We generalise the Jacob-Wick helicity formalism, which applies to sequential decays, to effective field theories of rare decays of the type B → K J K (→ Kπ)¯ 1 2 . This is achieved by reinterpreting local interaction verticesbΓ µ 1 ..µn s¯ Γ µ 1 ..µn as a coherent sum of 1 → 2 processes mediated by particles whose spin ranges between zero and n. We illustrate the framework by deriving the full angular distributions forB →K 1¯ 2 andB →K * (→Kπ) 1¯ 2 for the complete dimension-six effective Hamiltonian for non-equal lepton masses. Amplitudes and decay rates are expressed in terms of Wigner rotation matrices, leading naturally to the method of moments in various forms. We discuss how higher-spin operators and QED corrections alter the standard angular distribution used throughout the literature, potentially leading to differences between the method of moments and the likelihood fits. We propose to diagnose these effects by assessing higher angular moments. These could be relevant in investigating the nature of the current LHCb anomalies in R K = B(B → Kµ + µ − )/B(B → Ke + e − ) as well as angular observables in B → K * µ + µ − .

We provide an extensive study of the lifetimes of singly charmed baryons and mesons, within the heavy quark expansion with all known corrections included. A special attention is devoted to the choice of the charm mass and wavefunctions of heavy baryons. We give our predictions for lifetimes, lifetime ratios, and semileptonic branching ratios of singly charmed baryons. Our results accommodate the experimentally-favoured hierarchy of singly charmed baryon lifetimes$$ \tau \left({\Xi}_c^0\right)<\tau \left({\Lambda}_c^{+}\right)<\tau \left({\Omega}_c^0\right)<\tau \left({\Xi}_c^{+}\right), $$ τ Ξ c 0 < τ Λ c + < τ Ω c 0 < τ Ξ c + , in contrast to earlier theoretical findings. Predictions for charmed meson lifetimes and semileptonic decay rates are in agreement with a recent comprehensive study and experimental results within uncertainties.

In the 1990s, very low experimental values for the lifetime ratio τ(Λb)/τ(Bd) triggered a considerable amount of doubt in the applicability of the heavy quark expansion (HQE), which is based on the assumption of quark-hadron duality (QHD) for inclusive total decay rates. However, these low values turned out to be the result of purely experimental problems, and the current HFLAV average reads τ(Λb)/τ(Bd) = 0.969(6). In this work, we present the Standard Model predictions for the b-baryon lifetimes within the framework of the HQE. In particular, we include for the first time the contribution of the Darwin term and we update the estimates for the matrix elements of the dimension-six four-quark operators. Within experimental and theoretical uncertainties, we find excellent agreement between the data and the HQE predictions, and thus no indication for any visible violation of QHD. Our numerical results can be summarised by the ratios τ(Λb)/τ(Bd) = 0.955(14), $$ \tau \left({\varOmega}_b^{-}\right) $$ τ Ω b − /τ(Bd) = 1.081(42), and $$ \tau \left({\Xi}_b^0\right)/\tau \left({\Xi}_b^{-}\right) $$ τ Ξ b 0 / τ Ξ b − = 0.929(28).

The V-A structure of the weak interactions leads to definite amplitude hierarchies in exclusive heavy-to-light decays mediated by b → (d, s)γ and b → (d, s) ¯ . However, the extraction of right-handed currents beyond the Standard Model is contaminated by V-A long-distance contributions leaking into right-handed amplitudes. We propose that these quantum-number changing long-distance contributions can be controlled by considering the almost parity-degenerate vector meson final states by exploiting the opposite relative sign of left-versus right-handed amplitudes. For example, measuring the time-dependent rates of a pair of vector V (J P = 1 − ) and axial A(1 + ) mesons in B → (V, A)γ, up to an order of magnitude is gained on the theory uncertainty prediction, controlled by long-distance ratios to the righthanded amplitude. This renders these decays clean probes to null tests, from the theory side. referred to as short-distance (SD) contributions hereafter, obey exact algebraic relations, leading to accidental control in the SD part. However, sizeable tree-level four-quark operators with charm and up quarks, H eff ∼d L γ µ UŪ L γ µ b (U = u, c), induce genuine long-distance (LD) effects, which are more difficult to control. It was argued, based on studying the inclusivē B → X s γ decay, that such contaminations could be rather significant [12], whereas actual computations show smaller effects in exclusive channels [13][14][15][16][17].In this article, we show that these LD effects can be controlled by a symmetry that in turn also explains the smallness found in the concrete computation [13] quoted just above. The symmetry in question is the chiral restoration limit. The crucial point is that decays of opposite parity, such asB → ρ(1 −− )γ versusB → a 1 (1 ++ )γ, are opposite in sign in the righthanded amplitude between the exact SD and LD contributions (originating from the sizeable V-A part). 1 While decays of axial mesons have received some attention as complementary probes for RHC (e.g. [21-23]), we advocate that the combination of the two decay channels allows for a cleaner extraction of the relevant observables controlled by ratios of vector to axial LD amplitudes. In light-cone approaches, this necessitates axial vector meson distribution amplitudes (DAs) [24], whose symmetry relations with vector meson DAs can be studied rather systematically [25]. For a simplified discussion of the main ideas of this paper we refer the reader to [26].The paper is organised as follows. In section 2 it is shown, using the path integral, that the fraction of LD-over SD-RHC flips sign for parity doublers. In section 3, the parity doublers are listed (section 3.1), followed by a discussion of the sources of correction to the symmetry limit in section 3.2. Applications to the time-dependent rates ofB → (V, A)γ, a detailed breakdown ofB s → φ(f 1 )γ, and remarks on B → (V, A) ¯ are presented in sections 4.1, 4.2 and 4.3 respectively. The paper ends with conclusions in section 5, including comments on the experimental feasibility of...