Search for binary-channel metal-rich RR~Lyrae candidates

The existence of dynamically young and metal-rich RR Lyrae stars challenges conventional notions of these variable stars. One possible scenario for their formation and evolution is via binary channels involving mass transfer. This study presents the detection of nine fundamental-mode RR Lyrae stars residing in the thin disk of the Milky Way with metallicities higher than [Fe/H] > -1.0 dex and showing proper motion anomalies. Our thin disk classification is based on kinematics and supported by $\alpha$-element abundances, where possible. We searched for indications of the light-travel time effect (LTTE) in the available literature sources and the TESS photometric data of the stars but found no signs of periodic variations induced by companions within the expected period range. This could be because of a lack of observations as well as sparse measurements and large gaps in the data. We propose a continued search for signs of binarity and a subsequent long-term follow-up of nine targets that satisfy all of our search criteria. Beyond these targets, we also report the detection of slow phase changes in the Blazhko star ST Pic, which could be compatible with the LTTE.