Abstract
The LHC is exploring electroweak (EW) physics at the scale EW symmetry is broken. As the LHC and new high energy colliders push our understanding of the Standard Model to ever-higher energies, it will be possible to probe not only the breaking of but also the restoration of EW symmetry. We propose to observe EW restoration in double EW boson production via the convergence of the Goldstone boson equivalence theorem. This convergence is most easily measured in the vector boson plus Higgs production, $Vh$, which is dominated by the longitudinal polarizations. We define EW restoration by carefully taking the limit of zero Higgs vacuum expectation value (vev). EW restoration is then measured through the ratio of the $p_T^h$ distributions between $Vh$ production in the Standard Model and Goldstone boson plus Higgs production in the zero vev theory, where $p_T^h$ is the Higgs transverse momentum. As EW symmetry is restored, this ratio converges to one at high energy. We present a method to extract this ratio from collider data. With a full signal and background analysis, we demonstrate that the 14 TeV HL-LHC can confirm that this ratio converges to one to 40% precision while at the 27 TeV HE-LHC the precision will be 6%. We also investigate statistical tests to quantify the convergence at high energies. Our analysis provides a roadmap for how to stress test the Goldstone boson equivalence theorem and our understanding of spontaneously broken symmetries, in addition to confirming the restoration of EW symmetry.
Highlights
With the discovery of a Standard Model-like Higgs boson [1,2], we entered a new era of probing the nature of electroweak (EW) symmetry breaking
We propose a new study to test one of the central behaviors of the SM at high energy: restoration of EW symmetry
Symmetry restoration and the Goldstone boson equivalence theorem (GBET) is simplest in processes that are dominated by longitudinally polarized gauge bosons
Summary
With the discovery of a Standard Model-like Higgs boson [1,2], we entered a new era of probing the nature of electroweak (EW) symmetry breaking. As the above makes clear, the observation of EW symmetry restoration and the GBET is simplest in processes that are dominated by longitudinally polarized gauge bosons. Such a process is Higgs production in association with an EW gauge boson: qq 0 → Vh with V 1⁄4 WÆ; Z (Vh). The vector and Higgs bosons are intermediate states, and the collider observes their decay products These decays occur at the EW scale and the GBET is not valid. At high Higgs transverse momentum, we show that it is possible to observe the convergence of this signal strength to one, indicating that EW symmetry is restored.
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