http://arxiv.org/abs/2002.02935
The standard model particles can be gauged in an anomaly free way by three possible gauge symmetries namely ${L_e-L_\mu}$, ${L_e-L_\tau}$, and ${L_\mu-L_\tau}$. Of these, ${L_e-L_\mu}$ and ${L_e-L_\tau}$ forces can mediate between the Sun and the planets and change 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 which was tested from the observation of the perihelion advancement of the Mercury. We consider the Yukawa potential of ${L_e-L_{\mu,\tau}}$ force which arises between the Sun and the planets if the mass of the gauge boson is $M_{Z^{\prime}}\leq \mathcal{O}(10^{-19})\rm {eV}$. We derive the formula for the perihelion advancement for such Yukawa type fifth force. We find that perihelion advancement is proportional to the square of the semi major axis of the orbit for the Yukawa potential, unlike GR, where it is largest for the nearest planet. We take the observational limits of all planets for which the perihelion advancement is measured and we obtain the gauge boson coupling $g$ in the range $10^{-18}$ to $10^{-16}$ for the mass range $10^{-22}$eV to $10^{-18}$eV. 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.
T. Poddar, S. Mohanty and S. Jana
Mon, 10 Feb 20
36/59
Comments: 16 pages, 2 figures, 2 tables