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 − .
The coupled system of the quark-gluon vertex and quark propagator Dyson-Schwinger equations (DSEs) is investigated within Landau gauge QCD. The aim is to get a deeper insight into the mechanisms of quark confinement and dynamical chiral symmetry breaking and into a possible relation between these two phenomena. To this end an earlier study is extended by improving systematically on the truncations imposed on the quark-gluon vertex DSE. A clear infrared enhancement for all tensor structures of the quark-gluon vertex is obtained.Xth Quark Confinement and the Hadron Spectrum,
The quark-gluon vertex in Landau gauge QCD is investigated in the Dyson-Schwinger approach. The aim is to obtain a fully self-consistent solution of the quark propagator and the quark-gluon vertex Dyson-Schwinger equation (DSE) in the vacuum using the gluon propagator as input from other calculations. The truncation scheme used in an earlier study is systematically improved and the first decisive step towards a full solution is presented. First results for the quark propagator with a fully dressed quarkgluon vertex in a truncation that incorporates all twelve vertex tensorstructures are shown.
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