Interference effects in gluon-fusion Higgs boson production

This paper summarizes recent higher-order computational progress on signal-background interference effects in gluon-fusion Higgs boson production, demonstrating that destructive interference reduces the resonant production rates by approximately 1.6% in the $H \to \gamma\gamma$ channel and 3% in the $H \to Z\gamma$ mode.

The Gist

The Big Picture: A Noisy Concert Hall

Imagine the Large Hadron Collider (LHC) is a massive concert hall where scientists are trying to hear a specific, rare song: the "Higgs boson song."

Most of the time, the Higgs boson is created when two particles (gluons) smash together. This is the "signal." However, the concert hall is also filled with background noise—other random collisions that happen to look exactly like the Higgs song, even though they aren't. This is the "background."

Usually, scientists treat the signal and the background as two separate things: they count the signal, then subtract the background. But this paper explains that in the quantum world, these two don't just sit side-by-side; they interfere with each other, like two sound waves crashing together. Sometimes they cancel each other out, and sometimes they boost each other.

The authors of this paper calculated exactly how much this "cancellation" (interference) changes the final count of Higgs bosons, specifically for two rare ways the Higgs decays: turning into two photons (light particles) or a photon and a Z boson.

The Two Main Channels

The paper focuses on two specific "songs" the Higgs sings:

1. The Diphoton Channel ($H \to \gamma\gamma$): The Higgs turns into two flashes of light.
2. The Z-Photon Channel ($H \to Z\gamma$): The Higgs turns into a Z boson and a flash of light.

These are special because, unlike other ways the Higgs decays, these two processes are "loop-induced." In quantum mechanics, this means the particles don't just fly straight from A to B; they take a detour through a "loop" of heavy particles (like top or bottom quarks) before appearing. This makes the signal weaker and the interference with the background more significant.

The "Ghost" Effect: Real vs. Imaginary

The paper breaks the interference down into two parts, which the authors call the "Real" and "Imaginary" parts.

• The Real Part (The Shifty Peak): Imagine the Higgs signal is a bell ringing at a specific pitch. The "Real" interference doesn't change how loud the bell is; instead, it slightly shifts the pitch up or down. It makes the peak of the signal look like it's in a slightly different place than it actually is. The paper notes that while this is interesting for measuring the Higgs' mass, it doesn't change the total number of Higgs bosons we count.
• The Imaginary Part (The Volume Knob): This is the part that matters for the total count. The "Imaginary" interference acts like a volume knob that turns the signal down. In both channels studied, this interference is destructive, meaning the background noise cancels out some of the signal.

The Results: How Much Did They Lose?

The scientists ran complex calculations (using supercomputers and advanced math) to see how much the signal drops because of this cancellation.

• For the Two-Photon Channel ($H \to \gamma\gamma$):
  The interference reduces the number of Higgs bosons we see by about 1.6%.
  Analogy: If you expected to hear 100 people singing a specific note, the background noise actually cancels out 1.6 of them, so you only hear 98.4.

• For the Z-Photon Channel ($H \to Z\gamma$):
  The interference is even stronger here, reducing the count by about 3%.
  Analogy: In this case, the background noise is louder, so it cancels out 3 people out of every 100.

Why This Matters

For a long time, scientists thought these interference effects were too small to worry about, or they just ignored them in their error budgets. They treated the "production" of the Higgs and its "decay" as separate steps.

This paper argues that as our measurements get more precise (aiming for 1% accuracy or better), we can no longer ignore this "cancellation." If we don't account for it, our theoretical predictions will be slightly wrong.

• The Diphoton case: Since this is one of the most precisely measured channels, a 1.6% error is significant. We need to include this "cancellation" in our math to match the real data.
• The Z-Photon case: The effect is larger (3%), but because this is a very rare event, we don't have enough data yet to see this 3% drop clearly. However, the theory must still account for it to be accurate.

The Bottom Line

The authors conclude that to get the most accurate picture of the Higgs boson, we must stop treating the signal and the background as separate entities. We have to acknowledge that they "talk" to each other and cancel each other out.

• In the two-photon channel, this cancellation lowers the rate by ~1.6%.
• In the Z-photon channel, it lowers the rate by ~3%.

These numbers are now considered part of the standard "uncertainty budget" for Higgs physics, ensuring that future predictions match the high-precision data coming from the LHC.

Technical Summary

Technical Summary: Interference Effects in Gluon-Fusion Higgs Boson Production

Problem Statement
In the Standard Model (SM), the dominant Higgs boson production mechanism at the Large Hadron Collider (LHC) is gluon-gluon fusion ($gg \to H$). While significant theoretical effort has been dedicated to calculating higher-order Quantum Chromodynamics (QCD) corrections for the production cross-section, the theoretical uncertainty budget has traditionally treated the production stage and the decay stage as separate entities. This separation is justified when the target precision is above the percent level. However, as precision requirements tighten, effects that were previously neglected become relevant.

A critical, often overlooked source of uncertainty is the quantum interference between the resonant Higgs production signal ($gg \to H \to V_1V_2$) and the non-resonant continuum background ($gg \to V_1V_2$). This interference is particularly significant when the Higgs decay is loop-induced (e.g., $H \to \gamma\gamma$ and $H \to Z\gamma$), as the signal amplitude is suppressed by a loop factor relative to tree-level decays, making the relative impact of the interference larger. Previous studies established Next-to-Leading Order (NLO) effects in the diphoton channel, but these contributions were not consistently included in the theory uncertainty budget. Furthermore, higher-order corrections beyond NLO for these interference effects had not been fully characterized for the on-shell cross-section.

Methodology
The authors analyze signal-background interference effects for the processes $gg \to H \to \gamma\gamma$ and $gg \to H \to Z\gamma$ at the LHC. The scattering amplitude is decomposed into a signal term (mediated by the Higgs propagator) and a background term (continuum). The interference contribution ($I$) is separated into a real part ($I_{Re}$), which is antisymmetric around the resonance and affects the peak position (mass shift), and an imaginary part ($I_{Im}$), which is symmetric and contributes destructively to the total on-shell cross-section.

The calculations employ the following setup:

• Perturbative Orders: The study extends beyond previous NLO results. For the $H \to \gamma\gamma$ channel, results are presented up to NNLO (specifically using the soft-virtual approximation for the interference term). For the $H \to Z\gamma$ channel, results are presented at NLO accuracy.
• Approximations:
  • Production: Calculations for the signal cross-section utilize the infinite top-quark mass limit for NLO and beyond, justified by the smallness of finite mass effects at these orders. The exact NNLO signal is computed using the NNLOJET generator.
  • Decay: The Higgs decay is treated at Leading Order (LO) in the full SM, as QCD corrections to the decay amplitude are known to be small.
  • Background: For $H \to \gamma\gamma$, the LO interference is driven by massive bottom quarks (negligible), while NLO effects arise from two-loop diagrams with massless quarks. For $H \to Z\gamma$, light quark loops contribute at LO due to the massive $Z$ boson.
  • Soft-Virtual Approximation: For the interference terms at NNLO ($H \to \gamma\gamma$) and NLO ($H \to Z\gamma$), the authors employ the soft-virtual approximation. This includes contributions from loop diagrams and soft real emissions, capturing the dominant absorptive (imaginary) parts responsible for the interference.
• Parameters: The $G_\mu$ scheme is used for electroweak parameters. The strong coupling $\alpha_s(m_Z) = 0.118$ and PDFs (NNPDF31) are extracted from the PDF set. Renormalization and factorization scales are set to $\mu_R = \mu_F = m_{VV}/2$.
• Kinematics: Fiducial cuts are applied to mimic experimental selections (e.g., photon transverse momentum and invariant mass windows), though no isolation criteria are applied to avoid infrared singularities in the technical study.

Key Contributions and Results

1. $H \to \gamma\gamma$ Channel:

   • The study provides updated predictions for the interference effect at NNLO accuracy (soft-virtual).
   • At LO, the interference is negligible (well below 1%) because the absorptive part requires massive quarks and is mass-suppressed.
   • At NLO, large imaginary terms from two-loop background amplitudes with massless quarks appear, reducing the cross-section by more than 1%.
   • Result: At NNLO, the destructive interference reduces the on-shell signal rate by approximately 1.6% to 1.7% across LHC energies (7, 8, 13, and 13.6 TeV). This reduction is consistent across energies and represents a stable, negative shift in the predicted cross-section.

2. $H \to Z\gamma$ Channel:

   • Unlike the diphoton case, the presence of the massive $Z$ boson allows light quark loops to generate an imaginary part in the background amplitude at LO.
   • Result: The destructive interference is significantly larger, reducing the signal rate by approximately 3.1% to 4.3%.
   • At LO, the reduction is roughly 4.3%. At NLO, the reduction is approximately 3.1%. The authors attribute the reduction in the percentage impact at NLO to the signal K-factor being larger than that of the background and interference terms.

Significance and Claims
The paper argues that the theoretical uncertainty budget for gluon-fusion Higgs production must be updated to include signal-background interference effects, particularly for loop-induced decay modes.

• Magnitude: The interference effects are not negligible; they modify the on-shell cross-section by 1.6% ($H \to \gamma\gamma$) and ~3% ($H \to Z\gamma$). These magnitudes are comparable to other dominant sources of uncertainty, such as mixed QCD-electroweak corrections or finite top-mass effects.
• Recommendation: The authors recommend that fiducial cross-section measurements of central Higgs boson production at the LHC explicitly account for the destructive interference effect ($\delta_{int}$) reported in their tables.
• Limitations: The authors note that their analysis relies on the soft-virtual approximation, which provides a reliable description for inclusive observables (integrated cross-sections and line shapes) but precludes quantitative conclusions for differential observables (e.g., photon transverse momentum distributions) where hard radiation effects are significant.
• Context: While the $H \to Z\gamma$ channel shows a larger interference effect, the authors state that the total uncertainty in this channel is currently dominated by statistical limitations, making the observation of these interference effects unlikely in the near future. Conversely, the $H \to \gamma\gamma$ channel is among the most precisely measured, making the inclusion of this 1.6% correction crucial for high-precision SM tests.