118412914
Describing neutrino oscillations in matter with Magnus expansion
Abstract We present new formalism for description of the neutrino oscillations in matter with varying density. The formalism is based on the Magnus expansion and has a virtue that the unitarity of the S-matrix is maintained in each order of perturbation theory. We show that the Magnus expansion provides better convergence of series: the restoration of unitarity leads to smaller deviations from the exact results especially in the regions of large transition probabilities. Various expansions are obtained depending on a basis of neutrino states and a way one splits the Hamiltonian into the self-commuting and non-commuting parts. In particular, we develop the Magnus expansion for the adiabatic perturbation theory which gives the best approximation. We apply the formalism to the neutrino oscillations in matter of the Earth and show that for the solar oscillation parameters the second order Magnus adiabatic expansion has better than 1% accuracy for all energies and trajectories. For the atmospheric Δ m 2 and small 1–3 mixing the approximation works well ( sin 2 θ 13 = 0.01 ) outside the resonance region 2.7–8 GeV.
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.
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.
115887973
Solar neutrinos: Theoretical aspects
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.
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.
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 ) .
14611410
Four Loop Massless Propagators: a Numerical Evaluation of All Master Integrals
Abstract We present numerical results which are needed to evaluate all non-trivial master integrals for four-loop massless propagators, confirming the recent analytic results of Baikov and Chetyrkin (2010) [1] and evaluating an extra order in e expansion for each master integral.
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.
120006374
Contributions of scalar leptoquarks to the cross sections for the production of quark-antiquark pairs in electron-positron annihilation
AbstractThe contributions of scalar-leptoquark doublets to the cross sections 
$$\sigma _{Q\tilde Q} $$
, for the production of quark-antiquark pairs in electron-positron annihilation are calculated within the minimal model based on the four-color symmetry of quarks and leptons. These contributions are analyzed versus the scalar-leptoquark masses and the mixing parameters of the model at colliding-particle energies in the range 250–1000 GeV. It is shown that the contributions in question are of greatest importance for processes leading to t-quark production. In particular, it is found that, with allowance for the contribution of the scalar leptoquark of charge 5/3 and mass in the range 250–500 GeV, the cross section 
$$\sigma _{t\tilde t} $$
 calculated at a mixing-parameter value of kt ∼ 1 may be severalfold larger than the corresponding cross section 
$$\sigma _{t\tilde t}^{(SM)} $$
 within the Standard Model. The possibility of setting constraints on the scalar-leptoquark masses and on the mixing parameters by measuring such contributions at future electron-positron colliders is indicated.
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.