Search for heavy Majorana neutrinos at muon-proton colliders via lepton-number-violating signals

This paper proposes a novel search strategy for heavy Majorana neutrinos at future muon-proton colliders via lepton-number-violating signals, demonstrating that the facility can achieve significantly superior constraints on neutrino mixing parameters compared to existing LHC bounds for neutrino masses between 200 GeV and 3 TeV.

The Gist

Imagine the universe is a giant, high-speed train station where tiny particles are the passengers. For decades, scientists have been trying to find a specific, elusive passenger called the Heavy Majorana Neutrino. This particle is special because it is its own antiparticle (like a person who is both their own mother and father), and finding it would prove that the universe has a secret rule: sometimes, the number of "leptons" (a type of particle) can change by two units at once. This is called Lepton Number Violation.

Here is a simple breakdown of what this paper proposes to find this passenger.

1. The New Search Strategy: A "Muon-Proton" Train

Currently, the biggest particle colliders (like the LHC) smash protons into other protons. It's like trying to find a specific needle in a haystack by crashing two giant haystacks together. It creates a massive mess of debris (background noise), making it hard to spot the needle.

This paper suggests building a different kind of collider: a Muon-Proton collider.

• The Muon: Think of a muon as a "cleaner" version of an electron. It's heavier and behaves more predictably.
• The Proton: The heavy proton beam stays the same.
• The Advantage: Smashing a muon into a proton is like aiming a sniper rifle (the muon) at a moving target (the proton) rather than crashing two trucks together. It creates much less "noise" (background debris) and allows scientists to see the collision much more clearly.

2. The "Smoking Gun" Signal

The scientists are looking for a very specific event that breaks the rules of the Standard Model. They want to see a process where a muon hits a proton and creates a heavy neutrino ($N$), which then decays into a charged lepton (like an electron or muon) and a W boson.

The W boson then breaks apart into jets of particles (like a firework exploding into sparks).

• The "Light" Scenario (200–1000 GeV): If the heavy neutrino isn't too heavy, the W boson explodes into two distinct sparks (jets). The final scene looks like one charged particle + three distinct jets. It's a clear, clean signature.
• The "Heavy" Scenario (1000–3000 GeV): If the neutrino is very heavy (TeV scale), the W boson is moving so fast that its explosion gets squished together. Instead of two separate sparks, it looks like one giant, fat spark (a "fat-jet"). The final scene is one charged particle + one fat-jet.

3. The Detective Work (Filtering the Noise)

The paper describes a rigorous filtering process, similar to a bouncer at a club checking IDs.

1. The Setup: They simulate billions of collisions using supercomputers.
2. The Cuts: They apply strict rules to ignore the boring, common events (background noise) and keep only the weird, rare ones.
   • Rule: "We only want events with exactly one positive charged particle."
   • Rule: "The energy must be high enough to match our heavy neutrino theory."
   • Rule: "There should be almost no missing energy (which usually means a ghost particle escaped)."
3. The Result: After applying these filters, the "noise" from standard physics drops to almost zero. The signal (the heavy neutrino) stands out clearly against the silence.

4. The Results: Seeing the Unseen

The authors calculated how sensitive this new "Muon-Proton" collider would be compared to current machines like the LHC or future plans like the FCC (Future Circular Collider).

• The Reach: They found that this collider could detect heavy neutrinos with masses ranging from 200 GeV to 3000 GeV.
• The Sensitivity: It can detect these particles even if they interact very weakly with normal matter (a very small "mixing parameter").
• The Comparison: The paper claims this new strategy is much better than what we can do today. It can probe areas of physics that other colliders simply cannot reach, effectively opening a new window into the universe's secrets.

Summary Analogy

Imagine you are trying to hear a specific whisper in a crowded stadium.

• Current Colliders (LHC): You are in the middle of the crowd screaming. You can't hear the whisper because everyone else is shouting.
• This Paper's Proposal (Muon-Proton): You move to a quiet, soundproof booth (the muon beam) and use a super-sensitive microphone (the detector) to listen to a specific person (the proton). Even if the whisper is very faint, you can hear it clearly because the background noise is gone.

Conclusion: The paper argues that building a muon-proton collider is a powerful, complementary way to hunt for these heavy, mysterious neutrinos, potentially solving a major puzzle in physics that current machines cannot crack.

Technical Summary

Technical Summary: Search for Heavy Majorana Neutrinos at Muon-Proton Colliders via Lepton-Number-Violating Signals

Problem Statement
Heavy Majorana neutrinos are a natural prediction of various Beyond-Standard Model (BSM) scenarios, particularly those employing seesaw mechanisms to explain small neutrino masses. While neutrinoless double beta decay ($0\nu\beta\beta$) serves as a sensitive low-energy probe, high-energy colliders offer a unique avenue to explore the neutrino mass generation mechanism through clear lepton-number-violating (LNV) signatures. Current experimental limits on the mixing parameter $|V_{\ell N}|^2$ versus the heavy neutrino mass $m_N$ are largely derived from the Large Hadron Collider (LHC) and other facilities. However, there remains a need to probe intermediate to high mass ranges ($200 \text{ GeV} \le m_N \le 3000 \text{ GeV}$) with higher sensitivity and reduced background contamination. This work addresses the potential of future muon-proton ($\mu p$) colliders to fill this gap, leveraging their unique kinematic advantages over hadron and electron-proton colliders.

Methodology
The study employs the minimal Type-I seesaw framework, augmented by three right-handed neutrino singlets. The analysis focuses on a single heavy Majorana neutrino $N$ that mixes exclusively with electron and muon flavor active neutrinos ($|V_{eN}|^2 = |V_{\mu N}|^2 \neq 0$, $|V_{\tau N}|^2 = 0$), while the other two heavy neutrinos are decoupled.

The proposed search strategy targets the LNV process $\mu^- p \to j N \to j(\ell^+ W^-)$ at a future $\mu p$ collider with a center-of-mass energy of $\sqrt{s} \approx 5.3 \text{ TeV}$ (1 TeV muon beam, 7 TeV proton beam). The analysis is divided into two distinct kinematic regimes based on the mass of the heavy neutrino:

1. Resolved Jet Regime ($200 \text{ GeV} \le m_N \le 1000 \text{ GeV}$):

   • Signal Topology: The $W$ boson from the $N$ decay is not highly boosted, decaying into two resolved jets. The final state is $\ell^+ + 3j$ (one charged lepton and three jets).
   • Simulation: Signal and background events are generated using MadGraph5_aMC@NLO with NNPDF23L01 parton distribution functions. Detector effects are simulated using Delphes 3.4.2 with a dedicated $\mu p$ detector card. Jet reconstruction utilizes the anti-$k_t$ algorithm ($R=0.4$).
   • Selection: A sequence of kinematic cuts is applied, including requirements on lepton transverse momentum ($p_T$), jet $p_T$, missing transverse energy ($\not{E}_T < 20 \text{ GeV}$), and an invariant mass window around $m_N$ for the lepton-dijet system.

2. Fat-Jet Regime ($1000 \text{ GeV} \le m_N \le 3000 \text{ GeV}$):

   • Signal Topology: For TeV-scale neutrinos, the $W$ boson is highly boosted, causing its hadronic decay products to coalesce into a single "fat-jet" ($J$). The final state is $\ell^+ + J + j$ (one charged lepton, one fat-jet, and one light jet).
   • Simulation: Fat-jets are reconstructed using the Cambridge-Aachen algorithm with a cone radius $R=1.0$.
   • Selection: Cuts include high $p_T$ thresholds for the lepton and fat-jet, a fat-jet mass window consistent with the $W$ boson ($|M_J - m_W| < 15 \text{ GeV}$), low missing transverse energy, and a high invariant mass for the lepton-fat-jet system ($M_{\ell J} > 0.9 m_N$).

Backgrounds are dominated by Standard Model processes such as $\mu^- p \to \nu_\mu W^+ W^- j$, $\mu^- p \to \nu_\mu W^+ Z j$, and $\mu^- p \to \ell^+ \ell^- j \nu$. The sensitivity is quantified using the exclusion significance formula $Z_{exc} = \sqrt{2[s - b \ln(1 + s/b)]}$, where $s$ and $b$ are the expected signal and background event counts.

Key Contributions and Results
The paper provides a comprehensive signal and background analysis incorporating realistic detector effects to assess the search sensitivity for heavy Majorana neutrinos at a $\mu p$ collider.

• Cross Sections and Kinematics: The production cross section for the LNV signal decreases monotonically with increasing $m_N$. For a benchmark mass of $m_N = 500 \text{ GeV}$ and $|V_{\ell N}|^2 = 10^{-4}$, the cross section is approximately 1.83 fb. In the fat-jet regime, for $m_N = 2000 \text{ GeV}$, the cross section is approximately 0.14 fb.
• Background Suppression: The sequential kinematic cuts effectively suppress Standard Model backgrounds. In the resolved jet regime, the total background cross section is reduced to extremely low levels (e.g., $\sim 10^{-4}$ fb) after the final invariant mass cut. In the fat-jet regime, the dominant background ($\mu^- p \to \ell^+ \ell^- j \nu$) is similarly suppressed, resulting in total background cross sections of $\sim 0.0043 \text{ fb}$ for $m_N = 1000 \text{ GeV}$ and $\sim 2.6 \times 10^{-4} \text{ fb}$ for $m_N = 3000 \text{ GeV}$.
• Projected Exclusion Limits:
  • For an integrated luminosity of $1 \text{ ab}^{-1}$, the study projects $2\sigma$ exclusion limits on $|V_{\ell N}|^2$ ranging from $1.3 \times 10^{-6}$ to $7.4 \times 10^{-6}$ for $m_N$ between 200 GeV and 1 TeV.
  • For the TeV-scale range ($1000 \text{ GeV} \le m_N \le 3000 \text{ GeV}$), the $2\sigma$ upper limits on $|V_{\ell N}|^2$ evolve from $3.2 \times 10^{-6}$ to $8.8 \times 10^{-5}$ with $1 \text{ ab}^{-1}$ luminosity.
  • Even with a lower luminosity of $100 \text{ fb}^{-1}$, the $\mu p$ collider sensitivity surpasses global indirect constraints for masses up to 3 TeV.

Significance and Claims
The authors claim that the proposed search strategy at future $\mu p$ colliders offers a powerful and complementary approach to existing searches at hadron colliders (LHC, FCC-hh) and other lepton colliders (ILC, CLIC, FCC-eh).

• Superior Sensitivity: The results demonstrate that the $\mu p$ collider can achieve constraints on the mixing parameter $|V_{\ell N}|^2$ that are substantially superior to existing bounds from the LHC and other high-energy facilities, particularly in the mass range $200 \text{ GeV} \le m_N \le 3000 \text{ GeV}$.
• Unique Kinematic Advantages: The study highlights that $\mu p$ collisions benefit from higher center-of-mass energy and reduced QCD backgrounds compared to hadron colliders, while offering a higher energy reach than electron-proton colliders under similar proton beam conditions. The on-shell production of heavy neutrinos via $t$-channel $W$ exchange is noted as being more efficient than off-shell channels at the LHC.
• Complementary Strategy: The paper concludes that future $\mu p$ facilities represent a promising avenue for probing heavy Majorana neutrinos, capable of accessing previously inaccessible regions of the $|V_{\ell N}|^2 - m_N$ parameter space.