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.
119111785
Applications of FIESTA
Sector decomposition in its practical aspect is a constructive method used to evaluate Feynman integrals numerically. We present a new program performing the sector decomposition and integrating the expression afterwards. The program can be also used in order to expand Feynman integrals automatically in limits of momenta and masses with the use of sector decompositions and Mellin--Barnes representations. The program is parallelizable on modern multicore computers and even on multiple computers. Also we demonstrate some new numerical results for four-loop massless propagator master integrals.
16841546
Three-loop heavy quark potential ¤
We discuss the calculation of the three-loop corrections to the static potential of two heavy quarks.
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.
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.
5899166
An algorithm to construct Gröbner bases for solving integration by parts relations
This paper is a detailed description of an algorithm based on a generalized Buchberger algorithm for constructing Grobner-type bases associated with polynomials of shift operators. The algorithm is used to calculate Feynman integrals and has proved to be efficient in several complicated cases.
18100102
Reconstructing neutrino mass spectrum
Reconstruction 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 states. We discuss also possible relation between large mixing and existence of sterile neutrinos.
119498237
Radiative corrections to neutrino mass matrix in the standard model and beyond
We study the effect of radiative corrections on the structure of neutrino mass matrix. We analyze the renormalization of the matrix from the electroweak scale mZ to the scale m0 at which the effective operator that gives masses to neutrinos is generated. Apart from Standard Model and MSSM, non-standard extensions of SM are considered at a scale mX intermediate between mZ and m0. We find that the dominant structure of the neutrino mass matrix does not change. SM and MSSM corrections produce small (few percents) independent renormalization of each matrix element. Non-standard (flavor changing) corrections can modify strongly small (sub-dominant) matrix elements, which are important for the low energy phenomenology. In particular, we show that all sub-dominant elements can have purely radiative origin, being zero at m0. The set of non-zero elements at m0 can be formed by (i) diagonal elements (unit matrix); (ii) Mee and Mμτ; (iii)Mee and μτ-block elements; (iv) μτ-block elements. In the case of unit matrix, both atmospheric and solar mixing angles and mass squared differences are generated radiatively.
6485465
Leptonic CP violation: zero, maximal or between the two extremes
Discovery 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, δ. In this connection we discuss two extreme cases: the zero phase, δ = 0, and the maximal CP-violation, δ = ±π/2, and relate them to the peculiar pattern of the neutrino mixing. The maximal CP-violation can be related to the νμ−ντ reflection symmetry. We study various aspects of this symmetry and introduce a generalized reflection symmetry that can lead to an arbitrary phase that depends on the parameter of the symmetry transformation. The generalized reflection symmetry predicts a simple relation between the Dirac and Majorana phases. We also consider the possibility of certain relations between the CP-violating phases in the quark and lepton sectors.
16836336
Solar neutrinos: Interpretation of results
Abstract Recent SNO results give strong evidence that the solar neutrinos undergo flavor conversion. The main issue now is the identification of the mechanism of conversion. The LMA MSW solution with Δm 2 = (5–7)·10 −5 eV 2 , tan 2 ≡ = 0.35–0.45 looks rather plausible: it fits well the experimental data and our new theoretical prejudices. In the LMA case, KamLAND should see (0.5 – 0.7) reduced signal. VAC-QVO and LOW are accepted at about 3δ-level. The SMA solution is practically excluded. No sub-leading effects produced by U e 3 and admixture of sterile neutrino have been found. The fit becomes worse with an increase of U e 3 (for LMA) and a ν s admixture. Still a (30 – 50)% presence of the sterile neutrino is allowed. Solutions based on the neutrino spin-flip in the magnetic fields of the Sun as well as on non-standard neutrino interactions give a good fit of the data. If KamLAND confirms LMA MSW, the spin-flip and non-standard interactions can be considered (and will be searched for) as sub-leading effects.
12632665
Zenith angle distributions at Super-Kamiokande and SNO and the solution of the solar neutrino problem
We have performed a detailed study of the zenith angle dependence of the regeneration factor and distributions of events at SNO and SK for different solutions of the solar neutrino problem. In particular, we discuss the oscillatory behavior and the synchronization effect in the distribution for the LMA solution, the parametric peak for the LOW solution, etc. A physical interpretation of the effects is given. We suggest a new binning of events which emphasizes the distinctive features of the zenith angle distributions for the different solutions. We also find the correlations between the integrated day-night asymmetry and the rates of events in different zenith angle bins. The study of these correlations strengthens the identification power of the analysis.