Search for lepton-number-violating $B^-\to D^{(*)+}\mu^-\mu^-$ decays

Using 13 TeV proton-proton collision data corresponding to 5.4 fb$^{-1}$ of integrated luminosity, the LHCb experiment conducted a search for lepton-number-violating $B^-\to D^{(*)+}\mu^-\mu^-$ decays, observed no significant signal, and established 95% confidence level upper limits on the branching fractions of $4.6 \times 10^{-8}$ and $5.9 \times 10^{-8}$ for the $D^+$ and $D^{*+}$ modes, respectively.

The Gist

Imagine the universe as a giant, high-speed race track where tiny particles zoom around at nearly the speed of light. Physicists at CERN's LHCb experiment are like detectives watching this race, looking for a very specific, almost impossible rule-breaking event.

Here is the story of their latest investigation, explained simply.

The Mystery: A Forbidden Swap

In the world of particle physics, there is a fundamental rule called "Lepton Number Conservation." Think of this rule like a strict accounting system. In a normal transaction, if you take out two "negative" coins (electrons or muons), you must also release two "positive" neutrinos to balance the ledger.

However, some theories suggest that neutrinos might be their own antiparticles (like a coin that is heads on both sides). If this is true, the ledger could be balanced differently. Two "negative" coins could be created without any "positive" neutrinos being released. This is called lepton-number violation.

The scientists were looking for a specific "forbidden transaction": A heavy particle called a B-minus meson decaying into a lighter particle (a D-meson) and two muons (which are like heavy electrons), with no neutrinos in sight.

The Detective Work: Catching the Ghost

To find this rare event, the LHCb team used a massive dataset from 2016 to 2018, equivalent to watching 5.4 billion billion (5.4 fb⁻¹) collisions.

1. The Setup:
They built a giant, high-tech camera (the detector) to catch particles flying out of proton collisions. They looked for a specific signature: a B-meson that suddenly splits into a D-meson and two muons that have the same electric charge.

2. The Noise:
The problem is that the race track is incredibly crowded. Most of the time, particles decay in normal ways, or detectors get confused.

• The "Fake" Muons: Sometimes, a pion (a different type of particle) flies so fast it breaks apart into a real muon, or the detector mistakes a pion for a muon. This creates a "fake" signal that looks exactly like the forbidden event.
• The "Combinatorial" Clutter: Imagine a room full of people throwing balls. Sometimes, by pure chance, two random balls land in a bucket together. This is "combinatorial background"—random noise that looks like a pattern.

3. The Filters:
To find the real signal, the team used a "smart filter" (a machine learning tool called a Boosted Decision Tree).

• They taught the computer what a "fake" event looks like by studying millions of simulation runs.
• They checked the "footprints" (impact parameters) of the particles to ensure they all came from the exact same spot at the exact same time.
• They used a "normalization" event (a very common, well-understood decay) as a ruler to measure how efficient their camera was.

The Result: No Ghosts Found

After sifting through the data with these incredibly tight filters, the scientists looked at the results.

• The Verdict: They found zero clear evidence of the forbidden decay. The "signal" they saw was just random noise, consistent with what you'd expect if the rule-breaking event never happens.
• The Limit: Even though they didn't find it, they set a very strict "speed limit" on how often this could happen. They calculated that if this decay does occur, it happens less than 4.6 times out of every 100 million B-meson decays (for one type) and less than 5.9 times out of every 100 million (for the other).

Why This Matters (According to the Paper)

The paper states that while they didn't find the "ghost," this is still a victory for science.

• Better Tools: They improved their methods significantly compared to previous studies, specifically getting better at spotting when pions are pretending to be muons.
• Tighter Rules: They have now set the strictest limits in history on this specific type of decay.
• The Big Picture: While the theoretical predictions for this event are so rare that even this massive experiment is likely too small to see them, this work helps map out the "search space." It tells future scientists exactly where to look and how sensitive their next detectors need to be to finally catch a glimpse of these Majorana neutrinos.

In short: The detectives looked very hard for a rule-breaking particle swap, found nothing, and declared, "If it's happening, it's rarer than we thought." This helps refine the map of the universe's fundamental laws.

Technical Summary

Technical Summary: Search for Lepton-Number-Violating $B^- \to D^{(*)+} \mu^- \mu^-$ Decays

Problem and Motivation
The fundamental nature of neutrinos—whether they are Dirac or Majorana fermions—remains an open question in particle physics. Establishing the Majorana nature of neutrinos is a primary goal, typically pursued through the observation of neutrinoless double beta decay ($0\nu\beta\beta$). While $0\nu\beta\beta$ experiments probe couplings to electrons, analogous searches in the heavy-flavor sector can probe couplings to muons. This paper presents a search for lepton-number-violating (LNV) decays of the form $B^- \to D^{(*)+} \mu^- \mu^-$. Such processes are forbidden in the Standard Model (SM) and would indicate the existence of Majorana neutrinos. The analysis focuses on a specific topology where the charm meson and the two same-sign muons originate from a common vertex, corresponding to scenarios involving light ($m_N < m_\pi$) or heavy ($m_N > m_B$) Majorana neutrinos, as discussed in theoretical literature [11, 12].

Methodology
The analysis utilizes proton-proton collision data collected by the LHCb experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5.4 fb$^{-1}$ (2016–2018). The search reconstructs the signal decays via the charm-hadron channels $D^+ \to K^-\pi^+\pi^+$ and $D^{*+} \to D^0(\to K^-\pi^+)\pi^+$.

Key methodological components include:

• Event Selection: Candidates are selected requiring a common vertex for the $D^{(*)+}$ and two same-sign muons. Kinematic fits constrain the invariant masses of the intermediate charm states to known values. Tight impact parameter requirements ($\chi^2_{IP}$) and particle identification (PID) criteria are applied to suppress backgrounds from pions misidentified as muons.
• Background Suppression: A Boosted Decision Tree (BDT) classifier is employed to separate signal from combinatorial background. The training utilizes simulated signal samples and data-driven background samples (mass sidebands).
• Background Modeling: The dominant backgrounds arise from misidentified decays, specifically $B^- \to D^{(*)+} \pi^- \mu^- \nu_\mu$ (singly misidentified) and $B^- \to D^{(*)+} \pi^- \pi^-$ (doubly misidentified). The analysis introduces a sophisticated correction for pion-to-muon misidentification, accounting for pions decaying in flight. This involves a data-driven calibration of misidentification rates and a simulation-based smearing of momentum residuals to accurately model the kinematic distortions caused by decay-in-flight effects.
• Normalization: The branching fractions are measured relative to the normalization channel $B^- \to \psi(2S)(\to J/\psi(\to \mu^+\mu^-)\pi^+\pi^-)K^-$, which shares the same final-state particle content.
• Statistical Analysis: An extended unbinned maximum-likelihood fit is performed on the $B^-$ invariant-mass distributions. The signal yield is extracted while constraining the yields of misidentified backgrounds based on simulation and calibration data. Upper limits are set using the $CL_s$ method.

Key Contributions
This work represents a significant improvement over previous LHCb searches [4] in several areas:

1. Dataset Size: Utilization of a larger dataset (5.4 fb$^{-1}$ vs. previous smaller samples).
2. Background Estimation: A refined treatment of backgrounds from pions misidentified as muons. The paper explicitly addresses the momentum degradation effects of pions decaying in flight, a factor not fully accounted for in prior studies. This is achieved through a dedicated calibration sample and a momentum smearing procedure applied to simulation.
3. Selection Optimization: The implementation of a BDT classifier to suppress combinatorial background and tighter PID requirements to reduce pion misidentification probabilities to below 1% per track.
4. Systematic Control: A comprehensive evaluation of systematic uncertainties, including decay model dependence, PID calibration, and trigger efficiency variations.

Results
No significant signal is observed in either the $B^- \to D^+ \mu^- \mu^-$ or $B^- \to D^{*+} \mu^- \mu^-$ channels. The observed signal yields are consistent with background fluctuations ($9.0 \pm 5.3$ events for $D^+$ and $-1.7 \pm 2.1$ events for $D^{*+}$).

Consequently, upper limits on the branching fractions are set at the 95% confidence level (CL):

• $\mathcal{B}(B^- \to D^+ \mu^- \mu^-) < 4.6 \times 10^{-8}$
• $\mathcal{B}(B^- \to D^{*+} \mu^- \mu^-) < 5.9 \times 10^{-8}$

These limits represent an improvement of more than an order of magnitude compared to previous results [4].

Significance
The paper claims that while the achieved sensitivity is still far from the theoretical predictions for Majorana neutrino-induced decays (which are predicted to be at the level of $O(10^{-23})$ to $O(10^{-22})$), the results establish the most stringent limits to date on these specific LNV decay modes. The study demonstrates the experimental capability to perform model-independent searches for neutrinoless decays in the $B$-meson system and provides a refined strategy for future, more sensitive measurements. The improvements in background modeling and suppression serve as a foundation for subsequent analyses in the search for physics beyond the Standard Model.