Accidental Peccei-Quinn Symmetry from Chiral Gauge Symmetry and Mirror QCD

This paper proposes a novel solution to the strong CP problem where an accidental Peccei-Quinn symmetry emerges from a chiral U(1) gauge symmetry and is broken by mirror QCD dynamics, simultaneously explaining dark matter, baryogenesis, and generating observable gravitational waves and LHC signatures without requiring a light QCD axion or massless fermions.

The Gist

The Big Problem: The "Strong CP" Mystery

Imagine the universe is a giant, complex machine governed by rules. Most of these rules are perfectly symmetrical, meaning they work the same way whether you look at them in a mirror or run them backward in time. However, there is one specific rule in the "Strong Force" (the glue that holds atoms together) that should allow the machine to run differently in a mirror, but in reality, it doesn't.

Physicists call this the Strong CP Problem. It's like finding a screw on a car engine that is supposed to be loose, but it's tightened so perfectly that it's practically invisible. The question is: Why is it so perfectly tightened?

The most famous solution to this is the Axion. Think of the Axion as a magical "tuning knob" that automatically adjusts the screw until it's perfectly tight. However, for this knob to work, it needs a specific kind of symmetry (the Peccei-Quinn symmetry) to exist. The problem is, in standard physics, there's no good reason for this symmetry to exist, and if it does, it's very fragile and easily broken by tiny errors, which would ruin the tuning.

The Authors' Solution: A Mirror World with a Twist

The authors of this paper propose a new way to build this "tuning knob" without needing to fine-tune anything. They do this by introducing a Mirror World.

1. The Mirror World (The "Twin" Universe)

Imagine a universe that is an exact copy of ours, but everything is slightly heavier and runs on a different energy scale. Let's call this the "Mirror World."

• In our world, we have protons and neutrons.
• In the Mirror World, they have "Mirror Protons" and "Mirror Neutrons."
• Crucially, the authors introduce a rule (a Z2 symmetry) that swaps our world with the Mirror World. This ensures that if the "screw" is loose in our world, it's loose in the Mirror World too.

2. The "Accidental" Symmetry

Usually, physicists have to force the symmetry to exist by hand. The authors say, "Let's not force it. Let's build the machine so that the symmetry happens by accident."

They do this by adding a new, invisible force (a Chiral U(1) gauge symmetry) that acts like a strict bouncer at a club. This bouncer only lets certain particles in based on their "charges."

• Because of the strict rules of this bouncer, the particles in the Mirror World are forced to arrange themselves in a specific way.
• This arrangement accidentally creates the perfect "tuning knob" (the Peccei-Quinn symmetry) needed to fix the Strong CP problem.
• The Analogy: Imagine you are trying to balance a stack of plates. Usually, you have to hold them perfectly still. But if you put the stack inside a vibrating box with a specific shape, the vibration accidentally keeps the plates balanced without you doing anything. The "vibration" here is the new gauge symmetry.

3. The "Mirror QCD" Engine

In the Mirror World, the "glue" (Strong Force) is much stronger and operates at a higher energy level than in our world. This is called Mirror QCD.

• Because this force is so strong, it spontaneously breaks the symmetry, creating the "tuning knob" (the Axion).
• Because the Mirror World is so heavy and energetic, the Axion becomes very heavy. A heavy Axion is good because it is less sensitive to tiny errors (the "quality problem" mentioned earlier). It's like a heavy anchor that won't be moved by a gentle breeze.

Solving the "Domain Wall" Disaster

Previous models using Mirror Worlds had a major flaw: Domain Walls.

• The Problem: Imagine the Mirror World is a room with three different ways to arrange the furniture. When the universe cooled down, different parts of the universe might have chosen different arrangements. Where these different arrangements meet, you get a "wall" of energy. If these walls are stable, they would eventually swallow the entire universe, destroying everything.
• The Fix: In this new model, the "bouncer" (the U(1) symmetry) ensures that these walls are metastable. They are like a house of cards that looks stable but will eventually collapse. They decay before they can destroy the universe. This allows the universe to have a high temperature after the Big Bang, which is necessary for creating the matter we see today (baryogenesis).

The Hidden Treasures: Dark Matter and Gravitational Waves

This model doesn't just fix the Strong CP problem; it predicts new things we can look for.

1. Dark Matter Candidates
The model predicts two types of stable particles that could be Dark Matter:

• The "Ghost" Particle (NGB): A particle that barely interacts with anything, like a ghost. It is stable because of a hidden rule (U(1)T symmetry).
• The "Heavy Baryon": A heavy particle made of Mirror quarks.
• The Portal: There is a new "dark photon" (a particle associated with the U(1) symmetry) that acts as a bridge. It can mix slightly with our world's light (photons), allowing us to potentially detect these dark particles.

2. Gravitational Waves (The "Echo" of the Big Bang)
When the Mirror World cooled down, it underwent a phase transition (like water freezing into ice).

• Because this transition was violent (first-order), it created ripples in space-time called Gravitational Waves.
• The paper suggests these waves might be detectable by future observatories like LISA (a space-based gravitational wave detector). It's like hearing the "crack" of the universe freezing over.

3. Collider Signals (The LHC)
The model predicts heavy, colored particles (octets) that could be created at the Large Hadron Collider (LHC).

• If we smash protons together hard enough, we might create these heavy particles.
• They would decay into jets of particles, missing energy (the dark matter escaping), or displaced vertices (particles that travel a bit before decaying).
• Think of it like smashing two watches together and finding gears that shouldn't exist, which then fly off in specific patterns.

Summary

The authors have built a theoretical machine where:

1. A strict new rule (Chiral U(1) symmetry) forces the universe to accidentally create a solution to the Strong CP problem.
2. A Mirror World provides the heavy machinery needed to make this solution robust.
3. The dangerous "walls" that usually destroy such models are made unstable and decay safely.
4. The model naturally produces candidates for Dark Matter and predicts gravitational waves and new particles we might find at the LHC.

It is a self-contained story that solves an old mystery while opening new doors for experimental discovery, all without needing to "fine-tune" the universe by hand.

Technical Summary

1. Problem Statement

The paper addresses the Strong CP Problem, specifically the unexplained smallness of the QCD $\theta$ parameter ($|\theta| \lesssim 10^{-10}$).

• The Axion Quality Problem: The standard Peccei-Quinn (PQ) mechanism introduces a global $U(1)_{PQ}$ symmetry to dynamically relax $\theta$ to zero. However, this symmetry is not fundamental; it is an accidental symmetry that is explicitly broken by higher-dimensional operators (e.g., Planck-suppressed operators). Even tiny explicit breaking can shift the axion potential minimum away from $\theta=0$, reintroducing the Strong CP problem.
• Limitations of Previous Solutions:
  • Gauge Symmetry Approaches: Introducing gauge symmetries to forbid PQ-violating operators often requires intricate charge assignments or multiple gauge groups.
  • Mirror QCD Approaches: Models using a "Mirror QCD" sector to generate a heavy axion often suffer from the Domain Wall Problem (stable topological defects dominating the universe) and the production of stable colored relics (which are cosmologically dangerous).
• Goal: Construct a model that solves the Strong CP problem without fine-tuning, avoids the axion quality problem via an accidental symmetry derived from gauge structure, eliminates stable domain walls and colored relics, and allows for a high reheating temperature compatible with leptogenesis.

2. Methodology and Model Construction

The authors propose a model based on a Mirror Standard Model (SM') related to the SM by a $Z_2$ symmetry, coupled with a Chiral $U(1)_D$ Gauge Symmetry.

Key Components:

1. Mirror Sector & $Z_2$ Symmetry:
   • The SM is duplicated into a mirror sector ($SM'$). The $Z_2$ symmetry ensures the $\theta$ terms of both sectors are identical initially.
   • The mirror electroweak scale $v'$ is much larger than the SM scale $v$ ($v' \gg v$), leading to a mirror QCD scale $\Lambda' \gg \Lambda_{QCD}$.
2. Chiral Fermions:
   • Two pairs of vector-like fermions under $SU(3)_c \times SU(3)'_c$ are introduced: $(\psi_u, \psi_d)$ and $(\bar{\psi}_u, \bar{\psi}_d)$.
   • These fermions carry charges under a new chiral gauge symmetry $U(1)_D$.
   • Crucial Feature: A specific charge assignment (parameterized by $a$) forbids mass terms for these fermions at the renormalizable level.
3. Accidental PQ Symmetry:
   • The chiral $U(1)_D$ gauge symmetry, combined with the matter content, accidentally generates a global $U(1)_{PQ}$ symmetry.
   • This symmetry is explicitly broken only by the $SU(3)'_c$ anomaly (mirror QCD) and higher-dimensional operators.
   • Because the PQ symmetry is gauge-derived, lower-dimensional PQ-violating operators are forbidden, solving the axion quality problem.
4. Dynamics:
   • Mirror QCD ($SU(3)'_c$) undergoes chiral symmetry breaking at scale $\Lambda'$.
   • This breaks the accidental $U(1)_{PQ}$, generating a heavy "axion" (the $\eta'$ of mirror QCD) with mass $m_{\eta'} \sim 4\Lambda'$.
   • The large mass of the axion makes the $\theta=0$ solution robust against explicit breaking from higher-dimensional operators.

3. Key Contributions and Results

A. Resolution of Cosmological Pathologies

• No Stable Domain Walls: Unlike previous models using discrete symmetries (e.g., $Z_3$), the continuous $U(1)_D$ gauge symmetry prevents the formation of stable domain walls. While metastable domain walls may form, they decay via higher-dimensional operators before Big Bang Nucleosynthesis (BBN), avoiding the domain wall problem.
• No Stable Colored Relics: The model predicts that the lightest baryons are color singlets. Unlike the $Z_3$ model (which produced stable colored octet baryons), this setup ensures no stable particles carry Standard Model color charge, avoiding constraints from cosmic rays and underground detectors.
• High Reheating Temperature: The absence of stable domain walls allows the reheating temperature ($T_{RH}$) to exceed the mirror confinement scale $\Lambda'$. This is crucial for enabling Leptogenesis via mirror neutrino decays.

B. Particle Spectrum and Dark Matter Candidates

The model predicts a rich spectrum of pseudo-Nambu-Goldstone Bosons (pNGBs) and baryons:

1. 35 NGBs: Arising from the breaking of $SU(6)_L \times SU(6)_R \to SU(6)_V$.
   • Color Octets ($O, O_T, O_{T0}$): These are unstable and decay into SM particles (gluons, photons, leptons) or dark sector particles.
   • Stable Singlets ($T$): A complex scalar $T$ remains stable due to an accidental $U(1)_T$ symmetry.
2. Dark Matter Candidates:
   • Scenario 1: NGB Dark Matter ($T$): If $T$ is massive, it serves as a WIMP. It interacts with the SM via the $U(1)_D$ gauge boson ($A_D$), which kinetically mixes with the SM hypercharge. This provides a vector portal for indirect detection.
   • Scenario 2: Baryon Dark Matter ($B$): The lightest mirror baryon is a color singlet. It can be produced via the decay of unstable mirror quarks ($u', d'$) and serve as dark matter.

C. Phenomenological Signatures

The model offers distinct signatures across multiple experimental frontiers:

1. Collider Signals (LHC):
   • Octet NGBs: Pair-produced via QCD.
     • $O \to gg$: Leads to dijet resonances.
     • $O_T \to Tgg$: Leads to jets + missing energy (MET).
     • $O_{T0} \to A_D g$: Depending on the lifetime of $A_D$, this yields displaced vertices, multi-jets + leptons, or MET.
   • Constraints: Current LHC data constrains the octet masses to $m_O \gtrsim 1.4$ TeV.
2. Gravitational Waves (GW):
   • Metastable Domain Walls: Their decay generates a stochastic GW background. The peak frequency is low ($\sim$ nHz), but the high-frequency tail may be detectable by pulsar timing arrays or future space-based detectors.
   • Mirror QCD Phase Transition: The transition is predicted to be first-order, producing GWs with frequencies around 1 mHz, potentially detectable by LISA.
3. Electric Dipole Moments (EDM):
   • The model predicts non-zero neutron and proton EDMs, potentially within reach of future precision experiments.
4. Dark Matter Detection:
   • Direct Detection: $T$ scattering off nuclei is suppressed (below the neutrino floor) unless the kinetic mixing is large.
   • Indirect Detection: Constraints from Fermi-LAT on gamma rays from dark matter annihilation set a lower bound on the dark matter mass ($m_T > 100$ GeV).

4. Significance

This paper presents a theoretically robust and phenomenologically rich solution to the Strong CP problem. Its primary significance lies in:

1. Unification of Solutions: It successfully combines the "Mirror QCD" approach (heavy axion) with "Accidental Symmetry" (gauge-derived PQ) to solve the quality problem without fine-tuning.
2. Cosmological Viability: It resolves the two major cosmological flaws of previous mirror axion models: the domain wall problem and the stable colored relic problem.
3. Testability: Unlike many axion models that are difficult to probe, this model predicts a wide array of observable signals:
   • LHC: Dijet resonances, displaced vertices, and MET signatures.
   • GW Detectors: Signals from domain wall decay and first-order phase transitions.
   • Dark Matter: A viable WIMP candidate with a vector portal.
4. Baryogenesis: It naturally accommodates high-scale leptogenesis, linking the origin of matter-antimatter asymmetry to the Strong CP solution.

In summary, the authors propose a minimal extension of the Standard Model that not only solves the Strong CP problem but also provides testable explanations for Dark Matter, the Baryon Asymmetry, and potential Gravitational Wave signals, all while avoiding the theoretical pitfalls of global symmetries and stable topological defects.