Bounds on quantum gravity parameter from the SU(2) NJL effective model of QCD

Abstract

The existence of a minimal measurable length, as an effective cutoff in the ultraviolet regime, is a common feature of all approaches to the quantum gravity proposal. It is widely believed that this length scale will be of the order of the Planck length , where is a dimensionless parameter that should be fixed only by the experiments. This issue can be taken into account through the deformed momentum spaces with compact topologies. In this paper, we consider minimum length effects on the physical quantities related to three parameters of the SU(2) Nambu-Jona-Lasinio effective model of QCD by means of the deformed measure which is defined on the compact momentum space with S3 topology. This measure is suggested by the doubly special relativity theories, Snyder deformed spaces, and the deformed algebra that is obtained in the light of the stability theory of Lie algebras. Using the current experimental data of the particle physics collaboration, we constrain the quantum gravity parameter λ0 and we compare our results with bounds that are arisen from the other experimental setups.