Constraints on anomalous Higgs boson couplings to vector bosons and fermions using the $\gamma\gamma$ final state in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}$ = 13 TeV collected by the CMS experiment, this study constrains anomalous Higgs boson couplings to vector bosons and fermions via the diphoton decay channel, finding results consistent with Standard Model expectations.

The Gist

Imagine the universe is a giant, complex machine, and the Higgs boson is a crucial gear inside it. Scientists at CERN's Large Hadron Collider (LHC) have been studying this gear for years. They know it exists and roughly how it looks, but they want to know: Is it exactly the way the "Standard Model" (the rulebook of physics) says it should be, or is there a tiny, hidden flaw or a secret twist in its design?

This paper is like a high-stakes detective story where the CMS experiment team acts as forensic investigators. They are looking for "anomalous couplings"—weird, unexpected ways the Higgs boson might interact with other particles.

Here is a breakdown of what they did and what they found, using simple analogies:

1. The Crime Scene: The "Double Photon" Clue

The Higgs boson is unstable; it breaks apart almost instantly. To study it, the scientists had to look at the "debris" it leaves behind. In this study, they focused on a specific type of debris: two photons (particles of light) flying out in opposite directions.

• The Analogy: Imagine a magician (the Higgs) vanishing in a puff of smoke, leaving behind two specific colored balloons (the photons). Because light is so clean and easy to track, these "balloons" give a very clear picture of what the magician was doing right before they vanished. The scientists collected data from 138 "trillion" collisions (an enormous amount of data) to find these specific balloon pairs.

2. The Suspects: How the Higgs is Made

The Higgs boson doesn't just appear; it's created in different ways. The scientists looked at three main "manufacturing methods":

• Gluon Fusion (ggH): Two heavy particles smash together to make the Higgs. This is like two cars crashing to create a new object.
• Vector Boson Fusion (VBF): Two particles exchange a force carrier (like a ball being thrown) to create the Higgs. This leaves two "witnesses" (jets of particles) flying off to the sides.
• Associated Production (VH): The Higgs is made alongside another heavy particle (a vector boson). This is like a Higgs being born while holding hands with a partner.

The scientists wanted to see if the Higgs behaved differently depending on which "factory" made it.

3. The Investigation: Checking for "Twists"

The Standard Model predicts the Higgs is a specific shape (a scalar particle) and behaves in a specific way (it's "even" in a mathematical sense called CP-symmetry). The scientists were looking for two types of "twists":

• The "Odd" Twist (CP-violation): Imagine a spinning top. If it spins clockwise, that's "even." If it spins counter-clockwise, that's "odd." The Standard Model says the Higgs only spins clockwise. The scientists were checking if it ever spins counter-clockwise or spins in a weird mix of both.
• The "Stronger" Twist: They checked if the Higgs grabbed onto other particles (like gluons or W/Z bosons) harder or softer than the rulebook predicted.

To do this, they used AI and advanced math (like Deep Neural Networks) to sort millions of events. They created "bins" or categories, like sorting mail into different piles based on how the "witnesses" (the jets) were standing. They asked: "Do the events that look like they came from a 'twisted' Higgs appear more often than we expect?"

4. The Verdict: "Guilty of Being Normal"

After analyzing the data, the results were clear:

• No New Twists Found: The Higgs boson behaved exactly as the Standard Model predicted. It didn't show any signs of that "counter-clockwise" spin or any strange grabbing habits.
• The Limits: While they didn't find a "twist," they set very strict boundaries. It's like saying, "We didn't find a ghost in the house, but we can now say with 95% confidence that if a ghost is there, it must be smaller than a dust mote."
• The "Best" Measurement Yet: This study is significant because it used the "two photons" channel to measure these specific interactions for the first time with this level of precision. It tightened the net around the Higgs, making it harder for "weird" physics to hide.

5. The Takeaway

Think of the Higgs boson as a celebrity. For years, we've known who they are. This paper is like a paparazzi team taking thousands of high-definition photos from every possible angle to see if the celebrity is wearing a disguise or acting strangely.

The conclusion? The celebrity is exactly who they say they are. No disguise, no secret twin, no weird behavior. The "Standard Model" rulebook remains unchallenged by this specific investigation.

In short: The scientists looked for weird, new physics in the way the Higgs boson interacts with light and other particles. They found nothing unusual, which is actually a big deal because it confirms our current understanding of the universe is incredibly robust, even as we look for cracks in the foundation.

Technical Summary

Technical Summary: Constraints on Anomalous Higgs Boson Couplings to Vector Bosons and Fermions using the $\gamma\gamma$ Final State

Problem and Motivation
While the Higgs boson ($H$) discovered at the LHC is consistent with Standard Model (SM) predictions regarding its spin-parity ($J^{PC} = 0^{++}$), current precision allows for small anomalous couplings to electroweak gauge bosons ($HVV$, where $V=W, Z$) and gluons ($Hgg$). These couplings provide a window into interactions between the Higgs boson and fermions ($Hff$) and potential sources of CP violation. Previous studies in channels such as $H \to 4\ell$ and $H \to \tau\tau$ have constrained these parameters, but the $H \to \gamma\gamma$ decay channel offers a clean, fully reconstructible final state that can substantially improve sensitivity to such anomalous effects. This paper presents a search for anomalous couplings and CP-violating effects in the $H \to \gamma\gamma$ channel using proton-proton collision data at $\sqrt{s} = 13$ TeV.

Methodology
The analysis utilizes 138 fb$^{-1}$ of data collected by the CMS experiment during LHC Run 2. The study is divided into two separate analyses targeting different production mechanisms:

1. HVV Analysis (VBF and VH): This analysis targets Higgs bosons produced via Vector Boson Fusion (VBF) and associated production with a vector boson (VH). Events are categorized based on the decay mode of the vector boson (hadronic $V(qq)H$, leptonic $V(\ell\nu)H$ or $V(\ell\ell)H$, and missing transverse momentum $V(\nu\nu)H$).

   • Discriminants: The analysis employs Matrix Element Likelihood Approach (MELA) discriminants (e.g., $D_{0^-}$) to separate CP-even and CP-odd hypotheses, alongside Deep Neural Networks (DNNs) and Boosted Decision Trees (BDTs) to distinguish signal from background and SM from Beyond Standard Model (BSM) hypotheses.
   • Categorization: Events are binned into specific categories (e.g., "ggH-like," "qqH BSM-like," "V(qq)H BSM-like") to maximize sensitivity to specific anomalous coupling parameters (f_{a2}, f_{a3}, f_{\Lambda1}, f_{Z\gamma}_{\Lambda1}).

2. Hgg Analysis (Gluon Fusion): This analysis targets Higgs bosons produced via gluon fusion in association with two jets ($ggH + 2$ jets), a topology kinematically similar to VBF.

   • Selection: Events require at least two jets with specific transverse momentum thresholds.
   • Discriminants: The analysis utilizes MELA discriminants ($D_{ggH}^{0-}$, $D_{ggH}^{CP}$) and a multiclass BDT to separate CP-even and CP-odd signal processes from inclusive backgrounds. The $D_{ggH}^{CP}$ discriminant is specifically designed to probe the interference term, sensitive to the sign of the CP-odd coupling.

Phenomenological Framework
The study parametrizes anomalous interactions using an effective Lagrangian formalism. Instead of measuring coupling constants directly, the analysis measures effective cross-section fractions ($f_i$), defined as the ratio of the anomalous contribution to the total cross section.

• For HVV, the parameters are $f_{a2}$ (CP-even), $f_{a3}$ (CP-odd), $f_{\Lambda1}$, and f_{Z\gamma}_{\Lambda1}.
• For Hgg, the parameter is f_{ggH}_{a3}, representing the fraction of the CP-odd coupling. This is interpreted in terms of the effective cross-section fraction for Higgs-fermion couplings ($f_{Htt}^{CP}$), assuming top and bottom quark dominance in the loop.

A simultaneous extended maximum likelihood fit is performed on the diphoton invariant mass ($m_{\gamma\gamma}$) spectrum across all categories. Signal and background models are derived from simulation and data-driven methods (discrete profiling for background shape uncertainties), with systematic uncertainties treated as nuisance parameters.

Key Results
The results are consistent with Standard Model expectations, with no significant evidence of anomalous couplings or CP violation observed.

• HVV Constraints: The analysis sets 68% and 95% confidence level (CL) intervals on the anomalous HVV coupling fractions. For the CP-odd parameter $f_{a3}$, the observed 95% CL interval is $[-1.5, 1.5] \times 10^{-4}$. The results for $f_{a2}$, $f_{\Lambda1}$, and f_{Z\gamma}_{\Lambda1} also show no deviation from the SM. These constraints are reported to be the most stringent among CMS results published to date for these specific parameters in the $H \to \gamma\gamma$ channel.
• Hgg Constraints: The observed constraint on the CP-odd gluon coupling fraction f_{ggH}_{a3} is $0.45^{+0.46}_{-0.42}$ (stat) $^{+0.10}_{-0.08}$ (syst) at 68% CL, with a 95% CL interval of $[-0.65, 0.63]$. This represents a significant improvement over previous $H \to \gamma\gamma$ measurements and is comparable to the best constraints from other decay channels (e.g., $H \to 4\ell$, $H \to \tau\tau$).
• Signal Strengths: The signal strength modifiers for gluon fusion ($\mu_f$) and vector boson production ($\mu_V$) are found to be consistent with SM predictions ($\mu_f \approx 1.05$, $\mu_V \approx 1.37$ for the HVV fit; $\mu_f \approx 0.82$, $\mu_V \approx 1.22$ for the Hgg fit).

Significance and Claims
The paper claims that this work provides the first study of anomalous Higgs-vector boson couplings in the $H \to \gamma\gamma$ decay channel. By leveraging the high resolution and purity of the diphoton final state, the analysis achieves the most stringent constraints to date on several effective cross-section fractions (f_{a2}, f_{\Lambda1}, f_{Z\gamma}_{\Lambda1}) within the CMS collaboration. Furthermore, the constraints on the CP-odd Higgs-gluon coupling (f_{ggH}_{a3}) are comparable to the best existing CMS results from other channels, demonstrating the complementary power of the diphoton channel in probing the CP structure of the Higgs boson. The authors note that the measurements are currently limited by statistical precision, as systematic uncertainties largely cancel in the cross-section ratios.