Time dependence in B→VℓℓB\to V\ell\ell decays

We discuss the theory and phenomenology of $B_{d,s}\to V(\to M_1M_2)\ell\ell$ decays in the presence of neutral-meson mixing. We derive expressions for the time-dependent angular distributions for decays into CP eigenstates, and identify the relevant observables that can be extracted from time-integrated and time-dependent analyses with or without tagging, with a focus on the difference between measurements at $B$-factories and hadronic machines. We construct two observables of interest, which we call $Q_8^-$ and $Q_9$, and which are theoretically clean at large recoil. We compute these two observables in the Standard Model, and show that they have good potential for New Physics searches by considering their sensitivity to benchmark New Physics scenarios consistent with current $b\to s\ell\ell$ data. These results apply to decays such as $B_d\to K^*(\to K_S\pi^0)\ell\ell$, $B_s\to \phi (\to K_SK_L)\ell\ell$ and $B_s\to \phi(\to K^+K^-)\ell\ell$.Comment: 39 pages, 3 figures. Typos corrected. Matches published versio

Non-minimal 331331 model for Lepton Flavour Universality Violation in b→sℓℓb\to s\ell\ell decays

331 models constitute an extension of the Standard Model (SM) obtained by enlarging the SM gauge group $SU(3)_\text{C}\times SU(2)_\text{L}\times U(1)_Y$ to the group $SU(3)_\text{C}\times SU(3)_\text{L}\times U(1)_X$. We investigate how a non-minimal 331 model may embed lepton flavour universality violating contributions to $b\to s\ell\ell$ processes without introducing lepton flavour violation, as suggested by the recent LHCb measurements of the ratios $R_K$ and $R_{K^*}$. We discuss the model-independent scenarios of New Physics in $b\to s\ell\ell$ currently favoured by the data that could be accommodated by this model and consider a few phenomenological constraints on this model.Comment: 24 pages, 3 figures, 2 tables. Accepted for publication in Phys. Rev.

Isospin breaking in pion and Ke4K_{e4} form factors

Isospin breaking in the $K_{\ell 4}$ form factors induced by the difference between charged and neutral pion masses is discussed within a framework built on suitably subtracted dispersion representations. The $K_{\ell 4}$ form factors are constructed in an iterative way up to two loops in the low-energy expansion by implementing analyticity, crossing, and unitarity due to two-meson intermediate states. Analytical expressions for the phases of the two-loop form factors of the $K^\pm\to\pi^+\pi^- e^\pm \nu_e$ channel are presented, allowing one to connect the difference of form-factor phase shifts measured experimentally (out of the isospin limit) and the difference of $S$- and $P$-wave $\pi\pi$ phase shifts studied theoretically (in the isospin limit). The dependence with respect to the two $S$-wave scattering lengths $a_0^0$ and $a_0^2$ in the isospin limit is worked out in a general way, in contrast to previous analyses based on one-loop chiral perturbation theory. The results on the phases of the $K^\pm\to\pi^+\pi^- e^\pm \nu_e$ form factors obtained by the NA48/2 collaboration at the CERN SPS are reanalysed including isospin-breaking correction to extract values for the scattering lengths $a_0^0$ and $a_0^2$.Comment: 15 pages, 3 figures, prepared for the proceedings of the XIth Confinement and Hadron Spectrum Conference, Saint-Petersburg, Sept. 8-12, 201

Short-distance QCD corrections to K0Kˉ0K^0\bar{K}^0 mixing at next-to-leading order in Left-Right models

Left-Right (LR) models are extensions of the Standard Model where left-right symmetry is restored at high energies, and which are strongly constrained by kaon mixing described in the framework of the $|\Delta S|=2$ effective Hamiltonian. We consider the short-distance QCD corrections to this Hamiltonian both in the Standard Model (SM) and in LR models. The leading logarithms occurring in these short-distance corrections can be resummed within a rigourous Effective Field Theory (EFT) approach integrating out heavy degrees of freedom progressively, or using an approximate simpler method of regions identifying the ranges of loop momentum generating large logarithms in the relevant two-loop diagrams. We compare the two approaches in the SM at next-to-leading order, finding a very good agreement when one scale dominates the problem, but only a fair agreement in the presence of a large logarithm at leading order. We compute the short-distance QCD corrections for LR models at next-to-leading order using the method of regions, and we compare the results with the EFT approach for the $WW'$ box with two charm quarks (together with additional diagrams forming a gauge-invariant combination), where a large logarithm occurs already at leading order. We conclude by providing next-to-leading-order estimates for $cc$, $ct$ and $tt$ boxes in LR models.Comment: Accepted for publication in JHE

An analysis of B_{d,s} mixing angles in presence of New Physics and an update of Bs -> K0* anti-K0*

We discuss a simple approach to measure the weak mixing angles phi_s and phi_d of the Bs and Bd systems in the presence of New Physics. We present a new expression that allows one to measure directly the New Physics mixing angles if New Physics contributes significantly to the mixing only. We apply the method to specific penguin-mediated B->PP, B->PV and B ->VV modes. We provide a very stringent and simple bound on the direct CP asymmetries of all these modes, the violation of which is a signal of New Physics in decay. Within the same theoretical framework, an updated prediction for the branching ratio of Bs->K0* anti-K0* is presented, which can be compared with a recent LHCb analysis.Comment: 11 pages, 3 figure