Extended IDM theory with low scale seesaw mechanisms

This paper proposes an extended Inert Doublet Model that generates neutrino and charged fermion masses through multi-loop radiative seesaw mechanisms, explains CP violation and multi-component dark matter via discrete symmetries, and simultaneously addresses the 95 GeV diphoton excess and charged lepton flavor violation within current experimental limits.

The Gist

Imagine the Standard Model of physics as a giant, incredibly successful recipe book for the universe. It tells us how to cook up stars, planets, and even you. But, like any old recipe book, it has some missing pages and a few ingredients that don't quite make sense.

This paper proposes a "Special Edition" of that recipe book, adding a secret "Dark Kitchen" to the main kitchen. Here's how this new model works, broken down into simple concepts:

1. The Problem: The Missing Ingredients

The current recipe book has three big holes:

• The Ghostly Neutrinos: We know tiny particles called neutrinos have mass, but the book says they should be weightless.
• The Dark Matter Mystery: We know there's invisible "dark matter" holding galaxies together, but we don't know what it's made of.
• The "Strong CP" Glitch: There's a weird rule in the book about how particles behave that suggests the universe should be lopsided (like a coin that always lands on heads), but experiments show it's perfectly balanced. Why? Nobody knows.

2. The Solution: The "Dark Kitchen" Extension

The authors suggest adding a new room to the universe's kitchen: a Dark Sector. This room is separated from our main kitchen by a special door (a symmetry) that only opens under specific conditions.

Inside this Dark Kitchen, they introduce new "chefs" (particles) and "ingredients" (fields) that do the heavy lifting without messing up the main recipe.

3. How the Masses Work: The "Tiered" Cooking System

In our universe, some particles are heavy (like the top quark), and some are light (like the electron). The Standard Model can't explain why this hierarchy exists.

This new model uses a radiative seesaw mechanism. Think of it like a factory assembly line:

• The VIPs (3rd Generation): The heavy hitters (top quark, bottom quark, tau lepton) get their mass instantly at the "tree level" (the main counter). They are the VIPs who get served immediately.
• The Regulars (1st & 2nd Generation): The lighter particles (up, down, charm, strange quarks, electrons, muons) don't get served directly. Instead, they have to go through a one-loop process. Imagine them having to wait in a side kitchen where a special "Dark Chef" mixes their ingredients in a complex recipe before they get their mass. This delay makes them naturally lighter.
• The Ghosts (Neutrinos): These are so light they need an even more complex recipe. They go through a two-loop process (a double-side-kitchen detour) involving a "lepton number violation" (breaking a specific rule twice). This extra complexity makes their mass incredibly tiny, which matches what we observe.

4. Solving the "Strong CP" Glitch: The Silent Partner

The "Strong CP problem" is like a clock that should be ticking loudly but is completely silent. The authors propose that the main kitchen (our visible world) is perfectly symmetrical and silent at the start.

However, the Dark Kitchen is noisy and chaotic. The "noise" (CP violation) from the Dark Kitchen leaks into the main kitchen through a one-way pipe (loop corrections).

• The Magic Trick: The noise leaks in just enough to explain why we have a "weak force" that breaks symmetry (allowing the universe to exist as it is), but it never leaks enough to break the "strong force" symmetry.
• The Result: The strong force stays perfectly balanced (solving the glitch), while the weak force gets the necessary asymmetry. It's like having a noisy neighbor who only talks to you through a specific window, never disturbing the rest of the house.

5. The Dark Matter: A Two-Part Team

The model predicts two types of Dark Matter living in that Dark Kitchen:

1. The Scalar: A particle that acts like a wave (a boson).
2. The Fermion: A particle that acts like a solid matter (a fermion).

They are like a dynamic duo. They can annihilate each other (destroying themselves to create energy) in a way that perfectly matches the amount of dark matter we see in the universe today. Crucially, the model predicts they interact with our world so weakly that they haven't been caught by our most sensitive detectors yet, which fits current data perfectly.

6. The 95 GeV Diphoton Mystery: The "Ghost Signal"

Recently, the CMS experiment at CERN saw a strange "glitch" in their data: a bump at 95 GeV (a specific energy level) where two photons (light particles) appeared. It looked like a new particle, but it wasn't the Higgs boson.

This paper suggests that this bump is actually a new particle from the Dark Kitchen (a scalar singlet).

• Why we missed it: It's mostly invisible to normal matter. It only shows up when it decays into two photons, which is a rare event.
• The Fit: The model's math shows that if this particle exists with a mass of 95 GeV, it perfectly explains the signal strength observed by the CMS team.

7. The "Flavor" Test: Lepton Flavor Violation

The model also predicts that sometimes, a muon (a heavy electron) might turn into an electron and a photon. This is a forbidden dance in the old recipe book, but allowed here.

• The Good News: The model predicts this happens at a rate that is just low enough to have escaped detection so far, but just high enough that future, more sensitive experiments might catch it soon. It's a "Goldilocks" prediction—not too big, not too small.

Summary

In short, this paper builds a secret extension to the universe's rulebook.

• It explains why particles have different masses by making them wait in different "kitchens."
• It solves the Strong CP problem by keeping the main kitchen quiet while letting the dark kitchen do the noisy work.
• It provides two types of Dark Matter that fit the cosmic budget.
• It explains a recent experimental anomaly (the 95 GeV bump) as a new particle from that dark sector.

It's a unified theory that ties together the smallest particles, the invisible dark matter, and the fundamental symmetries of the universe into one elegant, albeit complex, story.

Technical Summary

Here is a detailed technical summary of the paper "Extended IDM theory with low scale seesaw mechanisms" by Huong et al.

1. Problem Statement

The Standard Model (SM) faces several critical unresolved issues:

• Fermion Mass Hierarchy: The SM cannot explain the vast hierarchy between the third-generation fermion masses (generated at tree level) and the first/second-generation masses.
• Neutrino Masses: The origin of tiny active neutrino masses remains unexplained.
• Strong CP Problem: The absence of a measurable neutron electric dipole moment implies the strong CP phase ($\theta_{QCD}$) is unnaturally small ($<10^{-10}$), a problem known as the Strong CP problem.
• Dark Matter (DM): The SM lacks a viable dark matter candidate.
• Anomalies: Recent experimental hints, such as the 95 GeV diphoton excess observed by CMS, require theoretical explanation.

2. Methodology and Model Construction

The authors propose an Extended Inert Doublet Model (IDM) that introduces new symmetries and particle content to address these issues simultaneously.

A. Symmetry Structure

The model extends the SM gauge group $SU(3)_C \times SU(2)_L \times U(1)_Y$ with:

1. Global $U(1)_X$ Symmetry: Spontaneously broken by the vacuum expectation value (VEV) of a scalar singlet $\sigma$. This breaking leaves a residual discrete symmetry $Z'_2$.
2. Discrete $Z_2$ Symmetry: An additional preserved symmetry.
   The combination of $Z_2$ and $Z'_2$ ensures the stability of dark matter candidates and dictates the radiative nature of fermion mass generation.

B. Particle Content

• Scalars:
  • SM Higgs doublet $\phi$.
  • Inert doublet $\eta$ (carrying odd $Z_2$ and $Z'_2$ charges).
  • Singlets $\sigma$ (breaks $U(1)_X$), $\phi_1, \phi_2, \phi_3$ (involved in radiative loops).
• Fermions:
  • Vector-like Fermions: Two up-type ($T_{1,2}$), two down-type ($B_{1,2}$), and two charged leptons ($E_{1,2}$).
  • Sterile Neutrinos: Right-handed Majorana neutrinos ($\nu_{R}, N_{R}$) and additional singlets ($\Psi, \Omega$) required for the two-loop inverse seesaw.

C. Mass Generation Mechanisms

The model employs a hierarchical generation of masses based on loop orders:

1. Tree Level (3rd Generation): The top, bottom, and tau masses are generated via standard Yukawa couplings to the SM Higgs $\phi$.
2. One-Loop Level (1st & 2nd Generations): Masses for lighter quarks and charged leptons arise from radiative corrections mediated by vector-like fermions and inert scalars. This is enforced by the $Z'_2$ symmetry, which forbids tree-level couplings for these generations.
3. Two-Loop Level (Neutrinos): Active neutrino masses are generated via a radiative inverse seesaw mechanism. The lepton-number violating Majorana mass term ($\mu$) is generated at the two-loop level, naturally suppressing the neutrino mass scale.

3. Key Contributions and Mechanisms

A. Solution to the Strong CP Problem

This is a central theoretical contribution. The authors demonstrate that:

• Tree Level: The SM sector conserves CP; thus, $\theta_{QCD} = 0$ at tree level.
• Loop Level: Explicit CP violation resides in the dark sector (specifically in the scalar potential involving $\eta, \phi_2, \sigma$).
• Transmission: CP-violating phases are transmitted to the SM quark sector via one-loop corrections.
• Protection: Due to the specific structure of the diagrams, the complex phases appear only in the first two columns of the quark mass matrices ($M_u, M_d$). The third column remains real.
• Result: The determinant of the mass matrices factorizes such that $\text{Arg}[\det(M_u M_d)] = 0$ up to three-loop order. The strong CP phase remains vanishing, while the weak CP phase (CKM phase) is generated dynamically.

B. Multi-Component Dark Matter

The preserved $Z_2 \times Z'_2$ symmetries stabilize two distinct dark matter candidates:

1. DM1: Carries odd $Z'_2$ charge (e.g., scalar $\phi_3$).
2. DM2: Carries odd $Z_2$ charge (e.g., mixed scalar $\rho_1$ from $\eta/\phi_2$ or fermion $\Omega_R$).
   The model allows for a two-component dark matter scenario. The relic abundance is calculated using the freeze-out mechanism, considering annihilation and conversion processes between the two components. The model is shown to be compatible with current direct detection limits (XENONnT, LZ, PandaX-4T).

C. Explanation of the 95 GeV Diphoton Excess

The model interprets the CMS 95 GeV diphoton excess as a scalar resonance ($\sigma_R$), the real component of the singlet $\sigma$.

• Production: Dominated by gluon fusion via loops of heavy vector-like quarks ($T, B$).
• Decay: The diphoton decay is enhanced by loops of vector-like leptons ($E$) and charged scalars ($H^\pm$).
• Signal Strength: The model successfully reproduces the observed signal strength ($\mu_{\gamma\gamma} \approx 0.35$) for charged scalar masses in the range of 850–2500 GeV and specific trilinear couplings, while suppressing decays to $b\bar{b}$ and $\tau\tau$ due to small mixing angles.

4. Results and Phenomenological Constraints

• CKM Matrix and CP Violation: The model successfully fits the CKM mixing angles and the CP-violating phase ($\delta_{CP}$). The phase is dynamically generated from the dark sector coupling $G \eta^\dagger \phi \phi_2^\dagger$. The fit yields $\delta_{CP} \approx 1.148$, consistent with experimental data.
• Neutrino Sector: The two-loop inverse seesaw generates correct neutrino mass squared differences ($\Delta m^2_{21}, \Delta m^2_{31}$). The model predicts a physical Majoron (massless Goldstone boson from $\sigma$) with couplings suppressed by the high scale $v_\sigma$, satisfying astrophysical constraints (e.g., SN1987A cooling).
• Charged Lepton Flavor Violation (cLFV): The branching ratio for $\mu \to e\gamma$ is calculated. The model predicts rates ($\sim 10^{-14}$) that are within current experimental sensitivity (MEG II) but below the exclusion limit, leaving room for future detection.
• Direct Detection: The spin-independent scattering cross-sections for the dark matter candidates are calculated. The singlet component ($\phi_3$) is constrained by Higgs portal interactions, while the doublet component ($\rho_1$) is constrained by gauge-mediated annihilation. The model finds viable parameter space consistent with XENONnT and LZ limits.

5. Significance

This work presents a unified framework that addresses multiple SM shortcomings without fine-tuning:

1. Naturalness: It explains the fermion mass hierarchy via loop suppression rather than arbitrary Yukawa couplings.
2. Strong CP Solution: It offers a novel solution where the strong CP phase is protected by symmetry and loop structure up to three loops, avoiding the need for an axion or PQ symmetry.
3. Dark Matter: It provides a stable, multi-component dark matter candidate compatible with direct detection.
4. Experimental Anomalies: It offers a concrete explanation for the 95 GeV diphoton excess and predicts testable signals for cLFV and neutrino properties.

The model demonstrates that the origin of CP violation, fermion masses, and dark matter can be interconnected through a specific extended scalar and fermion sector with discrete symmetries.