Probing new physics in the Boosted $HH \to b\bar{b}γγ$ channel at the LHC

This paper presents the first dedicated study of the boosted $HH \to b\bar{b}\gamma\gamma$ channel at the LHC, demonstrating that this topology enhances sensitivity to both non-resonant quartic gauge-Higgs coupling deviations and resonant heavy scalar decays, thereby improving constraints on new physics parameters and extending discovery reach in the high-energy double-Higgs regime.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle accelerator, smashing protons together to recreate the conditions of the early universe. Inside this cosmic collision zone, scientists are hunting for "Higgs boson pairs"—two of these mysterious particles created at the same time. Finding them is like trying to spot two specific fireflies in a storm of billions of other insects.

This paper, written by Mohamed Belfkir, introduces a new, sharper way to look for these pairs, specifically when they are flying apart at incredibly high speeds.

The Problem: The "Resolved" vs. The "Boosted"

To understand the new method, we first need to understand the old one.

The Old Way (Resolved):
Usually, when a Higgs boson decays, it splits into two "bottom quarks" (particles that act like tiny, heavy seeds). In the standard approach, scientists look for these two seeds as two separate, distinct objects. Imagine trying to identify two distinct marbles rolling on a table. This works great when the marbles are rolling slowly and far apart. This is called the "resolved" category.

The New Way (Boosted):
However, if the Higgs bosons are created with massive energy (a "boosted" state), they fly away so fast that their decay products get squished together. The two bottom quarks don't roll apart; they get smeared into a single, messy blob.

• The Analogy: Imagine two people running side-by-side holding hands. If they run slowly, you can clearly see two people. But if they sprint at the speed of sound, they might blur into a single, indistinguishable streak.
• The old method (looking for two separate marbles) fails here because the "marbles" have merged. The new method, the "boosted" category, looks for that single, fast-moving "blob" (a large jet) and analyzes its internal structure to realize, "Ah, this single blob is actually two Higgs decay products squashed together."

What They Are Looking For

The paper focuses on a specific "golden" signal: a Higgs pair that decays into two bottom quarks and two photons (particles of light).

• The photons are like bright, clean lighthouses that are easy to spot.
• The bottom quarks are the messy part that requires the special "boosted" or "resolved" techniques to identify.

The scientists are testing two main ideas about "New Physics" (things beyond our current understanding of the universe):

1. The "Tweaked" Rules (Non-Resonant): They are checking if the rules governing how Higgs bosons interact with other forces are slightly different than predicted. Specifically, they are looking for changes in a "knob" called $\kappa_{2V}$.

   • Analogy: Imagine a car engine that usually runs perfectly. The scientists are checking if the engine makes a specific, high-pitched whine when it revs to maximum speed. The "resolved" method misses this whine, but the "boosted" method can hear it clearly because it focuses on the high-speed engine noise.

2. The "Heavy Ghost" (Resonant): They are searching for a heavy, invisible particle (a "heavy scalar") that decays into two Higgs bosons.

   • Analogy: Imagine a heavy bowling ball (the new particle) that suddenly breaks apart into two lighter balls (the Higgs bosons). If the bowling ball is very heavy, the two lighter balls fly apart with huge force. The "boosted" method is the only one sensitive enough to catch these high-speed fragments.

The Results: Why the New Method Matters

The paper compares the old "resolved" method with the new "boosted" method:

• For the "Tweaked Rules" ($\kappa_{2V}$): The new boosted method is much better at spotting deviations when the particles are moving fast. It acts like a high-speed camera that captures details the slow-motion camera (resolved) misses.
• For the "Heavy Ghost" (Resonances): This is where the boosted method shines brightest. As the heavy particle gets heavier, the two Higgs bosons fly faster and merge tighter. The old method loses its grip and stops seeing them entirely. The boosted method, however, keeps working, allowing scientists to search for much heavier particles that were previously invisible.

The Bottom Line

This paper is the first to systematically apply this "boosted" technique to the $b\bar{b}\gamma\gamma$ channel (two bottom quarks + two photons).

The authors conclude that while the old method is still good for general searches, adding the new "boosted" method is like adding a specialized telescope to a regular pair of binoculars. It doesn't replace the binoculars, but it allows scientists to see into the "high-energy tail" of the data—where the most exciting new physics is hiding. By combining both methods, they can cast a much wider and deeper net for discovering new particles and understanding the universe's fundamental forces.

Technical Summary

Technical Summary: Probing New Physics in the Boosted HH → b$\bar{b}$γγ Channel at the LHC

Problem Statement
The interactions governing the Higgs sector, particularly the trilinear self-coupling ($\lambda_3$) and the quartic gauge–Higgs interaction, remain loosely constrained despite a decade of precision measurements at the LHC. While the double-Higgs production channel ($pp \to HH$) offers a unique laboratory to probe these couplings, existing experimental analyses of the $HH \to b\bar{b}\gamma\gamma$ final state have operated almost exclusively in the "resolved" reconstruction regime. In this regime, the two $b$-quarks from a Higgs decay are reconstructed as separate small-radius jets. However, this approach has limited sensitivity to the high-energy regime where deviations in the quartic gauge–Higgs coupling ($\kappa_{2V}$) or the decay of heavy scalar resonances ($X \to HH$) are expected to populate the high-$m_{HH}$ tail. In these high-momentum scenarios, the $b$-quarks become highly collimated, causing the resolved topology to lose efficiency as the decay products merge into a single large-radius jet.

Methodology
This study presents the first dedicated analysis of the boosted $HH \to b\bar{b}\gamma\gamma$ topology, utilizing a simulation framework based on $\sqrt{s} = 13.6$ TeV proton-proton collisions and an integrated luminosity of 308 fb$^{-1}$. The methodology is structured as follows:

• Theoretical Framework: The analysis investigates two classes of Beyond the Standard Model (BSM) scenarios:
  1. Non-resonant deviations: Parameterized by the coupling modifier $\kappa_{2V}$, affecting the vector-boson fusion (VBF) production amplitude.
  2. Resonant enhancement: Modeled via a heavy scalar state $X$ decaying to $HH$ within a Type-II Two-Higgs-Doublet Model (2HDM) framework, with masses ranging from 1 to 5 TeV.
• Event Generation: Signal samples include gluon-gluon fusion (ggF) and VBF processes generated with Powheg-Box and MadGraph5 aMC@NLO, normalized to NNLO/N$^3$LO cross-sections. Backgrounds include resonant single-Higgs production ($H \to \gamma\gamma$) and non-resonant continuum $\gamma\gamma + \text{jets}$.
• Reconstruction Strategies: Two mutually exclusive categories are defined to ensure orthogonality:
  • Resolved Category: Reconstructs $H \to b\bar{b}$ as two distinct small-radius ($R=0.4$) jets.
  • Boosted Category: Reconstructs $H \to b\bar{b}$ as a single large-radius ($R=1.0$) jet with groomed mass and substructure variables (trimming, pruning, soft-drop).
• Classification:
  • For the non-resonant search, an XGBoost classifier is trained separately for each category to define signal-enriched bins. The input features include kinematic variables of the diphoton system, VBF-tagged jets, and the hadronic Higgs candidate (either two small-$R$ jets or one large-$R$ jet).
  • For the resonant search, due to limited statistics at high transverse momentum and the distinctiveness of the signal topology, a simple rectangular-cut selection is employed without machine learning.
• Statistical Analysis: A binned likelihood fit using the pyhf framework is performed to derive 95% confidence level (CL) upper limits on signal strength ($\mu$) and constraints on $\kappa_{2V}$.

Key Contributions

• First Dedicated Boosted Study: This work establishes the first systematic assessment of the boosted $HH \to b\bar{b}\gamma\gamma$ channel, a topology previously unexplored in this specific final state despite its theoretical motivation.
• Orthogonal Categories: The definition of mutually exclusive resolved and boosted categories allows for a combined analysis that maximizes sensitivity across the full kinematic spectrum without double-counting events.
• Demonstration of High-Energy Sensitivity: The study explicitly demonstrates that the boosted category is essential for accessing the high-$m_{HH}$ phase space where BSM effects are most prominent, a region where the resolved topology suffers from vanishing acceptance.

Results

• Non-Resonant Analysis ($\kappa_{2V}$):
  • The resolved category provides the strongest constraint on the overall signal strength ($\mu_{HH} = 2.6$ at 95% CL), driven by the Standard Model (SM) peak near threshold.
  • The boosted category, while yielding a weaker inclusive limit ($\mu_{HH} = 6.5$), exhibits a pronounced response to deviations in $\kappa_{2V}$ far from the SM value ($\kappa_{2V}=1$).
  • The combined analysis improves the constraint on $\kappa_{2V}$ to the range $-0.4 < \kappa_{2V} < 2.6$ (95% CL), leveraging the complementary nature of the two categories.
• Resonant Analysis ($X \to HH$):
  • For heavy scalar masses ($m_X$) between 1 and 5 TeV, the boosted category provides significantly stronger exclusion limits than the resolved category.
  • The resolved selection loses efficiency rapidly as $m_X$ increases and the $b$-quarks merge, whereas the boosted selection maintains high acceptance.
  • The combined expected limits range from 1 fb at $m_X = 1$ TeV to 100 fb at $m_X = 5$ TeV, with the boosted analysis dominating the sensitivity in the high-mass region.

Significance and Claims
The paper claims that the boosted $HH \to b\bar{b}\gamma\gamma$ topology is an essential tool for future BSM searches in the Run-3 and High-Luminosity LHC (HL-LHC) programs. The authors emphasize that while the resolved category remains superior for measuring the inclusive SM cross-section, the boosted category is indispensable for probing new physics that manifests in the high-energy tail of the di-Higgs spectrum. By combining both approaches, the analysis establishes the $b\bar{b}\gamma\gamma$ channel as a competitive and complementary probe for new physics, offering a clean experimental signature and efficient trigger strategy that can access kinematic regions previously inaccessible to resolved-only analyses. The study does not claim to have discovered new physics but rather demonstrates the enhanced discovery reach and constraint capabilities provided by incorporating boosted reconstruction techniques.