Long term measurement of the $^{87}$Sr clock frequency at the limit of primary Cs clocks

We report on a series of 42 measurements of the transition frequency of the 429~THz (5s$^2$)~$^1$S$_0$--(5s5p)~$^3$P$_0$ line in $^{87}$Sr taken over three years from 2017 to 2019. They have been performed at the Physikalisch-Technische Bundesanstalt (PTB) between the laboratory strontium lattice clock and the primary caesium fountain clocks CSF1 and CSF2. The length of each individual measurement run has been extended by use of a hydrogen maser as flywheel to improve the statistical uncertainty given by the Cs clocks. We determine an averaged transition frequency of $429:228:004:229:873.00(0.07)$~Hz with $1.5times10^{-16}$ fractional uncertainty, at the limit of the current realization of the unit hertz. Analysis of the data provides an improved limit on the coupling of the gravitational potential of the Sun to the proton--electron mass ratio $mu$, and confirms the limits on its temporal drift.