Generalized helicity formalism, higher moments, and theB→KJK(→Kπ)

Abstract

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 − .

Lepton flavor violation in exclusive $$b\rightarrow s$$ b → s decays

“…[43], which is even more explicitly specified in Ref. [44] and fixed in such a way that they coincide with the conventions adopted in experiments at the LHC [2,3]. In the appendix of the present paper we give necessary details concerning the kinematics of this process.…”

A leptoquark model to accommodate R K exp < R K SM and R K ∗ exp < R K ∗

“…T /2, where we take into account the correct signs [34] to correctly compare with experimental results. In figure 3 we plot the resulting R K and R K * by relying only on the effective theory and on the value of C µµ 9 = −C µµ 10 obtained from the fit with the data as discussed above.…”

“…, and other similar decay modes [33,34]. As we mentioned in introduction, to obtain both R K < R SM K and R K * < R SM K * we need a NP contribution to the vector and axial Wilson coefficients, and in particular those coupling to the left-handed quark effective current, i.e.…”

B →Vℓ+ℓ− in the Standard Model from light-cone sum rules

“…refs. [26,77,78] for definitions of the angular observables) and the B + → K * + µ + µ − branching ratio are given in tables 6, 7 and 8 respectively. Crucially uncertainties are split into parametric, 16 FF and non-factorisable charm uncertainties as parameterised in 13 The problem is that the two effects are computed in two, slightly, different frameworks.…”