International Journal of Modern Physics A

Due to sphaleron processes in the high-temperature symmetric phase of the standard model the cosmological baryon asymmetry is related to neutrino properties. For hierarchical neutrino masses, with B-L broken at the unification scale Λ_GUT~10¹⁶ GeV, the observed baryon asymmetry n_B/s~10^-10 can be naturally explained by the decay of heavy Majorana neutrinos. We illustrate this mechanism with two models of neutrino masses, consistent with the solar and atmospheric neutrino anomalies, which are based on the two symmetry groups SU(5)×U(1)_F and SU(3)_c×SU(3)_L×SU(3)_R×U(1)_F. We also review related cosmological bounds on Majorana neutrino masses and the use of Boltzmann equations.

We describe a new method of calculation of generic multiloop master integrals based on the numerical solution of systems of difference equations in one variable. We show algorithms for the construction of the systems using integration-by-parts identities and methods of solutions by means of expansions in factorial series and Laplace transformation. We also describe new algorithms for the identification of master integrals and the reduction of generic Feynman integrals to master integrals, and procedures for generating and solving systems of differential equations in masses and momenta for master integrals. We apply our method to the calculation of the master integrals of massive vacuum and self-energy diagrams up to three loops and of massive vertex and box diagrams up to two loops. Implementation in a computer program of our approach is described. Important features of the implementation are: the ability to deal with hundreds of master integrals and the ability to obtain very high precision results expanded at will in the number of dimensions.

Symmetric vacua of heterotic M theory, characterized by vanishing cohomology classes of individual sources in the three-form Bianchi identity, are analyzed on smooth Calabi–Yau three-folds. We show that such vacua do not exist for elliptically fibered Calabi–Yau spaces. However, explicit examples are found for Calabi–Yau three-folds arising as intersections in both unweighted and weighted projective space. We show that such symmetric vacua can be combined with attractive phenomenological features such as three generations of quarks and leptons. Properties of the low energy effective actions associated with symmetric vacua are discussed. In particular, the gauge kinetic functions receive no perturbative threshold corrections, there are no corrections to the matter field Kähler metric and the associated five-dimensional effective theory admits flat space as its vacuum.