Sterile Neutrinos at MAPP in the B-L Model

This paper investigates the potential of the MAPP detector to discover sterile neutrinos via pair-production from $B-L$ and Standard Model $Z$ bosons, demonstrating sensitivity to active-sterile mixing strengths as low as $10^{-12}$ under specific coupling and mass conditions.

The Gist

Imagine the universe as a giant, bustling city. For decades, physicists have been mapping this city using a "Standard Model" blueprint. This blueprint explains almost everything: the buildings (atoms), the people (electrons and quarks), and the traffic laws (forces like gravity and electromagnetism).

But there's a problem. The blueprint has a missing piece: Neutrinos. These are ghostly particles that zip through everything without interacting. We know they exist, and we know they have a tiny bit of mass, but the Standard Model says they should be massless. It's like finding a car that drives without an engine. Something is missing from our understanding.

This paper proposes a solution and a new way to hunt for it. Here is the story in simple terms:

1. The Mystery Guest: The "Sterile" Neutrino

Physicists suspect there is a "cousin" to the known neutrinos, called a Right-Handed (or Sterile) Neutrino.

• The Analogy: Imagine the known neutrinos are like spies who wear uniforms and interact with the police (the Standard Model forces). The "Sterile" neutrino is a spy in a plain suit. It doesn't wear a uniform, so it ignores the police entirely. It only interacts with itself and a secret, hidden network.
• Because it ignores the police, it's very hard to catch. It's also very shy; it rarely shows up, and when it does, it disappears quickly.

2. The New Highway: The $B-L$ Model

To explain how these shy neutrinos get their mass, the authors suggest a new theory called the $B-L$ Model.

• The Analogy: Think of the Standard Model as a city with only one main highway. The $B-L$ model says, "Actually, there's a secret underground tunnel network!"
• This tunnel is mediated by a new particle called the $Z'$ boson. It's like a secret bus that can pick up our shy neutrinos and drop them off somewhere else.
• The paper also considers a "leak" in the system where the secret tunnel accidentally connects to the main highway (the Standard Model's $Z$ boson), allowing the shy neutrinos to hitch a ride on regular traffic.

3. The Hunting Ground: MAPP

Where do we look for these ghosts? The authors focus on a new detector called MAPP (MoEDAL's Apparatus for Penetrating Particles).

• The Analogy: Imagine the Large Hadron Collider (LHC) is a massive particle-smashing factory. When particles smash, they usually explode immediately. But our "shy" neutrinos are like slow-moving ghosts. They might travel a few meters or even tens of meters before they finally decide to "pop" (decay) into visible particles.
• Most detectors are right next to the explosion, so they miss the ghosts that travel far.
• MAPP is the "Ghost Trap" located far away. It's like setting up a camera 50 meters down the road, hidden behind a thick wall of rock. If a ghost travels that far and then pops, MAPP sees it. Because it's so far away and shielded, the background noise (other particles) is zero. It's a "no-background" zone.

4. The Big Discovery Potential

The paper runs computer simulations to see if MAPP can catch these ghosts.

• The Result: Yes! If the secret tunnel ($Z'$) exists and has a specific strength, MAPP could detect these neutrinos even if they are incredibly shy (mixing strengths as low as $10^{-12}$).
• Why it matters: Finding these neutrinos would solve the mystery of why neutrinos have mass. It would be like finding the engine for the ghost car. It would prove that our city blueprint (the Standard Model) is incomplete and that there is a whole new layer of physics (the "Beyond the Standard Model") waiting to be discovered.

Summary of the "Heist"

1. The Crime: Neutrinos have mass, but our current laws of physics say they shouldn't.
2. The Suspect: A "Sterile" neutrino that hides in a secret dimension.
3. The Accomplice: A new force carrier ($Z'$ boson) that helps create these neutrinos.
4. The Trap: A new detector (MAPP) placed far away from the crash site, waiting for the slow-moving suspects to reveal themselves.
5. The Goal: To catch the suspect, prove the secret tunnel exists, and finally understand the true nature of the universe's most elusive particles.

In short, this paper is a blueprint for a high-stakes game of hide-and-seek, where the "hider" is a fundamental piece of the universe's puzzle, and the "seeker" is a new, cleverly placed detector ready to catch it.

Technical Summary

Here is a detailed technical summary of the paper "Sterile Neutrinos at MAPP in the B −L Model":

1. Problem Statement

The lightness of active neutrinos suggests physics beyond the Standard Model (SM), often explained by the Type-I Seesaw Mechanism involving heavy right-handed (RH) Majorana neutrinos ($N$). In canonical seesaw scenarios, the mixing between active and sterile neutrinos ($V_{\ell N}$) is extremely small ($V^2 \sim 10^{-10} - 10^{-12}$) to satisfy light neutrino mass constraints.

• The Challenge: Such small mixing results in long-lived RH neutrinos that decay at macroscopic distances (centimeters to meters). However, in the SM, the production cross-section for these neutrinos is proportional to $V^4$, making them nearly impossible to produce in sufficient quantities for detection at colliders like the LHC.
• The Gap: While dedicated displaced vertex detectors (MAPP, FASER, MATHUSLA, CODEX-b) are designed to detect long-lived particles, their sensitivity in the SM-only scenario is often insufficient to probe the canonical seesaw region. The paper investigates whether extending the SM with a $U(1)_{B-L}$ gauge symmetry can enhance production rates sufficiently to make these neutrinos detectable.

2. Methodology

The authors employ a theoretical and simulation-based approach to evaluate the discovery potential of the MAPP (MoEDAL's Apparatus for Penetrating Particles) detector at the LHC.

• Theoretical Framework:

  • Model: The study utilizes the $U(1)_{B-L}$ model, which introduces a new gauge boson ($Z'$), a scalar field ($\chi$) to break the symmetry, and three RH neutrinos.
  • Production Channels: Two primary production mechanisms are analyzed:
    1. $Z'$ Portal: $pp \to Z' \to NN$. This process is governed by the $B-L$ gauge coupling ($g_{B-L}$) and is independent of the small active-sterile mixing $V_{\ell N}$.
    2. $Z$ Portal (Kinetic Mixing): $pp \to Z \to NN$. This occurs via kinetic and mass mixing between the SM $Z$ boson and the $Z'$, parameterized by an effective mixing angle $\alpha$.
  • Decay: The RH neutrinos decay via small active-sterile mixing into visible SM particles (e.g., $N \to \mu^\pm q\bar{q}$), creating displaced vertices.

• Simulation & Experimental Setup:

  • Event Generation: Used MadGraph5_aMC@NLO with the $B-L$ UFO model and PYTHIA for parton showering. Generated $10^5$ signal events.
  • Detector Geometry: Focused on MAPP-2 (Phase-2), a proposed detector for the High-Luminosity LHC (HL-LHC) located ~50m from the interaction point with a large fiducial volume (two polyhedra). MAPP-1 (Run-3) was also considered but found to have negligible sensitivity due to its smaller size.
  • Assumptions: A "no-background" assumption is applied, justified by the significant rock shielding and distance from the interaction point. Sensitivity is defined by observing $>3.09$ events at 95% confidence level (Poisson statistics).
  • Parameters:
    • Integrated Luminosity: $300 \text{ fb}^{-1}$ (MAPP-2).
    • Benchmark Couplings: $g_{B-L} = 10^{-3}$ (for $m_{Z'} > 10$ GeV) and $10^{-4}$(for$m_{Z'} < 10$ GeV), based on existing constraints.
    • Mass Ratios: Explored $m_N/m_{Z'}$ ratios of 0.1, 0.2, 0.3, and 0.4.

3. Key Contributions

• Enhanced Production Mechanism: Demonstrated that the $B-L$ gauge interaction allows for the efficient production of RH neutrinos via the $Z'$ portal, bypassing the suppression factor of $V^4$ inherent in SM-only production.
• Kinetic Mixing Analysis: Extended previous work by including the $Z-Z'$ mixing channel, showing that even a small mixing parameter ($\alpha \approx 0.002$) allows the SM $Z$ boson to serve as a viable portal for RH neutrino production.
• Comparative Sensitivity: Provided a comprehensive comparison of MAPP-2 against other proposed long-lived particle detectors (FASER-2, CODEX-b, MATHUSLA) specifically within the context of the $B-L$ model.

4. Results

The study yields the following quantitative sensitivities for the MAPP-2 detector:

• $Z'$ Mediated Channel ($pp \to Z' \to NN$):

  • With $g_{B-L} = 10^{-3}$, MAPP-2 can probe active-sterile mixing strengths as low as $V^2_{\mu N} \approx 10^{-12}$.
  • This sensitivity covers RH neutrino masses up to $m_N \lesssim 25$ GeV.
  • The sensitivity peaks when the mass ratio $m_N/m_{Z'} \approx 0.3$.
  • Crucially, this sensitivity reaches into the "Seesaw Band" (grey shaded region in figures), where light neutrino masses ($10^{-2}$ eV to 0.3 eV) are generated via the canonical Type-I seesaw mechanism.

• $Z$ Mediated Channel ($pp \to Z \to NN$):

  • Sensitivity is achieved for a gauge mixing parameter $\alpha \gtrsim 0.001$.
  • At $\alpha = 0.002$, the detector can probe $V^2_{\mu N} \gtrsim 10^{-13}$ for masses up to $m_N \lesssim 40$ GeV.

• Comparison with Other Detectors:

  • MAPP-2 vs. FASER-2: MAPP-2 outperforms FASER-2 because FASER-2's forward geometry requires high pseudo-rapidity ($\eta \approx 7$), which is less favorable for the specific kinematics of the $B-L$ model compared to MAPP's broader angular acceptance.
  • MAPP-2 vs. MATHUSLA: MATHUSLA (surface detector) shows sensitivity to even smaller mixing values due to its massive volume, but MAPP-2 offers a competitive probe specifically for the $B-L$ parameter space with a more compact footprint.
  • MAPP-2 vs. CODEX-b: CODEX-b has weaker sensitivity for the heavy $Z'$ masses considered due to its smaller angular acceptance.

• SM vs. $B-L$ Model:

  • In the absence of the $B-L$ gauge interaction (pure SM production), even ambitious projects like FCC-ee struggle to reach the canonical seesaw region.
  • The $B-L$ model's enhanced production rate allows MAPP-2 and MATHUSLA to probe a significant portion of the theoretically motivated seesaw parameter space.

5. Significance

• Probing the Origin of Neutrino Mass: The paper demonstrates that the MAPP detector, operating in the $B-L$ framework, is uniquely positioned to test the canonical Type-I Seesaw mechanism. This is a regime previously considered inaccessible to collider experiments due to the tiny mixing angles required.
• Validation of Extended Models: It highlights the importance of searching for sterile neutrinos not just as isolated SM extensions, but within the context of gauge extensions (like $B-L$) that provide efficient production mechanisms.
• Experimental Strategy: The results provide a strong physics case for the MAPP-2 detector design and its placement, validating its potential to discover new physics at the "lifetime frontier" of particle physics.
• Broader Impact: The findings suggest that similar enhancements in sensitivity apply to other experiments (SHiP, LHCb, ATLAS, CMS) if the $B-L$ model (or similar gauge extensions) is realized in nature, motivating a broader search strategy for displaced vertices.