Semileptonic and Rare BB-meson transitions in a QCD relativistic potential model

Using a QCD relativistic potential model, previously applied to the calculation of the heavy meson leptonic constants, we evaluate the form factors governing the exclusive decays $B\to\rho\ell\nu$, $B\to K^*\gamma$ and $B\to K^*\ell^+\ell^-$. In our approach the heavy meson is described as a $Q\bar q$ bound state, whose wave function is solution of the relativistic Salpeter equation, with an instantaneous potential displaying Coulombic behaviour at small distances and linear behaviour at large distances. The light vector meson is described by using a vector current interpolating field, according to the Vector Meson Dominance assumption. A Pauli-Villars regularized propagator is assumed for the quarks not constituting the heavy meson. Our procedure allows to avoid the description of the light meson in terms of wave function and constituent quarks, and consequently the problem of boosting the light meson wave function. Assuming as an input the experimental results on $B\to K^*\gamma$, we evaluate all the form factors describing the $B\to \rho, K^*$ semileptonic and rare transitions. The overall comparison with the data, whenever available, is satisfactory.Comment: Latex, 19 pages, 3 figure

The Isoperimetric Profile of a Noncompact Riemannian Manifold for Small Volumes

In the main theorem of this paper we treat the problem of existence of minimizers of the isoperimetric problem under the assumption of small volumes. Applications of the main theorem to asymptotic expansions of the isoperimetric problem are given.Comment: 33 pages, improved version after the referee comments, (Submitted

B Meson Transitions into Higher Mass Charmed Resonances

We use QCD sum rules to estimate the universal form factors describing the semileptonic B decays into excited charmed resonances, such as the $1^-$ and $2^-$ states $D_1^{*}$ and $D_2^{*}$ belonging to the $s_\ell^P={3/2}^-$ heavy quark doublet, and the $2^-$ and $3^-$ states $D_2^{*\prime}$ and $D_3$ belonging to the s_\ell^P={5\2}^- doublet.Comment: LaTex, 14 pages, 1 figur

Semileptonic and rare B meson decays into a light pseudoscalar meson

In the framework of a QCD relativistic potential model we evaluate the form factors describing the exclusive decays B => \pi l nu and B => K l+ l-. The present calculation extends a previous analysis of B meson decays into light vector mesons. We find results in agreement with the data, when available, and with the theoretical constraints imposed by the Callan-Treiman relation and the infinite heavy quark mass limit.Comment: 11 pages LaTeX + 2 figure

Evaluating the phase diagram of superconductors with asymmetric spin populations

The phase diagram of a non-relativistic fermionic system with imbalanced state populations interacting via a short-range S-wave attractive interaction is analyzed in the mean field approximation. We determine the energetically favored state for different values of the mismatch between the two Fermi spheres in the weak and strong coupling regime considering both homogeneous and non-homogeneous superconductive states. We find that the homogeneous superconductive phase persists for values of the population imbalance that increase with increasing coupling strength. In the strong coupling regime and for large population differences the energetically stable homogeneous phase is characterized by one gapless mode. We also find that the inhomogeneous superconductive phase characterized by the condensate $\Delta({\bf x}) \sim \Delta~\exp{(i \bf{q \cdot x})}$ is energetically favored in a range of values of the chemical potential mismatch that shrinks to zero in the strong coupling regime.Comment: 9 pages, 5 figure

Kaon Condensation in a Nambu--Jona-Lasinio (NJL) Model at High Density

We demonstrate a fully self-consistent microscopic realization of a kaon-condensed colour-flavour locked state (CFLK0) within the context of a mean-field NJL model at high density. The properties of this state are shown to be consistent with the QCD low-energy effective theory once the proper gauge neutrality conditions are satisfied, and a simple matching procedure is used to compute the pion decay constant, which agrees with the perturbative QCD result. The NJL model is used to compare the energies of the CFLK0 state to the parity even CFL state, and to determine locations of the metal/insulator transition to a phase with gapless fermionic excitations in the presence of a non-zero hypercharge chemical potential and a non-zero strange quark mass. The transition points are compared with results derived previously via effective theories and with partially self-consistent NJL calculations. We find that the qualitative physics does not change, but that the transitions are slightly lower.Comment: 21 pages, ReVTeX4. Clarified discussion and minor change

Hadronic decays of the tau lepton into K K pion modes within Resonance Chiral Theory

Tau decays into hadrons have a twofold interest: On the one hand, they are a clean environment for studying the hadronization of the left-handed current of QCD, while, on the other side, provide relevant dynamical information of the resonances that mediate these processes. Within an effective field theory-like framework, namely Resonance Chiral Theory, we analyse the decays ot the tau into K K pion modes and compare the results with CLEO and BaBar data. In this way, we provide bounds on the couplings entering our Lagrangian and predict the corresponding spectral functions. As a main result -and contrary to the bulk of theoretical studies and experimental analyses- we find vector current dominance on these decays.Comment: 7 pages, 1 figure, Prepared for the conference QCD@Work07 in Martina Franca, Bari, Italy. To appear in the Proceeding