Abstract
We study the differential decay rate for the rare Λ b → Λ(→ Nπ)ℓ + ℓ − transition, including a determination of the complete angular distribution, assuming unpolarized Λ b baryons. On the basis of a properly chosen parametrization of the various helicity amplitudes, we provide expressions for the angular observables within the Standard Model and a subset of new physics models with chirality-flipped operators. Hadronic effects at low recoil are estimated by combining information from lattice QCD with (improved) form-factor relations in Heavy Quark Effective Theory. Our estimates for large hadronic recoil — at this stage — are still rather uncertain because the baryonic input functions are not so well known, and non-factorizable spectator effects have not been worked out systematically so far. Still, our phenomenological analysis of decay asymmetries and angular observables for Λ b → Λ(→ Nπ)ℓ + ℓ − reveals that this decay mode can provide new and complementary constraints on the Wilson coefficients in radiative and semileptonic b → s transitions compared to the corresponding mesonic modes.
Highlights
Exclusive hadronic decays, by definition, are theoretically challenging because the calculation of decay amplitudes induces a number of hadronic uncertainties related to longdistance QCD dynamics
In the present article we have investigated the phenomenological potential of the rare decay Λb → Λ + − with a subsequent, self-analyzing Λ → N π transition
From the kinematics of the primary and secondary decay we have worked out the fully differential decay width that follows from the Standard Model (SM) operator basis for radiative b → s transitions and its chirality-flipped counterpart which may be relevant for physics beyond the SM
Summary
We assign particle momenta and spin variables for the baryonic states in the decay according to: Λb(p, sΛb) → Λ(k, sΛ) +(q1) −(q2) , Λ(k, sΛ) → N (k1, sN ) π(k2) ,. Si are the projections of the baryonic spins onto the z-axis in their rest frames. We end up with four independent kinematic variables, which can be chosen as the invariant mass q2, the helicity angles θΛ and θ , and the azimuthal angle φ, see figure 1, which are defined in the relevant Lorentz frames in appendix D. We introduce a set of virtual polarization vectors εμ(λ = t, +, −, 0) with q · ε(±) = q · ε(0) = 0, which in the dilepton rest frame take the canonical form as shown in appendix D.
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