Search for Higgs boson decays into two neutral scalars with unequal masses in final states with b quarks and tau leptons 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 detector, a search for Higgs boson decays into two neutral scalars of unequal masses in final states containing b quarks and tau leptors found no significant excess over the Standard Model, resulting in the setting of 95% confidence level upper limits on the relevant production cross sections and branching fractions.

The Gist

Imagine the universe is a giant, high-speed racetrack where tiny particles zoom around at nearly the speed of light. At CERN's Large Hadron Collider (LHC), scientists smash protons together like two cars crashing in slow motion to see what tiny fragments fly out. Usually, these crashes produce the famous Higgs boson, a particle discovered in 2012 that acts like a cosmic "glue" giving other particles their mass.

This paper is about a specific, high-stakes treasure hunt: Is the Higgs boson secretly hiding a family of lighter, invisible cousins?

The Big Idea: The "Magic Box" Theory

In the standard rules of physics (the Standard Model), the Higgs boson is a one-and-done particle. It's born, it decays, and it's gone. But many scientists suspect there are "beyond the Standard Model" rules. They think the Higgs might be a "magic box" that, instead of just disappearing, opens up to reveal two lighter, invisible particles (let's call them $\phi_1$ and $\phi_2$).

Think of the Higgs as a heavy, golden egg. When it cracks, instead of just breaking into dust, it might hatch two smaller, different-colored eggs.

• $\phi_2$ is the heavier of the two new eggs.
• $\phi_1$ is the lighter one.

Sometimes, the heavier egg ($\phi_2$) is unstable and immediately cracks open again to reveal two more of the lighter eggs ($\phi_1$). This is called a cascade decay (like a Russian nesting doll that keeps opening). Other times, the heavier egg just sits there and decays directly into normal matter.

The Detective Work: Following the Clues

The problem is, these new "eggs" ($\phi_1$ and $\phi_2$) are invisible to our detectors. We can't see them directly. However, we know what they eventually turn into. The paper focuses on two specific "fingerprints" they leave behind:

1. Bottom quarks ($b$): Heavy particles that turn into jets of debris.
2. Tau leptons ($\tau$): Heavy cousins of the electron that decay quickly.

The scientists are looking for a very specific crime scene:

• Scenario A (The Cascade): The Higgs splits into $\phi_1$ and $\phi_2$. The $\phi_2$ splits again into two more $\phi_1$s. So, we end up with three light particles ($\phi_1$). Two of them turn into pairs of bottom quarks (4 total), and one turns into a pair of tau leptons.
  • Result: A messy pile of 4 bottom quarks and 2 tau leptons.
• Scenario B (The Direct Split): The Higgs splits into $\phi_1$ and $\phi_2$. The $\phi_1$ turns into tau leptons, and the $\phi_2$ turns into bottom quarks.
  • Result: A pile of 2 bottom quarks and 2 tau leptons.

The Challenge: Finding a Needle in a Haystack

The LHC is a noisy place. Every second, billions of collisions happen, but 99.9% of them are just "background noise" (like a crowd of people shouting in a stadium). The signal the scientists are looking for is a whisper in that crowd.

To find it, the CMS team (the group of scientists who wrote this paper) used a massive dataset equivalent to 138 "inverse femtobarns" of data (a unit of collision volume) collected between 2016 and 2018.

They had to build a sophisticated filter to separate the signal from the noise:

1. The Trigger: Like a bouncer at a club, the computer system instantly decides which collisions are interesting enough to keep. They looked for events with specific combinations of electrons, muons, and tau particles.
2. The "Smart" Filter (BDT): Instead of just setting simple rules (e.g., "keep if energy is high"), they used a Boosted Decision Tree (BDT). Think of this as a super-smart AI detective that looks at dozens of clues at once—how the particles are spaced out, their angles, their missing energy—and learns to spot the subtle patterns of the "magic box" decay versus the background noise.
3. The "Cut-Based" Backup: They also tried a simpler method (just setting strict rules) to double-check their work, though the AI method was much better at finding the signal.

The Verdict: The Silence of the Higgs

After analyzing the data, the scientists looked for a "bump" in the statistics—a sudden spike in the number of events that matched their predicted "magic box" pattern.

The result? No bump.

The data looked exactly like the Standard Model predicted: just background noise. There was no evidence that the Higgs boson is decaying into these lighter, unequal-mass particles.

What Does This Mean?

Since they didn't find the "magic box," they didn't discover new physics. Instead, they set limits.

Imagine you are looking for a specific type of rare bird in a forest. You don't find it. You can't say, "The bird doesn't exist." But you can say, "If the bird exists, it is so rare that I would have seen it 95% of the time if it were common."

The paper sets strict upper limits on how often this exotic decay could be happening. They calculated that if this "Higgs-to-light-particles" decay happens, it must be less than 0.9 to 36.8 times per trillion Higgs bosons produced (depending on the mass of the particles).

Summary

• The Goal: Check if the Higgs boson secretly decays into two different, lighter invisible particles.
• The Method: Smashed protons together, looked for specific debris (bottom quarks and tau leptons), and used AI to filter out the noise.
• The Result: No new particles were found. The Higgs boson behaves exactly as the Standard Model predicts in this specific scenario.
• The Takeaway: We have ruled out a wide range of possibilities for "exotic" Higgs decays. If these lighter particles exist, they are even more elusive than we thought, or they don't interact with the Higgs in the way this theory predicted.

This is a "negative" result, but in science, knowing what isn't there is just as important as knowing what is. It tells theorists, "Don't waste time building models that predict this specific decay; the universe says it's not happening."

Technical Summary

Technical Summary: Search for Higgs Boson Decays into Two Neutral Scalars with Unequal Masses

Problem and Motivation
While the Standard Model (SM) successfully predicts the existence of a scalar Higgs boson ($H$) with a mass of 125 GeV, many theories beyond the SM (BSM) propose extended scalar sectors to address unresolved issues such as dark matter and matter-antimatter asymmetry. These models often predict that the observed Higgs boson decays into additional light neutral scalar particles. Previous searches have largely focused on symmetric decays ($H \to aa$) or specific final states. However, models such as the Two-Real-Singlet Model (TRSM) predict asymmetric decays into two neutral scalars with non-degenerate masses ($H \to \phi_1\phi_2$, where $m_{\phi_2} > m_{\phi_1}$). Depending on the mass hierarchy, $\phi_2$ may undergo a cascade decay into $\phi_1\phi_1$ or decay directly to SM fermions. This paper presents the first search using CMS data for these asymmetric decays in final states containing $b$ quarks and $\tau$ leptons.

Methodology
The analysis utilizes proton-proton collision data collected by the CMS detector at $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$ (2016–2018). The search targets the production of the Higgs boson via gluon-gluon fusion (ggF) and vector-boson fusion (VBF), followed by the decay chain $H \to \phi_1\phi_2$.

Two distinct decay scenarios are investigated:

1. Cascade Scenario ($m_{\phi_2} \ge 2m_{\phi_1}$): $\phi_2$ decays into two $\phi_1$ scalars. The final state signature is $H \to \phi_1\phi_2 \to 3\phi_1 \to 2\tau 4b$.
2. Non-Cascade Scenario ($m_{\phi_2} < 2m_{\phi_1}$): $\phi_2$ decays directly to SM particles. The final state signature is $H \to \phi_1\phi_2 \to 2\tau 2b$.

In both scenarios, one $\phi_1$ is required to decay into a pair of $\tau$ leptons. The analysis considers three final states based on $\tau$ decay modes: $\mu\tau_h$, $e\tau_h$, and $e\mu$ (where $\tau_h$ denotes hadronically decaying taus).

Event Selection and Categorization:
Events are selected using single-lepton and cross-trigger requirements. Offline selection requires two lepton candidates (muon/electron) and at least one hadronic $\tau$ candidate, along with at least one $b$-tagged jet. To enhance signal sensitivity, events are categorized based on the number of $b$-tagged jets (1b or $\ge$2b) and the specific decay channel.

A Boosted Decision Tree (BDT) is employed to discriminate between signal and background. The BDT is trained on kinematic variables including:

• The visible invariant mass of the combined leading $b$-jet and $\tau\tau$ candidate ($m_{\text{vis}}(\tau\tau b_1)$).
• Transverse mass variables ($m_T$) involving the missing transverse momentum ($p_T^{\text{miss}}$).
• The alignment variable $D_\zeta$, which measures the alignment of $p_T^{\text{miss}}$ with the $\tau\tau$ system.
• Angular separations ($\Delta R$) between objects and the variable $\Delta m$ (normalized mass difference between $b$-jet pairs and the $\tau\tau$ system).

The BDT score is used to define Signal Regions (SRs) with varying thresholds for each channel and $b$-jet multiplicity. A cut-based analysis is also performed as a cross-check.

Background Estimation:
Major backgrounds include Drell–Yan ($Z/\gamma^* \to \tau\tau$), top quark pair production ($t\bar{t}$), single top, and diboson processes.

• The $Z/\gamma^* \to \tau\tau$ background is estimated using an embedding technique where muons from data are replaced with simulated tau decays.
• Backgrounds from jets misidentified as $\tau_h$ are estimated using data-driven methods in sideband regions.
• QCD multijet backgrounds in the $e\mu$ channel are estimated using same-sign control regions.

Key Contributions and Results
The analysis performs a binned maximum likelihood fit to the reconstructed $\tau\tau$ invariant mass ($m_{\tau\tau}$) distribution in the defined SRs. No statistically significant excess over the SM background expectation is observed.

Upper limits are set at the 95% confidence level (CL) on the product of the Higgs production cross section ($\sigma$) and the relevant branching fractions:

• Cascade: $\sigma \mathcal{B}(H \to \phi_1\phi_2 \to 3\phi_1 \to 2\tau 4b)$
• Non-Cascade: $\sigma \mathcal{B}(H \to \phi_1\phi_2) \mathcal{B}(\phi_1 \to 2\tau) \mathcal{B}(\phi_2 \to 2b)$

The observed upper limits range between 0.9 and 36.8 pb, depending on the mass hypothesis ($m_{\phi_1}, m_{\phi_2}$) and the decay scenario. The sensitivity is dominated by statistical uncertainties and the normalization uncertainties of the misidentified $\tau_h$ background.

For the most sensitive non-cascade mass hypothesis ($m_{\phi_1}=30$ GeV, $m_{\phi_2}=40$ GeV), the observed upper limit on the branching fraction product is approximately 1.6% (assuming SM production cross sections). When interpreted within the TRSM benchmark scenario BP1, this excludes values of $\mathcal{B}(H \to \phi_1\phi_2)$ above 27.3% for this specific mass point.

Significance
This work represents the first search using CMS data for exotic Higgs boson decays into two light neutral scalar particles of unequal masses in final states involving $b$ quarks and $\tau$ leptons. The study extends previous constraints on Higgs exotic decays by probing the asymmetric mass region and the cascade decay topology. The results provide model-independent limits that can be used to constrain various BSM scenarios, including the TRSM, NMSSM, and models with axion-like particles. The BDT-based approach is shown to improve sensitivity by 20–30% compared to a traditional cut-based method.