Lepton flavor violating top quark FCNC at the $\mu$TRISTAN

This paper investigates charged lepton flavor violating top quark flavor-changing neutral current interactions at the proposed $\mu$TRISTAN collider, demonstrating that an integrated luminosity of $100~\text{fb}^{-1}$ could improve current LHC constraints on scalar, vector, and tensor four-fermion contact interactions by approximately an order of magnitude.

The Gist

Imagine the universe as a giant, high-stakes game of "Musical Chairs" played by tiny particles. In the Standard Model (the rulebook of physics), there are strict rules about who can sit in which chair. For example, a "muon" (a heavy cousin of the electron) is supposed to stay a muon, and a "top quark" (the heaviest particle) is supposed to stay a top quark. They rarely, if ever, swap places or change their identities.

However, physicists suspect that the rulebook might have hidden pages—clues to "New Physics" that explain why the universe is the way it is. This paper is a proposal for a new, ultra-precise experiment to catch these particles breaking the rules.

Here is the breakdown of the paper, translated into everyday language:

1. The Goal: Catching a "Double Cheat"

In this game, there are two types of cheating the authors are looking for:

• Lepton Flavor Violation (LFV): A muon turning into an electron (or vice versa). This is like a player suddenly changing their team jersey mid-game.
• Flavor-Changing Neutral Currents (FCNC): A top quark turning into a lighter quark (like an up or charm quark) without changing its electric charge. This is like a heavyweight champion suddenly shrinking into a lightweight without anyone noticing.

The authors want to see if these two cheats happen at the same time. They are looking for a process where a muon and an electron collide, and out pops a top quark and a lighter quark. It's a "double violation" that the current rulebook says shouldn't happen, but if it does, it proves the rulebook is incomplete.

2. The Venue: The µTRISTAN Collider

To catch these cheats, you need a very specific arena. The authors propose using a machine called µTRISTAN.

• The Setup: Imagine a racetrack where one car is a super-fast, heavy truck (the muon beam) and the other is a nimble, fast sports car (the electron beam). They are designed to crash into each other head-on.
• The Energy: They will collide at a specific energy (346 GeV), which is the "Goldilocks" zone—high enough to create heavy particles like the top quark, but low enough to keep the background noise manageable.
• The Advantage: Unlike the LHC (the current giant collider in Europe), which smashes protons together (like smashing two bags of marbles), this machine smashes clean, single particles (muons and electrons). It's like using a scalpel instead of a sledgehammer. This makes it much easier to spot the rare, specific "cheating" events.

3. The Strategy: The "Polarized Flashlight"

One of the paper's coolest ideas is using beam polarization.

• The Analogy: Imagine trying to hear a whisper in a noisy room. If you wear noise-canceling headphones that only let in sounds from a specific direction, you can hear the whisper clearly.
• The Physics: The muon and electron beams can be "polarized," meaning their internal spins are aligned in a specific direction (like a flashlight beam pointing only one way). By tuning these "flashlights," the physicists can:
  1. Drown out the noise: Reduce the background events that look like cheating but aren't.
  2. Highlight the culprit: Different types of "cheating" (Scalar, Vector, or Tensor interactions) react differently to the direction of the spin. By flipping the spin, they can tell exactly which type of new physics is causing the violation.

4. The Detective Work: The "Cut-Based" Analysis

Once the particles collide, the machine produces a chaotic mess of debris. The authors propose a set of rules (cuts) to filter the good stuff from the junk:

• The Clues: They look for specific debris patterns: one heavy "b-jet" (a jet of particles containing a bottom quark), one light jet, and a missing piece of energy (a neutrino).
• The Filter: They calculate the "invariant mass" (essentially the total weight of the debris). If the debris weighs exactly what a top quark should weigh, they keep it. If it looks like a common background event, they throw it away.
• The Result: Even with a modest amount of data, they predict they can spot these events much more clearly than the LHC can.

5. The Big Payoff: Why It Matters

The authors ran the numbers and found something exciting:

• Better than the LHC: Even with just a few years of data, this machine could set limits on these "cheating" interactions that are 10 times better than what the LHC can do today.
• The Future: If they run it longer (collecting 1,000 times more data), they could improve that sensitivity by another factor of 2 or 3.
• The Implication: If they find nothing, they have proven that the universe is even stricter than we thought. If they do find something, it's a smoking gun for new physics—perhaps revealing new particles like "Leptoquarks" (particles that are half-lepton, half-quark) or new forces (like a heavy Z' boson).

Summary

Think of this paper as a proposal to build a high-tech, polarized security camera at a specific racetrack. Instead of just watching the race, they are looking for a specific, impossible maneuver where a muon and an electron swap identities and create a top quark. By using the "spin" of the particles as a filter, they believe they can catch this rare event with a clarity that current giant colliders simply cannot match. It's a promise of a cleaner, sharper look into the deepest secrets of the universe.

Technical Summary

1. Problem Statement

The paper addresses the search for Charged Lepton Flavor Violation (cLFV) in conjunction with Top Quark Flavor-Changing Neutral Currents (FCNC).

• Context: In the Standard Model (SM), cLFV is strictly forbidden (assuming massless neutrinos), and top quark FCNCs are highly suppressed. Observing either would be a clear signal of New Physics (BSM).
• Gap: While individual searches for cLFV (e.g., $\mu \to e\gamma$) and top FCNCs exist, scenarios where both occur simultaneously (e.g., $t \to e\mu q$) are less constrained. Current LHC bounds on these combined processes are limited by background contamination and the complexity of hadronic collisions.
• Objective: To investigate the sensitivity of the proposed $\mu$TRISTAN collider (an asymmetric $\mu^+e^-$ collider) to the process $\mu^+ e^- \to tq$ (where $q=u, c$), mediated by effective four-fermion operators.

2. Methodology

A. Theoretical Framework

• Effective Field Theory (EFT): The study utilizes the Standard Model Effective Field Theory (SMEFT) framework. The authors focus on dimension-6 operators that generate the process $\mu^+ e^- \to tq$.
• Operator Classes: Three classes of simplified four-fermion contact interactions are analyzed:
  1. Scalar ($O_S$): Derived from $O^{(1)}_{LeQu}$.
  2. Vector ($O_V$): A sum of $O^{(1)}_{LQ}, O^{(3)}_{LQ}, O_{eu}, O_{Lu}, O_{Qe}$.
  3. Tensor ($O_T$): Derived from $O^{(3)}_{LeQu}$.
• Benchmark Points: Specific Wilson coefficients ($C/\Lambda^2$) are set to $0.01 \text{ TeV}^{-2}$ for signal generation, respecting current LHC exclusion limits.

B. Collider Setup and Simulation

• Facility: $\mu$TRISTAN, operating at $\sqrt{s} = 346$ GeV ($\mu^+$ at 1 TeV, $e^-$ at 30 GeV).
• Process: $\mu^+ e^- \to tq$, followed by the leptonic decay of the top quark ($t \to b \ell \nu$).
• Final State: Two jets (one $b$-tagged, one light jet), one charged lepton ($\ell = e, \mu$), and Missing Transverse Energy (MET).
• Simulation Chain:
  • Event Generation: FeynRules $\to$ UFO $\to$ MadGraph5_aMC@NLO.
  • Showering/Hadronization: Pythia8.
  • Detector Simulation: Delphes3 (using the ILCgen card as a proxy for $\mu$TRISTAN detector performance).
• Backgrounds: The dominant background is the SM process $\mu^+ e^- \to \ell \nu jj$ (via $W$ boson production).

C. Analysis Strategy

1. Cut-Based Analysis:

   • Selection: Exactly 1 lepton, 1 $b$-jet, 1 light jet.
   • Kinematic Cuts:
     • $M_{bj} > 100$ GeV (suppresses $W$-boson background).
     • $M_{\ell bj} > 200$ GeV (exploits the harder kinematic spectrum of the contact interaction signal).
   • Polarization: The study explicitly models beam polarization ($P_{\mu^+} \approx \pm 0.25$, $P_{e^-} \approx \pm 0.70$) to exploit chiral structures.
     • $P_{++}$ and $P_{--}$ enhance Scalar/Tensor operators.
     • $P_{+-}$ and $P_{-+}$ enhance Vector operators.

2. Statistical Analysis:

   • Likelihood Method: A binned likelihood analysis is performed using the azimuthal angle separation between jets ($\Delta \phi_{bj}$) as the discriminant observable.
   • Metric: Projected 95% Confidence Level (C.L.) limits on Wilson coefficients ($C/\Lambda^2$) and corresponding branching ratios for $t \to e\mu q$.

3. Key Contributions

• First Comprehensive Study at $\mu$TRISTAN: This is a dedicated phenomenological study of cLFV top FCNCs at the proposed $\mu$TRISTAN facility, leveraging its unique asymmetric $\mu^+e^-$ collision environment.
• Polarization as a Diagnostic Tool: The paper demonstrates how beam polarization can not only suppress backgrounds but also disentangle operator chiral structures. For instance, $P_{++}$ suppresses vector contributions while enhancing scalar/tensor ones, allowing for the identification of the underlying BSM physics.
• Superior Sensitivity: The study shows that the clean environment of a lepton collider, combined with optimized kinematic cuts and polarization, offers significantly better sensitivity than current hadron collider (LHC) limits.
• Mapping to Branching Ratios: The constraints on EFT coefficients are translated into projected limits on the rare top decay branching ratio $B(t \to e\mu q)$, providing a direct link to experimental observables.

4. Results

• Sensitivity to Wilson Coefficients:

  • For an integrated luminosity of 100 fb$^{-1}$, $\mu$TRISTAN improves upon current LHC bounds on the effective couplings by approximately one order of magnitude.
  • For 1 ab$^{-1}$, the sensitivity improves by an additional factor of 2–3.
  • Example (Scalar Operator $O_S^{e\mu tu}$):
    • LHC Limit: $0.24 \text{ TeV}^{-2}$.
    • $\mu$TRISTAN (100 fb$^{-1}$, unpolarized): $\sim 0.023 \text{ TeV}^{-2}$.
    • $\mu$TRISTAN (1 ab$^{-1}$, optimized polarization): $\sim 0.011 \text{ TeV}^{-2}$.

• Branching Ratio Limits:

  • The projected limits on $B(t \to e\mu q)$ reach the order of $10^{-10}$ for 1 ab$^{-1}$, representing an improvement of 2–3 orders of magnitude over current LHC limits ($\sim 10^{-7}$ to $10^{-8}$).
  • Tensor operators are generally the most tightly constrained due to their kinematic enhancement.

• Polarization Impact:

  • Polarized beams significantly reduce the required luminosity to achieve a given sensitivity.
  • Specific configurations (e.g., $P_{++}$ for scalars/tensors, $P_{+-}$ for vectors) allow for the isolation of specific operator contributions, which is difficult in unpolarized or hadronic environments.

5. Significance

• Probing New Physics: The results highlight $\mu$TRISTAN as a premier facility for exploring the intersection of the lepton and quark sectors. It can probe BSM scenarios such as Leptoquarks, $Z'$ bosons with flavor-dependent couplings, and Extended Higgs sectors that are difficult to constrain via low-energy experiments or the LHC alone.
• Complementarity: The study establishes that lepton colliders offer a "cleaner" environment for flavor physics, free from the high QCD backgrounds that plague hadron colliders, making them ideal for precision measurements of rare processes.
• Future Physics Reach: The projected sensitivity suggests that $\mu$TRISTAN could discover or severely constrain charged LFV top FCNCs well before the next generation of high-energy hadron colliders, potentially uncovering the flavor structure of new physics at the TeV scale.

In conclusion, the paper provides a robust case for the $\mu$TRISTAN collider's capability to perform high-precision searches for charged lepton flavor violation in top quark interactions, offering sensitivity far beyond current experimental limits through the strategic use of beam polarization and kinematic analysis.