https://doi.org/10.1140/epjc/s10052-021-09078-9
Regular Article – Theoretical Physics
Constraints on long range force from perihelion precession of planets in a gauged 
scenario
1
Theoretical Physics Division, Physical Research Laboratory, 380009, Ahmedabad, India
2
Département de Physique Théorique, Université de Genève, 24 quai Ernest Ansermet, 1211 Genève 4, Geneva, Switzerland
3
Discipline of Physics, Indian Institute of Technology, 382355, Gandhinagar, India
4
Department of Physics, Sitananda College, 721631, Nandigram, India
c soumyajana.physics@gmail.com, Soumya.Jana@etu.unige.ch
Received:
22
January
2021
Accepted:
20
March
2021
Published online:
3
April
2021
The standard model leptons can be gauged in an anomaly free way by three possible gauge symmetries namely 
, 
, and 
. Of these, and 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 
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 
. We derive the formula of perihelion advancement for Yukawa type fifth force due to the mediation of such 
gauge bosons. The perihelion advancement for Yukawa potential is proportional to the square of the semi major axis of the orbit for small 
, unlike GR where it is largest for the nearest planet. For higher values of , 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 
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.
© The Author(s) 2021
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