2365986
FIESTA 2: Parallelizeable multiloop numerical calculations
Abstract The program FIESTA has been completely rewritten. Now it can be used not only as a tool to evaluate Feynman integrals numerically, but also to expand Feynman integrals automatically in limits of momenta and masses with the use of sector decompositions and Mellin–Barnes representations. Other important improvements to the code are complete parallelization (even to multiple computers), high-precision arithmetics (allowing to calculate integrals which were undoable before), new integrators, Speer sectors as a strategy, the possibility to evaluate more general parametric integrals. Program summary Program title: FIESTA 2 Catalogue identifier: AECP_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AECP_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL version 2 No. of lines in distributed program, including test data, etc.: 39 783 No. of bytes in distributed program, including test data, etc.: 6 154 515 Distribution format: tar.gz Programming language: Wolfram Mathematica 6.0 (or higher) and C Computer: From a desktop PC to a supercomputer Operating system: Unix, Linux, Windows, Mac OS X Has the code been vectorised or parallelized?: Yes, the code has been parallelized for use on multi-kernel computers as well as clusters via Mathlink over the TCP/IP protocol. The program can work successfully with a single processor, however, it is ready to work in a parallel environment and the use of multi-kernel processor and multi-processor computers significantly speeds up the calculation; on clusters the calculation speed can be improved even further. RAM: Depends on the complexity of the problem Classification: 4.4, 4.12, 5, 6.5 Catalogue identifier of previous version: AECP_v1_0 Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 735 External routines: QLink [1], Cuba library [2], MPFR [3] Does the new version supersede the previous version?: Yes Nature of problem: The sector decomposition approach to evaluating Feynman integrals falls apart into the sector decomposition itself, where one has to minimize the number of sectors; the pole resolution and epsilon expansion; and the numerical integration of the resulting expression. Solution method: The sector decomposition is based on a new strategy as well as on classical strategies such as Speer sectors. The sector decomposition, pole resolution and epsilon-expansion are performed in Wolfram Mathematica 6.0 or, preferably, 7.0 (enabling parallelization) [4]. The data is stored on hard disk via a special program, QLink [1]. The expression for integration is passed to the C-part of the code, that parses the string and performs the integration by one of the algorithms in the Cuba library package [2]. This part of the evaluation is perfectly parallelized on multi-kernel computers. Reasons for new version: 1. The first version of FIESTA had problems related to numerical instability, so for some classes of integrals it could not produce a result. 2. The sector decomposition method can be applied not only for integral calculation. Summary of revisions: 1. New integrator library is used. 2. New methods to deal with numerical instability (MPFR library). 3. Parallelization in Mathematica . 4. Parallelization on multiple computers via TCP-IP. 5. New sector decomposition strategy (Speer sectors). 6. Possibility of using FIESTA to for integral expansion. 7. Possibility of using FIESTA to discover poles in d. 8. New negative terms resolution strategies. Restrictions: The complexity of the problem is mostly restricted by CPU time required to perform the evaluation of the integral Running time: Depends on the complexity of the problem References: [1] http://qlink08.sourceforge.net , open source. [2] http://www.feynarts.de/cuba/ , open source. [3] http://www.mpfr.org/ , open source. [4] http://www.wolfram.com/products/mathematica/index.html .
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.
2122861
Decoupling of heavy quarks in HQET
Decoupling of c-quark loops in b-quark HQET is considered. The decoupling coefficients for the HQET heavy-quark field and the heavy–light quark current are calculated with the three-loop accuracy. The last result can be used to improve the accuracy of extracting fB from HQET lattice simulations (without c-quark loops). The decoupling coefficient for the flavour-nonsinglet QCD current with n antisymmetrized γ-matrices is also obtained at three loops; the result for the tensor current (n = 2) is new.
9034286
Geometric approach to asymptotic expansion of Feynman integrals
We present an algorithm that reveals relevant contributions in non-threshold-type asymptotic expansion of Feynman integrals about a small parameter. It is shown that the problem reduces to finding a convex hull of a set of points in a multidimensional vector space.
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.
15195987
Leptonic Unitarity Triangle and CP-violation
The area of the unitarity triangle is a measure of CP-violation. We introduce the leptonic unitarity triangles and study their properties. We consider the possibility of reconstructing the unitarity triangle in future oscillation and non-oscillation experiments. A set of measurements is suggested which will, in principle, allow us to measure all sides of the triangle, and consequently to establish CP-violation. For different values of the CP-violating phase, {delta}{sub D}, the required accuracy of measurements is estimated. The key elements of the method include determination of |U{sub e3}| and studies of the {nu}{sub {mu}} - {nu}{sub {mu}} survival probability in oscillations driven by the solar mass splitting {Delta}m{sub sun}{sup 2}. We suggest additional astrophysical measurements which may help to reconstruct the triangle. The method of the unitarity triangle is complementary to the direct measurements of CP-asymmetry. It requires mainly studies of the survival probabilities and processes where oscillations are averaged or the coherence of the state is lost.
16247339
Where do we stand with solar neutrino oscillations
We determine parameters for MSW and vacuum oscillations (active and sterile neutrinos) that are allowed by separate, and collective, imposition of the constraints from total event rates in the chlorine, GALLEX, SAGE, and SuperKamiokande experiments (504 days), the SuperKamiokande energy spectrum, and the SuperKamiokande zenith-angle dependence. The small mixing angle MSW solution is acceptable at 7% C.L. (8% for sterile \ensuremath{\nu}'s) and the vacuum solution is acceptable at 6% C.L. The best-fit global MSW solution for active neutrinos is $\ensuremath{\Delta}{m}^{2}=5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}{\mathrm{eV}}^{2},$ ${\mathrm{sin}}^{2}2\ensuremath{\theta}=5.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ (and for sterile neutrinos $\ensuremath{\Delta}{m}^{2}=4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}{\mathrm{eV}}^{2},$ ${\mathrm{sin}}^{2}2\ensuremath{\theta}=7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}).$ For vacuum oscillations, the best-fit solution is $\ensuremath{\Delta}{m}^{2}=6.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}{\mathrm{eV}}^{2},$ ${\mathrm{sin}}^{2}2\ensuremath{\theta}=0.75.$ An arbitrary combination of undistorted (no oscillations) $pp,$ ${}^{7}\mathrm{Be},$ ${}^{8}\mathrm{B},$ and CNO neutrino fluxes is inconsistent with the combined data sets at the 3.5\ensuremath{\sigma} C.L., independent of astrophysical considerations. We use improved calculations of solar model fluxes, neutrino absorption cross sections and energy spectra, and a detailed evaluation of regeneration effects.
121442922
Resonant neutrino oscillations in matter
Abstract Review is devoted to the systematic representation of the theory (first part) and the applications (second part) of neutrino oscillations in matter. The evolution equations for mixed neutrinos in matter are deduced in different forms and analized. The consideration includes symmetries, limits of applications and some generalizations of equations. The analogies of the mixed neutrinos in matter have been found. We discuss in details the properties and the physical sense of the resonance in a system of mixed neutrinos. For homogeneous matter the effect of resonant enhancement of oscillations is described. Different representation of the adiabaticity condition, which determines a dynamics of neutrino oscillations, are given, and the adiabaticity parameter is introduced. Practically complete transformations of one neutrino species into another one are possible at the adiabatic (or near to adiabatic) crossing of resonance layer even at small vacuum mixing. The effect of non-oscillatory transition is remarked. Some results have been obtained for the adiabaticity violation regime. Also we review the exact solutions of the equations for special density distributions. The generalization of the theory for the case of three neutrino mixing is given. The effects of inelastic collisions as well as the divergence of neutrino wave packets are discussed. The theory of resonant conversion is applied then to the neutrino fluxes inside the Sun, the Earth and the collapsing stars. The distortion of the neutrino energy spectra by the matter filters with different density distributions are calculated. We describe the observable effects of conversion for solar and atmospheric neutrinos as well as for neutrinos from collapsing stars. The searching for these effects is considered as a method of measuring the neutrino masses and mixing. Resonant conversion may quite naturally solve the solar neutrino problem. The distinctions of resonance conversion effects and another mechanisms for solar ν e - flux reduction are considered, and in this connection the possibilities of solar neutrino spectroscopy are outlined. We discuss the consequences of ν - signal detection from supernova 1987A.
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
15323094
Neutrino physics: Open theoretical questions
We know that neutrino mass and mixing provide a window to physics beyond the Standard Model. Now this window is open, at least partly. And the questions are: what do we see, which kind of new physics, and how far "beyond"? I summarize the present knowledge of neutrino mass and mixing, and then formulate the main open questions. Following the bottom-up approach, properties of the neutrino mass matrix are considered. Then different possible ways to uncover the underlying physics are discussed. Some results along the line of seesaw, GUT and SUSY GUT are reviewed.