Performance of vertex reconstruction algorithms for detection of new long-lived particle decays within the ATLAS inner detector

Several theories beyond the Standard Model predict the existence of new particles with macroscopic lifetimes of $c\tau\gtrsim {\cal O}(1~{\rm mm})$ that could be created in $pp$ collisions at the Large Hadron Collider. These theories often give rise to signatures requiring dedicated tracking and vertexing techniques beyond conventional algorithms. This note presents a secondary vertex reconstruction algorithm designed to search for long-lived particles decaying within the ATLAS inner detector. Its performance is characterised across a range of theories beyond the Standard Model with unique final states that highlight various aspects of the reconstruction.