Search for the nonresonant and resonant production of a Higgs boson in association with an additional scalar boson in the $\gamma\gamma\tau\tau$ final state in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of 13 TeV proton-proton collision data from the CMS experiment, this study presents a search for nonresonant Higgs boson pair production and resonant production via new scalar bosons in the $\gamma\gamma\tau\tau$ final state, finding no evidence for signal and setting stringent 95% confidence level upper limits on various production cross sections and coupling parameters.

The Gist

Imagine the Large Hadron Collider (LHC) as a massive, high-speed particle racetrack. Inside, scientists smash protons together at nearly the speed of light, creating a chaotic explosion of energy that briefly forms new, exotic particles. The CMS experiment is like a team of ultra-precise detectives standing around the track, trying to spot specific, rare "suspects" hiding in the debris.

This paper is a report from those detectives. They were looking for a very specific, rare event: a collision that produces two Higgs bosons (the famous particles that give other particles mass) at the same time. Even more specifically, they were looking for these two Higgs bosons to decay into a "signature" that leaves behind two flashes of light (photons) and two heavy, short-lived particles called tau leptons.

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

The Three Main Mysteries They Solved

The detectives didn't just look for one thing; they set up three different "traps" to catch different types of suspects:

1. The "Double Trouble" Search (Nonresonant Production)

• The Scenario: Imagine two Higgs bosons just bumping into each other by pure chance, like two strangers accidentally colliding in a crowded room.
• The Goal: They wanted to measure how often this happens and check if the "strength" of their connection (a property called the trilinear self-coupling) matches the predictions of the Standard Model (the rulebook of physics).
• The Result: They found no evidence of this happening more often than the rulebook predicts. They set a limit: if this "Double Trouble" event is happening, it's doing so less than 33 times more often than the Standard Model says it should. They also narrowed down the possible values for the Higgs boson's "personality" (its self-interaction strength), ruling out extreme possibilities.

2. The "Heavy Parent" Search (Resonant X → HH)

• The Scenario: Imagine a heavy, invisible parent particle (let's call it X) that is so unstable it immediately splits apart into two Higgs bosons.
• The Goal: They scanned for a "parent" particle that could be anywhere from 260 to 1000 times heavier than a proton. They checked if this parent was a "spin-0" particle (like a ball) or a "spin-2" particle (like a spinning top).
• The Result: They found no heavy parents. They calculated the maximum weight this parent could have had without being detected, effectively ruling out certain theories that predicted such particles exist in that mass range.

3. The "Family Tree" Search (Resonant X → YH)

• The Scenario: This is a more complex family tree. A heavy parent (X) decays into a lighter child (Y) and a Higgs boson (H). Then, the child Y decays further.
  • Case A: The child Y turns into two tau leptons, while the Higgs turns into two photons.
  • Case B: The child Y turns into two photons, while the Higgs turns into two tau leptons.
• The Goal: They were looking for these specific family trees, which are predicted by theories like Supersymmetry (a theory suggesting every particle has a "super-partner").
• The Result: They found no definitive family trees. However, they did spot a few "glitches" in the data—small bumps that looked slightly suspicious (like a 3.2-sigma fluctuation). While these aren't strong enough to claim a discovery (they could just be random noise), they are interesting because they line up with other "glitches" the CMS team has seen elsewhere. They tightened the rules on how heavy these "children" could be, putting pressure on specific Supersymmetry theories.

How They Did It (The Detective Work)

• The Data: They analyzed a massive amount of data (138 "inverse femtobarns," which is like a library full of billions of collision records) collected between 2016 and 2018.
• The Filter: Since the signal they are looking for is incredibly rare (like finding a specific grain of sand on a beach), they used advanced computer algorithms (Machine Learning) to act as a sieve. These algorithms learned to distinguish the "signal" (the two photons and two taus) from the "background noise" (common collisions that look similar but aren't what they want).
• The Search: They didn't just look in one spot. They scanned a vast range of masses, checking millions of different possibilities for how heavy these new particles could be.

The Bottom Line

The paper concludes that nature is behaving exactly as the Standard Model predicts so far. They did not find the new particles they were hunting for.

• Did they find new physics? No.
• Did they find a new particle? No.
• What did they do? They drew a tighter fence around the possibilities. They told the theoretical physicists, "If your new particles exist, they must be heavier or rarer than we just proved they can't be."

While they didn't find the "Holy Grail" of new physics, they successfully eliminated a huge chunk of the "Where to look" map, forcing scientists to refine their theories and look in new places. The few small "glitches" they saw are like faint whispers in a noisy room—interesting enough to listen to again, but not loud enough to shout about yet.

Technical Summary

Technical Summary: Search for the Nonresonant and Resonant Production of a Higgs Boson in Association with an Additional Scalar Boson in the $\gamma\gamma\tau\tau$ Final State

Problem and Motivation
This paper presents a search for the production of two scalar bosons in the $\gamma\gamma\tau\tau$ final state using proton-proton collision data collected by the CMS experiment at $\sqrt{s} = 13$ TeV. The analysis addresses two primary physics goals: constraining the Higgs boson trilinear self-coupling ($\lambda_{HHH}$) through nonresonant Higgs pair ($HH$) production, and searching for new physics phenomena predicted by Beyond-the-Standard-Model (BSM) theories.

The trilinear coupling is a unique test of the Standard Model (SM) Higgs potential structure, yet it remains poorly constrained due to the small SM cross-section for $HH$ production ($31.1^{+2.1}_{-7.2}$ fb at NNLO). Furthermore, various BSM theories, such as the Randall–Sundrum (RS) bulk model and the Next-to-Minimal Supersymmetric Standard Model (NMSSM), predict additional scalar particles (denoted as $X$ and $Y$) that could decay into Higgs boson pairs or mixed states ($X \to HH$, $X \to YH$). Recent CMS results in other channels ($X \to Y(bb)H(\gamma\gamma)$ and searches for scalar decays to $\tau\tau$ or $\gamma\gamma$) have shown local excesses, motivating a complementary search in the $\gamma\gamma\tau\tau$ channel to probe these mass regions with high resolution.

Methodology
The analysis utilizes up to $138 \text{ fb}^{-1}$ of data recorded between 2016 and 2018. The event selection requires two photons and two tau leptons (or a single tau and an isolated track), with specific kinematic requirements on transverse momentum ($p_T$) and isolation. The diphoton invariant mass ($m_{\gamma\gamma}$) is required to be $>65$ GeV (or $>100$ GeV for most searches) to ensure trigger efficiency and background suppression.

Five distinct search strategies are employed:

1. Nonresonant $HH$ production: Via gluon-gluon fusion (ggF).
2. Resonant $X(0) \to HH$: Spin-0 resonance.
3. Resonant $X(2) \to HH$: Spin-2 resonance.
4. Resonant $X \to Y(\tau\tau)H(\gamma\gamma)$: Decay of a heavy scalar $X$ to a lighter scalar $Y$ (decaying to $\tau\tau$) and a SM Higgs (decaying to $\gamma\gamma$).
5. Resonant $X \to Y(\gamma\gamma)H(\tau\tau)$: Decay of $X$ to $Y$ (decaying to $\gamma\gamma$) and $H$ (decaying to $\tau\tau$). This search is split into low-mass ($m_Y \in [70, 125]$ GeV) and high-mass ($m_Y \in [125, 800]$ GeV) regimes due to trigger constraints.

Event Categorization and Modeling
To maximize sensitivity, the analysis employs machine learning classifiers:

• Nonresonant Search: A Boosted Decision Tree (BDT) trained on kinematic variables (excluding $m_{\gamma\gamma}$ to avoid sculpting the background) separates signal from background. Events are categorized into two bins (Cat 0 and Cat 1) based on BDT scores.
• Resonant Searches: A Parameterized Neural Network (pNN) is used. The pNN is trained simultaneously on signal samples across a wide range of mass hypotheses ($m_X$ and $m_Y$), using the mass values as additional input features. This allows a single network to adapt its discrimination power based on the specific mass hypothesis being tested.

Signal and background modeling are performed via maximum likelihood fits to the $m_{\gamma\gamma}$ distribution.

• Signal: Modeled using a Double Crystal Ball (DCB) function derived from simulation. For intermediate mass points not explicitly simulated, signal shapes and efficiencies are interpolated using splines.
• Background: The continuum background is modeled directly from data using the discrete profiling method, which accounts for the uncertainty in the choice of the analytic function (e.g., exponential, Bernstein polynomials). Single Higgs production ($H \to \gamma\gamma$) is treated as a resonant background modeled from simulation. In the $X \to Y(\gamma\gamma)H(\tau\tau)$ search, Drell–Yan background (where electrons are misidentified as photons) is estimated using an ABCD method.

Systematic uncertainties, including theoretical cross-section variations, luminosity, trigger efficiency, and object identification (photons, $\tau_h$, jets), are incorporated as nuisance parameters.

Key Contributions and Results
No significant evidence for signal was found in the data. The results are presented as 95% confidence level (CL) upper limits:

• Nonresonant $HH$ Production:

  • The observed (expected) upper limit on the $HH$ production cross section is $930$($740$) fb, corresponding to $33$($26$) times the SM prediction.
  • Limits on the Higgs self-coupling modifier $\kappa_\lambda$ exclude values outside the range $[-12, 17]$ (observed) and $[-9.4, 15]$ (expected) at 95% CL, assuming SM values for other couplings.
  • Limits were also set for 13 BSM benchmark scenarios involving effective field theory (EFT) operators.

• Resonant $X \to HH$ Searches:

  • For $X(0) \to HH$ and $X(2) \to HH$, observed (expected) limits on the production cross section $\sigma(pp \to X)\mathcal{B}(X \to HH)$ range from $160$–$2200$ fb ($200$–$1800$ fb) depending on $m_X$.
  • In the context of the RS bulk model, these results exclude specific mass ranges for radion and Kaluza-Klein graviton resonances.

• Resonant $X \to YH$ Searches:

  • For $X \to Y(\tau\tau)H(\gamma\gamma)$, observed (expected) limits on $\sigma \times \mathcal{B}$ vary between $0.059$–$1.2$ fb ($0.087$–$0.68$ fb).
  • For $X \to Y(\gamma\gamma)H(\tau\tau)$, limits on $\sigma(pp \to X \to YH)\mathcal{B}(Y \to \gamma\gamma)$ vary between $0.69$–$15$ fb ($0.73$–$8.3$ fb) for low $m_Y$ and $0.64$–$10$ fb ($0.70$–$7.6$ fb) for high $m_Y$.
  • In the low-mass $Y$ search, the observed limits are compared to maximally allowed cross-sections in the NMSSM. A region in the $(m_X, m_Y)$ parameter space is identified where the observed limits are tighter than previous constraints, providing new exclusion power for the NMSSM.

• Excesses:

  • Local significances of up to $3.2\sigma$ were observed in the $X \to Y(\gamma\gamma)H(\tau\tau)$ search at $(m_X, m_Y) = (525, 115)$ GeV and $(450, 161)$ GeV.
  • Excesses of $2.2\sigma$ and $2.3\sigma$ were seen at masses consistent with previous CMS excesses ($m_X \approx 600$–$650$ GeV, $m_Y \approx 95$ GeV).
  • However, the global significances for all searches are low ($0.1$–$2.2\sigma$), indicating no significant deviation from the background-only hypothesis when accounting for the look-elsewhere effect.

Significance
The paper claims to provide the first constraints on the $\gamma\gamma\tau\tau$ final state for these specific production modes, complementing previous searches in $bb\gamma\gamma$ and $\tau\tau$ channels. By utilizing a parameterized neural network, the analysis efficiently covers a wide mass range for resonant production without the need for separate training for every mass point. The results tighten constraints on the NMSSM and provide updated limits on the Higgs trilinear coupling and various BSM benchmark scenarios. While the local excesses observed are not statistically significant globally, their consistency with other CMS results motivates future measurements at these specific mass points.