[Paper Review] What does a non-vanishing neutrino mass have to say about the strong CP problem?

P. Q. Hung|arXiv (Cornell University)|Apr 21, 2017

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper proposes a non-axionic solution to the strong CP problem within the EW-νR model, where complex Yukawa couplings between Standard Model and mirror quarks via a Higgs singlet generate a small CP-violating phase. The resulting effective θ̄ parameter remains below 10⁻¹⁰ due to the seesaw suppression from the large ratio of Majorana to Dirac mass scales, offering testable LHC signatures through displaced decays of mirror fermions.

ABSTRACT

A new solution to the strong CP problem with distinct experimental signatures 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 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. $\barθ < 10^{-10}$ 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 invoking the Peccei-Quinn axion or explicit CP conservation.
• To explain why the effective CP-violating parameter θ̄ = θQCD + ArgDetM remains below 10⁻¹⁰ despite complex Yukawa couplings.
• To demonstrate that the smallness of ArgDetM arises naturally from the seesaw mechanism in a model with mirror fermions and a Higgs singlet.
• To provide a testable framework within the EW-νR model that links non-vanishing neutrino mass to strong CP violation.
• To show that the model avoids the Nielsen-Ninomiya no-go theorem and satisfies electroweak precision constraints.

Proposed method

• Introduces a two-sector framework with Standard Model (SM) quarks and mirror quarks, both transforming under the same gauge group SU(3)×SU(2)×U(1).
• Incorporates a Higgs singlet φS that mediates mixing between left-handed SM quarks and right-handed mirror quarks, generating Dirac masses.
• Uses the seesaw mechanism: the Dirac mass mD ∝ vS is much smaller than the Majorana mass MR ∝ vM, leading to mν ≈ mD²/MR.
• Calculates the CP-violating phase ArgDetM from the 6×6 quark mass matrices (SM and mirror), showing it is suppressed by mD/MR.
• Assumes diagonalization of the 6×6 mass matrices in the limit of small mixing, reducing to 4×4 blocks for each quark type.
• Demonstrates that ArgDetM ∝ mν / mquark, leading to θ̄ < 10⁻¹⁰ due to the hierarchy mD ≪ MR.

Experimental results

Research questions

• RQ1 Can the strong CP problem be solved without introducing the Peccei-Quinn axion or imposing CP conservation in the Lagrangian?
• RQ2 Why does the CP-violating phase ArgDetM remain below 10⁻¹⁰ even when Yukawa couplings are complex?
• RQ3 How does the seesaw mechanism in the EW-νR model suppress the effective θ̄ parameter to sub-10⁻¹⁰ levels?
• RQ4 Can the model be consistent with electroweak precision data and LHC phenomenology?
• RQ5 What are the experimental signatures of the mirror fermions and their displaced decays in this framework?

Key findings

• The effective CP-violating parameter θ̄ remains below 10⁻¹⁰ due to the seesaw suppression mD/MR, even with complex Yukawa couplings.
• ArgDetM vanishes when the Higgs singlet vacuum expectation value vS → 0, linking the smallness of θ̄ to the seesaw mechanism.
• The model avoids the Nielsen-Ninomiya no-go theorem by introducing mirror fermions that form vector-like pairs with SM fermions.
• Mirror quarks and leptons can decay via fᴹ → f + φS at displaced vertices due to small Yukawa couplings, offering a distinctive LHC signature.
• The CP-violating phase in the quark sector is proportional to mν / mquark, with neutrino mass generation via seesaw providing the necessary suppression.
• The model is consistent with the 125 GeV Higgs boson and electroweak precision constraints, as the mirror sector is embedded in a gauge-invariant framework.