Nnaturalness

TL;DR

N naturalness introduces N SM-like sectors with distributed Higgs mass parameters and a reheaton that preferentially heats the lightest sector, thereby solving the electroweak hierarchy problem through cosmological dynamics rather than new collider-scale particles. The framework predicts a reduced gravity cutoff $\\Lambda_G^2 \\sim M_{pl}^2/N$ and, for perturbative unification, $N \lesssim 10^4$, though much larger values (up to $\\sim 10^{16}$) are possible with low reheat temperatures. Explicit models (L_ell and L_phi) demonstrate how reheaton decays can be arranged to populate the lightest sector, with detailed analyses of cross-quartics, reheating bounds, and baryogenesis, alongside detailed cosmological constraints from DeltaN_eff and relic densities. The scenario yields distinct, testable cosmological signals in upcoming CMB and LSS surveys, potential SUSY signatures below ~10 TeV for certain UV completions, and a Heavy Axion option to address the strong CP problem across N sectors. Overall, N naturalness offers a cosmological route to naturalness, predicting new physics primarily via early-universe probes rather than direct collider signatures, while remaining compatible with grand unification and future experimental capabilities.

Abstract

We present a new solution to the electroweak hierarchy problem. We introduce $N$ copies of the Standard Model with varying values of the Higgs mass parameter. This generically yields a sector whose weak scale is parametrically removed from the cutoff by a factor of $1/\sqrt{N}$. Ensuring that reheating deposits a majority of the total energy density into this lightest sector requires a modification of the standard cosmological history, providing a powerful probe of the mechanism. Current and near-future experiments will explore much of the natural parameter space. Furthermore, supersymmetric completions which preserve grand unification predict superpartners with mass below $m_W \times M_{\text{pl}} / M_{\text{GUT}} \sim 10$ TeV.

Figures (5)

• Figure 1: A sketch of the $N$naturalness setup. The sectors have been ordered so that they range from $m_H^2 \sim \Lambda_H^2$ to $-\Lambda_H^2$. The sector with the smallest vacuum expectation value contains our copy of the SM.
• Figure 2: Feynman diagrams for the most important decays in the $\phi$ model. The left (right) column is for $\left\langle {H} \right\rangle \neq 0$$(\! \left\langle {H} \right\rangle = 0)$. The top (bottom) row is for $m_\phi \gg |m_H|$$(m_\phi \ll |m_H|)$.
• Figure 3: Energy density deposited in each sector as a function of sector number, normalized to the energy density in our sector. The left panel is for the $\phi$ model with $a=1$ MeV. The right panel is for the $L_4$ model with $\lambda\times \mu_E=1$ MeV, $M_L=400$ GeV, $M_{E, N}=500$ GeV, $Y_E=Y_N=0.2$, and $Y^c_E=Y^c_N=-0.5$. The solid lines are the result of a full numerical calculation. The dashed lines show the expected scalings. As discussed in the text, the steps in the $\phi$ model are proportional to Yukawa couplings due to the fact that $\phi$ decays via mixing with the Higgs. When $i \gtrsim 10^9$ in the $L_4$ model, the process $S^c \rightarrow 2\,e+\nu$ cannot proceed on-shell, which results in the deviation from the naive scaling as denoted by $m_S = 2\,m_e + m_\nu$. Both figures were made using the zero temperature branching ratios of the reheaton; thermal corrections are under control so long as $T_\text{RH}$ is smaller than the weak scale in our sector, as discussed at the end of Sec. \ref{['Models']}.
• Figure 4:
• Figure 5: $\Delta N_{\rm eff}$ contours as a function of reheaton mass and the $r$ parameter defined in Eq. (\ref{['eq:mHsqiScaling']}). $\Delta N_{\rm eff}\simeq 0.03$ corresponds to the sensitivity of CMB stage 4 experiments. The current upper bound at the CMB epoch is around $0.6$. The left panel is for the $\phi$ model with $a=1$ MeV. The right panel is for the $L_4$ model with $\lambda\times \mu_E=1$ MeV, $M_L=400$ GeV, $M_{E, N}=500$ GeV, $Y_E=Y_N=0.2$, and $Y^c_E=Y^c_N=-0.5$. As discussed in the text, the $L_4$ result is valid for a large range of $N$, namely $30 \lesssim N\lesssim 10^{9}$. Both figures were made using the zero temperature branching ratios of the reheaton; see the end of Sec. \ref{['Models']} for a discussion.