Search for light charged Higgs bosons decaying to charm and strange quarks in $\mathrm{t\bar{t}}$ events in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of proton-proton collision data at 13 TeV, this study presents the first direct search for light charged Higgs bosons decaying to charm and strange quarks in top quark pair events, setting the most stringent limits to date on the branching fraction $\mathcal{B}$(t $\to$ H$^\pm$ b) for masses between 70 and 110 GeV while finding no evidence of a signal beyond Standard Model predictions.

The Gist

The Great Particle Hunt: Searching for a "Ghost" in the Top Quark's Shadow

Imagine the universe as a giant, high-speed car race. In this race, the most important cars are called top quarks. They are the heaviest, most energetic particles we know. Usually, when these top quarks crash and break apart, they follow a very strict rulebook (the Standard Model of physics). They always split into a specific set of parts: a "bottom" particle and a "W" particle.

But what if there's a secret rulebook? What if, sometimes, a top quark decides to take a different path and split into a bottom particle and a mysterious, invisible "ghost" particle called a charged Higgs boson ($H^\pm$)?

This paper is the report from the CMS Collaboration (a team of thousands of scientists at CERN's Large Hadron Collider) who went looking for this ghost.

The Setup: A 138-Footprint Trail

The scientists didn't just look at a few cars; they analyzed a massive pile of data from 2016 to 2018. Imagine they had a camera that took 138 trillion snapshots (138 inverse femtobarns) of proton collisions. That's like taking a photo of every grain of sand on a beach, but for subatomic particles.

They were specifically looking for a scenario where:

1. Two top quarks are created.
2. One top quark breaks apart normally (into a bottom and a W).
3. The other top quark breaks apart strangely (into a bottom and a charged Higgs).
4. This mysterious Higgs then instantly dissolves into two lighter particles: a charm and a strange quark.

The Challenge: Finding a Needle in a Haystack

The problem is that the "normal" way top quarks break apart happens all the time. It's like trying to find a specific, rare type of red marble in a pile of a billion red marbles that look exactly the same.

The "ghost" Higgs would leave behind two jets of energy (sprays of particles) that look very similar to the jets left behind by the normal W particle. It's like trying to distinguish between two identical twins based on a blurry photo.

The Detective Work: Three New Tricks

To solve this, the scientists used three main tricks to sharpen their vision:

1. The Kinematic Fit (The Puzzle Solver):
   Imagine you have a broken toy car, and you want to know what it looked like before it broke. You measure the pieces and use math to "rebuild" the car in your mind, forcing the pieces to fit together perfectly according to the laws of physics. The scientists did this with every collision. By mathematically forcing the pieces to fit the "top quark" shape, they could clean up the blurry photos and make the signal clearer. This removed a lot of the "noise" that usually hides the ghost.

2. The "Charm" Detector (The ID Check):
   The ghost Higgs is supposed to turn into a charm quark. The scientists used a super-smart AI (called DeepJet) trained to recognize the "fingerprint" of a charm quark. It's like having a bouncer at a club who can tell the difference between a VIP guest (charm) and a regular visitor (light quarks) just by looking at their ID. They categorized events based on how confident the AI was that it saw a charm quark.

3. The BDT (The Smart Filter):
   Instead of just setting simple rules (like "if the particle is this heavy, keep it"), they used a Boosted Decision Tree (BDT). Think of this as a super-intelligent filter that looks at 18 different clues at once (speed, angle, energy, etc.) to decide: "Is this a normal top quark, or is it the ghost Higgs?" It learns from millions of computer simulations to spot the subtle differences that a human eye would miss.

The Results: The Ghost is Still Hiding

After running all their data through these high-tech filters, the scientists looked at the final results.

• Did they find the ghost? No.
• What did they see? They saw exactly what they expected to see if the ghost didn't exist. The number of "strange" events matched the predictions of the Standard Model perfectly. The data was consistent with the "normal" twins, not the rare ghost.

The Conclusion: Setting the Boundaries

Even though they didn't find the ghost, this is a huge success. By not finding it, they drew a very tight fence around where the ghost could be hiding.

• They proved that if this charged Higgs boson exists, it cannot be responsible for more than 0.07% to 1.12% of top quark decays in the mass range they checked (40 to 160 GeV).
• They set the strictest limits ever for the mass range of 70–110 GeV.
• They were the first to look for it in the 40–50 GeV range and found nothing there either.

In simple terms: The scientists looked very hard for a new particle that some theories say should exist. They didn't find it. This means that if this particle does exist, it is even rarer and more elusive than we thought. The "Standard Model" rulebook remains unbroken for now, and the search for new physics must continue in other directions.

Technical Summary

1. Problem Statement and Physics Motivation

The Standard Model (SM) of particle physics predicts a single Higgs doublet, resulting in one physical Higgs boson ($H$). However, many Beyond-the-Standard-Model (BSM) theories, particularly Two-Higgs-Doublet Models (2HDMs), predict the existence of additional scalar particles, including a charged Higgs boson ($H^\pm$).

• Production Mechanism: In many 2HDM scenarios, the charged Higgs boson can be produced via the decay of a top quark ($t \to H^+ b$). This is kinematically allowed only if $m_{H^\pm} < m_t$.
• Decay Channel: While the decay $H^\pm \to \tau \nu$ is often dominant, specific 2HDM scenarios (Type II and Type Y flipped models) predict a substantial branching fraction for $H^\pm \to c\bar{s}$ (charm and strange quarks), particularly in low and high $\tan\beta$ regions.
• The Challenge: Searching for $H^\pm \to c\bar{s}$ in top-quark pair ($t\bar{t}$) events is experimentally difficult because the final state (two light jets from the $H^\pm$, two $b$-jets, a lepton, and missing energy) is indistinguishable from the dominant SM background where both top quarks decay via $t \to W b$ (with $W \to q\bar{q}'$). The signal manifests as a resonance in the dijet invariant mass ($m_{jj}$) spectrum, but this is obscured by the broad $W$ boson peak and combinatorial background.

2. Methodology

Data and Simulation:

• Dataset: Proton-proton collision data collected by the CMS detector at $\sqrt{s} = 13$ TeV during 2016–2018, corresponding to an integrated luminosity of 138 fb$^{-1}$.
• Signal Simulation: Generated using MADGRAPH5_aMC@NLO at Next-to-Leading Order (NLO) for $m_{H^\pm}$ ranging from 40 to 160 GeV in 10 GeV steps. The branching fraction is assumed to be $B(H^\pm \to cs) = 100\%$.
• Background Simulation: SM $t\bar{t}$ (dominant, ~90%), single top, $W/Z$+jets, and QCD multijet processes generated using POWHEG and MADGRAPH5_aMC@NLO.

Event Selection:

• Topology: Events are selected in the lepton+jets channel, requiring exactly one isolated electron or muon, missing transverse momentum ($p_T^{miss}$), and at least four jets.
• Flavor Tagging: Events must contain at least two $b$-tagged jets (using the DEEPJET algorithm).
• Kinematic Fit: A kinematic fit is applied to resolve ambiguities in jet assignment. It minimizes a $\chi^2$ function by constraining the lepton-neutrino system to the $W$ mass and the $W$-jet systems to the top mass. This significantly improves the resolution of the dijet invariant mass ($m_{jj}$).
• Light Jet Definition: Jets not identified as $b$-jets are termed "light jets." The signal is reconstructed from the two light jets assigned to the hadronic boson candidate.

Event Categorization Strategies:
The analysis employs two complementary approaches to maximize sensitivity:

1. Cut-Based Method: Events are categorized based on charm-tagging (c-tagging) performance. Using CvsL (charm vs. light) and CvsB (charm vs. bottom) discriminators, events are sorted into "Loose," "Medium," and "Tight" categories based on the highest c-tag score of the two light jets.
2. Multivariate (BDT) Method: A Boosted Decision Tree (BDT) is trained to separate signal from the dominant SM $t\bar{t}$ background.
   • Inputs: 18 variables including kinematic properties ($p_T$, $\Delta\phi$, $\Delta R$), angular correlations, and c-tagging scores (CvsL, CvsB) for light and $b$-jets.
   • Training: Separate BDTs are trained for low-mass (40–70 GeV) and high-mass (80–160 GeV) hypotheses. The BDT output is used to create three exclusive categories (Loose, Medium, Tight) to optimize signal-to-background separation.

Statistical Analysis:

• A binned maximum likelihood fit is performed on the $m_{jj}$ distribution in the signal regions.
• The fit model includes the SM background (constrained by systematic uncertainties) and the signal hypothesis.
• Systematic Uncertainties: Major sources include Jet Energy Scale/Resolution (JES/JER), $b$- and $c$-tagging efficiencies, theoretical modeling (scale variations, PDFs), and luminosity. The QCD multijet background is estimated using a data-driven "AB method" (control regions with non-isolated leptons).

3. Key Contributions

• Extended Mass Range: This analysis probes the 40–50 GeV mass range, providing the first direct limits on charged Higgs bosons produced in top decays in this specific low-mass window. Previous searches often had lower mass thresholds around 60–80 GeV due to trigger or reconstruction limitations.
• Improved Sensitivity in 70–110 GeV: The results provide the most stringent limits to date in the 70–110 GeV range, surpassing previous ATLAS and CMS results.
• Advanced Techniques:
  • Implementation of a full kinematic fit to suppress high-mass tails in the $m_{jj}$ spectrum caused by incorrect jet pairing.
  • Utilization of charm-tagging discriminators (CvsL/CvsB) as a primary handle to distinguish $H^\pm \to cs$ from $W \to q\bar{q}'$ and light-flavor backgrounds.
  • Deployment of a multivariate BDT strategy alongside traditional cut-based methods to exploit correlations between kinematic and flavor variables.
• Full Dataset Usage: Utilization of the complete 2016–2018 Run 2 dataset (138 fb$^{-1}$), significantly increasing statistical power compared to previous 13 TeV analyses.

4. Results

• Observation: The observed yield in the $m_{jj}$ spectrum is consistent with Standard Model predictions. No significant excess or resonant structure indicative of a charged Higgs boson was found.
• Upper Limits: 95% Confidence Level (CL) upper limits were set on the branching fraction $B(t \to H^\pm b)$, assuming $B(H^\pm \to cs) = 100\%$.
  • The observed limits range from 0.07% to 1.12% across the 40–160 GeV mass range.
  • Specific Performance:
    • Limits are up to 75% better than previous CMS results (based on 2016 data).
    • Limits are 40–70% better than corresponding ATLAS results in the 70–110 GeV range.
• Exclusion: The analysis excludes specific regions of the 2HDM parameter space, particularly for low-mass charged Higgs bosons where previous constraints were weak or non-existent.

5. Significance

This paper represents a significant milestone in the search for extended Higgs sectors at the LHC. By successfully targeting the challenging $H^\pm \to c\bar{s}$ decay channel with high precision:

1. It closes a critical gap in the search for light charged Higgs bosons below 50 GeV, a region previously difficult to access.
2. It demonstrates the efficacy of charm-tagging and multivariate analysis in isolating rare BSM signals from overwhelming QCD and SM $t\bar{t}$ backgrounds.
3. The stringent limits significantly constrain the parameter space of Type II and Type Y 2HDMs, particularly in regions with low and high $\tan\beta$, guiding future theoretical models and experimental strategies for Run 3 and the High-Luminosity LHC.