Abstract
Muon decay is self-analyzing: the spectral-angular distribution of the emitted electron reveals the spin orientation of the polarized muon. Here, we show that the same feature applies to muons in non-plane-wave states and helps reveal the rich polarization opportunities available. We focus on the so-called vortex states, in which the muon carries a non-zero orbital angular momentum with respect to the average propagation direction and exhibits a cone structure in the momentum distribution. We compute the spectrum and the angular distribution of the electrons emitted in decays of vortex muons and show that the most revealing observable is not the angular distribution but the fixed-angle electron spectra. Even for very small cone opening angles of the vortex muons, it will be easy to observe significant modifications of the electron spectra which would allow one to distinguish vortex muons from approximately plane wave muons, as well as to differentiate among various polarization states. These features will be the key to tracking the evolution of vortex muons in external magnetic fields.
Highlights
Particle physics with carefully engineered nonplanewave states of initial particles is an emergent field whose full potential is still to be explored
The spin evolve, and how this evolution is affected by the inhomogeneities of the magnetic field of the ring. All these effects can be monitored through the decay of muons μ → eνeνμ, which is a self-analyzing process [43]; namely, the correlations between the spectrum and the angular distribution of the emitted electron reveal the orientation of the muon spin
We study how the spectrum and the angular distribution of the electron reveal the parameters of the vortex muon, including its polarization state
Summary
Particle physics with carefully engineered nonplanewave states of initial particles is an emergent field whose full potential is still to be explored. The spin evolve, and how this evolution is affected by the inhomogeneities of the magnetic field of the ring All these effects can be monitored through the decay of muons μ → eνeνμ, which is a self-analyzing process [43]; namely, the correlations between the spectrum and the angular distribution of the emitted electron reveal the orientation of the muon spin. It is this self-analyzing property which lies at the heart of several generations of experiments measuring the muon anomalous magnetic moment g − 2 with increasing precision [43,44]. We study how the spectrum and the angular distribution of the electron reveal the parameters of the vortex muon, including its polarization state. IV we discuss the results, briefly mention experimental prospects, and draw conclusions
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