Novel Signatures of Heavy Neutral Lepton at Muon Collider

This paper investigates novel same-sign multi-lepton signatures ($4\mu^\pm+4J$ and $3\mu^\pm\mu^\mp+2J$) arising from heavy neutral lepton production in the $Z'H$ channel at 3 TeV and 10 TeV muon colliders within gauged extension models.

The Gist

Imagine the universe as a giant, complex machine. For decades, scientists have had a "User Manual" called the Standard Model that explains how most of the machine works. But there's a glitch: the manual says tiny particles called neutrinos should have no weight, yet we know they have a tiny bit of mass. To fix this, physicists propose a hidden "upgrade" to the machine involving heavy, invisible particles called Heavy Neutral Leptons (N).

This paper is a proposal for how to find these hidden particles using a future super-powerful machine called a Muon Collider. Think of the Muon Collider as a high-speed particle racetrack where we smash muons (a cousin of the electron) together at incredible speeds to see what new parts pop out.

Here is the story of their discovery plan, explained simply:

1. The Setup: A New "Factory"

The authors suggest a specific upgrade to the machine called the $U(1)_{L_\mu - L_\tau}$ model.

• The Problem: In the old model, finding these heavy particles is like trying to find a needle in a haystack because they are so shy they barely interact with anything.
• The Solution: This new model adds two new "machinery parts" that act like a factory:
  1. A new force-carrier called $Z'$ (a heavy cousin of the Z boson).
  2. A new heavy particle called $H$ (a heavy cousin of the Higgs boson).
• The Process: When we smash muons together, we can create a pair of these new parts ($Z'$ and $H$) in a process called "Heavy Higgs-strahlung." It's like hitting two billiard balls together and suddenly producing two brand-new, heavier balls.

2. The Cascade: The "Domino Effect"

Once we create these heavy parts ($Z'$ and $H$), they don't stay around for long. They immediately break apart (decay) into other things, creating a chain reaction:

• The heavy parts break down into Heavy Neutral Leptons (N).
• These heavy leptons then break down further into muons (the particles we can detect) and jets (sprays of particles from broken-down W bosons).

The paper focuses on two specific "domino patterns" that would be very loud and clear in our detectors:

Pattern A: The "Four-Muon Fireworks" (Same-Sign Tetralepton)

• The Scenario: The factory produces four heavy leptons, which all decay into muons.
• The Signature: We see four muons all with the same electric charge (like four positive or four negative magnets) plus four sprays of particles (jets).
• Why it's special: In the normal universe, getting four muons with the same charge is incredibly rare. It's like flipping four coins and getting "Heads" every single time by pure luck. If we see this, it's a smoking gun that new physics is happening.
• The Catch: This pattern is very rare, so we need a lot of data to see it.

Pattern B: The "Three-Muon Signal" (Same-Sign Trilepton)

• The Scenario: One of the new parts ($Z'$) breaks directly into two muons, while the other part ($H$) breaks into two heavy leptons that turn into two more muons.
• The Signature: We see three muons with the same charge and one with the opposite charge, plus two sprays of particles.
• Why it's better: This happens much more often than the four-muon pattern. It's like flipping three coins and getting "Heads" twice. Because it happens more frequently, the authors say this is the best way to discover these new particles.

3. The Race Track: 3 TeV vs. 10 TeV

The paper compares two versions of the Muon Collider:

• The 3 TeV Collider: A slightly smaller track. The authors found this is actually better for finding lighter versions of these new particles. It's like a sprinter who is great at short distances.
• The 10 TeV Collider: A massive, high-speed track. This is needed to find the very heavy versions of the particles. It's like a marathon runner who can go further but needs more energy.

4. The Results: What Can We Find?

The authors ran simulations (computer models) to see if these signals would show up.

• The Good News: Both signals have very little "background noise." In a crowded room, it's hard to hear a whisper, but if the room is empty, even a whisper is loud. These signals are so unique that the background noise is almost zero.
• The Discovery:
  • If the new particles exist, the 3 TeV collider could find them if they are relatively light (around the size of the Higgs boson).
  • The 10 TeV collider could find them even if they are much heavier (up to several times the mass of the Higgs).
  • The "Three-Muon Signal" (Pattern B) is the most promising because it happens often enough to be seen with a high degree of certainty.

Summary Analogy

Imagine you are trying to find a rare, invisible animal in a forest.

• The Standard Model says the animal doesn't exist.
• This Paper says: "If we build a special trap (the Muon Collider) and use a specific bait (the $Z'$ and $H$ factory), the animal will get caught and leave a very specific footprint."
• The Footprints: Either a set of four identical tracks (rare but unique) or a set of three identical tracks plus one different one (more common and easier to spot).
• The Conclusion: If we build the 3 TeV or 10 TeV collider, we have a very high chance of catching this animal and proving that our "User Manual" for the universe needs a new chapter.

Important Note: The paper strictly discusses the theoretical possibility of finding these particles at a future collider. It does not claim these particles exist yet, nor does it discuss any medical or practical applications of this discovery. It is purely about how to look for them in the physics lab.

Technical Summary

Technical Summary: Novel Signatures of Heavy Neutral Lepton at Muon Collider

Problem Statement
The observation of tiny neutrino masses necessitates physics beyond the Standard Model (SM), often addressed via the seesaw mechanism by introducing heavy neutral leptons (HNLs), denoted as $N$. In the canonical seesaw scenario, the production of HNLs at colliders is governed by the mixing parameter $|V_{\ell N}|^2$, which is heavily suppressed ($|V_{\ell N}|^2 \simeq m_\nu/m_N$), rendering direct detection at current facilities like the LHC extremely difficult.

While gauge extensions of the seesaw mechanism (e.g., Left-Right Symmetric models or $U(1)_{B-L}$) allow for HNL production independent of this mixing, they are often tightly constrained by LHC searches due to direct couplings to quarks. An alternative is the leptophilic $U(1)_{L_\mu-L_\tau}$ symmetry, where the new gauge boson $Z'$ couples only to muon and tau flavors. Current LHC constraints on this model are weak ($m_{Z'} < 81$ GeV), but future multi-TeV muon colliders offer a promising environment to probe this symmetry and the associated heavy particles ($Z'$, heavy Higgs $H$, and HNLs $N$) without the suppression of the mixing parameter.

Methodology
The authors investigate the heavy Higgs-strahlung process $\mu^+\mu^- \to Z'H$ at future muon colliders with center-of-mass energies of 3 TeV and 10 TeV. The study is based on a $U(1)_{L_\mu-L_\tau}$ extended type-I seesaw model containing three HNLs ($N_e, N_\mu, N_\tau$), a new gauge boson $Z'$, and a heavy Higgs boson $H$.

1. Model Setup: The authors assume a simplified scenario where the Higgs mixing angle $\sin \alpha = 0$ and focus on the muon-flavored HNL ($V_{\mu N} \neq 0$). They analyze the decay properties of $Z'$ and $H$, noting that $Z'$ decays dominantly to $\mu^+\mu^-$ and $H$ decays to $NN$ (or $Z'Z'$ if kinematically allowed).
2. Signal Processes: Two primary lepton number violating (LNV) signatures are investigated:
   • Same-sign tetralepton: $\mu^+\mu^- \to Z'H \to NN + NN \to 4\mu^\pm + 4J$ (where $J$ are fat-jets from hadronic $W$ decays).
   • Same-sign trilepton: $\mu^+\mu^- \to Z'H \to \mu^+\mu^- + NN \to 3\mu^\pm\mu^\mp + 2J$.
3. Simulation and Analysis:
   • The model is implemented using FeynRules.
   • Signal events are generated at leading order using MadGraph5_aMC@NLO.
   • Parton showering and hadronization are performed with Pythia8.
   • Detector simulation is conducted using Delphes3 with a specific muon collider card.
   • Fat-jets are reconstructed using the Valencia algorithm with $R=1.2$.
   • Selection cuts include transverse momentum ($p_T > 20$ GeV for muons, $p_T > 50$ GeV for jets) and invariant mass windows for fat-jets ($50 < m_J < 110$ GeV).
   • Backgrounds are estimated to be negligible (assumed $N_B = 1$ for conservative significance calculation).
   • Mass reconstruction is performed using $\chi^2$ minimization on invariant masses of muon-jet pairs ($m_{\mu J}$) and reconstructed resonances.

Key Contributions and Results

• Production Cross Sections: The cross section for $\mu^+\mu^- \to Z'H$ peaks near the threshold $\sqrt{s} \sim m_{Z'} + m_H$ and decreases as $\sim 1/s$ at high energies. Consequently, the 3 TeV collider is found to be more sensitive to TeV-scale resonances than the 10 TeV collider for masses below the TeV scale, provided the luminosity is sufficient.
• Same-Sign Tetralepton Signature ($4\mu^\pm + 4J$):
  • This signature violates lepton number by four units.
  • It is background-free.
  • At 3 TeV, for $m_N = 200-400$ GeV (with $m_{Z'}=m_H=3m_N$ and $g'=0.6$), the significance reaches $12.6\text{--}18.6$ with $1 \text{ ab}^{-1}$ luminosity.
  • At 10 TeV, for $m_N = 500-1500$ GeV, the significance reaches $10.5\text{--}15.8$ with $10 \text{ ab}^{-1}$.
  • The 5$\sigma$ discovery region covers $g' \gtrsim 0.38$ for electroweak-scale HNLs at 3 TeV.
• Same-Sign Trilepton Signature ($3\mu^\pm\mu^\mp + 2J$):
  • This signature is found to be more promising than the tetralepton channel due to a significantly larger cross section (approximately two orders of magnitude larger for certain benchmarks) and higher detection efficiency from the direct $Z' \to \mu^+\mu^-$ decay.
  • Backgrounds remain negligible ($\sim 10^{-5}$ fb).
  • At 3 TeV, the significance exceeds 149 for $m_N = 200$ GeV with $1 \text{ ab}^{-1}$. Discovery is possible with less than $5 \text{ fb}^{-1}$.
  • At 10 TeV, the significance exceeds 100 for $m_N = 500-1500$ GeV with $10 \text{ ab}^{-1}$.
  • The 5$\sigma$ discovery region extends to $g' \gtrsim 0.14$ at 3 TeV and $g' \gtrsim 0.15$ at 10 TeV.
  • Crucially, this signature can probe the off-shell decay region where $m_H < 2m_N$ via the three-body decay $H \to N^*N$, a region inaccessible to the tetralepton signature.
• Mass Reconstruction: The authors demonstrate that the masses of $N$, $Z'$, and $H$ can be reconstructed. For $H$, the invariant mass of two HNLs ($m_{NN}$) provides a more precise reconstruction than the recoil mass method ($m_{rec}$) at TeV scales due to detector energy resolution effects.

Significance and Claims
The paper claims that the future muon collider is a powerful tool for probing the $U(1)_{L_\mu-L_\tau}$ gauged seesaw model. The authors emphasize that:

1. Novelty: The proposed signatures ($4\mu^\pm + 4J$ and $3\mu^\pm\mu^\mp + 2J$) offer clean, background-free channels to detect HNLs without relying on the suppressed mixing parameter $V_{\ell N}$.
2. Complementarity: The 3 TeV muon collider is particularly effective for electroweak-scale particles, while the 10 TeV collider, with higher luminosity, extends the reach to heavier TeV-scale particles.
3. Superiority of Trilepton Channel: The same-sign trilepton signature is identified as the most promising discovery channel due to its larger cross section and ability to probe off-shell decay regions ($m_H < 2m_N$).
4. Model Constraints: The results are specific to the $U(1)_{L_\mu-L_\tau}$ model. The authors note that while the results apply in principle to $U(1)_{B-L}$, current LHC dilepton constraints ($m_{Z'} > 5.1$ TeV) would exclude the promising regions at 3 TeV, leaving only a viable window at 10 TeV or higher energies (e.g., 30 TeV).

The study concludes that these signatures allow for the reconstruction of the full mass spectrum of the new particles ($Z', H, N$), providing a comprehensive test of the gauged seesaw mechanism at future muon colliders.