26897204
Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
Abstract We present a new program performing the sector decomposition and integrating the expression afterwards. The program takes a set of propagators and a set of indices as input and returns the epsilon-expansion of the corresponding integral. Program summary Program title: FIESTA Catalogue identifier: AECP_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AECP_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL v2 No. of lines in distributed program, including test data, etc.: 88 281 No. of bytes in distributed program, including test data, etc.: 6 153 480 Distribution format: tar.gz Programming language: Wolfram Mathematica 6.0 [3] and C Computer: from a desktop PC to supercomputer Operating system: Unix, Linux, Windows RAM: depends on the complexity of the problem Classification: 4.4, 4.12, 5, 6.5 External routines: QLink [1], Vegas [2] Nature of problem: The sector decomposition approach to evaluating Feynman integrals falls apart into the sector decomposition itself, where one has to minimize the number of sectors; the pole resolution and epsilon expansion; and the numerical integration of the resulting expression. Solution method: The sector decomposition is based on a new strategy. The sector decomposition, pole resolution and epsilon-expansion are performed in Wolfram Mathematica 6.0 [3]. The data is stored on hard disk via a special program, QLink [1]. The expression for integration is passed to the C-part of the code, that parses the string and performs the integration by the Vegas algorithm [2]. This part of the evaluation is perfectly parallelized on multi-kernel computers. Restrictions: The complexity of the problem is mostly restricted by the CPU time required to perform the evaluation of the integral, however there is currently a limit of maximum 11 positive indices in the integral; this restriction is to be removed in future versions of the code. Running time: Depends on the complexity of the problem. References: [1] http://qlink08.sourceforge.net , open source. [2] G.P. Lepage, The Cornell preprint CLNS-80/447, 1980. [3] http://www.wolfram.com/products/mathematica/index.html2 .
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.
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.
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.
122184451
Comments on reconstruction and origins of the neutrino mass spectrum
Abstract There are two main issues in the present day neutrino physics: (i) Reconstruction of the neutrino mass (and flavor) spectrum and (ii) Identification of origin of the neutrino mass and mixing, or in other terms, implications of the neutrino data for the fundamental theory. Present status and perspectives of the reconstruction are summarized. We comment on the see-saw and the “bulk-brane” mechanisms of neutrino mass generation.
14516817
NEUTRINO PHYSICS AFTER KAMLAND
The neutrino anomalies were driving force of the developments in neutrino physics during the last 30 - 35 years. I will consider status of the anomalies after the first KamLAND result. The main questions are "What is left?" and "What is the next?" In the new phase, the phenomenological objectives of neutrino physics consist of accomplishing the program of reconstruction of the neutrino mass and flavor spectrum and searches for physics beyond the ``standard'' picture. The latter includes searches for new (sterile) neutrino states, new neutrino interactions, effects of violation of the fundamental symmetries in the neutrino sector.
15825921
LARGE R-PARITY VIOLATING COUPLINGS AND GRAND UNIFICATION
Abstract We consider the possibility that R-parity violating interactions of particles which do not involve the first generation have large (up to 1) coupling constants, λ. Such couplings, if they exist, could have a number of phenomenological consequences: renormalization of the b − τ mass ratio, generation of ντ mass in the MeV region, etc. In grand unified models, where B- and L-violating couplings appear simultaneously, proton decay can be forbidden in virtue of the hierarchical flavor structure of λ. However, due to Cabibbo-Kobayashi-Maskawa mixing this decay is induced already at one loop. Present experimental data give the upper bound λ ⪅ 10−8 (or |λ′λ″| ⪅ 7 × 10−16, on products of certain L- and B-violating coupling constants, in a more general context). The bound can be avoided if there is an asymmetry between the L- and B-violating couplings of the usual matter fields. In the SU(5) model the asymmetry can be related to the doublet-triplet splitting.
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.
119354807
Neutrino masses and mixing: Singular mass matrices and quark lepton symmetry
Abstract We suggest an approach to explain the observed pattern of the neutrino masses and mixing which employs the weakly violated quark–lepton equality and does not require introduction of an ad hoc symmetry of the neutrino sector. The mass matrices are nearly equal for all quarks and leptons. They have very small determinant and hierarchical form with expansion parameter λ ∼ sin θ c ∼ m μ / m τ . The latter can be realized, e.g., in the model with U ( 1 ) family symmetry. The equality is violated at the ∼ λ 2 level. Large lepton mixing appears as a result of summation of the neutrino and charged lepton rotations which diagonalize corresponding mass matrices in contrast with the quark sector where the up quark and down quark rotations cancel each other. We show that the flip of the sign of rotation in the neutrino sector is a result of the seesaw mechanism which also enhances the neutrino mixing. In this approach one expects, in general, deviation of the 2-3 mixing from maximal, s 13 ∼ ( 1 – 3 ) λ 2 , hierarchical neutrino mass spectrum, and m e e 10 − 2 eV . The scenario is consistent with the thermal leptogenesis and (in SUSY context) bounds on lepton number violating processes, like μ → e γ .