Quantum gravity effects in the infrared: a theoretical derivation of the lowenergy fine structure constant and mass ratios of elementary particles
Abstract
We have recently proposed a prequantum, prespacetime theory as a matrixvalued Lagrangian dynamics on an octonionic spacetime. This theory offers the prospect of unifying internal symmetries of the standard model with pregravitation. We explain why such a quantum gravitational dynamics is in principle essential even at energies much smaller than Planck scale. The dynamics can also predict the values of free parameters of the lowenergy standard model: these parameters arising in the Lagrangian are related to the algebra of the octonions, which define the underlying noncommutative spacetime on which the dynamical degrees of freedom evolve. These free parameters are related to the exceptional Jordan algebra J_{3}(8 ) , which describes the three fermion generations. We use the octonionic representation of fermions to compute the eigenvalues of the characteristic equation of this algebra and compare the resulting eigenvalues with known mass ratios for quarks and leptons. We show that the ratios of the eigenvalues correctly reproduce the [square root of the] known mass ratios. In conjunction with the trace dynamics Lagrangian, these eigenvalues also yield a theoretical derivation of the lowenergy fine structure constant.
 Publication:

European Physical Journal Plus
 Pub Date:
 June 2022
 DOI:
 10.1140/epjp/s13360022028684
 arXiv:
 arXiv:2205.06614
 Bibcode:
 2022EPJP..137..664S
 Keywords:

 Physics  General Physics;
 High Energy Physics  Theory
 EPrint:
 v2: 67 pages, 11 figures, minor changes in text so as to improve clarity