On the robustness of the indirect determination of the width of the detected Higgs boson

This paper demonstrates that while relaxing the assumption of equal on-shell and off-shell Higgs coupling modifiers in Standard Model extensions can allow for a larger total width, realistic constraints still limit this increase to at most a factor of two compared to the standard indirect bounds.

The Gist

The Invisible Weight of the Higgs Boson: A Detective Story

Imagine the Higgs boson as a mysterious, invisible celebrity living in a crowded city (the Large Hadron Collider, or LHC). Scientists know this celebrity exists because they see the "ripples" it leaves behind when it interacts with other particles. But there's a big mystery: How heavy is this celebrity really?

In physics, "weight" is measured by something called width. A "wide" particle decays (falls apart) very quickly into many different things. A "narrow" one is more stable.

The Standard Detective Method

For years, scientists at the LHC (ATLAS and CMS experiments) have been trying to weigh this Higgs celebrity. They can't put it on a scale, so they use a clever trick called indirect determination.

Think of it like trying to guess how fast a car is driving by looking at two different things:

1. The On-Shell Signal: The car driving normally at a steady speed (the Higgs at its exact mass of 125 GeV).
2. The Off-Shell Signal: The car speeding up or slowing down wildly, creating a blur (the Higgs at higher, unstable energies).

The standard detective rule assumes that the car's engine behaves the same way whether it's cruising steadily or speeding up. In physics terms, this means the coupling modifiers (how strongly the Higgs talks to other particles) are the same in both the "steady" and "speeding" zones.

Using this rule, the detectives calculated a very strict speed limit: The Higgs is very light (narrow). If it were much heavier, the "blur" (off-shell signal) would look different than what they see.

The "What If?" Scenario

But what if the car has a secret turbo button? What if the engine behaves differently when it's speeding up compared to when it's cruising?

This is the question Panagiotis Stylianou and Georg Weiglein asked in their paper. They wondered: "What if the Higgs boson is actually much heavier than we think, but it's hiding because new, invisible physics is messing with the 'speeding up' zone?"

If new particles exist that only show up when the Higgs is "speeding up" (off-shell), they could cancel out the extra noise. This would make the Higgs look light and narrow, even if it's actually heavy and wide.

The Investigation: Three Suspects

The authors investigated three specific ways this "secret turbo" could work:

1. The Ghostly Resonance (An Extra Scalar):
   Imagine a second, invisible car (a new particle) that appears only when the Higgs speeds up. If this ghost car crashes into the Higgs in a very specific way, it could cancel out the extra noise, hiding the Higgs's true weight.

   • The Catch: For this to work, the ghost car has to be very light (around 200–300 GeV). But if it's that light, we should have already seen it in other experiments. The authors found that current searches for these light particles are so strict that this trick can only hide the Higgs's weight by a small amount (about 40%).

2. The Hidden Loop (A Colored Scalar):
   Imagine the Higgs is driving through a tunnel, and a new particle is running in circles inside the tunnel walls, changing the air pressure. This "loop" effect could also hide the Higgs's weight.

   • The Catch: This requires the new particle to be extremely light (around 100 GeV) and to interact strongly with the Higgs. However, particles that interact this strongly are like loud neighbors; we would have heard them by now. Direct searches for these particles rule them out almost completely.

3. The Mirror Effect (Loop in the Propagator):
   Imagine the Higgs is looking in a mirror, and the reflection is distorted by a new particle. This could change how the Higgs appears to us.

   • The Catch: To distort the reflection enough to hide a heavy Higgs, the new particle needs to be very heavy and interact very strongly. But if it interacts that strongly, it would break other rules of physics (like unitarity) or show up in other measurements.

The Verdict: The Hiding Spot is Tiny

After running thousands of simulations (like running the car through every possible scenario), the authors concluded:

The standard detective rule is mostly safe.

While it is theoretically possible for the Higgs to be heavier than we think, the "hiding spots" where this could happen are very small and very crowded.

• To hide a heavy Higgs, you need new particles that are light and strongly interacting.
• But the LHC has already looked for light, strongly interacting particles and hasn't found them.

The Final Conclusion:
Even if we throw out the assumption that the Higgs behaves the same way at all speeds, the total width of the Higgs boson cannot be more than about twice what the standard measurements say.

In everyday terms:
If the standard measurement says the Higgs weighs 10 pounds, the authors are saying, "Even if there are secret tricks we haven't thought of, it's impossible for the Higgs to actually weigh 100 pounds. It might be 12 or 15 pounds, but it's definitely not 100."

This gives scientists great confidence that their current measurements are robust. The "indirect" method is a reliable scale, even if the universe tries to play a little trick on it.

Technical Summary

Here is a detailed technical summary of the paper "On the robustness of the indirect determination of the width of the detected Higgs boson" (DESY-26-008).

1. Problem Statement

The indirect determination of the total width of the Higgs boson ($\Gamma_H$) at the LHC relies on a specific theoretical assumption: that the coupling modifiers for on-shell ($\kappa_{on}$) and off-shell ($\kappa_{off}$) Higgs production are identical ($\kappa_{i,on} = \kappa_{i,off}$).

• Current Status: Experiments (ATLAS and CMS) use the ratio of on-shell to off-shell signal strengths in the $gg \to H \to ZZ$ channel to constrain $\Gamma_H$. Under the assumption of equal modifiers, they have derived tight upper limits (e.g., $\Gamma_H < 2.5 \times \Gamma_H^{SM}$ at 95% CL).
• The Issue: Physics Beyond the Standard Model (BSM) could affect on-shell and off-shell regions differently. If new physics enhances on-shell couplings (increasing $\Gamma_H$) but simultaneously suppresses off-shell contributions (via destructive interference or loop effects), the experimental assumption of equal modifiers would be violated. This could lead to an underestimation of the true Higgs width, potentially allowing $\Gamma_H$ to be significantly larger than current bounds without contradicting data.
• Objective: The authors investigate how robust the indirect bounds on $\Gamma_H$ are when relaxing the assumption of equal on/off-shell coupling modifiers, considering realistic BSM scenarios constrained by existing experimental and theoretical limits.

2. Methodology

The authors analyze three specific classes of BSM scenarios where the off-shell $gg \to ZZ$ cross-section is modified relative to the on-shell region:

1. Additional Scalar Propagator (Tree-level):

   • Model: An additional singlet scalar $S$ coupled to top quarks and $Z$ bosons.
   • Mechanism: $S$ contributes to $gg \to ZZ$ via an $s$-channel propagator. It induces a resonant peak and, crucially, destructive interference with the SM continuum and the SM-like Higgs at high invariant masses ($m_{ZZ} > m_S$).
   • Constraint: A sum-rule ($\kappa_t \kappa_Z + C_{Stt}C_{SZZ} = 1$) relates the Higgs coupling modifiers to the BSM couplings to preserve unitarity in $t\bar{t} \to ZZ$ scattering.
   • Tools: Monte Carlo simulations using FeynRules, NLOCT, and MadGraph5_aMC@NLO. Constraints from direct scalar searches are applied using HiggsBounds.

2. Colored Scalar in Gluon-Fusion Loop:

   • Model: A colored complex scalar $S_c$ (SU(2) singlet, SU(3) triplet) coupling to the Higgs.
   • Mechanism: $S_c$ enters the gluon-fusion loop ($gg \to H$). This modifies the on-shell production cross-section differently than the weak boson fusion (WBF) process, creating a tension between on-shell signal strengths in different channels.
   • Analysis: The authors calculate the interference between the BSM loop diagrams and the SM box/Higgs diagrams in the off-shell region. They impose constraints from the 2D plane of on-shell signal strengths ($\mu_{ggF}$ vs. $\mu_{WBF}$).

3. Scalar Loop in Higgs Propagator:

   • Model: A singlet scalar $S$ coupled via a Higgs-portal interaction ($\lambda_S S^2 \Phi^\dagger \Phi$).
   • Mechanism: $S$ contributes to the Higgs self-energy (propagator correction) at one-loop level. This modifies the off-shell amplitude via a form factor involving the Passarino-Veltman function $B_0$.
   • Analysis: The impact on the off-shell signal strength ratio $R$ is calculated, and the resulting limits on coupling modifiers are translated into bounds on $\Gamma_H$.

General Approach:
For all scenarios, the authors:

• Parameterize the differential cross-section $d\sigma/dm_{ZZ}$ as a sum of SM, interference, and BSM-squared terms.
• Define a ratio $R = \sigma_{BSM} / \sigma_{SM}$ and enforce $R < R_{up}$ (derived from the experimental off-shell limit $\mu_{off} < 2.4$).
• Combine these off-shell constraints with on-shell signal strength measurements ($\mu_{on} \approx \kappa^2 / (\Gamma_H/\Gamma_H^{SM})$) to derive the maximum allowed $\Gamma_H/\Gamma_H^{SM}$.
• Apply direct search limits (e.g., for light scalars) and unitarity constraints.

3. Key Contributions

• Systematic Relaxation of Assumptions: The paper provides a rigorous quantitative assessment of the "flat direction" problem in Higgs width measurements by explicitly modeling BSM physics that breaks the $\kappa_{on} = \kappa_{off}$ equality.
• Unitarity and Sum-Rule Constraints: The analysis incorporates theoretical consistency conditions (sum-rules for scattering amplitudes) which tightly restrict the parameter space where large width enhancements are possible.
• Integration of Direct Searches: Unlike purely phenomenological studies, this work explicitly checks the viability of the "loophole" scenarios against existing direct search limits for new particles (e.g., light scalars, colored triplets) using HiggsBounds.
• Quantification of Robustness: The authors determine the maximum factor by which the current indirect bounds on $\Gamma_H$ can be weakened in realistic models.

4. Results

The analysis yields the following conclusions regarding the upper bound on the total Higgs width:

• Scalar Propagator Scenario:

  • Destructive interference from a light scalar ($m_S \lesssim 300$ GeV) can reduce the off-shell rate, allowing for a larger $\Gamma_H$.
  • However, direct search limits for such light scalars are severe.
  • Result: The maximum enhancement of $\Gamma_H/\Gamma_H^{SM}$ is limited to ~40% above the standard indirect bound for the lightest allowed masses. For heavier masses, the bound returns to the standard limit.

• Colored Scalar Loop Scenario:

  • A light colored scalar ($m_{Sc} \sim 90-100$ GeV) with specific couplings can create a tension between $ggF$ and WBF on-shell rates that allows for a larger width.
  • Result: While a width ratio of $\sim 7.5$ is theoretically possible in a narrow mass window, such light colored particles are excluded by direct searches for colored resonances and constraints on long-lived charged particles. For viable masses, the enhancement is limited to ~40-50%.

• Higgs Propagator Loop Scenario:

  • The effect is generally small unless the coupling $\lambda_S$ is very large ($\sim 5$) and the scalar is light ($\sim 200$ GeV).
  • Result: Even in the most favorable case, the enhancement of the width is small, and the shift in the on-shell signal strength remains within current experimental uncertainties. No significant weakening of the bound is found.

• Overall Conclusion:

  • In all realistic scenarios compatible with current experimental data (direct searches) and theoretical constraints (unitarity, electroweak precision), the indirect bound on $\Gamma_H$ is only weakened by a factor of up to ~2 compared to the standard assumption.
  • Significant deviations (factors $>2$) require light new particles with large couplings, which are already ruled out or severely constrained by LHC data.

5. Significance

• Validation of Current Limits: The paper validates the robustness of the ATLAS and CMS indirect width measurements. It confirms that while the assumption of equal coupling modifiers is theoretically fragile, realistic BSM physics cannot easily evade the current bounds without being detected by direct searches.
• Guidance for Future Searches: The authors highlight that the "loophole" regions (light new scalars) are precisely the regions targeted by direct resonance searches. Therefore, the indirect width measurement and direct searches are complementary; a failure to find new light particles reinforces the validity of the indirect width bound.
• Future Prospects: The study suggests that while the HL-LHC will improve precision, the fundamental limitation on the indirect width determination is not just statistical but relies on the absence of light BSM states. Future $e^+e^-$ Higgs factories remain the only path to a model-independent, direct measurement of the total width.
• Policy Implication: The authors conclude that for phenomenological studies, it is safe to apply an upper bound on $\Gamma_H$ that is twice the value obtained under the equal-modifier assumption to account for potential BSM effects, without needing to assume extreme or unphysical models.