119205696
Full result for the three-loop static quark potential
The three-loop corrections to the potential of two heavy quarks are computed. Analytic results for the most complicated master integrals are presented.
15948639
S-bases as a tool to solve reduction problems for Feynman integrals
We 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 reduction algorithm which uses Grobner bases. New results obtained with its help for a family of three-loop Feynman integrals are outlined.
55043207
DESIGN OF THE NUCLOTRON BOOSTER IN THE NICA PROJECT
NICA is the new complex being constructed on the JINR aimed to provide collider experiments with ions up to uranium at energy of 3.5x3.5 GeV/u. The NICA layout includes Electron String Ion Source, 6.2 Mev/u linac, 600 MeV/u booster synchrotron, upgraded Nuclotron and ion collider with average luminosity of 10 27 cm -2 s -1 . The main goals of the Booster are the following: accumulation of 4·10 9 Au 32+ ions; acceleration of the heavy ions up to energy required for effective stripping; forming of the required beam emittance with electron cooling system. The present layout makes it possible to place the Booster having 211 m circumference and four fold symmetry lattice inside the yoke of the Synchrophasotron (shut down in 2002). The features of this booster, the requirement to the main synchrotron systems and their parameters are presented in this paper.
18145511
On the reduction of Feynman integrals to master integrals
The 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 Grobner bases seem to be inefficient. An essential modification designed especially for this problem has been w orked out. It has been already applied in two- and three-loop calculations. We are also suggesting to combine our method with the Laporta’s algorithm.
1669343
Applying Gröbner bases to solve reduction problems for Feynman integrals
We describe how Grobner 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. Our approach is based on a generalized Buchberger algorithm for constructing Grobner-type bases associated with polynomials of shift operators. We illustrate it through various examples of reduction problems for families of one- and two-loop Feynman integrals. We also solve the reduction problem for a family of integrals contributing to the three-loop static quark potential.
119320601
The Number of Master Integrals is Finite
For a fixed Feynman graph one can consider Feynman integrals with all possible powers of propagators and try to reduce them, by linear relations, to a finite subset of integrals, the so-called master integrals. Up to now, there are numerous examples of reduction procedures resulting in a finite number of master integrals for various families of Feynman integrals. However, up to now it was just an empirical fact that the reduction procedure results in a finite number of irreducible integrals. It this paper we prove that the number of master integrals is always finite.
119540272
Self-induced spectral splits in supernova neutrino fluxes
In the dense-neutrino region above the neutrino sphere of a supernova (r < or approx. 400 km), neutrino-neutrino refraction causes collective flavor transformations. They can lead to 'spectral splits' where an energy E{sub split} splits the transformed spectrum sharply into parts of almost pure but different flavors. Unless there is an ordinary MSW resonance in the dense-neutrino region, E{sub split} is determined by flavor-lepton number conservation alone. Spectral splits are created by an adiabatic transition between regions of large and small neutrino density. We solve the equations of motion in the adiabatic limit explicitly and provide analytic expressions for a generic example.
14713509
Neutrino mixing and quark-lepton complementarity
As a result of the identification of the solution to the solar neutrino problem, a rather precise relation ${\ensuremath{\theta}}_{\mathrm{s}\mathrm{u}\mathrm{n}}+{\ensuremath{\theta}}_{C}=\ensuremath{\pi}/4$ between the leptonic 1-2 mixing angle ${\ensuremath{\theta}}_{\mathrm{s}\mathrm{u}\mathrm{n}}$ and the Cabibbo angle has emerged. It would mean that the lepton and the quark mixing angles add up to the maximal, suggesting a deep structure by which quarks and leptons are interrelated. We refer to the relation as ``quark-lepton complementarity'' (QLC) in this paper. We formulate general conditions under which the QLC relation is realized. We then present several scenarios which lead to the relation and elaborate on phenomenological consequences which can be tested by the future experiments. We also discuss implications of the QLC relation for the quark-lepton symmetry and the mechanism of neutrino mass generation.
119346649
Precise analytical description of the Earth matter effect on oscillations of low energy neutrinos
We present a formalism for the matter effects in the Earth on low energy neutrino fluxes which is both accurate and has all the advantages of a full analytic treatment. The oscillation probabilities are calculated up to the second order term in $ϵ(x)\ensuremath{\equiv}2V(x)E/\ensuremath{\Delta}{m}^{2}$, where $V(x)$ is the neutrino potential at position $x$. We show the absence of large undamped phases which makes the expansion in $ϵ$ well behaved. An improved expansion is presented in terms of the variation of $V(x)$ around a suitable mean value which allows one to treat energies up to those relevant for supernova neutrinos. We discuss also the case of three-neutrino mixing.
125403690
THE ADRON APPARATUS FOR RESEARCHING THE PRIMARY COSMIC RADIATION AND THE CHARACTERISTICS OF NUCLEAR INTERACTIONS IN THE ATMOSPHERE
6397128
Probing the neutrino mass hierarchy and the 13-mixing with supernovae
We consider in detail the effects of the 13-mixing (sin2?13) and of the type of mass hierarchy/ordering (sign[?m213]) on neutrino signals from the gravitational collapses of stars. The observables (characteristics of the energy spectra of ?e and e events) sensitive to sin2?13 and sign[?m213] have been calculated. They include the ratio of average energies of the spectra, rE?E/?, the ratio of widths of the energy distributions, r???/, the ratios of total numbers of ?e and e events at low energies, S, and in the high energy tails, Rtail. We construct and analyse scatter plots which show the predictions for the observables for different intervals of sin2?13 and signs of ?m213, taking into account uncertainties in the original neutrino spectra, the star density profile, etc. Regions in the space of observables rE, r?, S, Rtail exist in which certain mass hierarchy and intervals of sin2?13 can be identified or discriminated. We elaborate on the method of the high energy tails in the spectra of events. The conditions are formulated for which sin2?13 can be (i) measured, (ii) restricted from below, (iii) restricted from above. We comment on the possibility to determine sin2?13 using the time dependence of the signals due to the propagation of the shock wave through the resonance layers of the star. We show that the appearance of the delayed Earth matter effect in one of the channels (?e or e) in combination with the undelayed effect in the other channel will allow us to identify the shock wave appeareance and determine the mass hierarchy.