Abstract:
We present results of a lattice computation of the matrix elements of the vector and axial-vector currents which are relevant for the semi-leptonic decays $D \rightarrow K$ and $D \rightarrow K^*$. The computations are performed in the quenched approximation to lattice QCD on a $24^3 \times 48$ lattice at $\beta=6.2$ using an $O(a)$-improved fermionic action.

Abstract:
We use Omnes representations of the form factors f_+ and f_0 for exclusive semileptonic B to pi decays, paying special attention to the treatment of the B* pole and its effect on f_+. We apply them to combine experimental partial branching fraction information with theoretical calculations of both form factors to extract |Vub|. The precision we achieve is competitive with the inclusive determination and we do not find a significant discrepancy between our result, |Vub| =(3.90+/-0.32+/-0.18)10^(-3), and the inclusive world average value, (4.45+/-0.20+/-0.26)10^(-3).

Abstract:
We update the extraction of |Vub| from exclusive semileptonic B to pi decays, combining experimental partial branching fraction information with theoretical form factor calculations, using the recently revised HPQCD results for the form factors f_+ and f_0. We use Omnes representations to provide the required parametrisations of the form factors. The extracted value is 10^3 |Vub| = 3.47+/-0.29+/-0.03, in striking agreement with |Vub| extracted using all other inputs in CKM fits and showing some disagreement with |Vub| extracted from inclusive semileptonic B to pi decays.

Abstract:
We show how theoretical, principally lattice, calculations of the scalar form factors in semileptonic pseudoscalar-to-pseudoscalar decays can be used to extract information about the corresponding elastic s-wave scattering channels. We find values for the scattering lengths m_pi a = 0.179(17)(14), 0.26(26) and 0.29(4) for elastic s-wave isospin-1/2 K pi, B pi and D pi channels respectively. We also determine phase shifts. For the D K channel we find hints that there is a bound state which can be identified with the recently discovered D_{s0}^+(2317).

Abstract:
We study the semileptonic decays of the lowest-lying bc baryons to the lowest-lying cc baryons (Xi_{bc}^{(\prime*)}--> Xi_{cc}^{(*)} and Omega_{bc}^{(\prime*)}--> Omega_{cc}^{(*)}), in the limit m_b, m_c >> Lambda_{QCD} and close to the zero recoil point. The separate heavy quark spin symmetries make it possible to describe all these decays using a single form factor. We recover results derived previously by White and Savage in a manner which we think is more straightforward and parallels the method applied later to study Bc semileptonic decays. We further discuss the resemblance between the bc baryon decays and those of Bc mesons to eta_c and J/\psi mesons and comment on the relation between the slopes of the single functions describing each set of decays. Our results can straightforwardly be applied to the decays of bb baryons to bc baryons.

Abstract:
The Bethe-Salpeter equation restores exact elastic unitarity in the s- channel by summing up an infinite set of chiral loops. We use this equation to show how a chiral expansion can be undertaken by successive approximations to the potential which should be iterated. Renormalizability of the amplitudes in a broad sense can be achieved by allowing for an infinite set of counter-terms as it is the case in ordinary Chiral Perturbation Theory. Within this framework we calculate the $\pi \pi$ scattering amplitudes both for s- and p-waves at lowest order in the proposed expansion where a successful description of the low-lying resonances ($\sigma$ and $\rho$) and threshold parameters is obtained. We also extract the SU(2) low energy parameters ${\bar l}_{1,2,3,4}$ from our amplitudes.

Abstract:
We use a multiply-subtracted Omnes dispersion relation for the form factor f^+ in B->pi semileptonic decay, allowing the direct input of experimental and theoretical information to constrain its dependence on q^2. Apart from these inputs we use only unitarity and analyticity properties. We obtain |V(ub)|=(4.02 \pm 0.35)\times 10^{-3}, improving the agreement with the value determined from inclusive methods, and competitive in precision with them.

Abstract:
The $s-$wave meson-baryon scattering is analyzed for the strangeness S=0 sector in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry. Four channels have been considered: $\pi N$, $\eta N$, $K \Lambda$, $K \Sigma$. The needed two particle irreducible matrix amplitude is taken from lowest order Chiral Perturbation Theory in a relativistic formalism and low energy constants are fitted to the elastic $\pi N $ phase-shifts and the $\pi^- p \to \eta n$ and $\pi^- p \to K^0 \Lambda$ cross section data. The position of the complex poles in the second Riemann sheet of the scattering amplitude determine masses and widths of the $S_{11}-$ $N$(1535) and $-N$(1650) resonances, in reasonable agreement with experiment. A good overall description of data, from $\pi N$ threshold up to 2 GeV, is achieved keeping in mind that the two pion production channel has not been included.

Abstract:
Neutrinos propagating in matter acquire an effective electromagnetic vertex induced by their weak interactions with the charged particles in the background. In the presence of an external magnetic field the induced vertex affects the flavor transformations of mixed neutrinos in a way that, in contrast to the oscillations driven by an intrinsic magnetic moment interaction, preserve chirality. We derive the evolution equation for this case and discuss some of the physical consequences in environments such as a supernova. For small values of the square mass difference the resonance for neutrinos and antineutrinos occur within regions which are close. In that case, the resonance condition becomes independent of the vacuum parameters and is approximately the same for both.

Abstract:
We calculate the nucleon contribution to the electromagnetic vertex of a neutrino in a background of particles, including the effect of the anomalous magnetic moment of the nucleons. Explicit formulas for the form factors are given in various physical limits of practical interest. Several applications of the results are mentioned, including the effect of an external magnetic field on the dispersion relation of a neutrino in matter.