6355018
On the resolution of singularities of multiple Mellin–Barnes integrals
One 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 is implemented as a Mathematica code MBresolve.m
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.
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.
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.
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.
118729061
Neutrino production coherence and oscillation experiments
A bstractNeutrino oscillations are only observable when the neutrino production, propagation and detection coherence conditions are satisfied. In this paper we consider in detail neutrino production coherence, taking π → μν decay as an example. We compare the oscillation probabilities obtained in two different ways: (1) coherent summation of the amplitudes of neutrino production at different points along the trajectory of the parent pion; (2) averaging of the standard oscillation probability over the neutrino production coordinate in the source. We demonstrate that the results of these two different approaches exactly coincide, provided that the parent pion is considered as pointlike and the detection process is perfectly localized. In this case the standard averaging of the oscillation probability over the finite spatial extensions of the neutrino source (and detector) properly takes possible decoherence effects into account. We analyze the reason for this equivalence of the two approaches and demonstrate that for pion wave packets of finite width σxπ the equivalence is broken. The leading order correction to the oscillation probability due to σxπ ≠ 0 is shown to be ~ [vg/(vg−vπ )]σxπ/losc, where vg and vπ are the group velocities of the neutrino and pion wave packets, and losc is the neutrino oscillation length.
11791067
On the effective mass of the electron neutrino in beta decay
Abstract In 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 ν -schemes which describe the solar and atmospheric neutrino data, this distortion can be described by a single effective mass, under certain conditions. In the literature, two different definitions for the effective mass have been suggested. We show that for quasi-degenerate mass schemes (with an overall mass scale  m and splitting Δ m 2 ) the two definitions coincide up to (Δ m 2 ) 2 / m 4 corrections. We consider the impact of different effective masses on the integral energy spectrum. We show that the spectrum with a single mass can be used also to fit the data in the case of 4 ν -schemes motivated, in particular, by the LSND results. In this case the accuracy of the mass determination turns out to be better than (10–15)%.
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.
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.
120577993
Asymptotic behavior of amplitudes for longitudinal-leptoquark processes and structure of the scalar sector in the minimal model involving four-color symmetry
Within the minimal model based on the four-color symmetry of quarks and leptons of the Pati-Salam type, the asymptotic behavior of amplitudes for processes involving longitudinal leptoquarks (and W or Z′ bosons) is investigated, together with the mechanism according to which the growth of these amplitudes at high energies is suppressed by scalar fields. It is shown that, within the Higgs mechanism of mass generation and of the mass splitting of quarks and leptons, the four-color symmetry of quarks and leptons requires that scalar-leptoquark doublets, scalar-gluon doublets, and an extra color-singlet scalar doublet exist in addition to the standard Higgs doublet.