The $\hat{H}$-Parameter: An Oblique Higgs View

Understand

We study, from theoretical and phenomenological angles, the Higgs boson oblique parameter $\hat{H}$, as the hallmark of off-shell Higgs physics.

• $\hat{H}$ is defined as the Wilson coefficient of the sole dimension-6 operator that modifies the Higgs boson propagator, within a Universal EFT.
• Theoretically, we describe self-consistency conditions on Wilson coefficients, derived from the K\"{a}ll\'{e}n-Lehmann representation.
• Phenomenologically, we demonstrate that the process $gg\to h^\ast \to VV$ is insensitive to propagator corrections from $\hat{H}$, and instead advertise four-top production as an effective high-energy probe of off-shell Higgs behaviour, crucial to break flat directions in the EFT.