Real Singlet Scalar Benchmarks in the Multi-TeV Resonance Regime

Technical Summary: Real Singlet Scalar Benchmarks in the Multi-TeV Resonance Regime

Problem and Motivation
The measurement of the Higgs potential, specifically the cubic term via the Higgs trilinear coupling ($\lambda_{111}$) and di-Higgs production, is a primary long-term goal for the Large Hadron Collider (LHC) and future colliders. Deviations in these observables can signal physics beyond the Standard Model (SM). This paper investigates the simplest extension of the SM: the addition of a real gauge singlet scalar ($S$) with no additional symmetries (such as a $Z_2$ symmetry). Unlike $Z_2$-symmetric models, the absence of such symmetry introduces additional free parameters ($a_1, a_2, b_1, b_2, b_3, b_4$) that allow for greater flexibility in enhancing trilinear couplings and resonant di-Higgs production rates. The model is motivated by its potential to facilitate a strong first-order electroweak phase transition necessary for electroweak baryogenesis.

Methodology
The authors analyze the "Real Singlet Scalar Model" where the scalar potential couples the SM Higgs doublet ($\Phi$) and the singlet ($S$). After electroweak symmetry breaking (EWSB), the physical states are admixtures of the SM Higgs ($h$) and the singlet ($s$), resulting in two mass eigenstates: the observed Higgs ($h_1$, $m_1 = 125$ GeV) and a heavier scalar ($h_2$, $m_2 > 2m_1$).

The study employs a parameter scan over the mixing angle ($\theta$), the quartic coupling $a_2$, and the cubic/quartic singlet self-couplings ($b_3, b_4$), subject to the following constraints:

1. Theoretical Constraints: Vacuum stability (boundedness of the potential) and perturbative unitarity (limiting scattering amplitudes to $|Re(a_k)| \le 1/2$).
2. Global Minimization: Ensuring the electroweak vacuum $(v_{EW}, 0)$ is the global minimum.
3. Experimental Constraints:
   • Scenario S1: Current LHC constraints from precision Higgs signal strengths and direct scalar searches (using both "hard cut" and $\Delta\chi^2$ methods).
   • Scenario S2: Projected constraints at the High-Luminosity LHC (HL-LHC).
   • Scenario S3: HL-LHC combined with a circular $e^-e^+$ collider (CEPC or FCC-ee).
   • Scenario S4: HL-LHC combined with a 500 GeV linear $e^-e^+$ collider (ILC).

The analysis focuses on maximizing the resonant di-Higgs production rate ($pp \to h_2 \to h_1h_1$) and determining the allowed variation in the Higgs trilinear coupling ($\lambda_{111}$) across these scenarios. The narrow width approximation is enforced ($\Gamma_{h_2} \le 0.1 m_2$).

Key Contributions and Results

• Resonant Di-Higgs Rates:

  • Current LHC (S1): For resonance masses ($m_2$) up to 1 TeV, the resonant di-Higgs rate can still be an order of magnitude larger than the SM di-Higgs rate. Near the di-Higgs threshold, the gluon fusion rate can be $\sim 5-10$ times the SM rate, and the Vector Boson Fusion (VBF) rate $\sim 15-20$ times larger.
  • Future Colliders (S2-S4): The authors provide benchmark points for resonance masses up to 10 TeV. In the multi-TeV regime, the resonant production rates are significantly suppressed due to the "narrow width constraint," which forces the mixing angle $|\sin \theta|$ to decrease as $m_2$ increases ($|\sin \theta| \propto 1/m_2^2$). Consequently, for $m_2 \gtrsim 2.1$ TeV (HL-LHC) or $m_2 \gtrsim 5.7$ TeV (with lepton colliders), the resonant rate drops rapidly.

• Higgs Trilinear Coupling ($\lambda_{111}$) Variation:

  • Current LHC (S1): The trilinear coupling can be enhanced by up to a factor of 2.5 relative to the SM prediction for $m_2 < 1$ TeV.
  • HL-LHC (S2): In the mass range of $1.5 - 3.5$ TeV, $\lambda_{111}$ can be enhanced by a factor of three. This enhancement lies just at the projected $2\sigma$ sensitivity of the HL-LHC. Crucially, in this mass range, the resonant production rate is negligible, meaning the trilinear coupling deviation may be the only observable signature of new physics.
  • Lepton Collider Scenarios (S3, S4): When combined with precision measurements from FCC-ee or ILC, the allowed range for $\lambda_{111}$ tightens significantly, remaining within 50% of the SM prediction and within the $1\sigma$ projected bounds of the HL-LHC.

• Complementarity of Observables:
  The paper identifies a specific phenomenon where the trilinear coupling $\lambda_{111}$ is maximized while the resonant rate $pp \to h_2 \to h_1h_1$ becomes nearly zero. Analytical approximations show this occurs at specific resonance masses (e.g., $m_2 \approx 1.7$ TeV in certain scenarios) where the coupling $\lambda_{112}$ (governing the $h_2 \to h_1h_1$ decay) vanishes. This implies that non-resonant measurements of $\lambda_{111}$ and resonant searches for $h_2$ provide complementary information, probing different regions of the parameter space.

Significance
The paper provides an updated and extended benchmark analysis for the real singlet scalar model, moving beyond previous studies limited to the 1 TeV scale. Its primary significance lies in demonstrating that:

1. Large deviations in the Higgs trilinear coupling (up to $3\times$ SM) are theoretically viable in the multi-TeV regime, even when resonant production is unobservable.
2. The interplay between vacuum stability, perturbative unitarity, and the narrow width approximation creates distinct "kinks" and behaviors in the allowed parameter space that dictate the maximum possible rates and coupling variations.
3. Future colliders (HL-LHC combined with lepton colliders) will be essential to probe these high-mass scenarios where resonant searches lose sensitivity, making precision measurements of the Higgs trilinear coupling a critical probe for this class of new physics.

The authors note that while tree-level results are presented, higher-order corrections (potentially 50-100%) are expected, and a full one-loop calculation is required for definitive signal interpretation, which is left for future work.