Precise Characterization of a Nonuniversal Efimov State and Few-body Interactions in \textsuperscript{39}K

We perform precise studies of two- and three-body interactions near an intermediate-strength Feshbach resonance in \textsuperscript{39}K. We determine, with unprecedented accuracy, the location of the resonance to be $33.5821(13)$ Gauss. Measurement of dimer binding energies, spanning three orders of magnitude, enables the construction of a coupled-channel model for the determination of scattering lengths with low uncertainty. With the derived scattering length map, we discover that this ground Efimov resonance is located at $|a_-|/r_{vdW}=14.19(16)$ ($r_{vdW}$ is the van der Waals length), significantly deviating from the van der Waals universal value $9.73$. A three-body model is introduced to explain the origin of this anomaly. To enrich our understanding of this Efimov spectrum, we extend our study to positive scattering lengths where atom-dimer interactions give rise to additional complexities in scattering processes.