A complete description of P- and S-wave contributions to the B0 → K+π−ℓ+ℓ− decay

In this paper we present a detailed study of the four-body decay B0 → K+π−ℓ+ℓ−, where tensions with the Standard Model predictions have been observed. Our analysis of the decay with P- and S-wave contributions to the K+π− system develops a complete understanding of the symmetries of the distribution, in the case of massless and massive leptons. In both cases, the symmetries determine relations between the observables in the B0 → K+π−ℓ+ℓ− decay distribution. This enables us to define the complete set of observables accessible to experiments, including several that have not previously been identified. The new observables arise when the decay rate is written differentially with respect to $$ {m}_{K_{\pi }} $$ m K π . We demonstrate that experiments will be able to fit this full decay distribution with currently available data sets and investigate the sensitivity to new physics scenarios given the experimental precision that is expected in the future.The symmetry relations provide a unique handle to explore the behaviour of S-wave observables by expressing them in terms of P-wave observables, therefore minimising the dependence on poorly-known S-wave form factors. Using this approach, we construct two theoretically optimized S-wave observables and explore their sensitivity to new physics. By further exploiting the symmetry relations, we obtain the first bounds on the S-wave observables using two different methods and highlight how these relations may be used as cross-checks of the experimental methodology and the parametrization of the B0 → K+π−ℓ+ℓ− differential decay rate. We identify a zero-crossing point that would be at a common dilepton invariant mass for a subset of P- and S-wave observables, and explore the information on new physics and hadronic effects that this zero point can provide.

Lepton flavour violating $${\Lambda }_{{b}}$$ decays in non-universal $${Z}^{\prime }$$ model

Motivated by the recent LHCb results of lepton flavour violation on $$b\rightarrow s$$ b → s and $$b\rightarrow c$$ b → c transitions we study the lepton flavour violating (LFV) baryonic decays $${\Lambda }_{b}\rightarrow {\Lambda }l_{i}^{+}l_{j}^{-}$$ Λ b → Λ l i + l j - in non-universal $$Z^{\prime }$$ Z ′ model. We discuss the two-fold decay distribution of $${\Lambda }_{b}\rightarrow {\Lambda }l_{i}^{+}l_{j}^{-}$$ Λ b → Λ l i + l j - decays in terms of transversity amplitudes. From this distribution we study the differential branching ratio and lepton side forward-backward asymmetry in new physics (NP). The predicted values of the observables are very interesting and that might emboss the footprints of NP more aesthetically.

Lepton flavor violating $$\Lambda _b\rightarrow \Lambda \ell _1\ell _2$$ decay

Inspired by the recent hints of lepton flavor universality violation in $$b\rightarrow s\ell \ell $$b→sℓℓ and $$b\rightarrow c\ell \nu $$b→cℓν transitions, we study lepton flavor violating exclusive $$\Lambda _b\rightarrow \Lambda \ell _1^+\ell _2^-$$Λb→Λℓ1+ℓ2- ($$\ell _1\ne \ell _2$$ℓ1≠ℓ2) decay, which is forbidden in the Standard Model. Starting from a general effective Hamiltonian for a $$b\rightarrow s\ell _1^+\ell _2^-$$b→sℓ1+ℓ2- transition that includes vector and axial-vector operators, and scalar and pseudo-scalar operators, we derive a two-fold decay distribution of $$\Lambda _b\rightarrow \Lambda \ell _1^+\ell _2^-$$Λb→Λℓ1+ℓ2-. The distribution helps us to construct the differential branching ratio and the lepton-side forward–backward asymmetry, which are studied in a vector leptoquark model. The parameter space of the vector leptoquark model is constrained by low energy observables.