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 $pp\to \ell \overline{\ell }$ 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 $\mathrm{\Lambda }$ are within $\sim 15\%$ of the latest limits from the LHC experiments.

Figure 1

The thick blue line is the partonic cross section for $\widehat{\sigma }(u\overline{u}\to e^{+}{e}^{-})$, mediated by $Z,\gamma$, and a leptoquark $S_0$ of mass 2 TeV and ${\lambda }^2=1$ in the $t$-channel, and normalized to $\widehat{\sigma }$ for $Z,\gamma$ exchange. The dotted (dot-dashed) blue lines are the $\mathcal{O}({\widehat{s}}^2),\mathcal{O}({\widehat{s}}^3)$ terms of a “form-factor” approximation to leptoquark exchange [see Eq. (5)]. The solid black line (that exits the upper plot border) is the dimension-six CI approximation, and the dashed black line (that exits the lower border) includes the first correction in $\widehat{s}/m^2$ to the CI approximation. The leptoquark has destructive interference (first plot); for illustration, we also plot the same model but with constructive interference.

Figure 2

$2\sigma$-allowed ellipses for the $a,b$ parameters of Eq. (2), with fixed values of $c=1/m^2$, obtained from $e^{+}{e}^{-}$ (upper) and ${\mu }^{+}{\mu }^{-}$ (lower) data [2]. Decreasing ellipse size corresponds to $m=1,2,3,\infty \mathrm{TeV}$. The dotted 1 TeV ${\mu }^{+}{\mu }^{-}$ ellipse (lower plot) extends to $b\simeq 3.5$. The inner green ellipse (lower plot) is the $1\sigma$-allowed contour for the contact interaction. The parabolas, in decreasing width, represent models described by $b=1/4a^2,a^2,4a^2,10a^2$.