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

Four-body contributions to B -> Xs gamma at NLO

Ongoing efforts to reduce the perturbative uncertainty in the B -> Xs gamma decay rate have resulted in a theory estimate to NNLO in QCD. However, a few contributions from multi-parton final states which are formally NLO are still unknown. These are parametrically small and included in the estimated error from higher order corrections, but must be computed if one is to claim complete knowledge of the B -> Xs gamma rate to NLO. A major part of these unknown pieces are four-body contributions corresponding to the partonic process b -> s qbar q gamma. We compute these NLO four-body contributions to B -> Xs gamma, and confirm the corresponding tree-level leading-order results. While the NLO contributions arise from tree-level and one-loop Feynman diagrams, the four-body phase-space integrations make the computation non-trivial. The decay rate contains collinear logarithms arising from the mass regularization of collinear divergences. We perform an exhaustive numerical analysis, and find that these contributions are positive and amount to no more than 1% of the total rate in the Standard Model, thus confirming previous estimates of the perturbative uncertainty.Comment: 37 pages, 8 figure

Timelike-helicity B→ππB\to \pi\pi form factor from light-cone sum rules with dipion distribution amplitudes

We complete the set of QCD light-cone sum rules for $B\to \pi\pi$ transition form factors, deriving a new sum rule for the timelike-helicity form factor $F_t$ in terms of dipion distribution amplitudes. This sum rule, in the leading twist-2 approximation, is directly related to the pion vector form factor. Employing a relation between $F_t$ and other $B\to \pi\pi$ form factors we obtain also the longitudinal-helicity form factor $F_0$. In this way, all four (axial-)vector $B\to \pi\pi$ form factors are predicted from light-cone sum rules with dipion distribution amplitudes. These results are valid for small dipion masses with large momentum.Comment: 7 pages, 3 figure

Gauge-invariant implications of the LHCb measurements on Lepton-Flavour Non-Universality

We study the implications of the recent measurements of $R_K$ and $R_{K^*}$ by the LHCb collaboration. We do that by adopting a model-independent approach based on the Standard Model Effective Field Theory (SMEFT), in which the dominant new physics effects are encoded in the coefficients of dimension-six operators respecting the full Standard Model (SM) gauge symmetry. After providing simplified expressions for $R_K$ and $R_{K^\ast}$, we determine the implications of the recent LHCb results for these observables on the coefficients of the SMEFT operators at low and high energies. We also take into account all $b\to s \ell\ell$ data, which combined lead to effective New Physics (NP) scenarios with SM pulls in excess of 5~$\sigma$. Thus the operators discussed in this paper would be the first dimension-six terms in the SM Lagrangian to be detected experimentally. Indirect constraints on these operators are also discussed. The results of this paper transcend the singularity of the present situation, and set a standard for future analyses in $b\to s$ transitions when the NP is assumed to lie above the electroweak scale.Comment: 10 pages, 2 figures, 3 tables. v2: references added, typos corrected, improved discussion in Sec. V, corrected coefficient of C7 in formula for RKstar in the low-bin, new figure with global fit in terms of SMEFT coefficients. Conclusions unchanged. v3: minor addition, shorter version to be published in PR

Three-Body Non-Leptonic B Decays and QCD Factorization

We extend the framework of QCD factorization to non-leptonic $B$ decays into three light mesons, taking as an example the decay $B^+ \to \pi^+ \pi^+ \pi^-$. We discuss the factorization properties of this decay in different regions of phase space. We argue that, in the limit of very large $b$-quark mass, the central region of the Dalitz plot can be described in terms of the $B \to \pi$ form factor and the $B$ and $\pi$ light-cone distribution amplitudes. The edges of the Dalitz plot, on the other hand, require different non-perturbative input: the $B \to \pi \pi$ form factor and the two-pion distribution amplitude. We present the set-up for both regions to leading order in both $\alpha_s$ and $\Lambda_{\rm QCD} / m_b$ and discuss how well the two descriptions merge. We argue that for realistic $B$-meson masses there is no perturbative center in the Dalitz plot, but that a systematic description might be possible in the context of two-pion states. As an example, we estimate the $B\to\rho\pi$ branching fraction beyond the quasi-particle approximation. We also discuss the prospects for studies of three-body and quasi-two-body non-leptonic $B$ decays from QCD.Comment: 20 pages, 8 figures. Version published in Nucl.Phys.

B→ππB\to\pi\pi Form Factors from Light-Cone Sum Rules with BB-meson Distribution Amplitudes

We study $B\to\pi\pi$ form factors using QCD light-cone sum rules with $B$-meson distribution amplitudes. These form factors describe the semileptonic decay $B\to \pi\pi \ell\bar{\nu}_{\ell}$, and constitute an essential input in $B\to \pi\pi \ell^+\ell^-$ and $B\to \pi\pi\pi$ decays. We employ the correlation functions where a dipion isospin-one state is interpolated by the vector light-quark current. We obtain sum rules where convolutions of the $P$-wave $\bar{B}^0\to \pi^+\pi^0$ form factors with the time-like pion vector form factor are related to universal $B$-meson distribution amplitudes. These sum rules are valid in the kinematic regime where the dipion state has a large energy and a low invariant mass, and reproduce analytically the known light-cone sum rules for $B\to \rho$ form factors in the limit of $\rho$-dominance with zero width, thus providing a systematics for so-far-unaccounted corrections to $B\to\rho$ transitions. Using data for the pion vector form factor, we estimate finite width-effects and the contribution of excited $\rho$-resonances to the $B\to\pi\pi$ form factors. We find that these contributions amount up to $\sim 20\%$ in the small dipion mass region where they can be effectively regarded as a nonresonant ($P$-wave) background to the $B\to\rho$ transition.Comment: 28 pages, 3 figures. A few comments added. Version published in JHE

New Physics constraints from optimized observables in B -> K*ll at large recoil

B -> K*ll angular observables have become a key ingredient in global model-independent analyses of b->s transitions. However, as experimental precision improves, the use of theoretically clean quantities becomes a crucial issue. Global analyses that use clean observables integrated in small bins are already a reality, opening up a new chapter in our quest for New Physics.Comment: 6 pages, 7 figures. Talk presented at QCD@Work 2012, June 18-21, Lecce, Ital