Abstract
Planck scale modified dispersion relations are one way how to capture the influence of quantum gravity on the propagation of fundamental point particles effectively. We derive the time dilation between an observer's or particle's proper time, given by a Finslerian length measure induced from a modified dispersion relation, and a reference laboratory time. To do so, the Finsler length measure for general first order perturbations of the general relativistic dispersion relation is constructed explicitly. From this we then derive the time dilation formula for the $\kappa$-Poincar\'e dispersion relation in several momentum space bases, as well as for modified dispersion relations considered in the context of string theory and loop quantum gravity. Most interestingly we find that the momentum Lorentz factor in the present and future colliders can, in principle, become large enough to constrain the Finsler realization of the $\kappa$-Poincar\'e dispersion relation in the bicrossproduct basis as well as a string theory inspired modified dispersion relation, at Planck scale sensitivity with the help of the muon's lifetime.
Highlights
A major difficulty in the search for quantum gravity effects is that the scale at which they are expected to become relevant is at the Planck energy EP of order 1019 GeV, respectively at distance of the Planck length lP of order 10−35 m
Most interestingly we find that the momentum Lorentz factor in the present and future colliders can, in principle, become large enough to constrain the Finsler realization of the κ-Poincaredispersion relation in the bicrossproduct basis as well as a string theory inspired modified dispersion relation, at Planck scale sensitivity with the help of the muon’s lifetime
On the basis of a deformed relativity principle, which is implied by the Finsler geometric treatment of the modified dispersion relation,1 we find that the deformation parameter, κ or MQ, could be constrained by muon lifetime measurements at the colliders at the order of magnitude of the Planck energy, reaching Planck scale sensitivity for this quantum gravity phenomenology model with muon lifetimes
Summary
A major difficulty in the search for quantum gravity effects is that the scale at which they are expected to become relevant is at the Planck energy EP of order 1019 GeV, respectively at distance of the Planck length lP of order 10−35 m. In the absence of a complete theory of quantum gravity, phenomenological models which shall capture aspects of quantum gravity often employ Planck scale modified dispersion relations (MDRs) to effectively capture the interaction of particles, propagating through spacetime, with the quantum nature of gravity [1,2,3]. On the basis of a deformed relativity principle, which is implied by the Finsler geometric treatment of the modified dispersion relation, we find that the deformation parameter, κ or MQ, could be constrained by muon lifetime measurements at the colliders at the order of magnitude of the Planck energy, reaching Planck scale sensitivity for this quantum gravity phenomenology model with muon lifetimes.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
