Elastic Potential: A proposal to discover elastic production of top quarks at the Large Hadron Collider

In this letter, I present the motivation and an example analysis method for discovering the elastic production of top-quark pairs at the LHC using forward proton tags, including an overview of the current theoretical tools and experimental acceptance. I show that it is possible to discover the semi-elastic process with only 300 pb${^{-1}}$ of data but that the fully-elastic case is currently out of reach. I also illustrate how the use of forward proton tags can result in limits on the branching ratio for flavor changing neutral current decays of the top quark of the form $t\rightarrow u\gamma$ and $t\rightarrow c\gamma$ of $