[Paper Review] A Sinister Extension of the Standard Model to SU(3)XSU(2)XSU(2)XU(1)

Sheldon L. Glashow|ArXiv.org|Apr 29, 2005

Particle physics theoretical and experimental studies21 citations

TL;DR

This paper proposes a sinister extension of the Standard Model based on the gauge group $SU(3)\times SU(2)\times SU(2)'\times U(1)$, introducing 'terafermions'—heavy mirror partners to ordinary fermions—linked by a novel $CP'$ symmetry. Soft $CP'$ breaking in the Higgs sector generates large masses for terafermions and $W'$, $Z'$ bosons, while enabling small Dirac neutrino masses and predicting stable, electromagnetically bound terahelium atoms as viable dark matter candidates.

ABSTRACT

This paper describes work done in collaboration with Andy Cohen. In our model, ordinary fermions are accompanied by an equal number `terafermions.' These particles are linked to ordinary quarks and leptons by an unconventional CP' operation, whose soft breaking in the Higgs mass sector results in their acquiring large masses. The model leads to no detectable strong CP violating effects, produces small Dirac masses for neutrinos, and offers a novel alternative for dark matter as electromagnetically bound systems made of terafermions.

Motivation & Objective

• To resolve the strong $CP$ problem by introducing a symmetric mirror sector with $CP'$ invariance.
• To provide a natural mechanism for small Dirac neutrino masses without Majorana terms.
• To propose a novel dark matter candidate in the form of stable, electromagnetically bound terahelium atoms.
• To ensure compatibility with experimental constraints on heavy stable particles and dark matter searches.
• To explain the absence of strong $CP$ violation through exact cancellation between quarks and teraquarks.

Proposed method

• Introduce a gauge group $SU(3)\times SU(2)\times SU(2)'\times U(1)$ with two distinct $SU(2)$ factors for ordinary and terafermions.
• Postulate a new $CP'$ symmetry that maps ordinary fermions to $CP$ conjugates of their tera-equivalents and vice versa.
• Implement soft $CP'$ breaking via dimension-2 mass terms in a two-Higgs doublet sector: one $SU(2)$ doublet ($h$) and one $SU(2)'$ doublet ($h'$).
• Require conservation of the flavor current $\mathcal{F} = (B-L) - (B'-L')$ to forbid mixing between ordinary and terafermions.
• Enforce $\lambda' = \lambda^*$ via $CP'$ invariance, ensuring terafermion masses are $S$ times their ordinary counterparts.
• Use a large vacuum expectation value $\langle h' \rangle = S \langle h \rangle \gg 250~\text{GeV}$ to generate heavy terafermions with $S > 2\times 10^5$.

Experimental results

Research questions

• RQ1 Can a $CP'$-symmetric extension of the SM resolve the strong $CP$ problem without introducing new strong CP-violating phases?
• RQ2 Can the model naturally generate small Dirac neutrino masses while forbidding neutrinoless double beta decay?
• RQ3 Do stable, electromagnetically bound terahelium atoms—composed of $UUU^{++}$ nuclei and two $E^-$ electrons—constitute viable dark matter candidates?
• RQ4 What constraints do current dark matter and heavy stable particle searches place on the mass scale $S$ of the terafermion sector?
• RQ5 Can relic terafermions efficiently aggregate into stable, neutral terahelium atoms, and are such states consistent with cosmological and astrophysical bounds?

Key findings

• The strong $CP$ problem is solved via exact cancellation of $\bar{\theta}$ contributions between ordinary quarks and much heavier teraquarks.
• Neutrinos acquire tiny Dirac masses through a seesaw-like mechanism, and neutrinoless double beta decay is strictly forbidden.
• The least massive charged terafermion, the $E^-$, is stable with mass $S \times 511~\text{keV}$, requiring $S > 2 \times 10^5$ to satisfy constraints from heavy stable lepton searches.
• Teraquarks and teraleptons undergo exothermic exchange reactions, efficiently aggregating into $UUU$ baryons and $UUUEE$ terahelium atoms prior to nucleosynthesis.
• The predicted terahelium atom to photon ratio is $\eta_{B'} \approx 3 \times 10^{-13} S_6$, with $S_6 = S / 10^6$, indicating a high degree of aggregation.
• The dominant interaction cross-section for terahelium with nuclei arises from the magnetic dipole moment of the $UUU^{++}$ nucleus, requiring $S > 10^6$ (i.e., terahelium mass > 10 TeV) to evade current dark matter detection limits.