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The Mikheyev-Smirnov-Wolfenstein (MSW) EffectJan 31 2019Feb 04 2019Developments of main notions and concepts behind the MSW effect (1978 - 1985) are described. They include (i) neutrino refraction, matter potential, and evolution equation in matter, (ii) mixing in matter, resonance and level crossing; (iii) adiabaticity ... More

Leptonic CP violation: zero, maximal or between the two extremesOct 25 2006Jan 21 2007Discovery of the CP-violation in the lepton sector is one of the challenges of the particle physics. We search for possible principles, symmetries and phenomenological relations that can lead to particular values of the CP-violating Dirac phase, $\delta$. ... More

On the Effective Mass of the Electron Neutrino in Beta DecayNov 21 2002Mar 17 2003In the presence of mixing between massive neutrino states, the distortion of the electron spectrum in beta decay is, in general, a function of several masses and mixing angles. For $3\nu$-schemes which describe the solar and atmospheric neutrino data, ... More

Leptonic Unitarity Triangle and CP-violationJan 12 2002Jan 28 2002The area of the unitarity triangle is a measure of CP-violation. We introduce the leptonic unitarity triangles and study their properties. We consider the possibility of reconstructing the unitarity triangle in future oscillation and non-oscillation experiments. ... More

Fundamental solution and the weight functions of the transient problem on a semi-infinite crack propagating in a half-planeOct 05 2015The two-dimensional transient problem that is studied concerns a semi-infinite crack in an isotropic solid comprising an infinite strip and a half-plane joined together and having the same elastic constants. The crack propagates along the interface at ... More

Testing the Solar Neutrino Conversion with Atmospheric NeutrinosFeb 11 1999Feb 12 1999Neutrino oscillations with parameters relevant for the large mixing solution of the solar neutrino problem ($\Delta m^2_{21} = (2 - 20) \cdot 10^{-5}$ eV$^2$, $\sin^2 2\theta_{12} > 0.65$) can lead to observable (up to 10 - 12 %) excess of the e-like ... More

Neutrino Mass and New PhysicsMar 16 2006Dec 20 2006We review the present state of and future outlook for our understanding of neutrino masses and mixings. We discuss what we think are the most important perspectives on the plausible and natural scenarios for neutrinos and what may have the most promise ... More

Neutrino Mass Spectrum with $ν_μ$ $\to$ $ν_s$ Oscillations of Atmospheric NeutrinosDec 22 1997May 04 1998We consider the ``standard'' spectrum of the active neutrinos (characterized by strong mass hierarchy and small mixing) with additional sterile neutrino, $\nu_s$. The sterile neutrino mixes strongly with the muon neutrino, so that $\nu_{\mu} \leftrightarrow ... More

View on N-dimensional spherical harmonics from the quantum mechanical Pöschl-Teller potential wellJan 20 2019In this paper we propose an approach of obtaining of N-dimensional spherical harmonics based exclusively on the methods of solutions of differential equations and the use of the special functions properties. We deduce the Laplace-Beltrami operator on ... More

Solar neutrinos and grand unificationJul 24 1997Nov 28 1997We consider the Grand Unification (GU) scenario for neutrino masses which is based on the see-saw mechanism with the mass of the heaviest right handed (RH) neutrino at the GU-scale: $M_3 \sim \Lambda_{GU}$, and on the quark-lepton symmetry for fermions ... More

Neutrino Mass Spectrum and Future Beta Decay ExperimentsMay 11 2001May 26 2001We study the discovery potential of future beta decay experiments on searches for the neutrino mass in the sub-eV range, and, in particular, KATRIN experiment with sensitivity $m > 0.3$ eV. Effects of neutrino mass and mixing on the beta decay spectrum ... More

Neutrino mass spectrum and neutrinoless double beta decayMar 22 2000Oct 08 2000The relations between the effective Majorana mass of the electron neutrino, $m_{ee}$, responsible for neutrinoless double beta decay, and the neutrino oscillation parameters are considered. We show that for any specific oscillation pattern $m_{ee}$ can ... More

Parametric Resonance in Oscillations of Atmospheric Neutrinos?Mar 21 1998We consider a solution of the atmospheric neutrino problem based on oscillations of muon neutrinos to sterile neutrinos: $\nu_{\mu}$ $\leftrightarrow$ $\nu_s$. The zenith angle ($\Theta$) dependences of the neutrino and upward-going muon fluxes in presence ... More

Neutrino mass, mixing and discrete symmetriesMay 21 2013Status of the discrete symmetry approach to explanation of the lepton masses and mixing is summarized in view of recent experimental results, in particular, establishing relatively large 1-3 mixing. The lepton mixing can originate from breaking of discrete ... More

On the reduction of Feynman integrals to master integralsJul 26 2007The reduction of Feynman integrals to master integrals is an algebraic problem that requires algorithmic approaches at the modern level of calculations. Straightforward applications of the classical Buchberger algorithm to construct Groebner bases seem ... More

Applying Groebner Bases to Solve Reduction Problems for Feynman IntegralsSep 30 2005Jan 20 2006We describe how Groebner bases can be used to solve the reduction problem for Feynman integrals, i.e. to construct an algorithm that provides the possibility to express a Feynman integral of a given family as a linear combination of some master integrals. ... More

S-bases as a tool to solve reduction problems for Feynman integralsJun 22 2006We suggest a mathematical definition of the notion of master integrals and present a brief review of algorithmic methods to solve reduction problems for Feynman integrals based on integration by parts relations. In particular, we discuss a recently suggested ... More

On the Resolution of Singularities of Multiple Mellin-Barnes IntegralsJan 04 2009One of the two existing strategies of resolving singularities of multifold Mellin-Barnes integrals in the dimensional regularization parameter, or a parameter of the analytic regularization, is formulated in a modified form. The corresponding algorithm ... More

Two-Loop Static QCD Potential for General Colour StateDec 06 2004In this letter, we extend the known results for the QCD potential between a static quark and its antiquark by computing the two-loop corrections to the colour-octet state.

Hepp and Speer Sectors within Modern Strategies of Sector DecompositionDec 26 2008Hepp and Speer sectors were successfully used in the sixties and seventies for proving mathematical theorems on analytically or/and dimensionally regularized and renormalized Feynman integrals at Euclidean external momenta. We describe them within recently ... More

Decay of charged fields in de Sitter spacetimeDec 15 2004May 12 2005We study the decay of charged scalar and spinor fields around Reissner-Nordstrom black holes in de Sitter spacetime through calculations of quasinormal frequencies of the fields. The influence of the parameters of the black hole (charge, mass), of the ... More

Finalizing the proof of AGT relations with the help of the generalized Jack polynomialsJul 09 2013Aug 04 2013Original proofs of the AGT relations with the help of the Hubbard-Stratanovich duality of the modified Dotsenko-Fateev matrix model did not work for beta different from one, because Nekrasov functions were not properly reproduced by Selberg-Kadell integrals ... More

FIRE4, LiteRed and accompanying tools to solve integration by parts relationsFeb 24 2013New features of the Mathematica code FIRE are presented. In particular, it can be applied together with the recently developed code LiteRed by Lee in order to provide an integration by parts reduction to master integrals for quite complicated families ... More

The application of the electrodynamics of Born to the theory of the propagation of light in electromagnetic fields [Engl. transl. of kand. diss. (Ph.D. thesis), 1936]Aug 22 2017English translation of a Russian Ph.D. thesis from 1936. No original abstract, translator's abstract: The thesis consists of two chapters. In chapter I, general requirements to be imposed on any nonlinear electrodynamics and their implementation in the ... More

Counting the local fields in SG theory.Jan 16 1995Jan 18 1995In terms of the form factor bootstrap we describe all the local fields in SG theory and check the agreement with the free fermion case. We discuss the interesting structure responsible for counting the local fields.

Remarks on deformed and undeformed Knizhnik-Zamolodchikov equationsOct 09 1992Oct 21 1992Deformed and undeformed KZ equations are considered for $k=0$. It is shown that they allow the same number of solutions, one being the asymptotics of others. Essential difference in analitical properties of the solutions is explained.

Analytical Result for Dimensionally Regularized Massless On-Shell Planar Triple BoxMay 13 2003The dimensionally regularized massless on-shell planar triple box Feynman diagram with powers of propagators equal to one is analytically evaluated for general values of the Mandelstam variables s and t in a Laurent expansion in the parameter \ep=(4-d)/2 ... More

Analytical Result for Dimensionally Regularized Massless Master Non-planar Double Box with One Leg off ShellNov 03 2000Dec 22 2000The dimensionally regularized massless non-planar double box Feynman diagram with powers of propagators equal to one, one leg off the mass shell, i.e. with p_1^2=q^2\neq 0, and three legs on shell, p_i^2=0, i=2,3,4, is analytically calculated for general ... More

Asymptotic Expansions of Feynman Integrals on the Mass Shell in Momenta and MassesAug 21 1997A brief review of recent results on asymptotic expansions of Feynman integrals on the mass shell in momenta and masses and their application to 2-loop calculations is presented.

Differential Renormalization, the Action Principle and Renormalization Group CalculationsDec 07 1994General prescriptions of differential renormalization are presented. It is shown that renormalization group functions are straightforwardly expressed through some constants that naturally arise within this approach. The status of the action principle ... More

Neutrino oscillations: what is magic about the "magic" baseline?Oct 16 2006Oct 30 2006Physics interpretation of the ``magic'' baseline, $L_{magic}$, that can play important role in future oscillation experiments is given. The ``magic'' baseline coincides with the refraction length, $l_0$. The latter, in turn, approximately equals the oscillation ... More

An Algorithm to Construct Groebner Bases for Solving Integration by Parts RelationsFeb 09 2006This paper is a detailed description of an algorithm based on a generalized Buchberger algorithm for constructing Groebner-type bases associated with polynomials of shift operators. The algorithm is used for calculating Feynman integrals and has proven ... More

Towards the Solution of the Solar Neutrino ProblemSep 22 1998Sep 23 1998We discuss various aspects of the solar neutrino spectrum distortion and time variations of fluxes. (i) Oscillations of neutrinos which cross the mantle and the core of the Earth can be parametrically enhanced. The parametric effect gives correct physical ... More

Vector leptoquark mass limits and branching ratios of $ K_L^0, B^0, B_s \to l^+_i l^-_j $ decays with account of fermion mixing in leptoquark currentsJan 09 2018Jan 19 2018The contributions of the vector leptoquarks of Pati-Salam type to the branching ratios of $K_L^0, B^0, B_s \to l \, l^{\prime}$ decays are calculated with account of the fermion mixing in the leptoguark currents of the general type. Using the general ... More

Riddle of the Neutrino MassFeb 16 2015We discuss some known approaches and results as well as few new ideas concerning origins and nature of neutrino mass. The key issues include (i) connections of neutrino and charged fermions masses, relation between masses and mixing, energy scale of new ... More

On mass limits for leptoquarks from $ K_L^0 \to e^{\mp} μ^{\pm}, B^0 \to e^{\mp} τ^{\pm} $ decaysDec 28 2006Mar 04 2007The contributions of the scalar leptoquark doublets into widths of the $K^0_L \to e^{\mp} \mu^{\pm}$, $B^0 \to e^{\mp} \tau^{\pm}$ decays are calculated in MQLS model with Higgs mechanism of the quark-lepton mass splitting. The resulted mass limits for ... More

Neutrinos: "...annus mirabilis"Feb 25 2004Main results and achievements of 2002 - 2003 in neutrino physics are summarized. The field moves quickly to new phase with clear experimental and phenomenological programs, and with new theoretical puzzle which may lead us to discoveries of the fundamental ... More

Lepton Mixing: Small, Large, Maximal?Jul 10 1999The SuperKamiokande data on atmospheric neutrinos imply that $\nu_{\mu}$ has large (or even maximal) mixing. It is still open question whether this mixing is the flavor one or mixing with singlet state (sterile neutrino). Several tests exist to establish ... More

The homology of iterated loop spacesOct 06 2000The singular chain complex of the iterated loop space is expressed in terms of the cobar construction. After that we consider the spectral sequence of the cobar construction and calculate its first term over Z/p-coefficients and over a field of characteristic ... More

High-frequency hopping conductivity in the quantum Hall effect regime: Acoustical studiesMar 07 2000The high-frequency conductivity of Si delta-doped GaAs/AlGaAs heterostructures is studied in the integer quantum Hall effect (QHE) regime, using acoustic methods. Both the real and the imaginary parts of the complex conductivity are determined from the ... More

Analytical Evaluation of Double BoxesSep 16 2002Recent results on the analytical evaluation of double-box Feynman integrals and the corresponding methods of evaluation are briefly reviewed.

Analytical Result for Dimensionally Regularized Massive On-Shell Planar Double BoxNov 13 2001The dimensionally regularized master planar double box Feynman diagram with four massive and three massless lines, powers of propagators equal to one, all four legs on the mass shell, i.e. with p_i^2=m^2, i=1,2,3,4, is analytically evaluated for general ... More

`Strategy of Regions': Expansions of Feynman Diagrams both in Euclidean and Pseudo-Euclidean RegimesJan 15 2001The strategy of regions [1] turns out to be a universal method for expanding Feynman integrals in various limits of momenta and masses. This strategy is reviewed and illustrated through numerous examples. In the case of typically Euclidean limits it is ... More

Four-dimensional integration by parts with differential renormalization as a method of evaluation of Feynman diagramsMay 22 1996It is shown how strictly four-dimensional integration by parts combined with differential renormalization and its infrared analogue can be applied for calculation of Feynman diagrams.

E_\infty-structure and differentials of the Adams spectral sequenceJul 02 2001Jul 11 2001The Adams spectral sequence was invented by J.F.Adams fifty years ago for calculations of stable homotopy groups of topological spaces and in particular of spheres. The calculation of differentials of this spectral sequence is one of the most difficult ... More

Analytical Result for Dimensionally Regularized Massless Master Double Box with One Leg off ShellJul 04 2000Nov 03 2000The dimensionally regularized massless double box Feynman diagram with powers of propagators equal to one, one leg off the mass shell, i.e. with non-zero q^2=p_1^2, and three legs on shell, p_i^2=0, i=2,3,4, is analytically calculated for general values ... More

Asymptotic expansions of two-loop Feynman diagrams in the Sudakov limitMar 18 1997Recently presented explicit formulae for asymptotic expansions of Feynman diagrams in the Sudakov limit are applied to typical two-loop diagrams. For a diagram with one non-zero mass these formulae provide an algorithm for analytical calculation of all ... More

Gauge-Invariant Differential Renormalization: Abelian CaseMay 22 1996A new version of differential renormalization is presented. It is based on pulling out certain differential operators and introducing a logarithmic dependence into diagrams. It can be defined either in coordinate or momentum space, the latter being more ... More

Structure of Matrix Elements in Quantum Toda ChainMay 12 1998We consider the quantum Toda chain using the method of separation of variables. We show that the matrix elements of operators in the model are written in terms of finite number of ``deformed Abelian integrals''. The properties of these integrals are discussed. ... More

On localization properties of Fourier transforms of hyperfunctionsNov 09 2008In [Adv. Math. 196 (2005) 310-345] the author introduced a new generalized function space $\mathcal U(R^k)$ which can be naturally interpreted as the Fourier transform of the space of Sato's hyperfunctions on $R^k$. It was shown that all Gelfand--Shilov ... More

The MSW effect and Solar NeutrinosMay 09 2003The MSW (Mikheyev-Smirnov-Wolfenstein) effect is the effect of transformation of one neutrino species (flavor) into another one in a medium with varying density. Three basic elements of the effect include: the refraction of neutrinos in matter, the resonance ... More

Bounds on scalar leptoquark masses from S, T, U parameters in the minimal four-color quark-lepton symmetry modelMay 15 1998The contributions into radiative correction parameters S, T, U from the scalar leptoquarks are calculated in the minimal gauge model with the four-color quark-lepton symmetry. It is shown that the contributions into T and U from the scalar leptoquark ... More

Algorithm FIRE -- Feynman Integral REductionJul 21 2008Aug 02 2008The recently developed algorithm FIRE performs the reduction of Feynman integrals to master integrals. It is based on a number of strategies, such as applying the Laporta algorithm, the s-bases algorithm, region-bases and integrating explicitly over loop ... More

Mass limits for scalar and gauge leptoquarks from $ K_L^0 \to e^{\mp} μ^{\pm}, B^0 \to e^{\mp} τ^{\pm} $ decaysMay 02 2007The contributions of scalar and gauge leptoquarks into widths of $K^0_L \to e^{\mp} \mu^{\pm}$, $B^0 \to e^{\mp} \tau^{\pm}$ decays are calculated in the models with the vectorlike and chiral four color symmetry and with the Higgs mechanism of the quark-lepton ... More

Fourier transformation of Sato's hyperfunctionsJan 14 2004Sep 30 2004A new generalized function space in which all Gelfand-Shilov classes $S^{\prime 0}_\alpha$ ($\alpha>1$) of analytic functionals are embedded is introduced. This space of {\it ultrafunctionals} does not possess a natural nontrivial topology and cannot ... More

Bounds on scalar leptoquark and scalar gluon masses from S, T, U in the minimal four color symmetry modelFeb 25 2002The contributions into radiative correction parameters S, T, U from scalar leptoquark and scalar gluon doublets are investigated in the minimal four color symmetry model. It is shown that the current experimental data on S, T, U allow the scalar leptoquarks ... More

Neutrino mass spectrum and lepton mixingOct 10 2000The program of reconstruction of the neutrino mass and flavor spectrum is outlined and the present status of research is summarized. We describe the role of future solar and atmospheric neutrino experiments, detection of the Galactic supernovae and double ... More

Reconstructing Neutrino Mass SpectrumJan 03 1999Reconstruction of the neutrino mass spectrum and lepton mixing is one of the fundamental problems of particle physics. In this connection we consider two central topics: (i) the origin of large lepton mixing, (ii) possible existence of new (sterile) neutrino ... More

The Approximate Bilinear Algorithm of Length 46 for Multiplication of 4 x 4 MatricesNov 20 2014We propose the arbitrary precision approximate (APA) bilinear algorithm of length 46 for multiplication of 4 x 4 and 4 x 4 matrices. The algorithm has polynomial order 3 and 352 nonzero coefficients from total 2208.

Solar neutrinos: Oscillations or No-oscillations?Sep 08 2016The Nobel prize in physics 2015 has been awarded "... for the discovery of neutrino oscillations which show that neutrinos have mass". While SuperKamiokande (SK), indeed, has discovered oscillations, SNO observed effect of the adiabatic (almost non-oscillatory) ... More

Baxter equations and Deformation of Abelian DifferentialsFeb 07 2003In this paper the proofs are given of important properties of deformed Abelian differentials introduced earlier in connection with quantum integrable systems. The starting point of the construction is Baxter equation. In particular, we prove Riemann bilinear ... More

Infinite Quantum Group Symmetry of Fields in Massive 2D Quantum Field TheoryAug 20 1991Starting from a given S-matrix of an integrable quantum field theory in $1+1$ dimensions, and knowledge of its on-shell quantum group symmetries, we describe how to extend the symmetry to the space of fields. This is accomplished by introducing an adjoint ... More

Some recent results on evaluating Feynman integralsJan 31 2006Some recent results on evaluating Feynman integrals are reviewed. The status of the method based on Mellin-Barnes representation as a powerful tool to evaluate individual Feynman integrals is characterized. A new method based on Groebner bases to solve ... More

Asymptotic Expansions of Feynman Diagrams on the Mass Shell in Momenta and MassesAug 22 1996Jan 08 1997Explicit formulae for asymptotic expansions of Feynman diagrams in typical limits of momenta and masses with external legs on the mass shell are presented.

Evaluating double and triple (?) boxesSep 25 2002Sep 26 2002A brief review of recent results on analytical evaluation of double-box Feynman integrals is presented. First steps towards evaluation of massless on-shell triple-box Feynman integrals within dimensional regularization are described. The leading power ... More

Stasheff structures and differentials of the Adams spectral sequenceOct 23 2000The Adams spectral sequence was invented by J.F.Adams almost fifty years ago for calculations of stable homotopy groups of topological spaces and in particular of spheres. The calculation of differentials of this spectral sequence is one of the most difficult ... More

Euler characteristics of theta divisors of Jacobians for spectral curvesDec 27 2000May 30 2001We show how to calculate the Euler characteristic of an affine Jacobi variety of a spectral curve from its defining equations.

On kernel theorems for (LF)-spacesDec 25 2006A convenient technique for proving kernel theorems for (LF)-spaces (countable inductive limits of Frechet spaces)is developed. The proposed approach is based on introducing a suitable modification of the functor of the completed inductive topological ... More

Elliptic solitons and Heun's equationSep 20 2001Oct 19 2001We find a new class of algebraic geometric solutions of Heun's equation with the accessory parameter belonging to a hyperelliptic curve. Dependence of these solutions from the accessory parameter as well as their relation to Heun's polynomials is studied. ... More

The Minimal Quark-Lepton Symmetry Model and the Limit on Z'-massMar 06 1995A minimal extension of the Standard Model containing the four-color quark-lepton symmetry is proposed and discussed. The existence of a rather light extra $Z'$-boson originated from the four-color quark-lepton symmetry is shown to be compatible with the ... More

Generators of von Neumann algebras associated with spectral measuresNov 24 2011Feb 03 2013Let $P_E$ be the set of all values of a spectral measure $E$ and $A(P_E)$ be the smallest von Neumann algebra containing $P_E$. We give a simple description of all sets of generators of $A(P_E)$ in terms of the integrals with respect to $E$. The treatment ... More

Signature of entangled eigenstates in the magnetic response of two coupled flux qubitsDec 24 2003We study dissipative dynamics and a magnetic response of two coupled flux qubits interacting with a high quality tank in the framework of the impedance measurement technique (IMT). It is shown that the observation of the difference between a sum of IMT ... More

Bounds on scalar leptoquark and scalar gluon masses from current data on S, T, USep 28 2002The contributions into radiative correction parameters S, T, U from scalar leptoquark and scalar gluon doublets are investigated in the minimal four color symmetry model. It is shown that the existence of the relatively light scalar leptoquarks and scalar ... More

Solar Neutrinos: Interpretation of ResultsSep 12 2002Recent SNO results give strong evidence that the solar neutrinos undergo the flavor conversion. Main issue now is the identification of the mechanism of conversion. The LMA MSW solution with $\Delta m^2 = (5 - 7) \cdot 10^{-5}$ eV$^2$, $\tan^2 \theta ... More

Towards Euclidean Theory of Infrared Singular Quantum FieldsMay 18 2002Jan 21 2003A new generalized formulation of the spectral condition is proposed for quantum fields with highly singular infrared behavior whose vacuum correlation functions are well defined only under smearing with analytic test functions in momentum space. The Euclidean ... More

Neutrino Conversion and Neutrino AstrophysicsNov 10 1998We consider main ingredients which determine neutrino transformations in media. Strong transformations relevant for the astrophysics can be due to large depth oscillations, resonance conversion, parametric resonance effect, interplay of oscillations and ... More

Solar neutrinos: Oscillations or No-oscillations?Sep 08 2016Sep 19 2017The Nobel prize in physics 2015 has been awarded "... for the discovery of neutrino oscillations which show that neutrinos have mass". While SuperKamiokande (SK), indeed, has discovered oscillations, SNO observed effect of the adiabatic (almost non-oscillatory) ... More

Separation of variables for quantum integrable models related to $ U_q(\hat{sl}_N) $Sep 18 2001In this paper we construct separated variables for quantum integrable models related to the algebra $U_q(\hat{sl}_N)$. This generalizes the results by Sklyanin for $N=2,3$.

A new set of exact form factorsDec 06 1993Jan 07 1994Some mistaken reasonings at the end of the paper omitted.

Form Factors, deformed Knizhnik-Zamolodchikov equations and finite-gap integrationOct 09 1992Oct 15 1992We study the limit of asymptotically free massive integrable models in which the algebra of nonlocal charges turns into affine algebra. The form factors of fields in that limit are described by KZ equations on level 0. We show the limit to be connected ... More

What are we quantizing in integrable field theory?Jul 15 1993We continue study of the connection of classical limit of integrable asymptotically free field theory to the finite-gap solutions of classical integrable equations. In the limit the momenta of particles turn into the moduli of Riemann surfaces while their ... More

The Leading Power Regge Asymptotic Behaviour of Dimensionally Regularized Massless On-Shell Planar Triple BoxSep 17 2002The leading power asymptotic behaviour of the dimensionally regularized massless on-shell planar triple box diagram in the Regge limit t/s -> 0 is analytically evaluated.

Problems of the Strategy of RegionsJul 23 1999Problems that arise in the application of general prescriptions of the so-called strategy of regions for asymptotic expansions of Feynman integrals in various limits of momenta and masses are discussed with the help of characteristic examples of two-loop ... More

Analytical Result for Dimensionally Regularized Massless On-shell Double BoxMay 12 1999Jun 10 1999The dimensionally regularized massless on-shell double box Feynman diagram with powers of propagators equal to one is analytically evaluated for general values of the Mandelstam variables s and t. An explicit result is expressed either in terms of polylogarithms ... More

Recent Developments in Neutrino PhenomenologyFeb 05 2007The first phase of studies of the neutrino mass and mixing is essentially over. The outcome is the discovery of non-zero neutrino mass and determination of the dominant structure of the lepton mixing matrix. In some sense this phase was very simple, and ... More

Eigenfunction expansions for the Schrödinger equation with inverse-square potentialAug 31 2015Jun 03 2016We consider the one-dimensional Schr\"odinger equation $-f"+q_\kappa f = Ef$ on the positive half-axis with the potential $q_\kappa(r)=(\kappa^2-1/4)r^{-2}$. For each complex number $\vartheta$, we construct a solution $u^\kappa_\vartheta(E)$ of this ... More

Reduction by symmetries in singular quantum-mechanical problems: general scheme and application to Aharonov-Bohm modelNov 19 2014Dec 23 2015We develop a general technique for finding self-adjoint extensions of a symmetric operator that respect a given set of its symmetries. Problems of this type naturally arise when considering two- and three-dimensional Schr\"odinger operators with singular ... More

Neutrino 2012: Outlook - theoryOct 15 2012Ongoing developments in theory and phenomenology are related to the measured large value of 1-3 mixing and indications of significant deviation of the 2-3 mixing from maximal one. "Race" for the mass hierarchy has started and there is good chance that ... More

Neutrino masses and mixing: Leptons versus QuarksApr 25 2006Comparison of properties of quark and leptons as well as understanding their similarities and differences is one of the milestones on the way to underlying physics. Several observations, if not accidental, can strongly affect the implications: (i) nearly ... More

Solar neutrino spectroscopy (before and after SuperKamiokande)Nov 25 1996Results of solar neutrino spectroscopy based on data from four experiments are presented. Perspectives related to forthcoming experiments are discussed. Implications of the results for neutrino properties are considered.

Solar Neutrinos: Expecting 1996Sep 26 1995These are remarks (mainly on the solar neutrinos) written in anticipation of 1996 - the year which can be crucial for the neutrino physics. Recent results on solar neutrinos are discussed. The topics include: (solar) model independent approach to the ... More

Solar Neutrinos and Lepton MixingJul 06 1995With latest experimental data the solar neutrino problem enters new phase when crucial aspects of the problem can be formulated in an essentially (solar) model independent way. Original neutrino fluxes can be considered as free parameters to be found ... More

Minimal Quark-Lepton Symmetry Model and Possible Limits on Z'-Mass from TRISTAN and Lep200Sep 30 1994A minimal extension of the Standard Model containing the four-color quark-lepton symmetry is discussed. Some features of an additional $Z'$-boson originated from this symmetry are investigated and the limits on $m_{Z'}$ from the current TRISTAN data and ... More

A Gronwall-type Trigonometric InequalityOct 03 2017May 06 2018We prove that the absolute value of the $n$th derivative of $\cos(\sqrt{x})$ does not exceed $n!/(2n)!$ for all $x>0$ and $n = 0,1,\ldots$ and obtain a natural generalization of this inequality involving the analytic continuation of $\cos(\sqrt{x})$.

Localization properties of highly singular generalized functionsDec 19 2005May 24 2007We study the localization properties of generalized functions defined on a broad class of spaces of entire analytic test functions. This class, which includes all Gelfand--Shilov spaces $S^\beta_\alpha(\R^k)$ with $\beta<1$, provides a convenient language ... More

On the deformation of abelian integralsJan 02 1995We consider the deformation of abelian integrals which arose from the study of SG form factors. Besides the known properties they are shown to satisfy Riemann bilinear identity. The deformation of intersection number of cycles on hyperelliptic curve is ... More

Dual Baxter equations and quantization of Affine JacobianJan 21 2000A quantum integrable model is considered which describes a quantization of affine hyper-elliptic Jacobian. This model is shown to possess the property of duality: a dual model with inverse Planck constant exists such that the eigen-functions of its Hamiltonians ... More

Quasi-classical Study of Form Factors in Finite VolumeFeb 19 1998We construct the quasi-classical approximation of the form factors in finite volume using the separation of variables. The latter is closely related to the Baxter equation.

Asymptotic Expansions in Momenta and Masses and Calculation of Feynman DiagramsDec 07 1994General results on asymptotic expansions of Feynman diagrams in momenta and/or masses are reviewed. It is shown how they are applied for calculation of massive diagrams.

Evaluating multiloop Feynman integrals by Mellin-Barnes representationJun 04 2004The status of analytical evaluation of double and triple box diagrams is characterized. The method of Mellin-Barnes representation as a tool to evaluate master integrals in these problems is advocated. New MB representations for massive on-shell double ... More