A Finely-Predicted Higgs Boson Mass from A Finely-Tuned Weak Scale

TL;DR

<3-5 sentence high-level summary>The paper proposes that if SUSY is broken at a very high scale and the weak scale is determined by environmental selection, a supersymmetric boundary condition on the Higgs quartic coupling can tightly fix the Higgs mass to a narrow range, M_H ≈ 128–141 GeV, with the upper edge ~141 GeV corresponding to the Higgs residing predominantly in a single supermultiplet. Through two-loop RG running and controlled threshold effects, the prediction becomes remarkably insensitive to high-scale details, making mt and α_s the dominant current uncertainties; future precision measurements of these parameters could test the prediction to sub-GeV accuracy. The authors also show that mild extensions below tilde{m} or alternative UV realizations (PQ symmetry, single-Higgs multiplet in extra dimensions) can preserve or slightly shift the central value, while a measurement near 141 GeV with no new TeV-scale physics would strongly support a multiverse-driven explanation for the weak scale. They further discuss implications for axion DM, gauge unification, and the nature of fine-tuning in a universe with environmental selection.</- The last sentence ends with punctuation but should be a complete sentence.>

Abstract

If supersymmetry is broken directly to the Standard Model at energies not very far from the unified scale, the Higgs boson mass lies in the range 128-141 GeV. The end points of this range are tightly determined. Theories with the Higgs boson dominantly in a single supermultiplet predict a mass at the upper edge, (141 \pm 2) GeV, with the uncertainty dominated by the experimental errors on the top quark mass and the QCD coupling. This edge prediction is remarkably insensitive to the supersymmetry breaking scale and to supersymmetric threshold corrections so that, in a wide class of theories, the theoretical uncertainties are at the level of \pm 0.4 GeV. A reduction in the uncertainties from the top quark mass and QCD coupling to the level of \pm 0.3 GeV may be possible at future colliders, increasing the accuracy of the confrontation with theory from 1.4% to 0.4%. Verification of this prediction would provide strong evidence for supersymmetry, broken at a very high scale of ~ 10^{14 \pm 2} GeV, and also for a Higgs boson that is elementary up to this high scale, implying fine-tuning of the Higgs mass parameter by ~ 20-28 orders of magnitude. Currently, the only known explanation for such fine-tuning is the multiverse.

Figures (6)

• Figure 1: Evolution of the three gauge couplings, $g_a$ ($a=1,2,3$), in the SM. The $SU(5)$ normalization for the hypercharge gauge coupling is taken.
• Figure 2: The Higgs mass prediction in the SM for theories where the boundary condition for the quartic coupling at $\tilde{m}$ is given by Eq. (\ref{['eq:lambda-bc_beta']}), for fixed values of $\tilde{m} = 10^{14}~{\rm GeV}$ and $\alpha_s(M_Z) = 0.1176$. The solid red curve gives the Higgs mass prediction for $m_t = 173.1~{\rm GeV}$, while the shaded red band shows the uncertainty that arises from the experimental uncertainty in the top quark mass of $\pm 1.3~{\rm GeV}$. The horizontal blue lines show the corresponding asymptotes of the prediction for large $\tan\beta$. For $\tan\beta <1$, an identical figure results provided the horizontal axis is labeled by $\cot\beta$.
• Figure 3: The evolution of the quartic coupling with energy $E$ in the SM with the supersymmetric boundary condition of Eq. (\ref{['eq:lambda-bc']}), for fixed values of $\tilde{m} = 10^{14}~{\rm GeV}$, $m_t = 173.1~{\rm GeV}$ and $\alpha_s(M_Z) = 0.1176$. The solid curve is for $\delta = 0$, while the long (short) dashed curves are for $\delta = \pm 0.1$ ($\pm 0.2$).
• Figure 4: The explicit dependence of the Higgs mass prediction on $\tilde{m}$ in the SM, with $\alpha_s(M_Z) = 0.1176$. The narrow red shaded region has $m_t = 173.1~{\rm GeV}$, with the three solid curves corresponding to (from bottom) $\delta_s = 0$, $0.02$ and $0.04$. The upper (lower) dashed red curve shows the prediction when the top quark mass is increased (decreased) by $1.3~{\rm GeV}$. The vertical blue lines correspond to values of $\tilde{m}$ in the region suggested by gauge coupling unification in the SM, $M_u = 10^{14 \pm 1}~{\rm GeV}$.
• Figure 5: Contours of the shift in the Higgs mass prediction when additional fermions of mass $1~{\rm TeV}$ are added to the SM. These fermions contribute $\varDelta b_{1,2}$ to the $U(1)_Y$, $SU(2)_L$ beta functions, but do not have significant Yukawa couplings to the Higgs boson or top quark. (a) None of the additional fermions are colored. The bold dot represents the addition of a single vector-like lepton doublet. (b) The only additional colored fermions are a single vector-like triplet. The bold dots represent the addition of ${\bf 5} + {\bf \bar{5}}$ (lower) and ${\bf 5} + {\bf \bar{5}}$ with a vector-like lepton doublet (upper).