Search for heavy neutral leptons in B-meson decays

Using 5 fb⁻¹ of proton-proton collision data at 13 TeV collected by the LHCb experiment, this study searches for long-lived heavy neutral leptons in B-meson decays to a muon-pion final state, finding no significant excess and setting new constraints on their mixing with muon neutrinos in the 1.6–5.5 GeV mass range for both lepton-number-conserving and violating scenarios.

The Gist

Imagine the universe as a giant, bustling cosmic city. For decades, physicists have been the city planners, using a blueprint called the Standard Model to explain how everything works: the forces, the particles, the traffic flow. It's a brilliant blueprint, but it has some glaring holes. It can't explain why the universe is made of matter instead of antimatter, what dark matter is (the invisible scaffolding holding galaxies together), or why neutrinos (tiny, ghostly particles) have mass at all.

To fix these holes, scientists suspect there are "ghosts" living in the city—particles that don't show up on the standard blueprints. One of the most popular suspects is the Heavy Neutral Lepton (HNL). Think of an HNL as a "heavy ghost." It's a particle that barely interacts with anything, making it incredibly hard to catch, but if it exists, it could explain some of the universe's biggest mysteries.

This paper is a report from the LHCb collaboration, a team of scientists working at CERN's Large Hadron Collider (the world's most powerful particle accelerator). They went on a massive "ghost hunt" to see if they could find these Heavy Neutral Leptons.

The Hunt: Catching a Ghost in a Moving Train

Here is how they tried to catch these ghosts, explained through a simple analogy:

1. The Setup: The Particle Factory
Imagine the Large Hadron Collider as a high-speed train station where protons (tiny particles) are smashed together at nearly the speed of light. These collisions create a chaotic explosion of new particles, including B-mesons. Think of B-mesons as "unstable delivery trucks" that are born in the crash and immediately start driving away.

2. The Suspect: The Heavy Ghost (HNL)
The scientists are looking for a specific scenario:

• A B-meson (the delivery truck) decays (falls apart).
• Instead of just breaking into normal pieces, it might spit out a Heavy Neutral Lepton (HNL).
• Because the HNL is a "ghost," it doesn't stop immediately. It travels a short distance—maybe a few centimeters or even a few meters—before it finally decays (dies) into two visible particles: a muon (a heavy cousin of the electron) and a pion (a type of meson).

The Analogy: Imagine a delivery truck (B-meson) driving down a highway. Suddenly, it drops a secret package (the HNL). The package keeps rolling down the road for a while before it bursts open, revealing two distinct items: a red ball (muon) and a blue ball (pion). The scientists are trying to find that specific spot on the highway where the package burst open, far away from where the truck dropped it.

3. The Challenge: The Needle in a Haystack
The problem is that the highway is crowded. Millions of other trucks are dropping packages every second, and most of them drop red and blue balls right next to the truck (prompt decays). Finding the ones that rolled a bit further away (displaced decays) is like finding a specific needle in a haystack that is constantly on fire.

To make it harder, the "ghost" might be very shy. It might only appear if it mixes with a specific type of neutrino (the muon neutrino). The scientists had to tune their detectors to look for this specific "shyness."

The Tools: The Super-Spectrometer

The LHCb detector is like a giant, high-tech camera and radar system surrounding the train tracks.

• The Camera: It tracks the path of every particle. If a particle travels a bit before decaying, the camera sees a "kink" in the path.
• The Radar: It identifies what the particles are. Is that a muon? Is that a pion?
• The Filter (AI): Because there is so much data, they used a Neural Network (a type of artificial intelligence). Think of this AI as a super-smart bouncer at a club. It looks at every event and decides, "This looks like a normal crash, go away," or "This looks like a ghost package rolling down the road, let's investigate!"

The Search: Two Types of Ghosts

The scientists looked for two types of HNLs:

1. The "Dirac" Ghost: A standard ghost that behaves normally.
2. The "Majorana" Ghost: A special kind of ghost that is its own antiparticle. If this exists, it could break the rules of "lepton number" (a conservation law), essentially allowing the universe to create matter out of nothing in a way that explains why we exist at all.

They searched for two different "signatures" in the debris:

• Opposite Signs: A positive muon and a negative pion (normal behavior).
• Same Signs: Two positive muons (or two negative). This would be a smoking gun for the "Majorana" ghost, proving that lepton number was violated.

The Results: The Silence of the Ghosts

After analyzing data equivalent to 5.04 femtobarns (a massive amount of collision data collected between 2016 and 2018), the scientists looked at the results.

The Verdict: They found no ghosts.

They didn't see any excess of "kinks" in the particle paths that couldn't be explained by normal background noise. There was a tiny blip in the data (a 2.5 sigma fluctuation), but when they accounted for the fact that they were looking at thousands of different possibilities, it turned out to be just a random statistical fluke—like hearing a noise in the dark and realizing it was just the wind.

What Does This Mean?

Even though they didn't find the ghost, the hunt was a huge success. Here is why:

1. Ruling Out the "Easy" Suspects: They have now proven that if these Heavy Neutral Leptons exist, they are not as common or as "heavy" as some theories predicted in the mass range they searched (1.6 to 5.5 GeV). They have effectively closed the door on many specific versions of the "ghost" theory.
2. Setting the Rules: They have placed strict limits on how "shy" these particles can be. If an HNL exists in this mass range, it must be even more elusive than they thought.
3. Refining the Blueprint: By ruling out these possibilities, they are helping theorists refine their blueprints. If the "easy" ghosts aren't there, the real ones must be hiding in a different part of the city, perhaps with different masses or different behaviors.

The Bottom Line

The LHCb team acted like master detectives in a cosmic crime scene. They used the world's most advanced tools and artificial intelligence to look for a particle that could explain the origin of the universe. While the "heavy neutral lepton" remained invisible this time, the search has tightened the noose around the suspects.

It's like searching for a specific type of fish in the ocean. You didn't catch it, but you proved that if it's there, it's not in this part of the ocean, and it's not the size you thought. Now, the scientists know exactly where to look next, and they are ready for the next round of the hunt with even better equipment. The universe is still full of secrets, but we are getting closer to solving the puzzle.

Technical Summary

1. Problem and Motivation

The Standard Model (SM) of particle physics fails to explain several fundamental phenomena, including the origin of neutrino masses, the matter-antimatter asymmetry of the universe, and the nature of dark matter. Heavy Neutral Leptons (HNLs), denoted as $N$, are hypothetical fermions (singlets under SM gauge groups) proposed in extensions like the Type-I Seesaw mechanism and the $\nu$MSM (Minimal Neutrino Standard Model).

• Physics Goal: To search for HNLs produced in $B$-meson decays ($B \to \mu N$) that subsequently decay into a muon and a pion ($N \to \mu \pi$).
• Key Scenarios: The search targets both Lepton-Number Conserving (LNC) scenarios (Dirac-like, $\mu^+\mu^-$ final states) and Lepton-Number Violating (LNV) scenarios (Majorana-like, $\mu^\pm\mu^\pm$ final states).
• Mass Range: The analysis focuses on the mass range 1.6 to 5.5 GeV, a region where $B$-meson decays are the dominant production mode at the LHC. This range is particularly relevant for models predicting larger mixing angles ($|U_{\mu N}|^2 \sim 10^{-5} - 10^{-4}$) than those required for standard leptogenesis, such as symmetry-protected low-scale seesaws or models with gauged $B-L$.

2. Methodology

Data and Detector

• Dataset: Proton-proton collision data collected by the LHCb experiment at $\sqrt{s} = 13$ TeV during Run 2 (2016–2018).
• Integrated Luminosity: $5.04 \pm 0.10 \text{ fb}^{-1}$.
• Detector: The LHCb forward spectrometer, optimized for $b$-hadron physics, with high-precision vertexing (VELO) and particle identification (RICH, muon system, calorimeters).

Signal Topology and Categories

The search reconstructs the decay chain $B \to \mu N (\to \mu \pi) X$, where $X$ represents unobserved particles. The analysis is divided into two main reconstruction categories based on the HNL decay vertex location:

1. Long Category: HNL decays occur within the Vertex Locator (VELO). Candidates are reconstructed using "long tracks" (hits in VELO and downstream trackers). This offers superior mass and vertex resolution.
   • Requirement: Flight distance $FD_z(N) > 20$ mm.
2. Downstream Category: HNL decays occur after the VELO. Candidates use "downstream tracks" (hits only in downstream trackers). This extends sensitivity to longer lifetimes.
   • Requirement: $FD_z(N) \gtrsim 70$ cm.

The analysis considers both Opposite-Sign (OS) ($\mu^+\mu^-$) and Same-Sign (SS) ($\mu^\pm\mu^\pm$) muon pairs to probe Dirac and Majorana HNLs, respectively.

Event Selection and Machine Learning

• Trigger: A dedicated software trigger was developed for the downstream category to select displaced $B \to \mu N$ candidates with same-sign muons.
• Multivariate Analysis (MVA): A Neural Network (NN) classifier, implemented in PyTorch, is used to suppress combinatorial background.
  • Innovation: The NN is mass-parametrized. Instead of training separate classifiers for each mass hypothesis, the HNL mass ($m_N$) is included as an input feature. This allows the classifier to smoothly interpolate between simulated mass points and eliminates the need for discrete training sets.
  • Training: Signal is modeled using simulation; background is modeled using data sidebands ($m(\mu\mu\pi)$ above the signal region).
  • Optimization: Working points are optimized using the Punzi Figure of Merit to maximize sensitivity across the mass range.

Background Estimation

• Combinatorial Background: Modeled by an exponential or linear function, fitted in sliding windows around the signal mass.
• **Peaking Background:**主要来自 charm meson decays ($D^0 \to K^- \pi^+$) where a kaon or pion is misidentified as a muon.
  • ABCD Method: A data-driven technique is used to estimate peaking backgrounds. The sample is divided into four regions based on flight distance ($FD_z$) and invariant mass ($m(\mu\mu\pi)$). The background yield in the signal region is extrapolated from a control region of prompt-like decays ($FD_z < 20$ mm).

Signal Extraction

• A "bump hunt" is performed in the invariant mass spectrum of the $\mu\pi$ system ($m(\mu\pi)$).
• The signal shape is modeled by a modified Crystal Ball function.
• A simultaneous fit is performed across all reconstruction categories (OS/SS, Long/Downstream, $B^+/B_c^+/B^0/B_s^0$) using the zfit library.
• Limits are set using the $CL_s$ method.

3. Key Contributions and Technical Advances

1. Mass-Parametrized Neural Network: The implementation of a physics-variable parametrized NN allows for a continuous search across the mass spectrum without the statistical penalty of training separate models for each mass point.
2. Downstream Track Reconstruction: The analysis successfully extends sensitivity to HNLs with longer lifetimes (decay lengths up to ~2 m) by utilizing downstream tracks, a technique specifically optimized for this search.
3. Inclusive Semileptonic Analysis: The search includes partially reconstructed decays ($B \to \mu N X$), significantly increasing the signal yield compared to purely exclusive analyses, while managing the associated background via the ABCD method.
4. Comprehensive Coverage: The analysis covers both LNC and LNV scenarios and combines multiple $B$-meson species ($B^+, B^0, B_s^0, B_c^+$), leveraging the enhanced production of $B_c^+$ HNLs despite their lower fragmentation fraction.

4. Results

• Observation: No significant excess of events was observed over the expected background.
  • The largest local excess was found at $m_N = 2.93$ GeV in the Dirac OS channel with a significance of 2.5$\sigma$.
  • After accounting for the look-elsewhere effect, the global significance drops to 0.3$\sigma$, consistent with a statistical fluctuation.
• Exclusion Limits:
  • Upper limits on the squared mixing element $|U_{\mu N}|^2$ were set at the 95% Confidence Level (CL).
  • The limits exclude values of $|U_{\mu N}|^2$ down to the $10^{-5} - 10^{-4}$ level in the mass range 1.6–5.5 GeV.
  • Improvement: These results represent more than an order of magnitude improvement over previous LHCb limits in this mass range.
  • Comparison: The limits are competitive with or superior to previous beam-dump experiments (e.g., BEBC) and complement searches by ATLAS and CMS, which are typically more sensitive at higher masses (via $W/Z$ decays).

5. Significance

• Model Constraints: While the results do not probe the specific parameter space favored by standard $\nu$MSM leptogenesis (which requires very small mixings, $|U|^2 \lesssim 10^{-6}$), they strongly constrain alternative models that predict larger mixings, such as:
  • Symmetry-protected low-scale seesaws (e.g., inverse seesaw).
  • Flavour-structured models with dominant muon mixing.
  • Models with gauged $B-L$ symmetry.
• Future Prospects: The techniques developed (mass-parametrized NN, downstream track handling, inclusive background control) provide a robust framework for future HNL searches. With the upcoming LHCb Upgrade I and II, which will provide significantly larger datasets and improved displaced vertex reconstruction, the sensitivity is expected to improve by orders of magnitude, potentially reaching the parameter space relevant for leptogenesis.

In conclusion, this paper sets the most stringent limits to date on GeV-scale Heavy Neutral Leptons mixing with muon neutrinos produced in $B$-meson decays, effectively ruling out a significant portion of the parameter space for various Beyond-Standard-Model scenarios.