LHC Signatures of the Generic Georgi-Machacek Model

This paper proposes a generalized Georgi-Machacek Model without custodial symmetry to explain recent LHC excesses in vector-boson fusion channels by allowing mass splitting among new Higgs bosons, thereby accommodating observed signals in $W^\pm W^\pm$, $WZ$, and di-photon production while satisfying experimental constraints.

The Gist

Imagine the Standard Model of particle physics as a perfectly tuned orchestra. For decades, it has played the music of the universe flawlessly, predicting every note we've heard in our experiments. The discovery of the Higgs boson in 2012 was like finding the final, missing instrument in the ensemble.

But recently, the orchestra started playing a few strange, unexpected notes.

The Mystery Notes

Two giant listening stations at the Large Hadron Collider (LHC)—ATLAS and CMS—have been scanning the cosmic noise. They noticed something odd:

• ATLAS heard a faint, suspicious hum at two specific pitches: one around 450 GeV (in a "same-sign W boson" channel) and another around 375 GeV (in a "WZ" channel).
• CMS didn't hear a loud noise, but they noticed the "silence" in those areas wasn't as quiet as they expected. It was like a detective finding a crime scene where the security cameras were mysteriously blurry.

These "excesses" suggest there might be new, heavy Higgs bosons hiding in the shadows, but the standard theory says they shouldn't be there.

The Old Theory vs. The New Clue

For a long time, physicists have had a favorite theory called the Georgi-Machacek (GM) Model. Think of this model as a strict rulebook for how these new particles should behave.

• The Rulebook's Problem: The original GM Model is like a rigid marching band. It demands that all the new heavy particles (the "new Higgses") must march in perfect lockstep, meaning they must all have the exact same mass.
• The Reality: The data from ATLAS shows two different masses (450 GeV and 375 GeV). They are not marching in lockstep. The old rulebook says, "Impossible! If you see one, you must see the other at the exact same weight." Since the data shows they are different, the old rulebook is broken.

The Solution: The "Loose" Rulebook

The authors of this paper propose a Generalized Georgi-Machacek Model (gGMM).

Imagine the original model was a strict parent who said, "You and your sibling must wear the exact same size shoes." The new model is a more relaxed parent who says, "You can wear slightly different sizes, as long as you still walk together."

By loosening the rules (specifically, removing a symmetry called "custodial symmetry" from the math), the authors show that:

1. The heavy particles can have different masses.
2. The "450 GeV" signal can be explained by a doubly-charged Higgs (a particle with double the electric charge of a proton).
3. The "375 GeV" signal can be explained by a singly-charged Higgs.
4. Both can exist without breaking the laws of physics or contradicting other experiments.

The "Ghost" at 152 GeV

There is a third mystery. Some data suggests a new particle might exist at 152 GeV, appearing when a Higgs boson is produced alongside two photons (light particles).

The authors show that their "loose" model can also explain this! They propose that a different type of particle (from a "Y=0 triplet") is responsible for this 152 GeV signal. It's like finding a third musician in the orchestra who was playing a solo that no one noticed until now.

Why This Matters

If this paper is right, it means:

• The Universe is richer than we thought: We aren't just looking at one Higgs boson; we might have a whole family of them.
• The "Lockstep" is broken: Nature doesn't always follow the strictest symmetries we imagine.
• New Physics is near: These specific signals (W bosons fusing together) are considered a "smoking gun." If confirmed, it would be the first direct evidence of physics beyond the Standard Model in decades.

The Bottom Line

The authors took a complex mathematical theory, loosened its strictest rules, and showed that it can perfectly explain the weird, "noisy" signals ATLAS and CMS have been hearing. They are essentially saying: "Don't throw away the theory just because the particles have different weights. If we tweak the rules slightly, the whole story makes sense again."

Now, it's up to the LHC to keep listening and see if these "mystery notes" turn into a full-blown symphony of new physics.

Technical Summary

1. Problem Statement

The paper addresses a set of intriguing experimental anomalies observed at the Large Hadron Collider (LHC) that cannot be explained by the Standard Model (SM) or the canonical Georgi-Machacek (GM) Model:

• ATLAS Excesses: ATLAS reported a $3.3\sigma$ excess in the $W^\pm W^\pm$ channel at $\approx 450$ GeV and a $2.8\sigma$ excess in the $WZ$ channel at $\approx 375$ GeV. CMS reported weaker-than-expected limits in these mass regions.
• Associated Diphoton Excess: There is an indication of a new scalar resonance at $\approx 152$ GeV in associated production channels (specifically $H \to \gamma\gamma$).
• Theoretical Obstacle: The canonical GM model imposes custodial $SU(2)_C$ symmetry on the scalar potential. This symmetry enforces mass degeneracy among the new gauge-philic Higgs bosons (the doubly charged $H^{\pm\pm}$, singly charged $H^\pm$, and neutral $H^0$). Consequently, the canonical model cannot simultaneously explain the distinct mass peaks observed at 450 GeV and 375 GeV, nor can it easily accommodate the 152 GeV signal without conflicting with other constraints.

2. Methodology

The authors propose and analyze the Generic Georgi-Machacek Model (gGMM), which relaxes the requirement of custodial symmetry in the scalar potential.

• Model Construction: The model extends the SM by adding an $SU(2)_L$ triplet with hypercharge $Y=1$ ($\chi$) and a triplet with $Y=0$ ($\zeta$). Unlike the canonical GM model, the scalar potential does not enforce custodial symmetry, allowing the masses of the physical eigenstates to split.
• Approximation: The authors work in the limit of small mixing between the triplets and the SM Higgs doublet. They initially treat the $Y=1$ and $Y=0$ sectors as decoupled to simplify the phenomenology, setting mixing parameters ($\mu_{\chi\zeta}, \rho_4, \rho_5, \sigma_4$) to near zero.
• Constraints & Analysis:
  • Electroweak Precision Data (EWPD): The triplet VEVs ($v_\chi, v_\zeta$) are constrained by the $\rho$ parameter ($\rho \approx 1$). In the gGMM, $v_\chi \approx v_\zeta$ is required to cancel contributions to the $\rho$ parameter, allowing for sizable VEVs (tens of GeV) which enhance Vector Boson Fusion (VBF) cross-sections.
  • Experimental Limits: The study incorporates limits from ATLAS and CMS on VBF production of $W^\pm W^\pm$, $WZ$, $ZZ$, and $hh$ final states, as well as SM Higgs signal strength measurements and vacuum stability conditions.
  • Parameter Space Scan: The authors scan the parameter space, specifically the VEVs ($v_\chi, v_\zeta$) and mixing angles ($\alpha_{\phi\chi}, \alpha_{\phi\zeta}$), to find regions consistent with all data.

3. Key Contributions

• Resolution of Mass Degeneracy: By removing custodial symmetry, the model lifts the mass degeneracy, allowing the $Y=1$ triplet states to have distinct masses ($m_{H^{\pm\pm}} \neq m_{H^\pm} \neq m_{H^0}$).
• Unified Explanation of Anomalies: The paper demonstrates that a single theoretical framework (gGMM) can simultaneously explain:
  1. The $W^\pm W^\pm$ excess at 450 GeV via the doubly charged Higgs ($H^{\pm\pm}$) from the $Y=1$ triplet.
  2. The $WZ$ excess at 375 GeV via the singly charged Higgs ($H^\pm_\chi$) from the $Y=1$ triplet.
  3. The 152 GeV diphoton excess via the neutral Higgs ($H^0_\zeta$) from the $Y=0$ triplet.
• Mechanism for $WZ$ Enhancement: The authors show that if the charged Higgs states from the $Y=1$ and $Y=0$ triplets are close in mass, mixing between them can enhance the branching ratio $Br(H^\pm \to WZ)$, improving the fit to the $WZ$ excess data.

4. Key Results

• $W^\pm W^\pm$ and $WZ$ Channels:
  • Fixing $m_{H^{\pm\pm}} \approx 450$ GeV and $m_{H^\pm_\chi} \approx 375$ GeV allows for a best-fit VEV of $v_\chi \approx 23$ GeV.
  • This configuration yields a VBF production cross-section $\sigma_{VBF} \times Br(H^{\pm\pm} \to W^\pm W^\pm) \approx 72$ fb, consistent with ATLAS data and CMS limits.
  • The mass splitting ensures $Br(H^{\pm\pm} \to W^\pm W^\pm) \approx 100\%$ (suppressing the decay to $H^\pm W^\pm$).
  • The neutral partner $H^0_\chi$ is predicted to have a mass of $\approx 280$ GeV. Its VBF production into $ZZ$ is consistent with current limits for small positive mixing angles ($\alpha_{\phi\chi} \approx 0.15$).
• 152 GeV Diphoton Excess:
  • The $Y=0$ triplet neutral scalar ($H^0_\zeta$) with mass 152 GeV can explain the diphoton excess.
  • The model predicts a branching ratio $Br(H^0_\zeta \to \gamma\gamma) \approx 0.7\%$, achievable via Drell-Yan production and VBF.
  • Crucially, the gGMM resolves tensions found in pure $Y=0$ triplet models: it allows for the required branching ratio without violating vacuum stability or SM Higgs signal strength constraints, thanks to the interplay with the $Y=1$ sector.
• Global Fit:
  • The preferred regions for the $W^\pm W^\pm$ and $WZ$ channels overlap at the $2\sigma$ level.
  • If the charged Higgs masses are tuned to be close ($m_{H^\pm_\zeta} \approx m_{H^\pm_\chi}$), mixing enhances the $WZ$ signal, improving the global agreement with data.

5. Significance

• Phenomenological Viability: This work provides a concrete, testable scenario where the "smoking-gun" signatures of the GM model (VBF production of same-sign $W$ pairs and $WZ$) are realized without the restrictive mass degeneracy of the canonical model.
• New Physics Interpretation: It offers a compelling explanation for multiple independent LHC anomalies (450 GeV, 375 GeV, and 152 GeV) within a single, theoretically consistent extension of the SM.
• Future Probes: The model predicts specific correlations between the masses of the new scalars and their mixing angles. Future LHC runs can test these predictions by:
  • Searching for the neutral $H^0_\chi$ at $\approx 280$ GeV in $ZZ$ and $hh$ channels.
  • Measuring the precise mass splitting between $H^{\pm\pm}$ and $H^\pm$.
  • Investigating the 152 GeV resonance in associated production.
• Theoretical Flexibility: It highlights that relaxing custodial symmetry in the scalar potential is a viable and necessary step to accommodate emerging LHC data, suggesting that the true nature of electroweak symmetry breaking may involve a more complex scalar sector than previously assumed.