41885673
Quark and gluon form factors to three loops.
We compute the form factors of the photon-quark-anti-quark vertex and the effective vertex of a Higgs-boson and two gluons to three-loop order within massless perturbative quantum chromodynamics. These results provide building blocks for many third-order cross sections. Furthermore, this is the first calculation of complete three-loop vertex corrections.
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.
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.
17082137
Parametric resonance in oscillations of atmospheric neutrinos
Abstract We consider a solution of the atmospheric neutrino problem based on oscillations of muon neutrinos to sterile neutrinos: ν μ ↔ ν s . The zenith angle ( Θ ) dependences of the neutrino and upward-going muon fluxes in presence of these oscillations are studied. The dependences have characteristic form with two dips: at cos Θ =−0.6÷−0.2 and cos Θ =−1.0÷−0.8. The latter dip is due to parametric resonance in oscillations of neutrinos which cross the core of the earth. A comparison of predictions with data from the MACRO, Baksan and Super-Kamiokande experiments is given.
59164737
Recent developments in neutrino phenomenology
The first phase of studies of the neutrino mass and mixing is essentially over. The outcome is the discovery of non-zero neutrino mass and determination of the dominant structure of the lepton mixing matrix. In some sense this phase was very simple, and nature was very collaborative with us: Two main effects - the vacuum oscillations and the adiabatic conversion in matter (the MSW-effect) - provide complete interpretation of the experimental results. Furthermore, with the present accuracy of measurements the $3\nu-$mixing analysis is essentially reduced to the $2\nu$ consideration. I will present a concise and comprehensive description of this first phase. The topics include: (i) the concept of neutrino mixing in vacuum and matter; (ii) physics of the oscillations and adiabatic conversion; (iii) the experimental evidences of the flavor transformations and determination of the oscillation parameters. Some implications of the obtained results are discussed. Comments are given on the next phase of the field that will be much more involved.
9409416
Neutrino-2008: Where are we? Where are we going?
Our present knowledge of neutrinos can be summarized in terms of the 'standard neutrino scenario'. Phenomenology of this scenario as well as attempts to uncover physics behind neutrino mass and mixing are described. Goals of future studies include complete reconstruction of the neutrino mass and flavor spectrum, further test of the standard scenario and search for new physics beyond it. Developments of new experimental techniques may lead to construction of new neutrino detectors from table-top to multi-Megaton scales which will open new horizons in the field. With detection of neutrino bursts from the Galactic supernova and high energy cosmic neutrinos neutrino astrophysics will enter qualitatively new phase. Neutrinos and LHC (and future colliders), neutrino astronomy, neutrino structure of the Universe, and probably, neutrino technologies will be among leading topics of research.
120801039
Resonance Amplification of Oscillations in Matter and Spectroscopy of Solar Neutrinos
118565164
Cross Section and Forward-Backward Asymmetry of $t\bar{t}$ Production in the Model with Four Color Symmetry
The contributions to the cross section $\sigma_{t\bar{t}}$ and to the forward-backward asymmetry $A_{\rm FB}^{t \bar t}$ of $t\bar{t}$ production at the Tevatron from $Z'$-boson and scalar leptoquarks $S^{(\pm)}_a$ and scalar gluons $F_a$ predicted by the minimal model with four color quark-lepton symmetry are calculated. These contributions are shown to be small in tree approximation and can be significant with account of the 1-loop $gt\bar{t}$ effective vertex induced by the scalar doublets. The lower mass limit for scalar gluons $m_F \gtrsim 320\, GeV$ from the Tevatron data is obtained and it is shown that for $m_{F_1}\lesssim 990\,GeV$ the scalar gluon $F_1$ can be evident at LHC at the significance not less that $3\sigma$ (for $\sqrt{s}=14$ TeV, $L=10\,fb^{-1}$).