Constraints on long range force from perihelion precession of planets in a gauged L_{e}L_{μ ,τ} scenario
Abstract
The standard model leptons can be gauged in an anomaly free way by three possible gauge symmetries namely L_{e}L_{μ} , L_{e}L_{τ} , and L_{μ}L_{τ} . Of these, L_{e}L_{μ} and L_{e}L_{τ} forces can mediate between the Sun and the planets and change the perihelion precession of planetary orbits. It is well known that a deviation from the 1 /r^{2} Newtonian force can give rise to a perihelion advancement in the planetary orbit, for instance, as in the well known case of Einstein's gravity (GR) which was tested from the observation of the perihelion advancement of the Mercury. We consider the long range Yukawa potential which arises between the Sun and the planets if the mass of the gauge boson is M_{Z'}≤O (10^{19}) eV . We derive the formula of perihelion advancement for Yukawa type fifth force due to the mediation of such U (1_{) LeLμ,τ} gauge bosons. The perihelion advancement for Yukawa potential is proportional to the square of the semi major axis of the orbit for small M_{Z'}, unlike GR where it is largest for the nearest planet. For higher values of M_{Z'}, an exponential suppression of the perihelion advancement occurs. We take the observational limits for all planets for which the perihelion advancement is measured and we obtain the upper bound on the gauge boson coupling g for all the planets. The Mars gives the stronger bound on g for the mass range ≤10^{19}eV and we obtain the exclusion plot. This mass range of gauge boson can be a possible candidate of fuzzy dark matter whose effect can therefore be observed in the precession measurement of the planetary orbits.
 Publication:

European Physical Journal C
 Pub Date:
 April 2021
 DOI:
 10.1140/epjc/s10052021090789
 arXiv:
 arXiv:2002.02935
 Bibcode:
 2021EPJC...81..286P
 Keywords:

 High Energy Physics  Phenomenology;
 Astrophysics  Earth and Planetary Astrophysics;
 Astrophysics  High Energy Astrophysical Phenomena;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 19 pages, 3 figures, 2 tables