SHIFT@LHC: Searches for New Physics with Shifted Interaction on a Fixed Target at the Large Hadron Collider

New low-mass particles with very small couplings to standard model particles that travel significant distances before decaying are interesting candidates to address some of the most intriguing questions of modern physics. In this paper, I propose to extend the LHC's research program by installing a gaseous fixed target referred to as SHIFT at around 160 meters from the CMS interaction point. When the LHC proton beam collides with this target, interactions at a center of mass energy of $\approx$113 GeV would occur. The particles produced in such collisions, or their decay products, would travel through the rock and other material on their path, potentially reaching the CMS detector where they can be registered and studied. Such an approach would allow us to access otherwise uncovered regions of parameters phase space at a relatively low cost since it does not require constructing a new detector. Various aspects such as angular and lifetime coverage or material survival probability have been studied. The results are interpreted within two new physics models, namely, the Dark Photons and the Hidden Valley scenarios, and compared with the standard proton-proton physics program of CMS. A comparison is also made with the fixed target program at LHCb, as well as parasitic detectors such as FASER or MATHUSLA. The obtained results indicate that, despite assuming just 1% of the nominal CMS luminosity to be available to SHIFT, the physics reach could be extended by a factor of up to 150 (1000) for Dark Photon (Hidden Valley) scenarios, depending on the signal model parameters.