Lepton Flavor Violating Higgs decays at the Compact Linear Collider

This paper investigates the sensitivity of the future Compact Linear Collider (CLIC) to lepton flavor violating Higgs decays ($h\rightarrow e\mu$, $h\rightarrow\tau\mu$, and $h\rightarrow e\tau$), projecting that it could establish 95% confidence level upper limits on their branching fractions between $10^{-4}$ and $10^{-5}$ using integrated luminosities of 4 ab$^{-1}$ at 1.4 TeV and 5 ab$^{-1}$ at 3 TeV.

The Gist

Imagine the universe as a giant, high-speed racetrack where tiny particles zoom around and crash into each other. In this race, there are strict rules about who can change into whom. For example, a "muon" (a heavy cousin of the electron) is generally not allowed to just turn into an "electron" or a "tau" (another heavy cousin). This rule is called Lepton Flavor Conservation.

However, scientists suspect there might be a "secret cheat code" in the laws of physics that allows these particles to swap identities, but only under very specific, rare conditions. This paper is a blueprint for a future race track called the Compact Linear Collider (CLIC) to see if they can catch these rare swaps in action.

Here is a simple breakdown of what the paper does:

1. The Goal: Catching a "Ghost" Swap

The main character in this story is the Higgs boson, a particle discovered a few years ago that gives other particles their mass. Usually, the Higgs is a shy particle that decays (breaks apart) into things that are very easy to predict.

But, the scientists in this paper are looking for a "ghost" event: Lepton Flavor Violating (LFV) decays. This is when the Higgs boson breaks apart into two different types of light particles (leptons) that shouldn't be able to pair up. They are looking for three specific "forbidden" pairings:

• An electron and a muon ($h \to e\mu$)
• A tau and a muon ($h \to \tau\mu$)
• A tau and an electron ($h \to \tau e$)

If they find even one of these, it would be like finding a red car driving on a blue-only highway. It would prove that our current rulebook (the Standard Model) is incomplete and that there is new, hidden physics at play.

2. The Race Track: The CLIC

To find these rare events, you need a very powerful microscope. The paper studies a future machine called CLIC. Think of CLIC as a super-powered slingshot that fires electrons and positrons (anti-electrons) at each other at nearly the speed of light.

• The Energy: They plan to run this at two different speeds: a "fast" mode (1.4 TeV) and a "super-fast" mode (3 TeV).
• The Detector: Surrounding the crash zone is a giant, high-tech camera called CLIC_ILD. It's like a 360-degree security system with layers of sensors. It tracks every particle that flies out, measuring their speed, direction, and energy with incredible precision.

3. The Challenge: Finding a Needle in a Haystack

The problem is that the "forbidden" decays are incredibly rare. Imagine trying to find a single specific grain of sand on a beach, while millions of other grains of sand are constantly being thrown at you by a hurricane.

• The Signal: The "needle" is the Higgs decaying into the forbidden pair.
• The Haystack: The "haystack" is the background noise—millions of other particle crashes that look almost the same but aren't the real thing.

The paper details how the scientists use computer simulations to figure out how to separate the needle from the haystack. They use a "filter" (called a Boosted Decision Tree, or BDT) which is like a smart AI referee. This AI looks at the shape of the crash, the angles of the particles, and their energy to decide: "Is this a fake background event, or is this the real forbidden decay?"

4. The Results: How Good Are the Filters?

The paper runs the numbers for two different scenarios:

• Scenario A (1.4 TeV): With 4 years of data collection (4 ab⁻¹), they expect to be able to say with 95% confidence that if these decays happen, they happen less than 1 in 10,000 times (for the electron-muon pair) or 1 in 10,000 to 1 in 100,000 times (for the tau pairs).
• Scenario B (3 TeV): With the machine running at full speed (3 TeV) and 5 years of data, the sensitivity gets even sharper. They could rule out these decays happening more than 1 in 100,000 times.

The Comparison:
The paper compares their future "super-microscope" to the current ones at the Large Hadron Collider (LHC). They claim that their future machine could be 12 to 33 times more sensitive than what we can do today. It's like upgrading from a pair of binoculars to a high-powered telescope; you can see much fainter, rarer events.

5. The Conclusion

The paper concludes that if the Compact Linear Collider is built and runs as planned, it will be an incredibly powerful tool for hunting these "forbidden" particle swaps.

• If they find nothing: They will have set very strict new rules, telling us that these swaps are even rarer than we thought.
• If they find something: It would be a massive discovery, proving that the universe has secret rules we haven't discovered yet.

Important Note: The paper is a "sensitivity study." This means they are calculating what could happen if the machine is built. They are not claiming they have found these particles yet, nor are they suggesting this will lead to new medicines or technologies right now. They are simply saying, "If we build this, here is how well we will be able to look for this specific mystery."

Technical Summary

Technical Summary: Lepton Flavor Violating Higgs decays at the Compact Linear Collider

Problem Statement
Lepton flavor violation (LFV) is strictly forbidden at the tree level in the Standard Model (SM) and is suppressed to negligible levels by tiny neutrino masses in loop-level processes. Consequently, the observation of a Higgs boson decaying into two leptons of different flavors ($h \to e\mu$, $h \to \tau\mu$, $h \to e\tau$) would constitute a definitive signal of physics beyond the Standard Model (BSM). While current Large Hadron Collider (LHC) experiments (ATLAS and CMS) have set limits on these branching ratios (BR) at the $10^{-3}$ level, indirect constraints from $\mu \to e\gamma$ searches suggest even tighter bounds for $h \to e\mu$. This study investigates the potential sensitivity of the future Compact Linear Collider (CLIC) to these rare decay modes, aiming to probe the LFV Higgs sector with significantly improved precision.

Methodology
The study utilizes a phenomenological approach based on full detector simulation of the CLIC_ILD detector concept, adapted from the International Linear Collider (ILC) design. The analysis focuses on the dominant Higgs production mechanism at CLIC, $e^+e^- \to h\nu\bar{\nu}$, at two center-of-mass energy stages: $\sqrt{s} = 1.4$ TeV (with an integrated luminosity of $4 \text{ ab}^{-1}$) and $\sqrt{s} = 3$ TeV (with $5 \text{ ab}^{-1}$).

• Simulation and Reconstruction: Signal and background processes were generated using WHIZARD 1.95, with fragmentation handled by PYTHIA 6.4 and tau decays by TAUOLA. Detector simulation and event reconstruction were performed using the CLIC_ILD model and the MARLIN software package, with Pandora PFA for particle flow reconstruction. Pile-up from $\gamma\gamma \to \text{hadrons}$ was included.
• Signal Channels: Three decay channels were analyzed:
  1. $h \to e\mu$: A clean channel with stable final-state particles.
  2. $h \to \tau\mu$ and $h \to e\tau$: Inclusive channels requiring the reconstruction of the $\tau$ lepton via its decay products using the TauFinder algorithm.
• Backgrounds: The primary backgrounds considered are $e^+e^- \to \ell\ell\nu\nu$ (where $\ell = e, \mu$) and $e^+e^- \to qq\nu\nu$. Processes with hard initial-state photons were neglected.
• Selection Strategy:
  • Pre-selection: Cuts were applied on kinematic variables such as invariant mass ($m_{\ell\ell'}$), polar angle differences ($|\Delta\theta|$), azimuthal differences ($|\Delta\phi|$), visible energy ($E_{vis}$), and the helicity angle ($\cos\theta^*$). Specific thresholds were optimized for each energy stage to suppress backgrounds while retaining signal efficiency.
  • Multivariate Analysis: A Boosted Decision Tree (BDT) classifier was employed using a subset of kinematic variables (e.g., $m_{\ell\ell'}$, $\beta_{\ell\ell'}$, $\theta_{miss}$) to further separate signal from background. Correlation matrices were checked to ensure variable independence.
  • Statistical Interpretation: Expected 95% Confidence Level (CL) upper limits on the branching fractions were derived using the $CL_s$ method, assuming no signal observation. Systematic uncertainties on background normalization (1% and 2%) were also evaluated.

Key Contributions and Results
The paper provides the first detailed sensitivity study for LFV Higgs decays at CLIC using full detector simulation. The key results are as follows:

• $h \to e\mu$ Channel:

  • At 1.4 TeV ($4 \text{ ab}^{-1}$), the expected 95% CL upper limit is $\text{BR}(h \to e\mu) < 3.86 \times 10^{-5}$.
  • At 3 TeV ($5 \text{ ab}^{-1}$), the limit improves to $\text{BR}(h \to e\mu) < 1.44 \times 10^{-5}$.
  • The analysis indicates a sensitivity improvement of a factor of 1.5 over current ATLAS results at 1.4 TeV and a factor of 4.5 at 3 TeV.

• $h \to \tau\mu$ Channel:

  • At 1.4 TeV, the expected limit is $\text{BR}(h \to \tau\mu) < 1.50 \times 10^{-4}$.
  • At 3 TeV, the expected limit is $\text{BR}(h \to \tau\mu) < 6.94 \times 10^{-5}$.
  • This represents a sensitivity improvement of approximately 12 times at 1.4 TeV and 33 times at 3 TeV compared to current LHC limits.

• $h \to e\tau$ Channel:

  • At 1.4 TeV, the expected limit is $\text{BR}(h \to e\tau) < 1.69 \times 10^{-4}$.
  • At 3 TeV, the expected limit is $\text{BR}(h \to e\tau) < 1.16 \times 10^{-4}$.
  • Sensitivity improvements are estimated at a factor of 12 at 1.4 TeV and 17 at 3 TeV relative to current LHC constraints.

The study also quantified the impact of background normalization uncertainties, showing that even with a 2% uncertainty, the limits remain robustly within the $10^{-4}$ to $10^{-5}$ range.

Significance and Claims
The authors claim that CLIC offers a unique and powerful probe for LFV Higgs decays, capable of reaching sensitivities in the $10^{-4}$ to $10^{-5}$ range, which are significantly more restrictive than current LHC constraints. The study highlights that these projections are based on phenomenological simulations and do not yet incorporate the full range of detector-related systematic uncertainties present in complete experimental analyses. Therefore, the authors explicitly state that the comparison with LHC results should be regarded as "indicative rather than directly comparable."

However, the results underscore the significant potential of the CLIC facility to explore BSM physics in the Higgs sector. The authors note that these sensitivities could be further enhanced by the inclusion of polarized electron beams, a feature of the latest CLIC baseline scenarios. The work establishes a baseline for future experimental efforts to search for new physics through lepton flavor violation in Higgs decays.