SUGRA Grand Unification, LHC and Dark Matter

A brief review is given of recent developments related to the Higgs signal and its implications for supersymmetry in the supergravity grand unification framework. The Higgs data indicates that the allowed parameter space largely lies on focal curves and focal surfaces of the Hyperbolic Branch of radiative breaking of the electroweak symmetry where TeV size scalars naturally arise. The high mass of the Higgs leads to a more precise prediction for the allowed range of the spin independent neutralino -proton cross section which is encouraging for the detection of dark matter in future experiments with greater sensitivity. Also discussed is the status of grand unification and a natural solution to breaking the GUT group at one scale and resolving the doublet-triplet problem. It is shown that the cosmic coincidence can be compatible within a supersymmetric framework in a muticomponent dark matter picture with one component charged under $B-L$ while the other component is the conventional supersymmetric dark matter candidate, the neutralino.

💡 Research Summary

The paper provides a comprehensive review of recent developments in supersymmetric grand unification within the supergravity (SUGRA) framework, focusing on the implications of the 125 GeV Higgs boson discovered at the LHC. It begins by emphasizing that a Higgs mass of this magnitude forces the radiative electroweak symmetry breaking (REWSB) mechanism to operate in a very specific region of the supersymmetric parameter space known as the Hyperbolic Branch (HB). Within the HB, the so‑called focal curves and focal surfaces allow the universal scalar mass $m_0$ to become multi‑TeV while keeping the Higgsino mass parameter $\mu$ relatively small. This “focus‑point” behavior preserves naturalness despite heavy scalar superpartners and is precisely the region favored by current LHC limits on sparticle masses, flavor observables such as $B_s!\to!\mu^+\mu^-$, and the muon anomalous magnetic moment.

A detailed numerical scan incorporating the latest LHC bounds, low‑energy constraints, and dark‑matter relic density requirements shows that the viable points cluster on these HB focal structures. The authors then translate the Higgs mass constraint into a sharper prediction for the spin‑independent neutralino–proton scattering cross section, $\sigma^{\rm SI}_{\chi p}$. Because a heavy Higgs forces the neutralino to be more Bino‑like with limited Higgsino admixture, the predicted cross section is confined to the range $10^{-47}$–$10^{-45},\text{cm}^2$. This interval lies well within the projected sensitivities of upcoming direct‑detection experiments such as XENONnT, LZ, and DARWIN, making the model highly testable in the near future.

The discussion then moves to grand unification. The authors present a mechanism by which a single step of symmetry breaking can reduce a high‑rank GUT group (e.g., $SO(10)$ or $E_6$) directly to the Standard Model gauge group, thereby solving the notorious doublet‑triplet splitting problem. By assigning appropriate vacuum expectation values to GUT‑scale Higgs (or “flaton”) fields, the dangerous color‑triplet partners acquire GUT‑scale masses while the electroweak doublets remain light. This approach eliminates the need for fine‑tuned mass matrices or additional discrete symmetries, offering a more economical and natural solution.

Finally, the paper addresses the cosmic coincidence problem—the observation that the dark‑matter and baryon densities are of the same order of magnitude. It proposes a multicomponent dark‑matter scenario in which one component carries $B!-!L$ charge (either a light scalar or a gauge boson associated with a $U(1){B-L}$ symmetry) and the other component is the conventional neutralino. The $B!-!L$ charged particle can annihilate efficiently through the $Z{B-L}$ portal, while the neutralino contributes the remaining relic density. This framework preserves the successful supersymmetric dark‑matter phenomenology (e.g., correct relic density, viable direct‑detection rates) and simultaneously explains the coincidence through the interplay of two distinct relic populations.

In summary, the authors argue that the measured Higgs mass dramatically narrows the allowed supersymmetric parameter space to the HB focal regions, predicts a narrow band for the neutralino‑proton scattering cross section that upcoming experiments can probe, offers a clean one‑step GUT breaking solution to the doublet‑triplet problem, and presents a viable multicomponent dark‑matter model that naturally accommodates the cosmic coincidence. The paper thus links LHC Higgs physics, grand unification, and dark‑matter searches into a coherent, experimentally testable framework.