Abstract
The energy dependence of the electroweak gauge couplings has not been measured above the weak scale. We propose that percent-level measurements of the energy dependence of $\alpha_{1,2}$ can be performed now at the LHC and at future higher energy hadron colliders. These measurements can be used to set limits on new particles with electroweak quantum numbers without relying on any assumptions about their decay properties. The shape of the high invariant mass spectrum of Drell-Yan, $p p \rightarrow Z^*/\gamma^* \rightarrow \ell^+ \ell^-$, constrains $\alpha_{1,2}(Q)$, and the shape of the high transverse mass distribution of $p p \rightarrow W^* \rightarrow \ell \nu$ constrains $\alpha_{2}(Q)$. We use existing data to perform the first fits to $\alpha_{1,2}$ above the weak scale. Percent-level measurements are possible because of high precision in theoretical predictions and existing experimental measurements. We show that the LHC already has the reach to improve upon electroweak precision tests for new particles that dominantly couple through their electroweak charges. The 14 TeV LHC is sensitive to the predicted Standard Model (SM) running of $\alpha_2$, and can show that $\alpha_2$ decreases with energy at $2-3 \sigma$ significance. A future 100 TeV proton-proton collider will have significant reach to measure running weak couplings, with sensitivity to the SM running of $\alpha_2$ at $4-5 \sigma$ and sensitivity to winos with masses up to $\sim$ 1.3 TeV at $2\sigma$.
Highlights
Constrained using a variety of techniques including lattice QCD, deep inelastic scattering, studies of heavy quarkonia, e+e− production of jets, and Z-pole measurements [9, 10]
It is in this sense that we consider our approach as model-independent, as such a procedure is insensitive to how these states decay: our setup must assume only that the dominant coupling of new states is to EW gauge bosons such that, for instance, four-fermion operators are not generated at tree-level below the new states’ masses
Since we are using the leading order EW coupling dependence to derive the limits on Beyond the Standard Model (BSM) scenarios, the reach curves we show are sensitive to the scale choice for the couplings
Summary
We focus on the inference of new particles based on their contribution to the evolution of couplings above their mass thresholds It is in this sense that we consider our approach as model-independent, as such a procedure is insensitive to how these states decay: our setup must assume only that the dominant coupling of new states is to EW gauge bosons such that, for instance, four-fermion operators are not generated at tree-level below the new states’ masses. Rather, new states generate contact operators between SM fermions at tree-level, their effect on the mass distributions that we consider will appear as a power law rather than as a logarithmic one, allowing a discrimination of these scenarios through precise determination of event shapes. We employ a massindependent subtraction scheme throughout, such that beta functions undergo discrete changes across mass thresholds; details of these conventions for encoding coupling evolution in beta functions are included in appendix A
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