Role of heavy neutral lepton in lepton number violating $B$ meson decays

This paper investigates the potential of heavy neutral leptons (HNLs) to mediate lepton-number-violating $B$-meson decays, demonstrating that $B_c$ meson channels offer significantly enhanced sensitivity for detecting these physics beyond the Standard Model effects compared to other modes.

The Gist

The Mystery of the "Ghostly Twin": A Simple Guide to the Research

Imagine you are watching a high-stakes game of billiards. You hit the cue ball, it strikes the target ball, and the target ball rolls into the pocket. In the world of physics, we have a "rulebook" called the Standard Model. It tells us exactly how particles (like billiard balls) should move and interact.

However, physicists have noticed that sometimes, the balls seem to behave as if there are invisible, ghostly players on the table. These "ghosts" are what this paper is about: Heavy Neutral Leptons (HNLs).

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1. The Protagonist: The Heavy Neutral Lepton (The "Ghostly Twin")

In our universe, there are particles called neutrinos. They are like the "ghosts" of the particle world—they are incredibly light, they have no electric charge, and they can fly through solid walls without touching anything.

The researchers in this paper are looking for a specific type of ghost: a Heavy Neutral Lepton.

• The Analogy: Imagine if every ghost in a haunted house had a much heavier, more solid "twin" that only appeared for a split second before vanishing. We haven't seen these twins yet, but if they exist, they would explain why the "regular" ghosts behave so strangely.

2. The Crime Scene: Lepton Number Violation (The "Rule Breaker")

In the Standard Model rulebook, there is a law called Lepton Number Conservation. Think of this as a cosmic accounting system. If you create one "lepton" (a type of particle), you must also create an "anti-lepton" to keep the balance at zero. It’s like a rule that says, "For every person who enters a room, someone must leave, so the number of people stays the same."

But if these "Heavy Ghostly Twins" (Majorana neutrinos) exist, they can break this rule. They can act as their own anti-particles.

• The Analogy: Imagine a person walks into a room, but instead of someone leaving, two people suddenly appear out of nowhere. The "accounting" is broken! This is called Lepton Number Violation (LNV). Finding this would be a "smoking gun" proving that our current rulebook is incomplete.

3. The Investigation: B-Meson Decays (The "Microscopic Explosion")

How do you catch a ghost that only appears for a fraction of a second? You watch a "controlled explosion."

The researchers focus on B-mesons. These are unstable particles that exist for a tiny moment before decaying (exploding) into other, smaller particles.

• The Analogy: Think of a B-meson as a highly pressurized firecracker. When it goes off, it sprays out various pieces. The scientists are looking for a very specific, "illegal" spray pattern: instead of the usual pieces, they are looking for two identical particles (like two muons) flying out together. If they see that specific pattern, they know a "Heavy Ghost" must have been the middleman that caused the explosion.

4. The Findings: Which "Explosion" is Best?

The paper compares different types of B-meson explosions to see which one is most likely to reveal the ghost:

1. The $B^-$ decay: A standard explosion.
2. The $B_c^-$ decay: A much more powerful, specialized explosion.

The Result: The researchers found that the $B_c^-$ decay is like using a high-powered microscope instead of a magnifying glass. It is much more sensitive and provides a much clearer "signal" for the heavy ghost to leave behind.

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Summary: Why does this matter?

Right now, our understanding of the universe is like a jigsaw puzzle with several missing pieces. We know neutrinos have mass, but we don't know why or how.

By studying these specific "illegal" explosions in B-mesons, these scientists are providing a roadmap for future experiments (like those at the Large Hadron Collider). They are telling the world: "If you want to find the heavy ghosts that explain the mysteries of our universe, don't just look anywhere—look at these specific $B_c$ explosions!"

Technical Summary

This technical summary details the research paper "Role of heavy neutral lepton in lepton number violating B meson decays" by Panda, Mohapatra, and Mohanta.

1. Problem Statement

The Standard Model (SM) treats neutrinos as massless, but the observation of neutrino oscillations confirms they possess non-zero masses, signaling physics beyond the Standard Model (BSM). A primary open question is whether neutrinos are Dirac or Majorana particles. If neutrinos are Majorana, they can mediate Lepton Number Violating (LNV) processes, where the lepton number changes by two units ($\Delta L = 2$).

While various meson decays have been studied for LNV signatures, the authors identify a gap in the literature: the role of Heavy Neutral Leptons (HNLs) in purely leptonic $B$ meson decays as a means to constrain HNL parameter space and as a probe for LNV processes. Specifically, they aim to determine how HNLs affect $B$ and $B_c$ meson decays and which decay channels offer the best sensitivity to these new physics effects.

2. Methodology

The authors employ a theoretical and phenomenological approach based on the following framework:

• Theoretical Framework: They extend the SM by introducing a single heavy Majorana neutrino ($N$) that mixes with the active SM neutrinos. This is modeled using a $4 \times 4$ unitary mixing matrix, where the $3 \times 3$ PMNS sub-matrix exhibits effective non-unitarity.
• Decay Modeling:
  • Purely Leptonic Decays ($B \to \ell N$): They calculate the decay widths for $B^+ \to \ell^+ N$ (where $\ell = \mu, \tau$), accounting for the finite mass of the HNL and the resulting phase-space effects.
  • LNV Decays ($\Delta L = 2$): They investigate three-body decays ($B^{(-)}_c \to \pi^+ \mu^- \mu^-$) and four-body decays ($B^-_c \to J/\psi \pi^+ \mu^- \mu^-$).
  • Approximation: They utilize the Narrow-Width Approximation (NWA), assuming the HNL is produced on-shell ($m_\pi + m_\mu < M_N < m_{B(c)} - m_\mu$), allowing the decay rate to factorize into sequential sub-processes.
• Parameter Constraints: They use current experimental data from Belle, BABAR, and others to constrain the allowed regions in the $M_N$ (mass) vs. $|U_{\ell N}|^2$ (mixing) plane. They test two scenarios: Unitary (extended matrix is unitary) and Non-Unitary (no unitarity constraint imposed).

3. Key Contributions

• Constraint Mapping: The paper provides a detailed mapping of the allowed parameter space for $|U_{\mu N}|^2$ and $|U_{\tau N}|^2$ using $B \to \mu \nu$ and $B \to \tau \nu$ data.
• Channel Comparison: A systematic comparison of $B$ vs. $B_c$ meson decays to identify which provides higher sensitivity to HNLs.
• LNV Prediction: The derivation of branching ratios for specific LNV dimuon channels mediated by on-shell Majorana neutrinos.
• Hadronic Dynamics: Integration of heavy quark spin symmetry and QCD relativistic potential models to handle the hadronic form factors in $B_c$ decays.

4. Results

• Parameter Space:
  • For the $\tau$ sector ($B \to \tau N$), most of the parameter space is excluded by existing bounds, leaving only a small, phenomenologically disfavored non-unitary region.
  • For the $\mu$ sector ($B \to \mu N$), the allowed region is well-defined and shows little difference between unitary and non-unitary assumptions due to helicity suppression.
• Branching Ratios (BR): Using benchmark values ($|U_{\mu N}|^2 = 10^{-6}$ and $M_N = 2\text{--}3$ GeV), the predicted LNV branching ratios range from $\mathcal{O}(10^{-13})$ to $\mathcal{O}(10^{-8})$.
• Channel Sensitivity:
  • $B^-_c \to \pi^+ \mu^- \mu^-$: Shows the largest enhancement ($\mathcal{O}(10^{-8})$), making it the most promising channel for discovery.
  • $B^- \to \pi^+ \mu^- \mu^-$: Shows moderate sensitivity ($\mathcal{O}(10^{-11})$).
  • $B^-_c \to J/\psi \pi^+ \mu^- \mu^-$: Is strongly suppressed, with the BR dropping significantly as $M_N$ increases (from $10^{-10}$ to $10^{-13}$).

5. Significance

The study demonstrates that $B_c$ meson decays are superior probes for HNL-mediated lepton number violation compared to standard $B$ decays. The predicted branching ratios for $B^-_c \to \pi^+ \mu^- \mu^-$ are within a range that could potentially be explored by high-luminosity experiments like LHCb. This work provides a clear roadmap for experimentalists to search for the Majorana nature of neutrinos through specific, high-sensitivity hadronic channels.