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.
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.
16841546
Three-loop heavy quark potential ¤
We discuss the calculation of the three-loop corrections to the static potential of two heavy quarks.
2365986
FIESTA 2: Parallelizeable multiloop numerical calculations
Abstract The program FIESTA has been completely rewritten. Now it can be used not only as a tool to evaluate Feynman integrals numerically, but also to expand Feynman integrals automatically in limits of momenta and masses with the use of sector decompositions and Mellin–Barnes representations. Other important improvements to the code are complete parallelization (even to multiple computers), high-precision arithmetics (allowing to calculate integrals which were undoable before), new integrators, Speer sectors as a strategy, the possibility to evaluate more general parametric integrals. Program summary Program title: FIESTA 2 Catalogue identifier: AECP_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AECP_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL version 2 No. of lines in distributed program, including test data, etc.: 39 783 No. of bytes in distributed program, including test data, etc.: 6 154 515 Distribution format: tar.gz Programming language: Wolfram Mathematica 6.0 (or higher) and C Computer: From a desktop PC to a supercomputer Operating system: Unix, Linux, Windows, Mac OS X Has the code been vectorised or parallelized?: Yes, the code has been parallelized for use on multi-kernel computers as well as clusters via Mathlink over the TCP/IP protocol. The program can work successfully with a single processor, however, it is ready to work in a parallel environment and the use of multi-kernel processor and multi-processor computers significantly speeds up the calculation; on clusters the calculation speed can be improved even further. RAM: Depends on the complexity of the problem Classification: 4.4, 4.12, 5, 6.5 Catalogue identifier of previous version: AECP_v1_0 Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 735 External routines: QLink [1], Cuba library [2], MPFR [3] Does the new version supersede the previous version?: Yes 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 as well as on classical strategies such as Speer sectors. The sector decomposition, pole resolution and epsilon-expansion are performed in Wolfram Mathematica 6.0 or, preferably, 7.0 (enabling parallelization) [4]. 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 one of the algorithms in the Cuba library package [2]. This part of the evaluation is perfectly parallelized on multi-kernel computers. Reasons for new version: 1. The first version of FIESTA had problems related to numerical instability, so for some classes of integrals it could not produce a result. 2. The sector decomposition method can be applied not only for integral calculation. Summary of revisions: 1. New integrator library is used. 2. New methods to deal with numerical instability (MPFR library). 3. Parallelization in Mathematica . 4. Parallelization on multiple computers via TCP-IP. 5. New sector decomposition strategy (Speer sectors). 6. Possibility of using FIESTA to for integral expansion. 7. Possibility of using FIESTA to discover poles in d. 8. New negative terms resolution strategies. Restrictions: The complexity of the problem is mostly restricted by CPU time required to perform the evaluation of the integral Running time: Depends on the complexity of the problem References: [1] http://qlink08.sourceforge.net , open source. [2] http://www.feynarts.de/cuba/ , open source. [3] http://www.mpfr.org/ , open source. [4] http://www.wolfram.com/products/mathematica/index.html .
14569030
NEUTRINOLESS DOUBLE BETA DECAY AND THE SOLAR NEUTRINO PROBLEM
Abstract The MSW or vacuum oscillation solution of the solar neutrino problem can be reconciled with the possible existence of the ( ββ ) 0 ν decay with a half-life corresponding to an effective Majorana mass of the electron neutrino | m ee | ≅ (0.1−1.0) eV. The phenomenological consequences of such a possibility are analyzed and the implications for the mechanisms of neutrino mass generation are considered.
15202458
Matter effects of thin layers: Detecting oil by oscillations of solar neutrinos
We consider a possibility to use the solar neutrinos for studies of small scale structures of the Earth and for geological research. Effects of thin layers of matter with density contrast on oscillations of Beryllium neutrinos inside the Earth are studied. We find that change of the $^7Be$ neutrino flux can reach 0.1 % for layers with density of oil and size 20 km. Problems of detection are discussed. Hypothetical method would consist of measuring the $^7Be -$ flux by, {\it e.g.}, large deep underwater detector$-$submarine which could change its location.
37716395
Neutrino-Modulino Mixing
We suggest an existence of light singlet fermion, S, which interacts with observable matter only via Planck mass suppressed interaction: {approximately}m{sub 3/2}/M{sub P}, where m{sub 3/2} is the supergravity gravitino mass. If the mass of the singlet equals {approximately}m{sup 2}{sub 3/2}/M{sub P}, then {nu}{sub e}{r_arrow}S resonance conversion solves the solar neutrino problem or leads to observable effects. The {nu}S mixing changes supernova neutrino fluxes and has an impact on the primordial nucleosynthesis. The singlet S can originate as the supersymmetric partner of the moduli fields in supergravity or low energy effective theory stemming from superstrings. The {nu}S mixing may be accompanied by observable R-parity breaking effects. {copyright} {ital 1997} {ital The American Physical Society}
117912243
Medium-induced neutrino decays: physical and astrophysical effects.
17564745
Neutrinos from SN 1987 A , Earth matter effects and the LMA solution of the solar neutrino problem
We study properties of the oscillation effects in the matter of the Earth on antineu-trino fluxes from supernovae. We show that these oscillations can provide explanation of the difference in the energy spectra of the events detected by Kamiokande-2 and IMB detectors from SN1987A as well as the absence of high-energy events with E > ∼ 40 MeV. This explanation requires the neutrino oscillation parameters ∆m 2 and sin 2 2θ to be in the region of the LMA solution of the solar neutrino problem and the normal mass hierarchy if |U e3 | 2 > ∼ 10 −3. The hierarchy can be inverted if |U e3 | 2 ≪ 10 −3 .