation and obeys the Gross-Llewellyn-Smith sum rule., Comment: 6 pages, 1 table, 3 figures

We show results for the universal anomalous dimension gamma_{uni}(j) of Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills theory in the first three orders of perturbation theory. These expressions are obtained by extracting the most complicated contributions from the corresponding anomalous dimensions in QCD., Comment: 6 pages, published in the Proceedings of International Bogolyubov Conference "Problems of Theoretical and Mathematical Physics" (dedicated to the 100th anniversary of the birth of N.N. Bogolyubov (1909-1992)), Dubna, Russia, August 21 - 27, 2009 (Phys.Part.Nucl. in press)

Deep inelastic scattering data on F2 structure function from various fixed-target experiments were analyzed in the non-singlet approximation with a next-to-next-to-leading-order accuracy. The study of high statistics deep inelastic scattering data provided by BCDMS, SLAC, NMC and BFP collaborations was carried out separately for the first one and the rest, followed by a combined analysis done as well. For the coupling constant the following value \alpha_s(M_Z^2) = 0.1167 +/- 0.0021 (total exp.error) +0.0056/-0.0036(theor) was found, which in this approximation turns out to be slightly less than that obtained at the next-to-leading-order, as was generally anticipated. Ditto the theoretical uncertainties reduced with respect to those obtained in the case of the next-to-leading-order analysis thus confirming earlier observations., Comment: 23 pages, 6 figures, error in Eq.(8) corrected and Fig.1 changed accordingly, overall results kept intact

In the leading twist approximation of the Wilson operator product expansion with "frozen" and analytic strong coupling constants we show that Bessel-inspired behavior of the structure function F2 at small x, obtained for a flat initial condition in the DGLAP evolution equations, leads to good agreement with the deep inelastic scattering experimental data from HERA., Comment: 19 pages, 5 figures, published in the Proceedings of Workshop on Physics of Fundamental Interactions, Institute of High Energy Physics, Protvino, Russia, 22--25 December 2008 (Phys.Atom.Nucl. in press)

Recently, the O(alpha) and O(alpha^3 ln(alpha)) radiative corrections to the orthopositronium lifetime have been presented in closed analytical form, in terms of basic irrational numbers that can be evaluated numerically to arbitrary precision [Phys. Rev. Lett. 101, 193401 (2008)]. Here, we present the details of this calculation and reveal the nature of these new constants. We also list explicit transformation formulas for generalized polylogarithms of weight four, which may be useful for other applications., Comment: 23 pages, 1 figure, several misprints corrected, reference updated, accepted for publication in Phys. Rev. A

The spectrum of anomalous dimensions of gauge-invariant operators in maximally supersymmetric Yang-Mills theory is believed to be described by a long-range integrable spin chain model. We focus in this study on its $sl(2)$ subsector spanned by the twist-two single-trace Wilson operators, which are shared by all gauge theories, supersymmetric or not. We develop a formalism for the solution of the perturbative multiloop Baxter equation encoding their anomalous dimensions, using Wilson polynomials as basis functions and Mellin transform technique. These considerations yield compact results which allow analytical calculations of multiloop anomalous dimensions bypassing the use of the principle of maximal transcendentality. As an application of our method we analytically confirm the known four-loop result. We also determine the dressing part of the five-loop anomalous dimensions., Comment: 44 pages, v2: references added and typos fixed

Using the leading-twist approximation of the Wilson operator product expansion with "frozen" and analytic versions of the strong-coupling constant, we show that the Bessel-inspired behavior of the structure function F_2 and its slope\break partial ln(F_2)/partial ln(1/x) at small values of x, obtained for a flat initial condition in the DGLAP evolution equations, leads to good agreement with experimental data of deep-inelastic scattering at DESY HERA., Comment: new curves added to Figs. 1 and 2, minor changes to the text, accepted for publication in Phys. Lett. B

We consider the production of heavy-quark pairs in the collisions of polarized and unpolarized on-shell photons and present, in analytic form, the fully integrated total cross sections for total photon spins $J_z=0, \pm 2$ at next-to-leading-order in QCD. Phenomenological applications include $b\bar b$ production, which represents an irreducible background to standard-model intermediate-mass Higgs-boson production, as well as $t\bar t$ production., Comment: Revtex, 8 pages, 1 MATHEMATICA file, trivial typo for F_{16} in Eq. (4.6) corrected, one reference added, matches the published version

We study the heavy-quark contributions to the proton structure functions $F_2^i(x,Q^2)$ and $F_L^i(x,Q^2)$, with $i=c,b$, for small values of Bjorken's $x$ variable and provide compact formulas for their ratios $R_i=F_L^i/F_2^i$ that are useful to extract $F_2^i(x,Q^2)$ from measurements of the doubly differential cross section of inclusive deep-inelastic scattering at DESY HERA. Our approach naturally explains why $R_i$ is approximately independent of $x$ and the details of the parton distribution functions in the low-$x$ regime., Comment: 10 pages, 2 figures, in Pros. of II Helmholtz International Summer School "Heavy quark physics"

In the leading twist approximation of the Wilson operator product expansion with standard and "frozen" versions of strong copling constant we show that the Bessel-inspired behavior of the structure function $F_2$ at small $x$, obtained for a flat initial condition in the DGLAP evolution, leads to very good agreement with the deep inelastic scattering experimental data from HERA., Comment: 6 pages, 2 figures, in Proc. of XIX International Baldin Seminar "Relativistic Nuclear Physics and Quantum Chromodynamics"

We establish irrational constants, that contribute to the positronium lifetime at $O(\alpha)$ and $O(\alpha^2)$ order. In particular we show, that a new type of constants appear, which are not related to Euler--Zagier sums or multiple $\zeta$ values., Comment: Presented at 9th Workshop on Elementary Particle Theory: Loops and Legs in Quantum Field Theory, Sondershausen, 20-25 Apr 2008. 6 pages, 3 figures

We introduce a method to obtain the analytic solution of the higher-order Baxter equation for twist-two and twist-three operators of planar N=4 SYM. Our result proofs the conjectured formula for the three-loop anomalous dimension of twist-two operators. As such we derive the maximally transcendental part of the corresponding three-loop QCD result from the maximal supersymmetric gauge theory in four dimension purely by methods of integrability., Comment: 23 pages; v2: references added, appendix A improved

We present the O(alpha) and O(alpha^3 ln(alpha)) corrections to the total decay width of orthopositronium in closed analytic form, in terms of basic transcendental numbers, which can be evaluated numerically to arbitrary precision., Comment: 9 pages, 1 figure

We study the heavy-quark contribution to the proton structure functions F_2^i(x,Q^2) and F_L^i(x,Q^2), with i=c,b, for small values of Bjorken's x variable at next-to-lading order and provide compact formulas for their ratios R_i=F_L^i/F_2^i that are useful to extract F_2^i(x,Q^2) from measurements of the doubly differential cross section of inclusive deep-inelastic scattering at DESY HERA. Our approach naturally explains why R_i is approximately independent of x and the details of the parton distributions in the small-x regime., Comment: 11 pages, 1 figure

We use the unintegrated Parton Density Functions of the gluon obtained from a fit to measurements of the structure functions F2 and F2c at HERA to describe the experimental data for F2b, FL and FL at fixed W., Comment: To be published in Proceedings of DIS'07

We prove that the validity of the recently proposed dressed, asymptotic Bethe ansatz for the planar AdS/CFT system is indeed limited at weak coupling by operator wrapping effects. This is done by comparing the Bethe ansatz predictions for the four-loop anomalous dimension of finite-spin twist-two operators to BFKL constraints from high-energy scattering amplitudes in N=4 gauge theory. We find disagreement, which means that the ansatz breaks down for length-two operators at four-loop order. Our method supplies precision tools for multiple all-loop tests of the veracity of any yet-to-be constructed set of exact spectral equations. Finally we present a conjecture for the exact four-loop anomalous dimension of the family of twist-two operators, which includes the Konishi field., Comment: 20 pages, 2 tables, no figures; v2: references added, conjecture on exact four-loop twist-two result stated

We investigate the Eden-Staudacher equation for the anomalous dimension of the twist-2 operators at the large spin s in the N=4 super-symmetric gauge theory. This equation is reduced to a set of linear algebraic equations with the kernel calculated analytically. We prove that in perturbation theory the anomalous dimension is a sum of products of the Euler functions zeta(k) having the property of the maximal transcendentality with the coefficients being integer numbers. The radius of convergency of the perturbation theory is found. It is shown, that at g=infty the kernel has an essential singularity. The analytic properties of the solution of the Eden-Staudacher equation are investigated. In particular for the case of the strong coupling constant the solution has an essential singularity on the second sheet of the variable j appearing in its Laplace transformation. Similar results are derived also for the Beisert-Eden-Staudacher equation which includes the contribution from the phase related to the crossing symmetry of the underlying S-matrix. We show, that its singular solution at large coupling constants reproduces the anomalous dimension predicted from the string side of the AdS/CFT correspondence., Comment: 42 pages

First attempts are described to determine the unintegrated Parton Density Function of the gluon from a fit to measurements of the structure function $F_2(x,Q^2)$ and also $F_2^c(x,Q^2)$ measured at HERA. Reasonable descriptions of both structure functions are obtained, but the gluon densities determined are different., Comment: to be published in Proceedings of ICEHP 2006

We present in analytic form the matching conditions for the strong-coupling constant alpha_s^(n_f)(mu) at the flavor thresholds to four loops in the modified minimal-subtraction scheme. Taking into account the present knowledge on the coefficient beta_4 of the Callan-Symanzik beta function of quantum chromo-dynamics, we thus derive a five-loop formula for alpha_s^(n_f)(mu) together with appropriate relationships between the asymptotic scale parameters Lambda^(n_f) for different numbers of flavors n_f., Comment: 10 pages, 2 figures, to appear in Phys. Rev. Lett

Fully analytical results for the first two moments of the heavy-quark vacuum polarisation function at four loops in quantum chromo-dynamics are presented., Comment: 8 pages, 3 figures

In this paper we present a simple analytic expression for the (spin-averaged) neutrino-nucleon cross section for ultra-high energies at twist-2, obtained as the asymptotic limit of our previous findings. This expression gives values for the cross section in remarkable numerical agreement with the previous numerical evaluation in the energy region relevant for forthcoming neutrino experiments. Moreover, we discuss the role and the relevance of saturation and recombination effects in our approach, in comparison with other recent suggestions., Comment: 19 pages, 2 figures

We consider possible saturation effects in the structure function $F_L$ at fixed W in HERA energy range and in $b\bar b-$production at LHC energies in the framework of $k_T-$facrorization approach., Comment: 5 pages, 3 figures, prepared for the Proceedings of XXXV International Symposium on Multipaticle Dynamics 2005, Kromeriz, Czech Republic, Aug. 9-15, 2005

In this paper, we consider the two-loop sunset diagram with two different masses, m and M, at spacelike virtuality q^2 = -m^2. We find explicit representations for the master integrals and an analytic result through O(epsilon) in d=4-2epsilon space-time dimensions for the case of equal masses, m = M., Comment: 11 pages

An efficient method to calculate tadpole diagrams is proposed. Its capability is demonstrated by analytically evaluating two four-loop tadpole diagrams of current interest in the literature, including their $O(\epsilon)$ terms in $D=4-2\epsilon$ space-time dimensions., Comment: 12 pages, 3 figures

The results for structure function $F_L$, obtained in the $k_T$-factorization and collinear approaches, are compared with recent H1 experimental data at fixed $W$ values., Comment: 6 pages, 3 figures, Talk given at XVII Intern. Baldin Seminar "Relativistic Nuclear Physics and QCD", JINR, Sept. 27 - Oct. 2, 2004, Dubna, Russia

We present results for the three-loop universal anomalous dimension of Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills theory. These expressions are obtained by extracting the most complicated contributions from the three-loop anomalous dimensions in QCD. This result is in an agreement with the hypothesis of the integrability of N=4 Supersymmetric Yang-Mills theory in the context of AdS/CFT-correspondence., Comment: 8 pages. Talk given by A.V.K. at the Workshop Hadron Structure and QCD, Repino, St. Petersburg, Russia, 18-22 May 2004. To appear in the Proceedings, reference added

We derive the analytic continuation of the Mellin moments of deep inelastic structure functions at the next-to-next-to-leading order accuracy., Comment: 33 pages, 12 figures, minor changes

In this paper we present an analytic result for the evolution in $Q^2$ of the structure functions for the neutrino-nucleon interaction, valid at twist-2 in the region of small values of the Bjorken $x$ variable and for soft non-perturbative input. In the special case of flat initial conditions, we include in the calculation also the contribution of the twist-4 gluon recombination corrections, whose effect in the evolution is explicitly determined. Finally, we estimate the resulting charged-current neutrino-nucleon total cross section and discuss its behavior at ultra-high energies., Comment: 35 pages, 4 eps figures

We present results for the three-loop universal anomalous dimension of Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills model. These results are obtained by extracting the most complicated contributions from the three loop non-singlet anomalous dimensions in QCD which were calculated recently. Their singularities at j=1 agree with the predictions obtained from the BFKL equation for N=4 SYM in the next-to-leading order. The asymptotics of universal anomalous dimension at large j is in an agreement with the expectations based on an interpolation between weak and strong coupling regimes in the framework of the AdS/CFT correspondence., Comment: LaTeX file, 13 pages, no figures. Some corrections, additional remarks and references. In the last version the analysis of anomalous dimension at j -> 2 was improved

We use results for the structure functions $F_L$ for a gluon target having nonzero transverse momentum square at order $\alpha_s$, obtained in our previous paper, to compare with recent H1 experimental data for $F_L$ at fixwd W values and with collinear GRV predictions at LO and NLO approximation., Comment: 10 pages, 4 figures

Higher twist corrections to the structure function F_2 at small x are studied for the case of a flat initial condition for the twist-two QCD evolution in the next-to-leading order approximation. We present an analytical parameterization of the contributions from the twist-two and higher twist operators of the Wilson operator product expansion. Higher twist terms are evaluated using two different approaches, one motivated by BFKL and the other motivated by the renormalon formalism. The results of the latter approach are in very good agreement with deep inelastic scattering data from HERA., Comment: 46 pages, 9 figures, typeset using REVTeX. Misprints corrected, new results, discussions, references and acknowledgements added, 2 pictures replaced. The conclusions remain unchanged

We present the perturbative parts of the structure functions F_2^c and F_L^c for a gluon target having nonzero transverse momentum squared at order \alpha _s. The results of the double convolution (with respect to the Bjorken variable x and the transverse momentum) of the perturbative part and the unintegrated gluon densities are compared with HERA experimental data for F_2^c and F_L at low x values and with predictions of other approaches. The contribution from F_L^c structure function ranges 10\div30% of that of F_2^c at the HERA kinematical range., Comment: 15 pages, 4 figures, latex. Talk presented at the International School "Heavy Quark Physics", Dubna, Russia, May-June 2002

We study the Q^2 evolution of parton distributions at small x values, obtained in the case of flat initial conditions. The contributions of twist-two and (renormalon-type) higher-twist operators of the Wilson operator product expansion are taken into account. The results are in good agreement with deep inelastic scattering experimental data from HERA., Comment: 6 pages, 2 figures, latex. Talk presented at the XVI International Baldin Seminar on High Energy Physics Problems ``Relativistic Nuclear Physics and Quantum Chromodynamics'', Dubna, Russia, June 2002

We reanalyze deep inelastic scattering data of BCDMS Collaboration by including proper cuts of ranges with large systematic errors. We perform also the fits of high statistic deep inelastic scattering data of BCDMS, SLAC, NM and BFP Collaborations taking the data separately and in combined way and find good agreement between these analyses. We extract the values of both the QCD coupling constant \alpha_s(M^2_Z) up to NLO level and of the power corrections to the structure function F_2., Comment: 3 pages, 2 figures, latex. Talk presented at the 8th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2002), Moscow, Russia, June 2002

I discuss a progress in calculations of Feynman integrals based on the Gegenbauer Polynomial Technique and the Differential Equation Method., Comment: 2 pages, 1 figure, latex. Talk presented at the 8th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2002), Moscow, Russia, June 2002

We present the results of two-loop calculations of the anomalous dimension matrix for the Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills theory for polarized and unpolarized cases. This matrix can be transformed to a triangle form by the same similarity transformation as in the leading order. The eigenvalues of the anomalous dimension matrix are expressed in terms of an universal function with its argument shifted by integer numbers. In the conclusion we discuss relations between the weak and strong coupling regimes in the framework of the AdS/CFT correspondence., Comment: LaTeX file, 10 pages, no figures

We derive the DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory in the next-to-leading approximation. The eigenvalue of the BFKL kernel in this model turns out to be an analytic function of the conformal spin |n|. Its analytic continuation to negative |n| in the leading logarithmic approximation allows us to obtain residues of anomalous dimensions \gamma of twist-2 operators in the non-physical points j=0,-1,... from the BFKL equation in an agreement with their direct calculation from the DGLAP equation. Moreover, in the multi-color limit of the N=4 model the BFKL and DGLAP dynamics in the leading logarithmic approximation is integrable for an arbitrary number of particles. In the next-to-leading approximation the holomorphic separability of the Pomeron hamiltonian is violated, but the corresponding Bethe-Salpeter kernel has the property of a hermitian separability. The main singularities of anomalous dimensions \gamma at j=-r obtained from the BFKL and DGLAP equations in the next-to-leading approximation coincide but our accuracy is not enough to verify an agreement for residues of subleading poles., Comment: 45 pages, latex. In the last version the expression (16) for the t-channel partial wave of the process e+e- --> \mu+\mu- in the double-logarithmic approximation at QED is corrected and its derivation is given in the Appendix D