Indications for new scalar resonances at the LHC and a possible interpretation

This paper proposes a minimalistic model containing four scalar multiplets to simultaneously explain multiple excesses observed at the LHC (notably at 95 GeV and 650 GeV), arguing that these hints disfavor common scalar extensions while predicting specific charged scalars that make the theory testable and falsifiable despite current data limitations.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle microscope. For over a decade, scientists have been using it to look at the fundamental building blocks of the universe. In 2012, they found the "Holy Grail" of this search: the Higgs boson, a particle that gives mass to everything else. It was like finding the missing piece of a giant jigsaw puzzle.

But recently, the scientists (specifically the ATLAS and CMS teams) have started seeing some strange, blurry shapes in the background of their data. They aren't sure if these shapes are real new particles or just random static (noise) in the image. However, these "ghosts" are appearing in the same spots often enough that the physicists are taking them very seriously.

This paper is like a detective story where the authors try to solve the mystery of these ghosts using a new theory. Here is the breakdown in simple terms:

1. The Mystery: The "Ghost" Particles

The authors are looking at four specific "ghosts" (resonances) that have shown up in the data:

• The 95 GeV Ghost: A light particle seen in a few different experiments. It's like a faint whisper that keeps repeating.
• The 650 GeV Ghost: A heavy, broad particle. This is the loudest whisper, with a statistical "significance" of about 4 sigma. In the world of particle physics, this is like hearing a shout that is very likely real, though not quite a "discovery" yet (which requires a 5-sigma shout).
• The 320 GeV and 400 GeV Ghosts: Two other hints, one of which might be a "mirror image" (CP-odd) of the others.

The problem is that the Standard Model (our current rulebook for how particles work) only has one Higgs boson. If these ghosts are real, the rulebook is incomplete.

2. The Old Solutions Don't Fit

Physicists have tried to explain these ghosts using existing "extensions" to the rulebook, like adding more Higgs particles (like adding extra wheels to a car).

• The Problem: The authors show that simple additions (like just adding more standard Higgs particles) break the laws of physics. Specifically, they violate a rule called Unitarity.
• The Analogy: Imagine you are trying to balance a seesaw. If you put a heavy weight (the 650 GeV particle) on one side, the seesaw tips over and breaks unless you add a counterweight on the other side. The authors found that the 650 GeV particle is so heavy and interacts so strongly with other particles that the "seesaw" of the universe would break unless there is a specific, hidden counterweight: a doubly-charged scalar (a particle with double the electric charge of an electron).

3. The New Theory: The "2HDeGM" Model

Since the simple solutions don't work, the authors propose a new, slightly more complex model called the 2-Higgs Doublet extended Georgi-Machacek (2HDeGM) model.

Think of the Standard Model as a house with one room.

• Old Idea: Maybe we just added a second room (a second Higgs doublet).
• The Problem: The "ghosts" are too big for just two rooms.
• The New Idea: The authors propose a house with two rooms (two Higgs doublets) AND a garden (triplets of particles).
  • The "rooms" interact with normal matter (quarks and electrons).
  • The "garden" (the triplets) is special because it keeps the "seesaw" (the unitarity sum rules) balanced. It provides that necessary doubly-charged counterweight without breaking the symmetry of the universe.

4. The Detective Work: Fitting the Puzzle

The authors didn't just invent a model; they tried to force the data into it. They treated the experimental numbers like clues.

• They asked: "If this new model is true, what must the properties of these ghosts be?"
• They found that the model is extremely picky. It's like a lock that only opens with a very specific key.
• The Result: The data is so precise (even with large error bars) that it severely limits the possible answers. They found that for the model to work, the "garden" (the triplet particles) must have a specific size, and the "rooms" must be arranged in a very specific way.
• The Twist: The model predicts that the 650 GeV particle should decay into pairs of lighter particles (like the 95 GeV and 125 GeV particles) rather than just disappearing into energy. This gives scientists a specific way to test if the model is right or wrong.

5. The Conclusion: A "Falsifiable" Guess

The authors are very honest: We don't know for sure if these ghosts are real yet.

• If future data proves the ghosts are real, this model is a strong candidate because it explains all of them at once, including the need for those mysterious doubly-charged particles.
• If the ghosts turn out to be just noise (static), the model falls apart.
• The beauty of this paper is that it makes a testable prediction. It tells the ATLAS and CMS teams exactly what to look for next:
  • Look for the doubly-charged particles (the counterweights).
  • Look for the 650 GeV particle decaying into two lighter scalars.

Summary Analogy

Imagine you are a mechanic looking at a car engine that is making strange knocking sounds (the 95, 320, 400, and 650 GeV hints).

• Old Mechanics said, "It's just a loose bolt," or "It's a bad spark plug."
• These Authors say, "No, the engine is built with a specific design flaw. If these sounds are real, the engine must have a hidden, double-gear system (the doubly-charged scalar) that we haven't seen yet to keep the engine from exploding."
• They propose a new blueprint (2HDeGM) that includes this hidden gear. They show that if you build the engine this way, all the knocking sounds make sense. But they also say, "If you open the hood and don't find that hidden gear, our blueprint is wrong."

It is a bold, "all-or-nothing" theory that turns vague hints into a concrete, testable roadmap for the future of particle physics.

Technical Summary

1. Problem Statement

The Large Hadron Collider (LHC) experiments (ATLAS and CMS) have reported several unconfirmed excesses in the search for new scalar resonances beyond the Standard Model (SM). While none have reached the $5\sigma$ discovery threshold, specific hints have accumulated statistical significance worthy of serious theoretical investigation. The primary anomalies include:

• $h_{95}$: A resonance near 95 GeV observed in $\gamma\gamma$ and $\tau^+\tau^-$ channels (CMS) and $Zb\bar{b}$ (LEP).
• $H_{650}$: A broad resonance near 650 GeV observed decaying to $W^+W^-$, $ZZ$, and $h_{95}h_{125}$.
• $A_{400}$ and $H_{320}$: Hints of a CP-odd scalar at 400 GeV and a CP-even scalar at 320 GeV.
• Charged Scalars: Mild hints of singly ($H^+$ at ~375 GeV) and doubly ($H^{++}$ at ~450 GeV) charged scalars.

The central problem addressed is whether these multiple, simultaneous indications can be accommodated within a minimal, renormalizable extension of the SM scalar sector. The authors demonstrate that standard minimal extensions (e.g., Multi-Higgs Doublet Models or the canonical Georgi-Machacek model) fail to explain the data due to constraints from unitarity sum rules and custodial symmetry.

2. Methodology

The authors employ a phenomenological approach combining experimental data constraints with theoretical consistency requirements:

• Data Aggregation: They calculate combined global significances for the resonances by combining $p$-values from independent channels (accounting for the Look-Elsewhere Effect). They find global significances of $\sim 3\sigma$ for $h_{95}$ and $\sim 4\sigma$ for $H_{650}$.
• Unitarity Sum Rules: They analyze the scattering amplitudes of longitudinal gauge bosons ($W_L W_L \to W_L W_L, Z_L Z_L$). They utilize sum rules (e.g., $\sum g^2_{WW\phi} - \sum g^2_{WW\phi^{--}} = g^2 M_W^2$) to show that a large coupling of a heavy neutral scalar ($H_{650}$) to $W^+W^-$ necessitates the existence of doubly charged scalars to preserve unitarity.
• Model Construction (2HDeGM):
  • They propose the 2-Higgs Doublet extended Georgi-Machacek (2HDeGM) model.
  • Field Content: Two $SU(2)_L$ doublets ($\Phi_1, \Phi_2$), one real triplet ($\Xi$), and one complex triplet ($X$).
  • Symmetry Breaking: Unlike the canonical Georgi-Machacek (GM) model, they impose custodial symmetry (CS) only on the gauge sector, not the scalar potential. This allows the custodial multiplets (5-plet, 3-plets) to be non-degenerate in mass, enabling the specific mass spectrum required by the data.
  • Yukawa Sector: They explore Type-I, II, X, and Y Yukawa structures, ultimately favoring Type-I to satisfy constraints on the triplet Vacuum Expectation Value (VEV).
• Parameter Space Scan: They perform a numerical scan to determine the mixing matrix elements ($x_{ij}$) and VEVs ($v_1, v_2, u$) that satisfy:
  • SM-like couplings for $h_{125}$.
  • Observed signal strengths for $h_{95}$ and $H_{650}$.
  • Unitarity sum rules.
  • Constraints from LEP and LHC searches (e.g., $H_{650} \to ZZ$ limits).

3. Key Contributions

• Ruling out Minimal Models: The paper rigorously demonstrates that simple extensions (Singlets, Doublets, or the canonical GM model) cannot simultaneously explain the $h_{95}$ and $H_{650}$ data. Specifically, the canonical GM model predicts a $ZZ$ coupling for $H_{650}$ that is too large (violating experimental limits) or requires a specific alignment that contradicts the observed $W^+W^-$ excess.
• Necessity of Doubly Charged Scalars: The authors prove that the observed $H_{650} \to W^+W^-$ signal, if interpreted within a renormalizable theory, predicts the existence of a doubly charged scalar. This is a direct consequence of the unitarity sum rules.
• The 2HDeGM Model: They introduce a specific, minimal extension (2HDeGM) that accommodates all hints. Key features include:
  • Breaking of mass degeneracy in custodial multiplets to allow $H_{650}$ to have the required couplings.
  • A large triplet VEV ($u \sim 69\text{--}78$ GeV), which is larger than typical GM model limits but allowed due to new decay channels.
  • Identification of the four CP-even scalars as $h_{95}, h_{125}, H_{320}, H_{650}$.
• Resolution of Tensions via Di-scalar Decays: A major finding is that satisfying all constraints (specifically the tension between $H_{650} \to ZZ$ limits and $h_{95} \to ZZ$ limits) requires significant di-scalar decay widths (e.g., $H_{650} \to h_{95}h_{125}$ or $H_{320} \to h_{125}h_{125}$). This reduces the branching ratio to gauge bosons, evading exclusion limits.

4. Results

• Global Significances:
  • $h_{95}$: Combined global significance $\approx 2.75\sigma$ (conservative) to $3\sigma$.
  • $H_{650}$: Combined global significance $\approx 4.08\sigma$.
  • $A_{400}$: $\approx 3.17\sigma$.
• Model Constraints:
  • The model requires a Type-I Yukawa structure to allow for a sufficiently large triplet VEV ($u \gtrsim 65$ GeV) while keeping couplings real and perturbative.
  • The mixing matrix $X$ is highly constrained. The solution space is narrow; for instance, the coupling $\kappa_{H_{650}}^Z$ must be very small ($\lesssim 0.1$) to avoid $4\ell$ exclusion limits, while $\kappa_{H_{650}}^W$ must be large ($\sim 0.9\text{--}1.0$) to match the $WW$ excess.
  • Benchmark Points: The authors provide specific benchmark points (e.g., Table V) where:
    • $u \approx 69$ GeV, $v_1 \approx 14$ GeV, $v_2 \approx 104$ GeV.
    • $H_{650}$ has a branching ratio to lighter scalars ($\sim 6\%$) to suppress $ZZ$ decays.
    • $H_{320}$ has a large width ($\sim 250\%$ increase) dominated by decays to $h_{125}h_{125}$.
• Charged Scalars: The model predicts charged scalars ($H^+, H^{++}$) with masses potentially as low as 375 GeV and 450 GeV, respectively. The standard CMS lower bounds ($m_{H^{++}} > 2$ TeV) are evaded because the doubly charged scalars can decay into $H^+ W^+$ or $H^+ H^+$, reducing the $H^{++} \to W^+W^+$ branching ratio.

5. Significance and Conclusion

• Falsifiability: Despite the complexity of the model, the scant data with large error bars severely constrains the parameter space. The model makes sharp predictions (e.g., specific mass ranges for charged scalars, specific di-scalar decay rates) that can be tested or falsified with future LHC data.
• Exploratory Value: The paper highlights the extreme difficulty of fitting multiple resonances simultaneously, even in "next-to-minimal" extensions. It illustrates that the "alignment limit" (where $h_{125}$ is SM-like) combined with new heavy resonances creates severe tension that usually requires non-standard mechanisms (like large di-scalar decays or broken custodial degeneracy).
• Future Prospects: The authors suggest prioritizing searches for:
  • $H_{650} \to W^+W^-$ and $ZZ$.
  • $H_{320} \to h_{125}h_{125}$ (specifically $b\bar{b}\gamma\gamma$ or $b\bar{b}\tau\tau$).
  • Charged scalars in the 300–500 GeV range.
  • The existence of the predicted doubly charged scalar $H^{++}$.

In summary, the paper argues that if the LHC excesses at 95 GeV and 650 GeV are real, they point towards a 2HDeGM scenario with broken custodial mass degeneracy, a large triplet VEV, and significant decays into pairs of lighter scalars, necessitating the discovery of doubly charged Higgs bosons.