[Paper Review] Mirror fermions and the strong CP problem: A new axionless solution and experimental implications

P. Q. Hung|arXiv (Cornell University)|Dec 27, 2017

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper proposes an axionless solution to the strong CP problem using the EW-νR model, where CP violation from complex Yukawa couplings is naturally suppressed by the seesaw mechanism. The smallness of the effective θ parameter (⟨θ̄⟩ < 10⁻¹⁰) arises from the hierarchy between Dirac and Majorana mass scales, leading to long-lived mirror fermions as key experimental signatures at the LHC.

ABSTRACT

A new solution to the strong CP problem with distinct experimental signatures (long-lived particles) at the LHC is proposed. It is based on the Yukawa interactions between mirror quarks, Standard Model (SM) quarks and Higgs singlets. (Mirror quarks and leptons which include non-sterile right-handed neutrinos whose Majorana masses are proportional to the electroweak scale, form the basis of the EW-$ν_R$ model.) The aforementioned Yukawa couplings can in general be complex and can contribute to $Arg\, Det M$ ($\barθ = θ_{QCD} + Arg\, Det M$) at tree-level. The model contains a Peccei-Quinn-type global symmetry which allows it to rotate away $θ_{QCD}$.The crux of matter in this manuscript is the fact that {\em no matter how large} the CP-violating phases in the Yukawa couplings might be, $Arg\, Det M$ can remain small i.e. $\barθ &lt; 10^{-10}$ for reasonable values of the Yukawa couplings and, in fact, vanishes when the VEV of the Higgs singlet (responsible for the Dirac part of the neutrino mass in the seesaw mechanism) vanishes. The smallness of the contribution to $\barθ$ is {\em principally due} to the smallness of the ratio of the two mass scales in the seesaw mechanism: the Dirac and Majorana mass scales.

Motivation & Objective

• To resolve the strong CP problem without introducing an axion, addressing the fine-tuning of θ̄ < 10⁻¹⁰.
• To demonstrate that CP-violating phases in Yukawa couplings do not lead to large contributions to the effective θ parameter due to mass scale hierarchy.
• To identify experimentally testable signatures—specifically long-lived mirror fermions—within the EW-νR model.
• To show that the seesaw mechanism naturally suppresses ArgDetM, linking small θ̄ to small neutrino masses.
• To provide a framework within the SM gauge group SU(3)×SU(2)×U(1) that avoids the Nielsen-Ninomiya theorem and enables lattice realizations.

Proposed method

• Introduces a Peccei-Quinn-type global symmetry that allows rotation of θQCD to zero at tree level, without requiring a dynamical axion field.
• Utilizes Yukawa couplings between SM quarks, mirror quarks, and Higgs singlets to generate CP-violating phases in the quark mass matrices.
• Applies the seesaw mechanism via a Higgs singlet with VEV vS, leading to a small Dirac mass mD ≪ MR, which suppresses ArgDetM.
• Assumes diagonalization of 4×4 mass matrices for up and down quarks, including mixing between SM and mirror quarks via off-diagonal terms proportional to vS.
• Demonstrates that ArgDetM vanishes when vS → 0, and remains < 10⁻¹⁰ for realistic Yukawa couplings and mass hierarchies.
• Predicts displaced vertex decays of mirror fermions due to their long lifetimes, arising from small couplings to the Higgs singlet.

Experimental results

Research questions

• RQ1 Can the strong CP problem be solved without introducing an axion, relying solely on symmetry and mass hierarchies?
• RQ2 Why does the contribution to ArgDetM remain small despite large CP-violating phases in Yukawa couplings?
• RQ3 Can the EW-νR model provide a viable, testable framework for the seesaw mechanism within the SM gauge group?
• RQ4 What are the distinct experimental signatures of this axionless solution at the LHC?
• RQ5 How does the seesaw mechanism suppress the effective θ parameter to below 10⁻¹⁰?

Key findings

• The effective θ parameter remains below 10⁻¹⁰ due to the small ratio of Dirac to Majorana mass scales in the seesaw mechanism.
• ArgDetM vanishes when the Higgs singlet VEV vS → 0, indicating that the smallness of θ̄ is a consequence of the seesaw hierarchy.
• The model predicts long-lived mirror quarks and leptons that decay at displaced vertices, offering a unique experimental signature at the LHC.
• The solution relies on a global chiral symmetry that allows θQCD to be rotated to zero, without requiring a dynamical axion field.
• The EW-νR model provides a consistent, anomaly-free extension of the SM gauge group that avoids the Nielsen-Ninomiya no-go theorem.
• The constraint on Yukawa couplings gSq and gSl < 10⁻⁴ leads to observable long-lived particle decays, aligning with the LHC LLP community's search initiatives.