The standard model leptons 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 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 \(M_{Z^{\prime }}\le \mathcal {O}(10^{-19})\mathrm {eV}\). We derive the formula of perihelion advancement for Yukawa type fifth force due to the mediation of such \(U(1)_{L_e-L_{\mu ,\tau }}\) gauge bosons. The perihelion advancement for Yukawa potential is proportional to the square of the semi major axis of the orbit for small \(M_{Z^{\prime }}\), unlike GR where it is largest for the nearest planet. For higher values of \(M_{Z^{\prime }}\), 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 \(\le 10^{-19}\mathrm {eV}\) 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.

可以通过三种可能的规范对称性来规范标准模型轻子，即\（{L_e-L_ \ mu} \），\（{L_e-L_ \ tau} \）和\（{L_ \ mu- L_ \ tau} \）。其中\（{L_e-L_ \ mu} \）和\（{L_e-L_ \ tau} \）力可以在太阳和行星之间进行调解，并改变行星轨道的近日点进动。众所周知，与\（1 / r ^ 2 \）的偏差牛顿力会引起行星轨道近日点前进，例如，爱因斯坦引力（GR）的著名案例就是通过观察水星近日点前进来测试的。如果规范玻色子的质量为\（M_ {Z ^ {\ prime}} \ le \ mathcal {O}（10 ^ {-19}）\，我们考虑在太阳与行星之间产生的远川汤川势。 mathrm {eV} \）。由于这种\（U（1）_ {L_e-L _ {\ mu，\ tau}} \）玻色子的介导，我们得出了Yukawa型第五力近日点推进的公式。对于小\（M_ {Z ^ {\ prime}} \），汤川势的近日脑前进与轨道半长轴的平方成正比。，而GR与最近的行星最大。对于\（M_ {Z ^ {\ prime}} \）较高的值，会发生对近日点推进的指数抑制。我们对测量了近日点前进的所有行星采取观测极限，并获得所有行星的标准玻色子耦合g的上限。对于质量范围\（\ le 10 ^ {-19} \ mathrm {eV} \），火星在g上给出了更强的界线，并获得了排除图。规范玻色子的质量范围可能是模糊暗物质的可能候选者，因此可以在行星轨道的进动测量中观察到其影响。