Naturally Heavy Scalars in Supersymmetric Grand Unified Theories

TL;DR

This work tackles naturalness in supersymmetry by proposing an inverted scalar hierarchy generated radiatively through renormalization-group evolution. Scalars with large Yukawa couplings flow toward a light scale $m_{ m light}$, while first- and second-generation scalars remain heavy, controlled by high-scale boundary conditions and fixed points of the RGEs. The authors demonstrate this both in the MSSM with a right-handed neutrino and in GUT scenarios above the unification scale (SO(10) and SU(5)), obtaining suppression factors $S$ up to about $20$ below $M_G$ and roughly $2$ above $M_G$. The mechanism widens the natural parameter space by allowing multi-TeV scalar masses without sacrificing naturalness for the third generation, reducing several experimental tensions and outlining distinctive high-scale boundary conditions that could guide model-building.

Abstract

The supersymmetric flavor, CP and Polonyi problems are hints that the fundamental scale of the soft supersymmetry breaking parameters may be above a TeV, in apparent conflict with naturalness. We consider the possibility that multi-TeV scalar masses are generated by Planck- or unification-scale physics, and find the conditions under which the masses of scalars with large Yukawa couplings are driven, radiatively and asymptotically, to the weak scale through renormalization group evolution. Light third generation scalars then satisfy naturalness, while first and second generation scalars remain heavy to satisfy experimental constraints. We find that this mechanism is beautifully realized in the context of grand unified theories. In particular, the existence of right-handed neutrinos plays an important role in allowing remarkably simple scenarios. For example, for SO(10) boundary conditions with the squared masses of Higgs scalars double those of sleptons and squarks, we find that the entire scalar mass scale may be increased to 4 TeV at the unification scale without sacrificing naturalness.

Figures (4)

• Figure 1: The renormalization group evolution of the Higgs (dashed) and third generation squark (solid) and slepton (dotted) squared masses in the MSSM with a right-handed neutrino for the boundary conditions of Eq. (\ref{['mssmbc']}) with $h_G = 2$ and $m_N = 10^{13}\text{ GeV}$. First and second generation scalar masses (not shown) are approximately renormalization group invariant. At the weak scale, $m_L = 1270\text{ GeV}$, $m_E = 830\text{ GeV}$, $m_{H_u} = 710\text{ GeV}$, $m_D = 690\text{ GeV}$, $m_Q = 570\text{ GeV}$, $m_U = 420\text{ GeV}$, and $m_{H_d} = 50\text{ GeV}$. Note, however, that neglected effects of order $m_{\rm light}^2$ modify solutions in the shaded region. The suppression factor for this case is $S=20$ (see text).
• Figure 2: The suppression factor $S$ defined in the text for the MSSM with a right-handed neutrino $N$ with initial boundary conditions given by Eq. (\ref{['mssmbc']}). The parameter $m_N$ is the scale at which the right-handed neutrino decouples, and $h_G$ is the value of the universal Yukawa coupling at the GUT scale $M_G \simeq 2 \times 10^{16}$.
• Figure 3: The suppression factor $S$ for SO(10) models evolving from $M_\ast = 2.4 \times 10^{18}\text{ GeV}$ to $M_G \simeq 2 \times 10^{16} \text{ GeV}$ with boundary conditions given by Eq. (\ref{['so10I']}). The parameter $b_{10}$ is the one-loop $\beta$-function coefficient parametrizing this class of models, and $h_\ast$ is the value of the universal Yukawa coupling at the scale $M_\ast$.
• Figure 4: The suppression factor $S$, as in Fig. \ref{['fig:so10IS']}, but for SU(5) theories with the boundary conditions of Eq. (\ref{['su5']}).