A modified naturalness principle and its experimental tests

TL;DR

This paper reframes the naturalness problem by adopting finite naturalness, which ignores uncomputable quadratic divergences and focuses on finite Higgs-mass corrections. It computes Higgs mass corrections within the SM and examines how extensions motivated by neutrino masses, dark matter, axions, vacuum stability, and inflation fare under the finite naturalness criterion, deriving explicit mass bounds for new states. Across see-saw scenarios, Minimal Dark Matter, scalar and fermion singlet dark matter, and axion models (KSVZ/DFSZ), the authors identify TeV-scale targets and correlations with relic abundance and direct-detection signals, highlighting experimental prospects for LHC and astroparticle searches. The results suggest that finite naturalness can be compatible with current data and guide expectations for new particles near the weak scale, while reinforcing that the cosmological constant problem remains outside this framework.

Abstract

Motivated by LHC results, we modify the usual criterion for naturalness by ignoring the uncomputable power divergences. The Standard Model satisfies the modified criterion ('finite naturalness') for the measured values of its parameters. Extensions of the SM motivated by observations (Dark Matter, neutrino masses, the strong CP problem, vacuum instability, inflation) satisfy finite naturalness in special ranges of their parameter spaces which often imply new particles below a few TeV. Finite naturalness bounds are weaker than usual naturalness bounds because any new particle with SM gauge interactions gives a finite contribution to the Higgs mass at two loop order.

Figures (3)

• Figure 1: The SM satisfies 'finite naturalness' for the observed values of its parameters (small ellipse), while a large fine-tuning would be present for a lighter Higgs.
• Figure 2: Scalar singlet DM model. In the ($M,\sigma_{\rm SI}$) plane we plot the region excluded by the Xenon direct search experiment, the band favored by the thermal DM abundance, the upper bound on the DM mass following from finite naturalness for $\Delta=1$ and $\Delta=100$.
• Figure 3: Fermion singlet DM model. In the ($M,\sigma_{\rm SI}$) plane we plot the region excluded by the Xenon direct search experiment and the upper bound on the DM mass following from finite naturalness for fine-tuning $\Delta=1$ (dashed line) and $\Delta=100$ (continuous line). We assume $m_{S_2}=300\,{\rm GeV}$ (left) or $1\,{\rm TeV}$ (right). This does not fix all parameters of the model such that the region where the DM thermal density can reproduce the cosmological DM density (green band) becomes wide at $M>m_{S_2}$. We demand compatibility with electroweak precision data.