33 research outputs found
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