The Higgs boson in the CP-violating NB-LSSM

This paper investigates the lightest and second-lightest Higgs bosons within a CP-violating next-to-minimal B-L supersymmetric model (NB-LSSM), demonstrating how CP-violating phases and specific parameters induce significant mixing in the Higgs sector to successfully fit both the 125 GeV SM-like Higgs data and the hypothetical 95 GeV excess.

The Gist

Imagine the universe as a giant, complex orchestra. For decades, physicists have been trying to figure out the sheet music for this orchestra. In 2012, they finally found the conductor's baton: the Higgs boson, a particle that gives mass to everything else. We found one at a specific weight (125 GeV), and it sounded exactly like the Standard Model (the current "sheet music") predicted.

But, there's a problem. The orchestra is playing a few extra notes that don't fit the sheet music.

The Mystery Notes (The 95 GeV Excess)

While listening to the music, the LHC (a giant particle collider) and older experiments heard a faint, mysterious "hum" at a lower pitch (around 95 GeV). It's not loud enough to be a confirmed discovery yet (it's like a whisper in a noisy room), but it's there. It appears in two specific ways:

1. The "Diphoton" whisper: A burst of light.
2. The "Bottom-quark" whisper: A specific type of heavy particle decay.

The Standard Model can't explain this whisper. So, physicists need a new theory to explain why this extra note exists.

The New Theory: The "Next-to-Minimum" Model

The authors of this paper propose a new theory called the NB-LSSM. Think of the Standard Model as a simple house with a few rooms. The NB-LSSM is like adding a secret attic, a basement, and a few extra wings to that house.

• The Expansion: They add new particles (like extra "sneutrinos" and "singlets") and new forces to the mix.
• The Twist (CP Violation): Here is the most important part. In the Standard Model, the rules of physics are mostly symmetrical (like a mirror image). But in this new model, the authors introduce CP Violation.
  • Analogy: Imagine a spinning top. In a normal world, if you spin it clockwise, it behaves the same as if you spun it counter-clockwise in a mirror. But in this new model, the top is slightly "wobbly" or "tilted." It doesn't look the same in the mirror. This tilt is called CP Violation.

The Big Mix-Up

Because of this "tilt" (CP violation), the different types of Higgs particles in this new model start to mix like colors of paint.

• Normally, you might have a "Red" Higgs and a "Blue" Higgs.
• In this model, because of the tilt, they swirl together to make "Purple" and "Orange" Higgses.
• This mixing changes their weights (masses) and how they talk to other particles (their couplings).

The paper calculates a massive 10x10 matrix (a giant spreadsheet of numbers) to figure out exactly how these particles mix. It's like trying to solve a Rubik's cube where the colors keep changing as you turn the sides.

The Results: A Perfect Harmony?

The authors ran the numbers to see if this new, wobbly, expanded model could explain the mystery.

1. The 125 GeV Note: They found that the "second-lightest" Higgs in their model still looks and sounds exactly like the one we found in 2012. It fits the data perfectly.
2. The 95 GeV Whisper: They found that the "lightest" Higgs in their model naturally settles at around 95 GeV. Because of the mixing, this particle interacts with light and bottom-quarks in just the right way to explain the "whispers" (the excess signals) seen at the LHC and LEP.

The "Knobs" of the Universe

The paper shows that the universe in this model has many "knobs" (parameters) that scientists can turn to get the music right.

• Tuning the Pitch: By adjusting values like the strength of new forces ($g_{YB}$) or the "tilt" angles (CP phases), they can make the 95 GeV particle appear exactly where the experiments see it.
• The Sweet Spot: They found a specific set of settings (a "best-fit" point) where the model predicts the 125 GeV Higgs perfectly and explains the 95 GeV mystery simultaneously.

Why This Matters

If this model is correct, it means:

1. The Universe is richer than we thought: There are hidden particles (like the extra wings of the house) that we haven't fully seen yet.
2. Symmetry is broken: The universe has a fundamental "tilt" (CP violation) that might explain why there is more matter than antimatter (why we exist at all).
3. The Mystery is Solved: The strange 95 GeV signals aren't just noise; they are the first glimpse of this new, complex physics.

In short: The authors built a more complex, slightly "wobbly" version of the Standard Model. They showed that this wobble causes Higgs particles to mix in a way that creates a new, lighter particle at 95 GeV. This new particle perfectly explains the mysterious signals physicists have been hearing, while keeping the famous 125 GeV Higgs exactly as we know it. It's like finding the missing piece of a puzzle that makes the whole picture suddenly make sense.

Technical Summary

Here is a detailed technical summary of the paper "The Higgs boson in the CP-violating NB-LSSM" by Dong et al.

1. Problem Statement

The paper addresses two major anomalies in experimental particle physics data:

1. The 125 GeV Higgs Boson: While the Standard Model (SM) Higgs boson was discovered at ~125 GeV, precise measurements of its signal strengths in various decay channels (diphoton, $ZZ$, $WW$, $b\bar{b}$, $\tau\bar{\tau}$) are being scrutinized for deviations that could indicate New Physics (NP).
2. The 95 GeV Excesses: Experimental data from LEP, Tevatron, and the LHC (specifically CMS and ATLAS) have reported local excesses around 95 GeV.
   • CMS observed a $2.8\sigma$ local excess in the diphoton channel at 95.3 GeV.
   • LEP reported a $2.3\sigma$local excess in the$b\bar{b}$ final state around 95.4 GeV.
   • Combined ATLAS/CMS data suggests a signal strength $\mu_{\gamma\gamma}(95) \approx 0.24$.

The challenge is to construct a theoretical framework that can simultaneously explain the properties of the 125 GeV SM-like Higgs boson and the 95 GeV excesses without violating other experimental constraints (e.g., $Z'$ mass limits, flavor physics, EDMs). The authors specifically investigate the Next-to-Minimal B-L Supersymmetric Model (NB-LSSM) with CP violation.

2. Methodology

The authors employ a rigorous theoretical and numerical approach within the NB-LSSM framework:

• Model Framework:

  • The NB-LSSM extends the MSSM by introducing a local $U(1)_{B-L}$ gauge symmetry, three singlet Higgs superfields ($\hat{\eta}, \hat{\bar{\eta}}, \hat{S}$), and three generations of right-handed neutrino superfields.
  • CP Violation: The study incorporates CP violation in the Higgs potential. This leads to mixing between CP-even and CP-odd Higgs fields, preventing the diagonalization of the mass matrix into pure CP eigenstates.
  • Mass Matrix: Due to the extended Higgs sector (5 doublets/singlets) and CP mixing, the neutral Higgs boson mass matrix becomes a $10 \times 10$ complex symmetric matrix.

• Theoretical Calculations:

  • Tree-Level: The Higgs potential is constructed, and the tree-level mass squared matrix ($M_h^{(0)}$) is derived in the basis of CP-even and CP-odd fields.
  • Radiative Corrections: To achieve precision, the authors include:
    • One-loop corrections: Dominated by top/stop and bottom/sbottom loops.
    • Two-loop corrections: Calculated using the effective potential approach, including contributions from gluinos and squarks.
  • Diagonalization: The full mass matrix ($M_h^2 = M_h^{(0)} + M_h^{(1)} + M_h^{(2)}$) is diagonalized by a unitary matrix $Z_H$ to obtain physical mass eigenstates.

• Phenomenological Analysis:

  • Signal Strengths ($\mu$): Calculated for both the 125 GeV ($h_{125}$) and 95 GeV ($h_{95}$) states. The signal strength is defined as the ratio of production cross-sections and branching ratios in the NP model versus the SM.
  • $\chi^2$ Analysis: A statistical fit is performed comparing theoretical predictions ($\mu_{\text{theo}}$) with experimental measurements ($\mu_{\text{exp}}$) for:
    • $h_{125}$: Mass, $\gamma\gamma, WW^*, ZZ, b\bar{b}, \tau\bar{\tau}$.
    • $h_{95}$: $\gamma\gamma$ (LHC) and $b\bar{b}$ (LEP).
  • Constraints: The parameter space is constrained by:
    • $Z'$ mass limits ($M_{Z'} \geq 5.15$ TeV).
    • Flavor physics ($\bar{B} \to X_s \gamma$).
    • Direct SUSY searches (gluinos, squarks, charginos, neutralinos).
    • Electric Dipole Moments (EDMs) (though noted as a separate future study, parameters are chosen to satisfy current limits).

3. Key Contributions

1. CP-Violating Mixing in NB-LSSM: The paper provides a comprehensive derivation of the $10 \times 10$neutral Higgs mass matrix in the presence of CP-violating phases ($\theta_{1-8}$). This mixing is crucial for generating the light scalar states required to explain the 95 GeV excess.
2. Simultaneous Explanation of Excesses: The study demonstrates that the NB-LSSM can naturally accommodate both the 125 GeV SM-like Higgs and the 95 GeV scalar excesses within the same parameter space.
3. Parameter Sensitivity Analysis: The authors identify specific parameters that are most sensitive to the Higgs masses and signal strengths:
   • Couplings: $g_{YB}$ (kinetic mixing), $\tan\beta$, $T_\kappa$, and $T_\lambda$.
   • Soft Terms: Trilinear couplings $A_t, A_b$ and CP-violating phases $\theta_{1,2,3,6,7,8}$.
   • Sparticle Masses: $\tilde{M}_{Q3}, \tilde{M}_t, \tilde{M}_b, M_{\tilde{g}}$.
4. Coupling Mechanism: The paper elucidates how CP violation alters the couplings of the Higgs bosons to fermions and gauge bosons. Specifically, it shows how the mixing allows the 95 GeV state to have enhanced couplings to $b\bar{b}$ and $\gamma\gamma$ while the 125 GeV state remains SM-like.

4. Results

• Best-Fit Point: The numerical analysis yields a best-fit point with $\chi^2_{\text{best}} = 1.336$, indicating an excellent agreement with experimental data.
  • Masses: $m_{h_{125}} \approx 125.14$ GeV and $m_{h_{95}} \approx 93.6$ GeV.
  • Signal Strengths (125 GeV): $\mu_{\gamma\gamma} \approx 1.05$, $\mu_{WW} \approx 1.07$, $\mu_{ZZ} \approx 1.08$, $\mu_{b\bar{b}} \approx 0.86$, $\mu_{\tau\bar{\tau}} \approx 0.86$. These are well within $3\sigma$ experimental limits.
  • Signal Strengths (95 GeV): $\mu_{\gamma\gamma} \approx 0.14$ and $\mu_{b\bar{b}} \approx 0.13$, which successfully explain the observed LEP and LHC excesses.
• Parameter Constraints:
  • $g_{YB}$ and $T_\kappa$: Highly constrained to narrow ranges ($g_{YB} \approx -0.31$, $T_\kappa \approx -0.727$ TeV).
  • $\tan\beta$ and $T_\lambda$: Correlated; larger $T_\lambda$ requires specific $\tan\beta$ values to maintain the mass hierarchy.
  • CP Phases: The phases $\theta_1, \theta_2, \theta_3$ (related to VEVs) are tightly constrained to very small values (near zero) by the mass constraints, while phases related to soft terms ($\theta_6, \theta_7, \theta_8$) also have restricted ranges but significantly influence signal strengths.
• Sparticle Masses: The fit prefers squark masses ($\tilde{M}_{Q3}, \tilde{M}_t, \tilde{M}_b$) in the 2–3.5 TeV range and gluino masses $>2$ TeV to satisfy LHC direct search limits while allowing sufficient radiative corrections to the Higgs mass.

5. Significance

• Validation of NB-LSSM: The study reinforces the NB-LSSM as a viable extension of the MSSM, capable of solving the $\mu$-problem, generating neutrino masses via the seesaw mechanism, and providing dark matter candidates, all while accommodating recent experimental anomalies.
• Role of CP Violation: It highlights that CP violation in the Higgs sector is not just a theoretical curiosity but a necessary mechanism to mix CP-even and CP-odd states, thereby allowing a light scalar (95 GeV) to exist without conflicting with the properties of the 125 GeV Higgs.
• Future Prospects: The paper suggests that the specific parameter space identified (particularly the values of $g_{YB}$, $T_\kappa$, and the CP phases) offers a clear target for future LHC runs and high-luminosity experiments. The simultaneous fit of the 95 GeV and 125 GeV sectors provides a compelling motivation for searching for additional Higgs bosons and supersymmetric particles in the multi-TeV range.

In conclusion, this work provides a robust theoretical explanation for the 95 GeV excesses within a well-motivated supersymmetric framework, demonstrating that CP-violating effects in the extended Higgs sector are key to reconciling these anomalies with the observed 125 GeV Higgs boson.