Abstract
Beauty baryons are being observed in large numbers in the LHCb detector. The rich kinematic distributions of their multibody decays are therefore becoming accessible and provide us with new opportunities to search for CP violation. We analyse the angular distributions of some three- and four-body decays of spin-$1/2$ baryons using the Jacob-Wick helicity formalism. The asymmetries that provide access to small differences of CP-odd phases between decay amplitudes of identical CP-even phases are notably discussed. The understanding gained on processes featuring specific resonant intermediate states allows us to establish which asymmetries are relevant for what purpose. It is for instance shown that some CP-odd angular asymmetries measured by the LHCb collaboration in the $\Lambda_b \to \Lambda\,\varphi \to p\,\pi\, K^+ K^-$ decay are expected to vanish identically.
Highlights
Certain imaginary parts of decay amplitude interferences become accessible through T -even angular distributions, in terms proportional to this T -odd polarisation component of the decaying particle
We have studied the angular distributions of some three- and four-body decays of spin-1/2 states, focusing on the discrete symmetry transformation properties of the different contributions
Special attention has been devoted to the two types of angular asymmetries that could serve to access small differences of CP-odd phases between decay amplitudes of identical CP-even phases
Summary
The following four- and three-body decays (depicted in figure 1) will be considered: 01/2 −→ a1/2,3/2 b1 −→ 11/2 20 31/2 41/2, −→ 11/2 20 30 40, 01/2 −→ a1/2,3/2 b1 −→ 11/2 20 b1, −→ a1/2,3/2 b0 −→ 11/2 20 b0, where the superscripts of particle labels specify their spins. When appearing as a final-state particle, in the three-body decays we consider, the b1 vector is taken massless so that it has no λb = 0 zero helicity state (and the A± amplitudes defined below are absent). In each four-body process considered here, for the b1 decay, there is one single independent combination of squared helicity amplitudes: either |Mb(1/2, −1/2)|2 + |Mb(−1/2, 1/2)|2, or |Mb(0, 0)|2. Note a relative complex conjugation of the amplitudes defined here and there, as well as the use of the Jacob-Wick convention there which leads to expressions identical to the ones we obtain with the Jackson convention for the terms compared when φΛ is set to 0 there Both table 7 and the A± dependence of table 3 agree with eq (16) and (21) of ref.
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