Searching for Lepton Flavor Violating decays of the Higgs Boson into $\mu\tau$, $e\tau$, and $e\mu$ final states at FCC-ee

This paper investigates the projected sensitivity of the FCC-ee at $\sqrt{s}=240$ GeV with 5 ab$^{-1}$ luminosity to Lepton Flavor Violating Higgs decays into $\mu\tau$, $e\tau$, and $e\mu$ final states, establishing 95% CL upper limits on their branching ratios and demonstrating that FCC-ee constraints surpass low-energy searches for the $e-\tau$ and $\mu-\tau$ channels, while remaining less stringent for the $e-\mu$ channel.

The Gist

Imagine the universe is built like a giant, complex Lego set. For decades, physicists have been following the instruction manual known as the Standard Model, which explains how the tiny pieces (particles) snap together. In 2012, they found the final, crucial piece: the Higgs boson. It's like the "glue" that gives other particles their mass.

However, the manual has some missing pages. It doesn't explain things like why neutrinos have mass, what dark matter is, or why the universe is made of matter instead of antimatter. This suggests there are "secret instructions" (New Physics) hidden somewhere.

The Mystery: Lepton Flavor Violation

In the Standard Model, particles called leptons (electrons, muons, and taus) are like distinct families. They are very polite; they never change their identity or swap places with their cousins. An electron stays an electron; a muon stays a muon.

This paper investigates a "rude" behavior called Lepton Flavor Violation (LFV). It asks: What if the Higgs boson is a mischievous matchmaker that forces these families to swap identities? Specifically, could a Higgs boson decay into a muon and a tau, or an electron and a tau, or an electron and a muon?

If we see this happen, it's a smoking gun. It proves the Standard Model is incomplete and that "New Physics" exists.

The Detective Work: The FCC-ee

To catch this mischievous Higgs, the authors propose using a future machine called the FCC-ee (Future Circular Collider). Think of this as a super-powered, ultra-clean racetrack for particles.

• The Environment: Unlike the Large Hadron Collider (LHC), which is like a chaotic, dusty demolition derby, the FCC-ee is a pristine, high-speed track. It smashes electrons and positrons together at a specific energy (240 GeV) to create Higgs bosons.
• The Strategy: The team simulates what happens when these collisions occur. They look for a specific "signature": a Higgs boson that instantly splits into four light particles (leptons).
  • Two of these leptons come from a "Z boson" (a partner particle).
  • The other two come from the Higgs itself.
  • If the Higgs is being mischievous, those two will be a mismatched pair (like a muon and a tau).

The Challenge: Finding a Needle in a Haystack

The problem is that the "haystack" (background noise) is huge. Most of the time, the particles behave politely and don't swap families. The team had to design a filter to ignore the polite behavior and only keep the rude, mismatched events.

They used two main "nets" to catch the signal:

1. The Z-Mass Net: They look for events where the two "partner" leptons have a combined weight exactly matching the Z boson (about 91 GeV). This catches the most common way Higgs bosons are made.
2. The Low-Mass Net: They also look for events where the partner leptons are lighter. This catches a different production method where the particles scatter off each other, which becomes important for heavier Higgs bosons.

For the tricky cases involving tau particles (which are heavy and decay into invisible neutrinos, like a ghost), they used a special math trick called "collinear mass reconstruction." Imagine trying to guess the speed of a car by looking at its tire tracks and the direction of the wind; this method helps them reconstruct the missing pieces of the puzzle.

The Results: How Good is the Net?

The team ran a massive simulation with the equivalent of 5 years of data (5 ab⁻¹). Here is what they found regarding the "rude" Higgs decays:

• The Limits: They calculated the strictest possible "speed limits" for how often these swaps could happen. If the Higgs did swap flavors, it would have to be incredibly rare.

  • For Muon-Tau swaps: Less than 1 in 1,700 Higgs bosons.
  • For Electron-Tau swaps: Less than 1 in 1,600 Higgs bosons.
  • For Electron-Muon swaps: Less than 1 in 13,000 Higgs bosons.

• The Comparison: They compared their "future detector" results with current "low-energy" experiments (which look for similar swaps in other particle decays).

  • The Win: For the Muon-Tau and Electron-Tau channels, the FCC-ee is a much better detective than current low-energy searches. It can see much further.
  • The Loss: For the Electron-Muon channel, current low-energy searches are actually better. The FCC-ee can't beat them there yet.

The Theory: The "Type-III 2HDM"

To make sense of their numbers, the authors plugged them into a specific theory called the Type-III Two-Higgs-Doublet Model. Think of this theory as a specific set of "secret instructions" that allows the Higgs to be mischievous.

• Their results show that if this theory is true, the FCC-ee would be able to rule out huge chunks of the "allowed" space for these secret instructions, especially for the Tau-related swaps.

The Bottom Line

This paper is a "proof of concept" for a future experiment. It says: "If we build the FCC-ee and run it for a few years, we will be able to hunt for these specific, forbidden particle swaps with incredible precision. We might not find them (which would be a discovery in itself, proving the Standard Model is rigid), but if we do, we will have found the first crack in the foundation of modern physics."

The authors emphasize that because the machine doesn't exist yet, they had to make some educated guesses about how well the detectors would work, but the potential for discovery is very high.

Technical Summary

Technical Summary: Searching for Lepton Flavor Violating Decays of the Higgs Boson at FCC-ee

Problem Statement
The discovery of the 125 GeV Higgs boson ($h$) completed the Standard Model (SM), yet phenomena such as neutrino masses, dark matter, and baryon-antibaryon asymmetry suggest the existence of physics beyond the SM (BSM). Lepton Flavor Violating (LFV) decays of the Higgs boson ($h \to e\mu, e\tau, \mu\tau$) are strictly forbidden in the SM but are predicted in various BSM frameworks, including the Type-III Two-Higgs-Doublet Model (2HDM), extra-dimension models, and supersymmetry. While the Large Hadron Collider (LHC) has placed constraints on these decays, the Future Circular Collider in $e^+e^-$ mode (FCC-ee) offers a cleaner environment to probe these rare processes with higher precision, particularly for additional Higgs bosons ($H$) with masses in the 110–200 GeV range.

Methodology
The authors investigate the projected sensitivity of the FCC-ee operating at a center-of-mass energy of $\sqrt{s} = 240$ GeV with an integrated luminosity of 5 ab$^{-1}$. The analysis focuses on the inclusive process $e^+e^- \to \ell^+\ell^-H$, where the final state consists of four light leptons ($\ell\ell\ell\ell'$), originating from the associated production of a Higgs boson ($h$ or $H$) and a lepton pair.

• Production Modes: The study considers both Higgs-strahlung ($ZH$) and Vector Boson Fusion (VBF) production channels, including their interference effects. The VBF contribution becomes increasingly significant for Higgs masses $m_H \gtrsim 150$ GeV.
• Signal and Background Simulation: Signal and background processes are generated using MadGraph5 aMC@NLO at leading order (LO). Parton showering, $\tau$ decays, and detector response are simulated using Pythia8 and Delphes (IDEA detector card), respectively. Initial State Radiation (ISR) and beamstrahlung effects are included.
• Event Reconstruction:
  • For channels involving $\tau$ leptons ($H \to \mu\tau e$ and $H \to e\tau\mu$), the collinear mass approximation is employed to reconstruct the Higgs mass, as neutrinos from $\tau$ decays carry away momentum.
  • For the $H \to \mu e$ channel, the invariant mass of the two prompt leptons is used directly.
• Event Selection: Events are categorized into two orthogonal regions based on the invariant mass of the associated lepton pair ($M(\ell\ell_A)$):
  • Z-mass category: $M(\ell\ell_A) \in [81, 101]$ GeV (targeting on-shell $Z$ bosons).
  • Low-mass category: $M(\ell\ell_A) \in [21, 81]$ GeV (targeting off-shell $Z$ bosons and VBF contributions).
    Specific cuts on transverse momentum ($p_T$), missing transverse energy ($E_T^{miss}$), and azimuthal angle differences ($\Delta\phi$) are applied to suppress backgrounds, particularly $ZZ$, $Zh$, triboson ($ZWW$), and Vector Boson Scattering (VBS) processes.
• Statistical Analysis: Expected 95% Confidence Level (CL) upper limits on branching ratios are calculated using the Higgs Combine tool, incorporating a 2% luminosity uncertainty and a conservative 10% systematic uncertainty on backgrounds.

Key Contributions and Results
The paper provides projected upper limits on the branching ratios for LFV Higgs decays across the mass range $110 \le m_H \le 200$ GeV.

• Sensitivity at $m_H = 125$ GeV: For the 125 GeV Higgs boson, the study finds the following 95% CL upper limits:
  • $B(h \to \mu\tau) < 5.92 \times 10^{-4}$
  • $B(h \to e\tau) < 6.27 \times 10^{-4}$
  • $B(h \to e\mu) < 7.48 \times 10^{-5}$
    The $H \to \mu e$ channel demonstrates superior sensitivity (an order of magnitude better) due to the absence of neutrinos and lower background levels.
• Mass Dependence: The sensitivity degrades as $m_H$ increases due to the falling production cross-section. For masses above 150 GeV, the VBF channel becomes the dominant production mode. The analysis notes that for $m_H \ge 190$ GeV, the integrated luminosity is insufficient to constrain the branching ratios meaningfully, leading to unphysical limits in some cases.
• BSM Interpretation (Type-III 2HDM): The results are interpreted within the Type-III 2HDM framework. The study derives constraints on the mixing angle $\sin \alpha$ and the LFV Yukawa couplings ($Y_{\ell\ell'}$).
  • Comparison with Low-Energy Searches: The FCC-ee sensitivity for the $e-\tau$ and $\mu-\tau$ channels is found to be superior to current and projected constraints from low-energy searches for $\ell \to \ell'\gamma$ decays. Conversely, for the $e-\mu$ channel, low-energy searches currently offer stronger constraints.

Significance
The paper claims that the FCC-ee, with its clean multi-lepton final states and high luminosity, offers a unique opportunity to probe LFV Higgs decays that are complementary to LHC searches. Specifically, the FCC-ee can provide tighter constraints on the LFV couplings in the $\tau$-involving sectors than low-energy experiments. The study highlights that while the $e-\mu$ channel is currently better constrained by low-energy data, the FCC-ee provides a critical test for the $\tau$-involving channels and extends the search to heavier Higgs bosons ($H$) up to 200 GeV, a mass range where LHC sensitivity is limited by the $Z$-boson off-shell suppression in Higgs-strahlung. The authors conclude that these projections provide new insights into BSM physics, though they acknowledge that systematic uncertainties for the future collider require further study.