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

TL;DR

This paper investigates how minimal length effects from quantum gravity theories influence parameters in the $SU(2)$ NJL model of QCD, constraining the quantum gravity parameter using experimental data.

Contribution

It introduces a deformed measure on compact momentum space to incorporate minimal length effects into the NJL model of QCD, providing new bounds on quantum gravity parameters.

Findings

Quantum gravity parameter $\lambda_0$ constrained by experimental data.

Deformed measure affects physical quantities in the NJL model.

Results are compared with bounds from other experimental setups.

Abstract

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 $\lambda=\lambda_0\,l_{_{\rm Pl}}$, where $\lambda_0\sim{\mathcal O}(1)$ 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 compact momentum space with ${\mathbf S}^3$ 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 constraint quantum gravity parameter $\lambda_0$ and we compare our results with bounds that are arisen from the other experimental setups.