14611410
Four Loop Massless Propagators: a Numerical Evaluation of All Master Integrals
Abstract We present numerical results which are needed to evaluate all non-trivial master integrals for four-loop massless propagators, confirming the recent analytic results of Baikov and Chetyrkin (2010) [1] and evaluating an extra order in e expansion for each master integral.
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.
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.
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.
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.
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.
16064284
Paradoxes of neutrino oscillations
Despite the theory of neutrino oscillations being rather old, some of its basic issues are still being debated in the literature. We discuss a number of such issues, including the relevance of the “same energy” and “same momentum” assumptions, the role of quantum-mechanical uncertainty relations in neutrino oscillations, the dependence of the coherence and localization conditions that ensure the observability of neutrino oscillations on neutrino energy and momentum uncertainties, the question of (in)dependence of the oscillation probabilities on the neutrino production and detection processes, and the applicability limits of the stationary-source approximation. We also develop a novel approach to calculation of the oscillation probability in the wave-packet approach, based on the summation/integration conventions different from the standard one, which allows a new insight into the “same energy” vs. “same momentum” problem. We also discuss a number of apparently paradoxical features of the theory of neutrino oscillations.
43358400
Neutrino mass spectrum and lepton mixing
Abstract The 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 beta decay searches in accomplishing this program. The LSND result and four-neutrino mass spectra are considered in connection with recent searches for the sterile components in the solar and atmospheric neutrino fluxes.
119297880
Theory of neutrino masses and mixing
In spite of enormous experimental progress in determination of the neutrino parameters, theory of neutrino mass and mixing is still on the cross-roads. Guidelines could be (i) the connection between zero neutrino charges (and therefore a possibility to be Majorana particle), smallness of the neutrino mass and large lepton mixing, (ii) joint description of leptons and quarks, (iii) existence of the right handed (RH) neutrinos without special quantum numbers. Properties of the RH neutrinos and the UV completion of the seesaw may turn out to be the key to understand the neutrino mass and mixing. In view of the
122988289
Solar neutrinos in four dimensions and beyond
Abstract Recent data give some indications in favor of the Large Mixing Angle (LMA) MSW-solution of the solar neutrino problem. Signatures of this solution are considered in details and confronted with experimental results. Recent theoretical developments - theories with low fundamental scale of quantum gravity and large extra dimensions - give new “bulk-brane” mechanism of generation of neutrino mass. In this framework new solution of the solar neutrino problem is possible via resonance conversion of the electron neutrino in the bulk states. The solution implies that one of extra dimensions has the size about 0.1 mm.
6112047
SNO: Predictions for ten measurable quantities
We calculate the range of predicted values for 10 quantities that will be measured by the Sudbury Neutrino Observatory ~SNO!. We use neutrino oscillation solutions ~vacuum and MSW; active and sterile neutrinos! that are globally consistent with all available neutrino data and estimate realistic theoretical and experimental uncertainties. The neutral current to charged current double ratio is predicted to be more than 9 s from the no-oscillation solution for all of the currently favored neutrino oscillation solutions. The best-fit oscillation solutions predict a CC day-night rate difference between 20.1% and 112.5% and a NC day-night difference ,0.01%. We present also the predicted range for the first and the second moments of the charged current electron recoil energy spectrum, the charged current, the neutral current, and the n-e scattering rates, the seasonal dependence of the charged current rate, and the double ratio of neutrino-electron scattering rate to charged current rate. What can one learn from measurements with the Sudbury Neutrino Observatory ~SNO !@ 1#? What are the most likely quantitative results for each of the different experiments that can be carried out with SNO? The main goal of this paper is to help answer these questions by providing quantitative predictions for the most important diagnostic tests of neutrino oscillations that can be performed with SNO. SNO is not an experiment. Like the LEP and SuperKamiokande, SNO is a series of experiments. We calculate the currently favored range of predictions for 10 quantities that are affected by neutrino oscillations and which SNO will measure. For the impatient reader, we list here the quantities that are sensitive to neutrino oscillations which we investigate ~definitions are given later in the text!: first and second moments of the recoil energy spectrum, the charged current ~CC!, the neutral current ~NC!, and the neutrino-electron scattering rates, the difference between the day and the night rates for both the CC and the NC, the difference in the winter-summer CC rates, the neutral current ~NC! to charged current ~CC! double ratio, and the neutrino-electron scattering to CC double ratio. The simultaneous analysis of all the SNO results, measured values and upper limits, will be a powerful technique for constraining neutrino oscillation parameters. As an initial step in this direction, we analyze the combined results for five especially informative pairs of oscillation parameters. A. SNO reactions The SNO Collaboration will study charged current ~CC! neutrino absorption by deuterium, n e1d! p1 p1e 2 , ~1!