18803649
Low-energy moments of heavy quark current correlators at four loops
Abstract We describe several techniques for the calculation of multi-loop integrals and their application to heavy quark current correlators. As new results, we present the four-loop correction to the second and third physical moments in the low-energy expansions of vector, axial-vector and scalar quark current correlators. Using the Ward identity, we obtain the third and fourth moments for the pseudo-scalar correlator. We briefly discuss the impact of these results on the determination of the charm quark mass and the strong coupling constant using lattice simulations for the current correlators and of the charm- and bottom-quark mass from experimental data for σ ( e + e − → hadrons ) .
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.
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.
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.
116859657
Scalar Leptoquark Contributions into $l_i\to l_j\gamma$ Processes
The contributions of scalar leptoquarks in lepton flavor violating (LFV) processes of type $l_i\to l_j \gamma$ are investigated in frame of the minimal model with the four color symmetry and Higgs mechanism of quark and lepton mass generation. It is shown that experimental data on the decays $\mu\to e \gamma$, $\tau \to \mu \gamma$, $\tau\to e \gamma$ allow the existence of light scalar leptoquarks of type under consideration, with masses of order 1 TeV or below.
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.
3221192
Probing the seesaw mechanism with neutrino data and leptogenesis
In the framework of the seesaw mechanism with three heavy right-handed Majorana neutrinos and no Higgs triplets we carry out a systematic study of the structure of the right-handed neutrino sector. Using the current low-energy neutrino data as an input and assuming hierarchical Dirac-type neutrino masses mDi, we calculate the masses Mi and the mixing of the heavy neutrinos. We confront the inferred properties of these neutrinos with the constraints coming from the requirement of a successful baryogenesis via leptogenesis. In the generic case the masses of the right-handed neutrinos are highly hierarchical: Mi∝mDi2; the lightest mass is M1 ≈ 103−106 GeV and the generated baryon-to-photon ratio ηB10−14 is much smaller than the observed value. We find the special cases which correspond to the level crossing points, with maximal mixing between two quasi-degenerate right-handed neutrinos. Two level crossing conditions are obtained: mee ≈ 0 (1-2 crossing) and d12 ≈ 0 (2-3 crossing), where mee and d12 are respectively the 11-entry and the 12-subdeterminant of the light neutrino mass matrix in the basis where the neutrino Yukawa couplings are diagonal. We show that sufficient lepton asymmetry can be produced only in the 1-2 crossing where M1 ≈ M2 ≈ 108 GeV,M3 ≈ 1014 GeV and (M2−M1)/M210−5.
122714200
Limits on the scalar-leptoquark and scalar-gluon masses from the parameters S, T, and U in the minimal model based on four-color symmetry
The contributions to the parameters S, T, and U of radiative corrections from the doublets of scalar leptoquarks and scalar gluons are analyzed within the minimal model based on four-color symmetry of the Pati-Salam type. It is shown that current experimental data on the parameters S, T, and U admit the existence of relatively light scalar leptoquarks and scalar gluons (of mass lower than 1 TeV), the best fit to experimental data being attained at mass values not greater than 400 GeV. In particular, the existence of scalar leptoquarks of mass below 300 GeV is found to be compatible with data on the parameters S, T, and U at χ2 < 3.1 (3.2) for mH = 115 (300) GeV as against χSM2 = 3.5 (5.0) in the Standard Model. The mass of the lightest scalar gluon is then predicted to be less than 850 (720) GeV. It is emphasized that the aforementioned doublets of scalar leptoquarks and scalar gluons can play a significant role in processes involving a t quark at LHC.
1489492
Large lepton mixings induced by sterile neutrino
Abstract We assume that the mass matrix of active neutrinos has hierarchical form with small mixings, similar to quark mass matrix. We show that the large mixings between ν μ and ν τ as well as between ν e and certain combination of ν μ and ν τ required by the present data can appear due to the presence of a sterile neutrino state. Two realizations of this possibility are considered: (i) Large flavor mixing appears as a result of sterile neutrino “decoupling” ( m ss ⪢ m a ), so that the active-sterile mixings are negligible. (ii) Sterile neutrino has a mass of O (1) eV and its mixing with active neutrinos can be observable. In the second case, the (3+1) scheme of neutrino mass, which also accommodates the LSND result, can be reproduced, provided the hierarchy of the mass matrix of active neutrinos is not strong (the ratio of largest to smallest elements is about two orders of magnitude). The enhancement of lepton mixing via coupling with sterile neutrino can be realized in Grand Unified theories with the see-saw mechanism of neutrino mass generation.