Interpreting the 650 GeV and 95 GeV Higgs anomalies in the next-to-two-Higgs-doublet model

This paper demonstrates that the Next-to-Two-Higgs-Doublet Model (N2HDM) can simultaneously explain the LHC and LEP anomalies at 95 GeV and the 650 GeV excess by predicting a heavy CP-even Higgs boson decaying into a 125 GeV Higgs and a 95 GeV scalar, a scenario consistent with current experimental constraints and offering distinct testable signatures for future collider runs.

The Gist

The Big Picture: A Cosmic "Missing Puzzle Piece" Hunt

Imagine the Standard Model of particle physics as a giant, mostly complete jigsaw puzzle. For decades, scientists have been trying to fit the last few pieces together. In 2012, they found the "King" piece: the famous 125 GeV Higgs boson. This confirmed how the universe gets its mass.

But recently, while looking at the edges of the puzzle box, scientists at the Large Hadron Collider (LHC) and the older LEP collider noticed some strange "glitches." They saw faint, blurry hints of two new, invisible puzzle pieces that shouldn't be there according to the current rules:

1. A light piece weighing about 95 GeV.
2. A heavy piece weighing about 650 GeV.

These aren't just random noise; they appear in specific ways (like decaying into pairs of photons or bottom quarks). The question is: Are these real new particles, or just statistical flukes?

The Theory: The "Next-to-Two-Higgs-Doublet Model" (N2HDM)

To explain these glitches, the authors propose a new theory called the N2HDM.

The Analogy: The Family House
Think of the Standard Model's Higgs sector as a small house with two rooms (two "Higgs doublets"). This is the standard setup.
The N2HDM suggests that this house actually has a secret attic (an extra "singlet" field) that we didn't know about.

• The Standard House (2HDM): Has two rooms.
• The N2HDM House: Has two rooms plus a secret attic.

This extra attic changes the architecture. It allows for three different types of "Higgs guests" to live there instead of just two:

1. The Light Guest (h1): Weighs ~95 GeV.
2. The Famous Host (h2): Weighs 125 GeV (the one we already found).
3. The Heavy Guest (h3): Weighs ~650 GeV.

The Mystery: How Do They Connect?

The paper investigates a very specific scenario to explain the glitches:

The "Heavy Guest" Drop-Off
Imagine the Heavy Guest (650 GeV) arrives at the party. Instead of staying, they immediately split into two smaller groups:

1. They drop off the Famous Host (125 GeV).
2. They drop off the Light Guest (95 GeV).

The Light Guest then quickly turns into a pair of bottom quarks (detectable as "b-b"), and the Famous Host turns into two photons (detectable as "gamma-gamma").

This creates a unique signature: Two photons + Two bottom quarks. This is exactly what the CMS experiment at the LHC saw as a "glitch" at 650 GeV.

The Investigation: Testing the Theory

The authors ran a massive computer simulation (a "parameter scan") to see if this "House with an Attic" theory could actually work without breaking the laws of physics. They had to check:

• Stability: Does the house collapse? (Vacuum stability).
• Rules: Does it break known physics rules? (Flavor physics, Electroweak precision).
• The "Tau" Test: There was a search for a similar process involving "tau particles" (heavy cousins of electrons) that came up empty. The theory had to predict a rate low enough to avoid this "no-go" zone.

The Result:
They found that the theory works, but only in two specific "neighborhoods" of the theory (called Type-II and Type-Y).

• In these neighborhoods, the math lines up perfectly.
• The Heavy Guest (650 GeV) can decay into the Famous Host and the Light Guest.
• The Light Guest (95 GeV) can explain the old LEP and LHC glitches in the photon and bottom-quark channels.
• Crucially, the theory predicts that the "tau" search should come up empty, which matches reality.

The "Ghost" Alternative:
The authors also checked if the Heavy Guest could be a "ghost" (a CP-odd particle). They found that if it were a ghost, the math would clash with other experiments. So, the Heavy Guest must be a normal particle (CP-even), not a ghost.

What This Means for the Future

This paper is like a detective saying, "We have a suspect, and we know exactly where to look for them next."

1. The Prediction: If this theory is right, we should see specific patterns in the data coming from the LHC's current run (Run 3) and the future High-Luminosity LHC.
2. The Correlation: The theory predicts that if you see the "Two Photons + Two Bottoms" signal, you should also see a specific, correlated signal in "Two Photons + Two Taus" (though the tau signal is harder to see).
3. The Verdict: The N2HDM is a strong candidate for explaining these anomalies. It's a "minimal" extension (adding just one extra piece to the house) that solves multiple problems at once without breaking the existing rules.

Summary in One Sentence

The authors propose that the universe has a slightly larger "Higgs family" than we thought, featuring a heavy particle that splits into our known Higgs and a new, lighter 95 GeV particle, perfectly explaining recent mysterious signals at the LHC while staying within the rules of physics.

Technical Summary

1. Problem Statement

Recent experimental data from the Large Hadron Collider (LHC) and previous Large Electron-Positron (LEP) collider have revealed intriguing anomalies suggesting the existence of new scalar resonances beyond the Standard Model (SM) 125 GeV Higgs boson ($H_{SM}$):

• ~95 GeV Excess: Observed in $b\bar{b}$ channels at LEP, and in $\gamma\gamma$ and $\tau^+\tau^-$ channels at CMS and ATLAS.
• ~650 GeV Excess: Observed by CMS in the $\gamma\gamma b\bar{b}$ final state, suggesting a heavy resonance decaying into a pair of Higgs bosons or a SM-like Higgs plus a lighter scalar.

The challenge is to explain these anomalies simultaneously within a consistent theoretical framework that respects all existing experimental constraints (including the properties of the 125 GeV Higgs, flavor physics, and Electroweak Precision Observables).

2. Methodology

The authors investigate the Next-to-Two-Higgs-Doublet Model (N2HDM), an extension of the SM featuring two complex $SU(2)_L$ Higgs doublets ($H_1, H_2$) and one real singlet scalar ($S$).

• Model Structure:

  • The model introduces three CP-even neutral scalars ($h_1, h_2, h_3$), one CP-odd scalar ($A$), and a charged Higgs pair ($H^\pm$).
  • The authors assume $h_2$ corresponds to the observed 125 GeV SM-like Higgs.
  • Two specific scenarios are tested for the 650 GeV resonance:
    1. CP-even interpretation: $h_3 \approx 650$ GeV decays via $h_3 \to h_2 h_1$, where $h_1 \approx 95$ GeV.
    2. CP-odd interpretation: $A \approx 650$ GeV decays via $A \to h_2 Z$.
  • The study focuses on Type-II and Type-Y (Flipped) Yukawa structures to avoid Flavor Changing Neutral Currents (FCNCs).

• Analysis Tools & Constraints:

  • ScannerS: Used for parameter scans and theoretical constraints (perturbative unitarity, boundedness from below, vacuum stability).
  • HiggsBounds & HiggsSignals: Used to apply direct search limits from LEP, Tevatron, and LHC, and to fit the 125 GeV Higgs signal rates.
  • N2HDECAY: Calculates branching ratios (BRs) and total widths.
  • SusHi: Computes production cross-sections ($ggF$ and $bbF$) at NNLO in QCD.
  • Constraints Applied:
    • 125 GeV Higgs signal strength ($\Delta\chi^2 < 6.18$).
    • Direct searches for heavy neutral Higgs ($A \to hZ$, $H \to ZZ$, etc.).
    • Flavor physics ($B \to X_s\gamma$, $B_s \to \mu\mu$).
    • Electroweak Precision Observables (S, T, U parameters).
    • Specific CMS limits on the $\tau^+\tau^- b\bar{b}$ channel to constrain the 650 GeV resonance.

3. Key Contributions

• Simultaneous Interpretation: The paper demonstrates that the N2HDM can simultaneously accommodate the 95 GeV and 650 GeV excesses, a feat difficult in more minimal models like the 2HDM or NMSSM without fine-tuning.
• Exclusion of CP-odd Scenario: The authors rigorously show that the CP-odd interpretation ($A \to h_2 Z$) is effectively ruled out by current LHC searches for heavy neutral Higgs bosons decaying to $hZ$ and $t\bar{t}Z$.
• Validation of CP-even Cascade: The viable solution is identified as a CP-even cascade: $gg \to h_3 \to h_2 h_1$, followed by $h_2 \to \gamma\gamma$ and $h_1 \to b\bar{b}$.
• Yukawa Structure Comparison: The study provides a comparative analysis of Type-II and Type-Y frameworks, identifying specific parameter regions where both can explain the data.

4. Results

• Viability of CP-even Scenario:

  • The CP-even interpretation ($h_3 \approx 650$ GeV) remains viable in both Type-II and Type-Y N2HDM.
  • The predicted cross-section for the $\gamma\gamma b\bar{b}$ channel ($\sigma_{\gamma\gamma b\bar{b}}$) falls within the experimental 2$\sigma$ interval reported by CMS ($\sim 0.35$ fb).
  • Type-II: Achieves cross-sections up to $\sim 0.12$ fb with $BR(h_3 \to h_1 h_2) \approx 20\%$ and moderate $\tan\beta$ ($1.0 - 3.7$).
  • Type-Y: Similar viability but with slightly lower cross-sections ($\sim 0.10$ fb) and a slightly different optimal $\tan\beta$ range ($1.3 - 3.6$).

• Branching Ratios & Dynamics:

  • The light scalar $h_1$ ($\approx 95$ GeV) must have a dominant $b\bar{b}$ decay ($BR \gtrsim 80\%$) and a suppressed coupling to gauge bosons to satisfy LEP constraints while maintaining the $\gamma\gamma$ signal.
  • The heavy scalar $h_3$ is produced primarily via gluon-gluon fusion. Its decay to $h_1 h_2$ is enhanced at moderate $\tan\beta$ due to the suppression of the dominant $t\bar{t}$ channel.
  • The singlet-doublet mixing is crucial: it allows $h_1$ to have the necessary singlet fraction to suppress $ZZ$ couplings (evading LEP limits) while retaining sufficient fermion couplings for LHC signals.

• Benchmark Points (BPs):

  • The authors provide four Benchmark Points for each Yukawa type (Type-II and Type-Y).
  • These points satisfy all theoretical constraints and experimental limits, including the recent CMS search for the inverted channel ($h_3 \to h_2(b\bar{b})h_1(\gamma\gamma)$), where the predicted rates are well below exclusion limits.

• Future Projections:

  • The model predicts correlated rates in complementary channels: $\gamma\gamma b\bar{b}$, $\tau^+\tau^- b\bar{b}$, $b\bar{b} \gamma\gamma$, and $\gamma\gamma \tau^+\tau^-$.
  • HL-LHC projections indicate that a subset of the viable parameter space will be testable via precision measurements of the 125 GeV Higgs couplings ($|c_{h_2 VV}|$ and $|c_{h_2 \tau\tau}|$).

5. Significance

This work provides a robust, non-supersymmetric explanation for multiple Higgs anomalies using the N2HDM. By systematically excluding the CP-odd hypothesis and validating the CP-even cascade, it narrows the search space for new physics. The identification of specific, testable predictions for Run 3 and the High-Luminosity LHC (HL-LHC) offers a clear path for experimentalists to either confirm the existence of this extended scalar sector or further constrain the N2HDM parameter space. The results highlight the importance of the singlet-doublet mixing mechanism in reconciling low-mass excesses with high-mass resonance searches.