Search for the nonresonant production of a pair of additional Higgs bosons in the Type-X two-Higgs-doublet model 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, this study found no evidence for the nonresonant production of a pair of additional Higgs bosons decaying to $\tau$ lepton pairs, thereby ruling out the Type-X two-Higgs-doublet model alignment scenario as an explanation for the muon anomalous magnetic moment tension.

The Gist

The Big Picture: Hunting for "Ghost" Particles to Solve a Mystery

Imagine the Standard Model of physics as a massive, incredibly detailed instruction manual for how the universe works. For decades, this manual has been spot-on. But recently, scientists found a tiny, stubborn typo in the section about muons (a type of subatomic particle similar to an electron, but heavier).

When they measured how a muon spins (its "magnetic moment"), the real-world number didn't match the number predicted by the manual. It was off by a tiny bit, but enough to suggest that the manual is missing a page. Something invisible is influencing the muon, and physicists suspect it's a new, undiscovered particle.

The Suspect: The "Type-X" Two-Higgs-Doublet Model

To fix the manual, scientists proposed a new theory called the Type-X Two-Higgs-Doublet Model (2HDM). Think of the current Higgs boson (the famous particle discovered in 2012) as the "Star Player" of the team. This new theory suggests there are actually five players on the field, not just one.

• The Star Player: The one we already found (the 125 GeV Higgs).
• The New Players: Two extra neutral particles and two charged ones.

The theory says these new players interact very strongly with tau leptons (heavy cousins of electrons) but barely interact with quarks (the stuff protons and neutrons are made of). This specific setup is called "Type-X" because it's "lepton-specific."

The Strategy: The "Off-Shell Z" Backdoor

Usually, when scientists look for new particles at the Large Hadron Collider (LHC), they smash protons together and look for the new particles popping out directly. However, in this specific "Type-X" theory, if you try to make just one of these new particles, it's like trying to hear a whisper in a hurricane—the signal is too weak to detect because the production rate is so low.

So, the CMS team (the group running this experiment) decided to try a different tactic. Instead of looking for a single new particle, they looked for a pair of them being born together from a "ghost" particle.

The Analogy:
Imagine you are trying to catch two elusive squirrels (the new Higgs bosons) that are hiding in a park.

• Old Method: You wait for a squirrel to run out of a hole. But these squirrels are shy; they rarely come out alone.
• New Method: You wait for a specific tree branch (an off-shell Z boson) to snap. When it snaps, it doesn't just fall; it launches two squirrels into the air at the same time. Even though the branch itself is invisible (it's "off-shell" or virtual), the two squirrels flying out are a clear sign it happened.

The paper focuses on this specific "branch snapping" event: $Z^* \to \phi A$.

The Investigation: The "Four-Tau" Crime Scene

Once these two new particles ($\phi$ and $A$) are created, they don't stick around. They immediately decay (fall apart). In the Type-X model, they almost always turn into tau leptons.

Since tau leptons are unstable, they decay again almost instantly. The team looked for events where four tau leptons appeared in the detector at once.

The Challenge:
Detecting four taus is like trying to find four specific types of needles in a haystack, where the needles are also changing shape and disappearing.

• Some taus turn into electrons or muons (easy to spot).
• Some turn into hadrons (particles that look like jets of debris, harder to spot).
• The background noise (other particle collisions) is massive.

The team used a sophisticated "particle-flow" algorithm (a digital reconstruction tool) to piece together the tracks of these four particles. They looked for a specific signature: a total energy balance that matched the "ghost branch" snapping, rather than just random noise.

The Results: The Manual is Still Missing a Page

After analyzing 138 inverse femtobarns of data (which is like looking at 138 trillion proton collisions), the team found nothing.

• The Observation: The number of "four-tau" events they saw matched exactly what the Standard Model predicted. There were no extra events that could be blamed on the new Higgs bosons.
• The Exclusion: Because they didn't see the signal, they could draw a line in the sand. They said, "If these new particles exist, they cannot be this heavy, or they cannot have these specific interaction strengths."

The Verdict:
The paper concludes that this specific version of the "Type-X" theory cannot be the explanation for the muon mystery. The "allowed" area where this theory could have fixed the muon's magnetic moment has been completely ruled out by this search.

Summary in a Nutshell

1. The Mystery: Muons are spinning slightly differently than our physics manual predicts.
2. The Theory: Maybe there are extra Higgs bosons (Type-X model) helping them spin.
3. The Plan: Smash protons together to see if we can create a pair of these extra Higgs bosons via a virtual Z boson, which then decay into four tau particles.
4. The Outcome: We looked, but we didn't find them.
5. The Conclusion: This specific theory is dead. It cannot explain why the muon is acting up. The search for the real cause of the muon anomaly must continue elsewhere.

Technical Summary

Technical Summary: Search for Nonresonant Production of Additional Higgs Bosons in the Type-X 2HDM

Problem and Motivation
The combined measurement of the muon magnetic moment ($g-2$) currently exhibits a discrepancy of five standard deviations from the Standard Model (SM) prediction provided by the Muon $g-2$ Theory Initiative. While tensions exist between different theoretical calculations, this deviation remains a potential indicator of Beyond-the-Standard-Model (BSM) physics. The Type-X Two-Higgs-Doublet Model (2HDM), also known as the "lepton-specific" model, offers a potential explanation by introducing additional Higgs bosons that contribute loop corrections to the muon magnetic moment.

However, the parameter space required to resolve the muon $g-2$ anomaly in the Type-X 2HDM typically demands large values of $\tan\beta$ ($\gtrsim 90$ in the normal scenario and $\gtrsim 120$ in the inverted scenario). In this regime, couplings to quarks are suppressed, rendering traditional single Higgs boson production modes (gluon fusion and $b$-associated production) negligible. Consequently, existing LHC searches targeting "MSSM-like" models or single Higgs production lack sensitivity to this specific region. Furthermore, standard di-Higgs searches often rely on tagging a SM-like Higgs boson ($H_{125}$) or target final states without $\tau$ leptons, which are incompatible with the Type-X 2HDM where additional Higgs bosons decay dominantly to $\tau$ lepton pairs.

Methodology
This analysis presents a search for the nonresonant production of a pair of additional Higgs bosons ($\phi$ and $A$) originating from an off-shell $Z$ boson ($Z^* \to \phi A$), where both bosons decay exclusively to $\tau$ lepton pairs ($Z^* \to \phi A \to \tau\tau\tau\tau$). This production mode is advantageous because its cross-section is independent of $\tan\beta$, while the decay branching fractions to $\tau$ leptons are enhanced at high $\tan\beta$.

The search utilizes proton-proton collision data collected by the CMS detector at $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of $138 \text{ fb}^{-1}$ from 2016–2018. The analysis reconstructs six primary $\tau\tau\tau\tau$ final states ($\tau_h\tau_h\tau_h\tau_h$, $e\tau_h\tau_h\tau_h$, $\mu\tau_h\tau_h\tau_h$, $e\mu\tau_h\tau_h$, $\mu\mu\tau_h\tau_h$, and $ee\tau_h\tau_h$), accounting for approximately 87% of the total branching fraction, plus an additional channel for events where one $\tau_h$ candidate is lost due to reconstruction inefficiencies.

Key selection criteria include:

• Triggering: Events are selected based on single electron, single muon, or $\tau_h$ pair triggers.
• Background Suppression: Events with $b$-jets are vetoed to reduce top-quark pair ($t\bar{t}$) backgrounds. Channels with light leptons are categorized by charge (same-sign vs. opposite-sign) to separate signal from backgrounds like $Z/\gamma^* \to \ell\ell$ and $t\bar{t}$.
• Discriminating Variable: The total transverse mass ($m_T^{tot}$) is used as the primary discriminant, defined as the quadrature sum of the transverse masses of all pairs of $\tau$ decay objects and missing transverse momentum.
• Background Modeling: The dominant background from jets misidentified as hadronic $\tau$ leptons ($\text{jet} \to \tau_h$) is estimated using a machine learning-enhanced "Fake Factor" (FF) method derived from data. Other backgrounds (e.g., $ZZ$, $t\bar{t}$, dibosons) are modeled using Monte Carlo simulations normalized to theoretical cross-sections at NLO or NNLO precision.
• Statistical Analysis: A profiled extended binned likelihood fit is performed using the COMBINE tool, treating systematic uncertainties as nuisance parameters.

Key Contributions

• Novel Topology: This work addresses a critical gap in experimental coverage by targeting the unique nonresonant $Z^* \to \phi A \to 4\tau$ topology, which has not been previously targeted by multi-$\tau$ analyses.
• Model Independence of Production: By leveraging a production mode independent of $\tan\beta$, the analysis probes the high-$\tan\beta$ regime where the Type-X 2HDM explains the muon $g-2$ anomaly, a region inaccessible to single-Higgs searches.
• Comprehensive Channel Reconstruction: The analysis combines multiple decay channels and employs advanced machine learning techniques for background estimation to maximize sensitivity across a wide mass range.

Results
No significant deviation from the Standard Model background prediction was observed in the data. Upper limits at the 95% confidence level (CL) were set on the product of the production cross-section and branching fractions ($\sigma \times \mathcal{B}$).

• The observed limits range from $190 \text{ fb}$ (for $m_A = 40 \text{ GeV}, m_\phi = 60 \text{ GeV}$) to $0.4 \text{ fb}$ (for $m_A = 600 \text{ GeV}, m_\phi = 800 \text{ GeV}$).
• Exclusion contours were derived in the $m_A$-$\tan\beta$ plane for a fixed $m_\phi = 200 \text{ GeV}$ and in the $m_A$-$m_\phi$ plane.
• The analysis excludes a diagonal region in the $m_A$-$m_\phi$ plane with an approximate width of $100 \text{ GeV}$, extending from the lowest searched masses ($m_A=40 \text{ GeV}, m_\phi=60 \text{ GeV}$) up to $m_A \approx m_\phi \approx 360 \text{ GeV}$.

Significance and Claims
The paper claims that the combination of these new results with constraints from previous searches (specifically $H/A \to \tau\tau$ single Higgs searches) excludes a large portion of the Type-X 2HDM alignment scenario parameter space. Crucially, the authors state that the allowed regions for the normal and inverted scenarios that accommodate the current muon anomalous magnetic moment measurement (as detailed in Ref. [9]) are contained entirely within the observed exclusion contours ($\tan\beta > 15$). Consequently, this search rules out the Type-X 2HDM alignment scenario as an explanation for the muon anomalous magnetic moment within the tested mass ranges. The results demonstrate that the specific parameter space required to resolve the $g-2$ tension via this mechanism is incompatible with current LHC data.