A New Probe of Naturalness

TL;DR

The paper addresses the electroweak hierarchy problem by proposing a weak-scale effective theory with scalar top partners that cancel the top-quark quadratic divergences. It shows these partners induce a physical Higgs wave-function renormalization that, after canonical normalization, rescale Higgs couplings in a measurable way, enabling indirect tests of naturalness through precision Higgs measurements at a Linear Collider. The key mechanism is a leading $c_H$ operator with $c_H(m_\phi) = n_\phi |\lambda_\phi|^2 /(96 \pi^2)$, which yields shifts in the Higgs–gauge and Higgs–fermion couplings, notably affecting the $e^+e^- \to hZ$ cross-section $\sigma_{Zh}$. The work demonstrates that even gauge-singlet top partners can be probed at the percent level, offering a robust indirect route to test electroweak naturalness and constrain or reveal new Higgs-sector physics.

Abstract

Any new scalar fields that perturbatively solve the hierarchy problem by stabilizing the Higgs mass also generate new contributions to the Higgs field-strength renormalization, irrespective of their gauge representation. These new contributions are physical and their magnitude can be inferred from the requirement of quadratic divergence cancellation, hence they are directly related to the resolution of the hierarchy problem. Upon canonically normalizing the Higgs field these new contributions lead to modifications of Higgs couplings which are typically great enough that the hierarchy problem and the concept of electroweak naturalness can be probed thoroughly within a precision Higgs program. Specifically, at a Linear Collider this can be achieved through precision measurements of the Higgs associated production cross-section. This would lead to indirect constraints on perturbative solutions to the hierarchy problem in the broadest sense, even if the relevant new fields are gauge singlets.

Figures (2)

• Figure 1: Sample counterterm diagrams that depend on the Higgs self-energy.
• Figure 2: Scalar top-partner corrections to the Higgs associated production cross-section at a $250$ GeV linear collider as a function of the top-partner mass $m_\phi$ in the effective theory of naturalness of Eq. (\ref{['eq:L']}). Corrections are shown for $n_\phi = 1,..,6$ top partners. Estimates for the measurement precision of $2.5 \%$Peskin:2012weILCTRD and $0.5\%$Klute:2013cx are also shown. It is remarkable that with current precision estimates a large portion of model-independent parameter space for Higgs naturalness can be probed. In particular, if one compares with the tuning estimates of Eq. (\ref{['eq:benchmarks']}), this broadly corresponds to probing $10 \%$ tuned regions for a single scalar top partner and close to $25 \%$ tuned regions for $n_\phi = 6$ scalar top partners as in SUSY. Optimistically, if the precision could be improved to $\delta \sigma_{Zh} \sim 0.1 \%$, then virtually all parameter space for generic natural scalar theories with up to $\sim10\%$ tunings could be probed.