Majorana neutrino textures from numerical considerations: the CP conserving case

Phenomenological bounds on the neutrino mixing matrix U are used to determine numerically the allowed range of real elements (CP conserving case) for the symmetric neutrino mass matrix Mn (Majorana case). For this purpose an adaptive Monte Carlo generator has been used. Histograms are constructed to show which forms of the neutrino mass matrix Mn are possible and preferred. We confirm results found in the literature which are based on analytical calculations, though a few differences appear. These cases correspond to some textures with two zeros. The results show that actually both normal and inverted mass hierarchies are still possible at 3 sigma confidence level.Comment: 12 pages, 10 figures, changes in Section 2, some references added, to appear in PR

Mass-flavour transitions of supernova neutrino states in the terrestrial matter

Neutrinos coming from the distant astrophysical objects reach the Earth in incoherent mass states. Simple approximations for transitions between mass and flavour states in the Earth are given

Differential equations and massive two-loop Bhabha scattering: the B5l2m3 case

The two-loop box contributions to massive Bhabha scattering may be reduced to two-loop box master integrals (MIs) with five, six, and seven internal lines, plus vertices and self energies. The self-energy and vertex MIs may be solved analytically by the differential equations (DE) method. This is true for only few of the box masters. Here we describe some details of the analytical determination, including constant terms in ep=(4-d)/2, of the complicated topology B5l2m3 (with 5 lines, 2 of them being massive). With the DE approach, three of the four coupled masters have been solved in terms of (generalized) standard Harmonic Polylogarithms.Comment: 5 pages, 2 figures, contribution to RADCOR 2005, Oct 2-7, 2005, Shonan Village, Japan, to appear in Nucl. B (Proc. Suppl.

On the tensor reduction of one-loop pentagons and hexagons

We perform analytical reductions of one-loop tensor integrals with 5 and 6 legs to scalar master integrals. They are based on the use of recurrence relations connecting integrals in different space-time dimensions. The reductions are expressed in a compact form in terms of signed minors, and have been implemented in a mathematica package called hexagon.m. We present several numerical examples.Comment: Latex, 7 pages, 2 eps figures. Contribution to the proceedings of `Loops and Legs in Quantum Field Theory', April 2008, Sondershausen, German

AMBRE: A Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals.

The Mathematica toolkit AMBRE derives Mellin-Barnes (MB) representations for Feynman integrals in d=4-2eps dimensions. It may be applied for tadpoles as well as for multi-leg multi-loop scalar and tensor integrals. AMBRE uses a loop-by-loop approach and aims at lowest dimensions of the final MB representations. The present version of AMBRE works fine for planar Feynman diagrams. The output may be further processed by the package MB for the determination of its singularity structure in eps. The AMBRE package contains various sample applications for Feynman integrals with up to six external particles and up to four loops.Comment: 26 pages, 10 figures, 1 table, in v2 typos in Eqn. 48 and Eqn. 57 corrected; the corresponding sample files are unchange

New results for loop integrals: AMBRE, CSectors, hexagon

We report on the three Mathematica packages hexagon, CSectors, AMBRE. They are useful for the evaluation of one- and two-loop Feynman integrals with a dependence on several kinematical scales. These integrals are typically needed for LHC and ILC applications, but also for higher order corrections at meson factories. hexagon is a new package for the tensor reduction of one-loop 5-point and 6-point functions with rank R=3 and R=4, respectively; AMBRE is a tool for derivations of Mellin-Barnes representations; CSectors is an interface for the package sector_decomposition and allows a convenient, direct evaluation of tensor Feynman integrals.Comment: 9 pages, 1 figure, subm. to PoS(ACAT08)12

News on Ambre and CSectors

Mellin-Barnes and sector decomposition methods are used to evaluate tensorial Feynman diagrams in the Euclidean kinematical region. Few software packages are shortly described and few examples demonstrate their use.Comment: 5 pages, 2 figures, 2 tables, contrib. to proceedings of "Loops and Legs in Quantum Field Theory'', 10th DESY Workshop on Elementary Particle Theory, 25-30 April 2010, Woerlitz, German