2085821
Applying Mellin-Barnes technique and Gröbner bases to the three-loop static potential
The Mellin‐Barnes technique to evaluate master integrals and the algorithm called FIRE to solve IBP relations with the help of Grobner bases are briefly revie wed. In FIRE, an extension of the classical Buchberger algorithm to construct Grobner ba ses is combined with the well-known Laporta algorithm. It is explained how both techniques are used when evaluating the three-loop correction to the static QCD quark potential. First results are presented: the coefficients of n 3 and n 2 , where nl is the number of light quarks.
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.
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.
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.
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.
119308192
Restricting the LSND and MiniBooNE sterile neutrinos with the IceCube atmospheric neutrino data
A bstractWe study oscillations of the high energy atmospheric neutrinos in the Earth into sterile neutrinos with the eV-scale mass. The MSW resonance and parametric enhancement of the $ \overline{\nu} $μ → $ \overline{\nu} $s oscillations lead to distortion of the zenith angle distribution of the muon-track events which can be observed by IceCube. Due to matter effect, the IceCube signal depends not only on the mixing element Uμ4 relevant for LSND and MiniBooNE but also on Uτ4 and the CP-violating phase δ24. We show that the case with Uτ4 = δ24 = 0 leads to the weakest IceCube signal and therefore should be used to bound Uμ4. We compute the zenith angle distributions of the νμ − events for different energy intervals in the range (0.1 - 10) TeV and find that inclusion of the energy information (binning in energy) improves the sensitivity to νs drastically. We estimate that with already collected (during 3-4years) IceCube statistics thebound |Uμ4|2<0.01(99% C.L.)canbeestablished and the mixing required by LSND and MiniBooNE can be excluded at (4–6)σ confidence level.
122307796
3ν oscillations in matter and solar neutrino data
Abstract A method of searching for 3ν solutions of the solar neutrino problem in terms of 2ν solutions is proposed. It gives “iso-SNU strips” on the plot of Δm 2 versus sin 2 2θ. A combined analusis of ClAr experiment data and results of the 8 B neutrino flux measurement by νe scattering (Kamiokande II) is presented.
120381841
Neutrino physics: Recent theoretical developments
Some recent developments in theory and phenomenology of neutrino mass and mixing are described. These include new results in theory of neutrino propagation: neutrino oscillograms of the Earth and non-linear neutrino physics with applications to supernova neutrinos. Results of the bottom-up approach to understanding neutrino masses and mixing are summarized. Emergence of the “standard neutrino scenario” and searches for physics beyond this scenario are discussed.
118758893
Minimal four-color model with quark-lepton symmetry and constraints on the Z{prime}-boson mass
A minimal model with quark-lepton symmetry is considered. This model, which describes unified electroweak and strong interactions, is a minimal extension of the standard model that involves four-color symmetry of quarks and leptons. Predicted relations between the masses of leptoquarks and W{sup +-}, Z, and Z{prime} bosons are studied, and the contributions of an additional Z{prime} boson to the cross sections for e{sup +}e{sup -} annihilation and the asymmetry A{sub FB} at TRISTAN and LEP200 energies are analyzed. Experimental data are shown to be consistent with the existence of a relatively light Z{prime} boson associated with four-color quark-lepton symmetry. 12 refs., 3 figs., 1 tab.
123279554
Chiral color quark symmetry and possible constraints on the G′-boson mass from tevatron and LHC data
A gauge model featuring a chiral color symmetry of quarks was considered, and possible manifestations of this symmetry in proton-antiproton and proton-proton collisions at the Tevatron and LHC energies were studied. The cross section $$\sigma _{t\bar t}$$ for the production of $$t\bar t$$ quark pairs at the Tevatron and the forward-backward asymmetry $$A_{FB}^{p\bar p}$$ in this process were calculated and analyzed with allowance for the contributions of the G′-boson predicted by the chiral color symmetry of quarks, the G′-boson massmG′ and the mixing angle θG being treated as free parameters of the model. Limits on mG′ versus θG were studied on the basis of data from the Tevatron on $$\sigma _{t\bar t}$$ and $$A_{FB}^{p\bar p}$$, and the region compatible with these data within one standard deviation was found in the mG′-θG plane. The region ofmG′-mass values that is appropriate for observing the G′-boson at LHC is discussed.