# A Golden Probe of Nonlinear Higgs Dynamics

## TL;DR

This paper performs the first fit of Wilson coefficients in nonlinear Higgs dynamics using LHC data from the golden H to 4L decay channel, constraining the decay constant and exploring the structure of the Higgs sector.

## Contribution

It introduces a novel analysis combining rate and shape information to constrain Wilson coefficients and the decay constant in nonlinear Higgs models using LHC Run 2 data.

## Key findings

- Current LHC data constrains the decay constant $f$ and Wilson coefficients.
- Including shape information broadens the allowed parameter space.
- Future high-luminosity LHC could improve constraints and enable multi-coefficient fits.

## Abstract

The most salient generic feature of a composite Higgs boson resides in the nonlinearity of its dynamics, which arises from degenerate vacua associated with the pseudo-Nambu-Goldstone (PNGB) nature of the Higgs boson. It has been shown that the nonlinear Higgs dynamics is universal in the IR and controlled only by a single parameter $f$, the decay constant of the PNGB Higgs. In this work we perform a fit, for the first time, to Wilson coefficients of ${\cal O}(p^4)$ operators in the nonlinear Lagrangian using the golden H $\to$ 4L decay channel. By utilizing both the "rate" information in the signal strength and the "shape" information in the fully differential spectra, we provide limits on the Goldstone decay constant $f$, as well as ${\cal O}(p^4)$ Wilson coefficients, using Run 2 data at the LHC. In rate measurements alone, the golden channel prefers a negative $\xi =v^2/f^2$ corresponding to a non-compact coset structure. Including the shape information, we identify regions of parameter space where current LHC constraint on $f$ is still weak, allowing for $\xi \lesssim 0.5$ or $\xi \gtrsim -0.5$. We also comment on future sensitivity at the high-luminosity upgrade of the LHC which could allow for simultaneous fits to multiple Wilson coefficients.