Finite-Size Effects on Nucleation in a First-Order Phase Transition

We discuss finite-size effects on homogeneous nucleation in first-order phase transitions. We study their implications for cosmological phase transitions and to the hadronization of a quark-gluon plasma generated in high-energy heavy ion collisions. Very general arguments allow us to show that the finite size of the early universe has virtually no relevance in the process of nucleation and in the growth of cosmological bubbles during the primordial quark-hadron and the electroweak phase transitions. In the case of high-energy heavy ion collisions, finite-size effects play an important role in the late-stage growth of hadronic bubbles.Comment: 6 pages, no figures, 1 reference adde

An S4 model for quarks and leptons with maximal atmospheric angle

We consider a model for quark and lepton masses and mixings based on S4 flavor symmetry. The model contains six Higgs doublets where three of them give mass to the leptons and the other three gives mass to the quarks. Charged fermion and quark masses arise from renormalizable interactions while neutrino Majorana masses are generated through effective dimension five Weinberg operator. From the study of the minimization of the scalar potential we found a residual mu-tau symmetry in the neutrino sector predicting zero reactor angle and maximal atmospheric angle and for the quark sector we found a four-zero texture. We give a fit of the mass hierarchies and mixing angles in the quark sector.Comment: some misprinting corrected, one reference and one commment added, version to be published on Phys. Rev.

Lp-norms, Log-barriers and Cramer transform in Optimization

We show that the Laplace approximation of a supremum by Lp-norms has interesting consequences in optimization. For instance, the logarithmic barrier functions (LBF) of a primal convex problem P and its dual appear naturally when using this simple approximation technique for the value function g of P or its Legendre-Fenchel conjugate. In addition, minimizing the LBF of the dual is just evaluating the Cramer transform of the Laplace approximation of g. Finally, this technique permits to sometimes define an explicit dual problem in cases when the Legendre-Fenchel conjugate of g cannot be derived explicitly from its definition

Transient photon production in a QGP

We discuss the shortcomings of a formula that has been used in the literature to compute the number of photons emitted by a hot or dense system during a finite time, and show that the transient effects it predicts for the photon rate are unphysical.Comment: 4 pages, to appear in the proceedings of Hadron Physics - RANP 2004, Angra dos Reis, Brazi