15966773
Fermionic contributions to the three-loop static potential
Abstract We consider the three-loop corrections to the static potential which are induced by a closed fermion loop. For the reduction of the occurring integrals a combination of the Grobner and Laporta algorithm has been used and the evaluation of the master integrals has been performed with the help of the Mellin–Barnes technique. The fermionic three-loop corrections amount to 2% of the tree-level result for top quarks, 8% for bottom quarks and 27% for the charm quark system.
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.
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.
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.
118529983
ON MASS LIMIT FOR CHIRAL COLOR SYMMETRY G'-BOSON FROM TEVATRON DATA ON $t\bar t$ PRODUCTION
The contributions of G'-boson predicted by the chiral color symmetry of quarks to the cross section $\sigma_{t\bar{t}}$ and to the forward–backward asymmetry $A_{{\rm FB}}^{p \bar p}$ of $t\bar{t}$ production at the Tevatron are calculated with account of the difference of the strengths of the $\bar q q G$ and $\bar q q G^\prime$ interactions. The results are analyzed in dependence on two free parameters of the model, the mixing angle θG and G' mass mG'. The G'-boson contributions to $\sigma_{t\bar{t}}$ and $A_{{\rm FB}}^{p \bar p}$ are shown to be consistent with the Tevatron data on $\sigma_{t\bar{t}}$ and $A_{{\rm FB}}^{p \bar p}$, the allowed region in the mG' - θG plane is discussed and around mG' = 1.2 TeV, θG = 14° the region of 1σ consistency is found.
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.
119273437
Neutrino Masses and a Fourth Generation of Fermions
Abstract We study neutrino mass generation in models with four chiral families of leptons and quarks and four right handed neutrinos. Generically, in these models there are three different contributions to the light neutrino masses: the usual see-saw contribution, the tree-level contribution due to mixing of light neutrinos with neutrino of the fourth generation, and the two loop contribution due to the Majorana mass term of the fourth neutrino. We study properties of these contributions and their experimental bounds. The regions of the parameters (mixings of the fourth neutrino, masses of RH neutrino components, etc.) have been identified where various contributions dominate. New possibilities of a realisation of the flavour symmetries in the four family context are explored. In particular, we consider applications of the smallest groups, e.g. SG ( 20 , 3 ) , with irreducible representation 4 .
118848163
Improving the neutrino mass hierarchy identification with inelasticity measurement in PINGU and ORCA
Multimegaton scale in under-ice and underwater detectors of atmospheric neutrinos with a few GeV energy threshold (PINGU, ORCA) open up new possibilities in the determination of neutrino properties, and in particular the neutrino mass hierarchy. With a dense array of optical modules it will be possible to determine the inelasticity, y, of the charged current nu(mu) events in addition to the neutrino energy E-nu and the muon zenith angle theta(mu). The discovery potential of the detectors will substantially increase with the measurement of y. It will enable (i) a partial separation of the neutrino and antineutrino signals, (ii) a better reconstruction of the neutrino direction, (iii) the reduction of the neutrino parameters degeneracy, (iv) a better control of systematic uncertainties, and (v) a better identification of the nu(mu) events. It will improve the sensitivity to the CP-violation phase. The three-dimensional (E-nu, theta(mu), y), nu(mu) oscillograms with the kinematical as well as the experimental smearing are computed. We present the asymmetry distributions in the E-nu - theta(mu) plane for different intervals of y and study their properties. We show that the inelasticity information reduces the effect of degeneracy of parameters by 30%. With the inelasticity, the total significance of establishing mass hierarchy may increase by (20-50)%, thus effectively increasing the volume of the detector by a factor of 1.5-2.
17592505
Bounds on Scalar Leptoquark Masses from S T U in the Minimal Model With the Four Color Symmetry
The contributions into radiative correction S T U parameters from the scalar leptoquarks are considered in frame of the minimal model with the four color gauge symmetry Taking the current exper imental data on S T U into account the bounds on the scalar lep toquark masses are obtained and discussed In particular it is shown that the current experimental data on S T U allow the existence of relatively light scalar leptoquark with electric charge The search for a new physics beyond the Standard Model SM is now one of the aims of the high energy physics It is interesting to know what kind of the new physics can manifest itself as the energy of the colliding particles increase What are the possible manifestations of such new physics at attainable energies One of the possible variants of the new physics beyond the SM can turn out to be the variant induced by the possible four color symmetry between quarks and leptons The main feature of the four color gauge symmetry is the prediction of the vector leptoquarks with the masses of about the mass scale Mc of the four color symmetry breaking In the models induced by the grand uni cation ideas the four color symmetry can manifest itself as an intermediate E mail asmirnov univ uniyar ac ru symmetry with mass scaleMc expected to be usually very high For instance in SO model it is of about Mc GeV but it can be essentially lowered up to Mc GeV by appropriate scheme of the symmetry breaking In the models regarding the four color symmetry as a primary symmetry the lower limit on the mass scale Mc is determined mainly by the low energy experimental data and it can be essentially lower for example of about TeV or about TeV or slightly less or even of about TeV The four color symmetry can manifest itself not only by the vector lep toquark physics but also due to the scalar leptoquarks Some of the scalar leptoquarks should have SU doublet structure and hence can mani fest themselves in the oblique radiative corrections in particular a ecting the S T U parameters of Peskin and Takeuchi Taking into account the rather stringent current experimental limits on S T U it is interesting to know what bounds on the scalar leptoquark masses can be extracted from the current experimental data on S T U For this purpose it is interesting to know the e ect of the scalar leptoquarks on S T U in some simple gauge model predicting these particles In this talk I would like to consider the contributions into S T U pa rameters from the scalar leptoquarks in frame of a minimal model with the four color symmetry in comparison with the current experimental data on S T U and to discuss the bounds on scalar leptoquark masses which can be extracted in this model from these data The minimal quark lepton symmetry model MQLS model to be used here as a minimal extension of the SM containing the four color gauge symmetry is based on the gage group SUV SUL UR The fermion sector of the model contains only the known fermions quarks and leptons whereas the gauge sector predicts the new gauge particles vector leptoquarks V with electric charge and an extra neutral Z boson The scalar sector of the model contains in general the four multiplets a a a transforming according to the representations of the SUV SUL UR group and having the VEV s respectively the content of the multiplets and notations can be found in more detail in Refs As regards the S T U parameters the most intersting of these multiplets is the muliplet which has been introduced to split the masses of quarks and leptons This multiplet contains fteen doublets which can be arranged into two scalar leptoquark doublets S a and S a with the SM hy percharge Y SM and respectively eight scalar gluon doublets Fja j with Y SM and the doublet a which in admixture with a gives the SM doublet SM with SM VEV p p GF GeV and an additional scalar doublet In addition to the scalar leptoquark doublets S a of the multiplet the multiplets and contain the singlet scalar leotoquarks S and S with electric charge which give in admixture with S S the Goldstone mode S and three mass eigenstate leptoqurk elds S S S As a result in the unitary gauge we obtain in general ve scalar leptoquarks S S with electric charge and respectively and Sk k with electric charge The resulting contributions into S T U from leptoquarks can be pre sented in the form S LQ nc X X k jC k j Y SM ln m m k X