15962053
Hepp and Speer sectors within modern strategies of sector decomposition
Hepp and Speer sectors were successfully used in the sixties and seventies for proving mathematical theorems on analytically or/and dimensionally regularized and renormalized Feynman integrals at Euclidean external momenta. We describe them within recently developed strategies of introducing iterative sector decompositions. We prove that Speer sectors are reproduced within one of the existing strategies.
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.
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.
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.
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}
7456908
Light Singlet Fermions and Neutrino Physics
The existence of a light singlet fermion mixed with the electron neutrino is hinted by the simultaneous explanation of various neutrino anomalies. We show that supersymmetry can provide a natural framework for the existence and the desired properties of such a fermion. Quasi Goldstone fermions (QGF) of spontaneously broken global symmetries like the Peccei-Quinn symmetry or lepton number can mix properly with the neutrinos provided the presence of the R-parity breaking term $\e LH_2$. The lightness of QGF can be a consequence of non-minimal K\"ahler potentials like that of no-scale supergravity. In order to keep R-parity, such a sterile component has to be placed in a new singlet superfield with no vacuum expectation value. In the context of the standard seesaw mechanism the lightness of such a singlet can be understood by imposing a $R$-symmetry.
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.
15376747
ON A POSSIBLE MANIFESTATION OF THE FOUR-COLOR SYMMETRY Z' BOSON IN μ+μ- EVENTS AT THE LHC
The cross section of the μ+μ- pair production in pp-collisions at the LHC is calculated with account of the Z' boson induced by the minimal four-color quark–lepton symmetry (MQLS). The μ+μ- invariant mass spectrum with account of the MQLS Z' boson is analyzed in dependence on the Z' mass. The mass region for the MQLS Z' boson observable at the LHC is found in dependence on the significance and on the integrated luminosity.
18429197
Solar Neutrinos and Lepton Mixing
With latest experimental data the solar neutrino problem enters new phase when crucial aspects of the problem can be formulated in an essentially (solar) model independent way. Original neutrino fluxes can be considered as free parameters to be found from the solar neutrino experiments. Resonance flavour conversion gives the best fit of all experimental results. Already existing data allow one to constraint both the neutrino parameters and the original neutrino fluxes. The reconciliation of the solution of the solar neutrino problem with other neutrino mass hints (atmospheric neutrino problem, hot dark matter etc.) may require the existence of new very light singlet fermion. Supersymmetry can provide a framework within which the desired properties of such a light fermion follow naturally. The existence of the fermion can be related to axion physics, mechanism of $\mu$-term generation etc..