[Paper Review] Missing (up) Mass, Accidental Anomalous Symmetries, and the Strong CP Problem

Tom Banks, Yosef Nir+1 more|ArXiv.org|Mar 1, 1994

Particle physics theoretical and experimental studies18 citations

TL;DR

This paper proposes that a massless up quark, enforced by an anomaly-free horizontal symmetry, leads to an accidental anomalous U(1) symmetry that protects both real and imaginary parts of the up quark mass from perturbative generation. It shows that nonperturbative QCD dynamics generate these masses, and that the resulting CP-violating effects are suppressed by a factor of order (αw/π)²(mₛ²/m_W⁴), making the strong CP problem naturally solved if m_u = 0 at high energy.

ABSTRACT

We reconsider the massless up quark solution of the strong CP problem. We show that an anomaly free horizontal symmetry can naturally lead to a massless up quark and to a corresponding accidental anomalous symmetry. Reviewing the controversy about the phenomenological viability of $m_u=0$ we conclude that this possiblity is still open and can solve the strong CP problem. To appear in the Proceedings of The Yukawa Couplings and the Origins of Mass Workshop.

Motivation & Objective

• To re-evaluate the viability of a massless up quark in solving the strong CP problem, challenging the assumption that m_u = 0 is phenomenologically ruled out.
• To demonstrate that an anomaly-free horizontal symmetry can lead to an accidental anomalous U(1) symmetry, which protects the up quark mass from perturbative generation.
• To assess whether the imaginary part of the up quark mass, generated nonperturbatively, leads to observable CP violation inconsistent with neutron electric dipole moment bounds.
• To resolve the ambiguity in low-energy chiral Lagrangian parametrization that previously hindered determination of m_u from data.

Proposed method

• Use of a first-order chiral Lagrangian to extract low-energy quark masses (μ_i) from experimental hadron data, distinguishing them from high-scale quark mass parameters (m_i).
• Analysis of the additive contribution μ_u ∝ m_d m_s / Λ_χSB, showing that μ_u can be nonzero even if m_u = 0 at high energy.
• Application of operator analysis to determine how high-energy CP violation can induce low-energy θ_QCD via irrelevant CP-odd operators.
• Feynman diagram computation involving W and top quark loops to estimate the induced imaginary part of the up quark mass, with suppression by m_t²/m_W² when m_t < m_W.
• Estimation of the induced imaginary mass as Im m_u ∼ (Re m_u) Λ_χSB² Δ³_u, with Δ³_u ∼ (α_w/π)² (m_s² / m_W⁴), consistent with earlier estimates.
• Use of symmetry arguments and loop expansion to show that only nonperturbative QCD processes generate the real and imaginary parts of m_u, ensuring naturalness.

Experimental results

Research questions

• RQ1 Can a massless up quark be consistent with low-energy hadron phenomenology, given that the low-energy parameter μ_u can still be nonzero?
• RQ2 Does the accidental anomalous U(1) symmetry arising from a horizontal symmetry prevent perturbative generation of the up quark mass, thereby protecting the strong CP solution?
• RQ3 What is the size of the induced imaginary part of the up quark mass from high-energy CP violation, and is it compatible with neutron electric dipole moment bounds?
• RQ4 Can the ambiguity in second-order chiral Lagrangian parametrization be resolved by low-energy data alone, or is additional physics required?
• RQ5 How does the suppression of CP-violating effects from top and W boson loops affect the viability of the m_u = 0 solution?

Key findings

• The low-energy up quark mass parameter μ_u can be nonzero even if the high-scale up quark mass m_u = 0, due to a contribution μ_u = β m_d m_s / Λ_χSB with β ≈ 2, which is consistent with current data.
• The ambiguity in second-order chiral Lagrangian parametrization cannot be resolved solely from low-energy data, leaving the possibility m_u = 0 phenomenologically viable.
• The imaginary part of the up quark mass is generated only by nonperturbative QCD dynamics, and its size is estimated as Im m_u ∼ (Re m_u) Λ_χSB² Δ³_u with Δ³_u ∼ (α_w/π)² (m_s² / m_W⁴), which is highly suppressed.
• The induced CP-violating effects from high-energy sources are suppressed by a factor of order (α_w/π)² (m_s² / m_W⁴), making them compatible with experimental bounds on the neutron electric dipole moment.
• The accidental anomalous U(1) symmetry ensures that both real and imaginary parts of m_u are protected from perturbative generation, providing a natural solution to the strong CP problem.
• The model remains viable even if m_t < m_W, as the suppression factor m_t²/m_W² further reduces the induced CP violation, aligning with estimates by Shabalin [11].