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.
5899166
An algorithm to construct Gröbner bases for solving integration by parts relations
This paper is a detailed description of an algorithm based on a generalized Buchberger algorithm for constructing Grobner-type bases associated with polynomials of shift operators. The algorithm is used to calculate Feynman integrals and has proved to be efficient in several complicated cases.
16841546
Three-loop heavy quark potential ¤
We discuss the calculation of the three-loop corrections to the static potential of two heavy quarks.
73596822
Transverse laser cooling by synchro-betatron coupling
Transverse laser cooling with the use of a synchrobetatron coupling is being carried out at S-LSR. Bunched 40 keV Mg beams are cooled by a co-propagating laser with a wavelength of 280 nm. Synchrotron oscillation and horizontal betatron oscillation are coupled by an RF drifttube at a finite dispersive section (D = 1.1 m) in order to transmit longitudinal cooling force to the horizontal degree of freedom. The time evolution of horizontal beam size during laser cooling are measured by a CCD camera. The measured beam size after 35 s is reduced to 0.55 mm on the resonance, compared to 0.85 mm measured or larger at non-resonance conditions. Momentum spreads are 1.7 × 10−4 on the resonance otherwise 1.2 × 10−4. These results indicate that the horizontal heat is connected to the longitudinal direction by the synchro-betatron coupling, which is cooled down by a longitudinal bunched beam laser cooling.
6485465
Leptonic CP violation: zero, maximal or between the two extremes
Discovery of the CP-violation in the lepton sector is one of the challenges of the particle physics. We search for possible principles, symmetries and phenomenological relations that can lead to particular values of the CP-violating Dirac phase, δ. In this connection we discuss two extreme cases: the zero phase, δ = 0, and the maximal CP-violation, δ = ±π/2, and relate them to the peculiar pattern of the neutrino mixing. The maximal CP-violation can be related to the νμ−ντ reflection symmetry. We study various aspects of this symmetry and introduce a generalized reflection symmetry that can lead to an arbitrary phase that depends on the parameter of the symmetry transformation. The generalized reflection symmetry predicts a simple relation between the Dirac and Majorana phases. We also consider the possibility of certain relations between the CP-violating phases in the quark and lepton sectors.
119420362
Neutrinoless Double Beta Decay Potential in a Large Mixing Angle World
We discuss the possibility of reconstructing the neutrino mass spectrum from the complementary processes of neutrino oscillations and double beta decay in view of the new data of Super-Kamiokande presented at the Neutrino2000 conference. Since the large mixing angle solution is favored, now, the prospects to observe double beta decay and provide informations on the absolute mass scale in the neutrino sector have been improved.
121364048
Radiative mechanisms for the 17 keV neutrino and the MSW mass scale
Abstract We present the simplest SU (2) ⊗ U (1) models with a spontaneously broken global U (1)-symmetry which naturally account for the 17 keV anomalies in beta decays and for the explanation of the solar neutrino deficit through resonant ν e conversions into an ultralight sterile neutrino. Two scales of neutrino masses arise naturally from radiative corrections in one- and two-loop levels associated to the exchange of new Higgs bosons. One of the models predicts the possibility of having exotic rare decay modes of the tau lepton, τ → e + J where J is the majoron, τ → e + γ and τ →3 e with branching ratios accessible to experiment.
118671206
Probing non-standard interaction of neutrinos with IceCube and DeepCore
A bstractWe consider effects of the Non-Standard Interactions (NSI) on oscillations of the high energy atmospheric neutrinos. The νμ-oscillograms are constructed and their dependence on the NSI strength parameters ϵαβ studied. We computed the zenith angle distributions of the νμ-events in the presence of NSI in different energy regions. The distributions are confronted with the IceCube-79 (high energy sample) and the DeepCore (low energy sample) data and constraints on the strength parameters |ϵμτ|≲ 6 × 10−3 and |ϵμμ − ϵττ| ≲ 3 × 10−2 (90% C.L.) have been obtained. Future measurements of the zenith angle distributions by DeepCore in several energy bins will allow to improve the bounds by factor 2–3. We discuss the signatures of NSI in the zenith angle and energy distributions of events which allow to discriminate them from the effects of sterile neutrinos.
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.