Abstract
We consider two-body and quasi-two-body decays of the type f_1 rightarrow f_2 B, where f_1 and f_2 are spin-1/2 fermions and B a spin-0 or spin-1 boson. After recalling the non-covariant formalism for decay amplitudes, we derive the expression of the differential decay width and of the polarizations of the final spinning particles, both on- and off-shell. We find an intriguing geometrical interpretation of the results about the polarization. We also illustrate some methods for measuring the polarizations of the resonances and for optimizing data analysis. Then we propose applications to semi-leptonic weak decays, with a major attention to the T-odd component of the polarization; this may help to find, simultaneously, possible time-reversal violations and hints to physics beyond the standard model. We suggest also a CPT test. Last, we discuss some T-odd observables for the production process of f_1 and for the study of the strong final state interactions of non-leptonic decays.
Highlights
The search for new physics (NP) beyond the standard model (SM) is especially stimulating that the Higgs boson has been found [1,2]
We establish a relation between some measurable angle and a given quantum-mechanical phase; we single out some T -odd observables, including the above mentioned angle, that are sensitive to NP; we indicate the most favorable conditions for exploiting the available data, even when the statistics is not so rich
We resume the main results of our paper, concerning thetwo-body decays (2)
Summary
The search for new physics (NP) beyond the standard model (SM) is especially stimulating that the Higgs boson has been found [1,2]. In the past few years, some data concerning semi-leptonic decays exhibited strong tensions with the SM predictions [7,8,9,10,11] Confirmations to such hints are expected from the polarization of spinning particles produced in weak decays, the semi-leptonic ones, like t → b ν , b → c ν. Where fi are spin-1/2 fermions and B is a spin-0 (S) or spin (V ) boson This includes the decays (1) – assuming they occur through the W -boson and through the charged Higgs H -, and non-leptonic decays like b → J/ψ, b → cρ−, c → π +(K +). Our main aim is to apply such results to specific semileptonic decays of the type (2), quite suitable for testing the SM; non-leptonic decays like (3) could give important information about the T -odd effects of the strong interactions.
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