Two-body decays in deformed relativity

Abstract

Deformed relativistic kinematics is a framework which captures effects, that are expected from particles and fields propagating on a quantum spacetime, effectively. They are formulated in terms of a modified dispersion relation and a modified momentum conservation equation. In this work we use Finsler geometry to formulate deformed relativistic kinematics in terms of particle velocities. The relation between the Finsler geometric velocity dependent formulation and the original momentum dependent formulation allows us to construct deformed Lorentz transformations between arbitrary frames. Moreover, we find the corresponding compatible momentum conservation equation to first order in the Planck scale deformation of special relativity based on the $\kappa$-Poincaré algebra in the bicrossproduct basis. We find that the deformed Lorentz transformations, as well as the deformed time dilation factor, contain terms that scale with the energy of the particle under consideration to the fourth power. We derive how the distributions of decay products are affected when the deformed relativity principle is satisfied and find, for the case of a pion decaying into a neutrino and a muon, that the ratio of expected neutrinos to muons with a certain energy is just slightly modified when compared to the predictions based on special relativity. We also discuss the phenomenological consequences of this framework for cosmic-ray showers in the atmosphere.

27+4 pages, 1 figure. Title and abstract were modified. 3 new appendices. Important modifications in the second half of the paper: absence of strong threshold effects. Matches version published in JHEP

References in corpus (12)

• Testing Hadronic Interactions at Ultrahigh Energies with Air Showers Measured by the Pierre Auger Observatory
• Lorentz-violation-induced arrival delays of cosmological particles
• Realization of DSR-relativistic symmetries in Finsler geometries
• Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes
• Probing Quantum Gravity with Imaging Atmospheric Cherenkov Telescopes
• Beyond Special Relativity at second order
• A bound on Planck-scale deformations of CPT from muon lifetime
• Dispersion relations in finite-boost DSR
• Bounds on Relativistic Deformed Kinematics from the Physics of the Universe Transparency
• An experimental test of gravity at high energy
• Planck-scale deformation of CPT and particle lifetimes
• Robust constraints on Lorentz Invariance Violation from H.E.S.S., MAGIC and VERITAS data combination

Cited by in corpus (8)

• White Paper and Roadmap for Quantum Gravity Phenomenology in the Multi-Messenger Era
• Massless Dirac Perturbations in a Consistent Model of Loop Quantum Gravity Black Hole: Quasinormal Modes and Particle Emission Rates
• Quantum Configuration and Phase Spaces: Finsler and Hamilton Geometries
• Modified particle lifetimes as a signature of deformed relativity
• Revisiting Legendre transformations in Finsler geometry
• Weak equivalence principle and nonrelativistic limit of general dispersion relations
• Muon accelerators -- Muon lifetime measurements as window to Planck scale physics
• Experimental Bounds on Deformed Muon Lifetime Dilation