Systematic-free limit on new light scalar bosons via isotope shift spectroscopy in Ca$^+$

We report a precise measurement of the isotope shifts in the $4^2$S$_{1/2} \rightarrow 3^2$D$_{3/2}$ electric quadrupole transition at 732~nm in $^{40 - 42,44,48}$Ca$^+$ via high-resolution laser spectroscopy of co-trapped ions, finding measured shifts of 2,775,392,374.8(6.0), 5,347,679,835.1(5.9), and 10,003,129,115.1(5.7)\,Hz between $^{42,44,48}$Ca$^+$and $^{40}$Ca$^+$, respectively. When combined with prior measurements on the $4^2$S$_{1/2} \rightarrow 3^2$D$_{5/2}$ transition [Phys. Rev. A 100, 022514 (2019), https://journals.aps.org/pra/abstract/10.1103/PhysRevA.100.022514] a King Plot analysis shows the data to be consistent with linearity below the level of parts per billion. This observed linearity, which is free of nuclear systematics, improves the previous isotope-shift based limits of Ca$^+$ for couplings of a scalar boson beyond the Standard Model to electrons and neutrons by a factor of 3. Our new limit excludes part of the coupling range remaining for a new physics interpretation after accounting for one higher-order nuclear term in the nonlinear King plot of Yb/Yb$^+$.