Of contact interactions and colliders

The hierarchy of scales which would allow dimension-six contact interactions to parametrize new physics may not be verified at colliders. Instead, we explore the feasibility and usefulness of parametrizing the high-energy tail of distributions at the LHC using form factors. We focus on the process $pp\ensuremath{\rightarrow}\ensuremath{\ell}\overline{\ensuremath{\ell}}$ in the presence of $t$- (or $s$)-channel new physics, guess a form factor from the partonic cross section, and attempt to use data to constrain its coefficients, and the coefficients to constrain models. We find that our choice of form factor describes $t$-channel exchange better than a contact interaction, and the coefficients in a particular model can be obtained from the partonic cross section. We estimate bounds on the coefficients by fitting the form factors to available data. For the parametrization corresponding to the contact interaction approximation, our expected bounds on the scale $\mathrm{\ensuremath{\Lambda}}$ are within $\ensuremath{\sim}15%$ of the latest limits from the LHC experiments.