16064284
Paradoxes of neutrino oscillations
Despite the theory of neutrino oscillations being rather old, some of its basic issues are still being debated in the literature. We discuss a number of such issues, including the relevance of the “same energy” and “same momentum” assumptions, the role of quantum-mechanical uncertainty relations in neutrino oscillations, the dependence of the coherence and localization conditions that ensure the observability of neutrino oscillations on neutrino energy and momentum uncertainties, the question of (in)dependence of the oscillation probabilities on the neutrino production and detection processes, and the applicability limits of the stationary-source approximation. We also develop a novel approach to calculation of the oscillation probability in the wave-packet approach, based on the summation/integration conventions different from the standard one, which allows a new insight into the “same energy” vs. “same momentum” problem. We also discuss a number of apparently paradoxical features of the theory of neutrino oscillations.
18492548
Pontecorvo's original oscillations revisited
Abstract We show that a left-handed neutrino ν L can oscillate into its CPT -conjugate state ν R with maximal amplitude, in direct analogy with K 0 − K 0 oscillations. Peculiarities of such oscillations under different conditions are studied.
115887973
Solar neutrinos: Theoretical aspects
59164737
Recent developments in neutrino phenomenology
The first phase of studies of the neutrino mass and mixing is essentially over. The outcome is the discovery of non-zero neutrino mass and determination of the dominant structure of the lepton mixing matrix. In some sense this phase was very simple, and nature was very collaborative with us: Two main effects - the vacuum oscillations and the adiabatic conversion in matter (the MSW-effect) - provide complete interpretation of the experimental results. Furthermore, with the present accuracy of measurements the $3\nu-$mixing analysis is essentially reduced to the $2\nu$ consideration. I will present a concise and comprehensive description of this first phase. The topics include: (i) the concept of neutrino mixing in vacuum and matter; (ii) physics of the oscillations and adiabatic conversion; (iii) the experimental evidences of the flavor transformations and determination of the oscillation parameters. Some implications of the obtained results are discussed. Comments are given on the next phase of the field that will be much more involved.
31519375
Multiple spectral splits of supernova neutrinos.
Collective oscillations of supernova neutrinos swap the spectra f(nu(e))(E) and f(nu[over ](e))(E) with those of another flavor in certain energy intervals bounded by sharp spectral splits. This phenomenon is far more general than previously appreciated: typically one finds one or more swaps and accompanying splits in the nu and nu[over ] channels for both inverted and normal neutrino mass hierarchies. Depending on an instability condition, swaps develop around spectral crossings (energies where f(nu(e))=f(nu(x)), f(nu[over ](e))=f(nu[over ](x)) as well as E-->infinity where all fluxes vanish), and the widths of swaps are determined by the spectra and fluxes. Washout by multiangle decoherence varies across the spectrum and splits can survive as sharp spectral features.
119540272
Self-induced spectral splits in supernova neutrino fluxes
In the dense-neutrino region above the neutrino sphere of a supernova (r < or approx. 400 km), neutrino-neutrino refraction causes collective flavor transformations. They can lead to 'spectral splits' where an energy E{sub split} splits the transformed spectrum sharply into parts of almost pure but different flavors. Unless there is an ordinary MSW resonance in the dense-neutrino region, E{sub split} is determined by flavor-lepton number conservation alone. Spectral splits are created by an adiabatic transition between regions of large and small neutrino density. We solve the equations of motion in the adiabatic limit explicitly and provide analytic expressions for a generic example.
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.
119111785
Applications of FIESTA
Sector decomposition in its practical aspect is a constructive method used to evaluate Feynman integrals numerically. We present a new program performing the sector decomposition and integrating the expression afterwards. The program can be also used in order to expand Feynman integrals automatically in limits of momenta and masses with the use of sector decompositions and Mellin--Barnes representations. The program is parallelizable on modern multicore computers and even on multiple computers. Also we demonstrate some new numerical results for four-loop massless propagator master integrals.
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.
41885673
Quark and gluon form factors to three loops.
We compute the form factors of the photon-quark-anti-quark vertex and the effective vertex of a Higgs-boson and two gluons to three-loop order within massless perturbative quantum chromodynamics. These results provide building blocks for many third-order cross sections. Furthermore, this is the first calculation of complete three-loop vertex corrections.