First evidence of the decay $B^+\to\pi^+ e^+ e^-$

Using 9 fb$^{-1}$ of proton-proton collision data from the LHCb experiment, researchers report the first evidence of the rare decay $B^+\to\pi^+ e^+ e^-$ with a significance of 3.2$\sigma$ and a measured branching fraction consistent with Standard Model predictions.

The Gist

Imagine the universe as a giant, high-speed racetrack where tiny particles zoom around at nearly the speed of light. The LHCb experiment at CERN is like a team of ultra-precise traffic cameras and detectives stationed on the side of this track, watching for rare and strange events that happen when these particles crash into each other.

This paper is a report from those detectives announcing they have finally caught a glimpse of a very rare, almost invisible event: a specific type of particle decay called $B^+ \to \pi^+ e^+ e^-$.

Here is the story of what they found, explained simply:

The "Ghost" Particle Hunt

In the world of physics, there are rules (called the Standard Model) that predict how particles should behave. Most of the time, particles follow these rules perfectly. However, physicists love looking for the "ghosts"—events that are so rare they barely happen, or events that might break the rules, hinting at new, undiscovered physics.

The particle they were hunting is a $B^+$ meson. Think of a $B^+$ meson as a heavy, unstable suitcase. Usually, when it breaks apart, it drops its contents in predictable ways. But sometimes, very rarely, it drops a specific, hard-to-find combination: a pion (a light particle) and two electrons (the stuff that makes up electricity).

This specific breakup is special because it's a "forbidden" dance in the standard rulebook. It happens so rarely that it's like trying to find a specific grain of sand on a beach the size of a continent.

The Challenge: Finding a Needle in a Haystack

The LHCb team collected data from billions of collisions (like watching billions of car crashes) to find this specific event. But there was a massive problem: noise.

Imagine trying to hear a whisper in a stadium full of screaming fans. The "screaming fans" in this experiment are other particle decays that look almost exactly like the one they want, but aren't.

• Some particles look like electrons but are actually pions (a case of mistaken identity).
• Some particles break apart in similar ways but involve different ingredients.

To filter out the noise, the scientists used a digital sieve (called a "Boosted Decision Tree"). Think of this as a super-smart bouncer at a club. It checks every single particle candidate against a long list of rules:

• "Did you come from the right place?"
• "Do you have the right energy?"
• "Are you moving in the right direction?"

If a particle didn't pass the bouncer's strict test, it was thrown out.

The Discovery: "We See a Shadow"

After sifting through 9 years' worth of data (9 "inverse femtobarns" of information—a unit that represents a massive amount of collisions), the team found a signal.

They didn't find a giant, undeniable explosion of evidence. Instead, they found a statistical bump. Imagine you are counting people entering a room. You expect 100 people. You count 103. Is that a new trend? Maybe. But if you count 130, you are sure something is happening.

In this case, the team saw a bump that was 3.2 times larger than what random chance would produce. In the language of physics, this is called "3.2 sigma."

• What this means: It's not a "discovery" yet (which usually requires 5 sigma, or a 99.9999% certainty). It is "evidence." It's like seeing a shadow that is almost certainly a person, but you haven't quite seen their face clearly enough to say, "I know who that is" with 100% confidence.

The Result: A Match with the Rules

The team measured how often this rare decay happens (the "branching fraction"). They found it happens about 2.4 times out of every 100 million $B^+$ mesons.

Crucially, this number matches the prediction made by the Standard Model perfectly.

• Why this matters: Sometimes, when we find a rare event, it breaks the rules and points to "New Physics" (like dark matter or extra dimensions). Here, the event followed the rules exactly. This is actually good news! It confirms that our current understanding of the universe is solid, even for these incredibly rare, difficult-to-see events.

The Bottom Line

The LHCb collaboration has successfully spotted the first clear evidence of the $B^+ \to \pi^+ e^+ e^-$ decay.

• They used a massive dataset from the Large Hadron Collider.
• They used advanced computer filters to remove the "noise" of fake signals.
• They found a signal that is very likely real (3.2 sigma).
• The frequency of the event matches the Standard Model's predictions perfectly.

It's a successful hunt for a ghost, proving that even the most elusive particles in the universe play by the rules we already know.

Technical Summary

1. Problem and Motivation

The paper addresses the search for the rare decay $B^+ \to \pi^+ e^+ e^-$. This process is mediated by a flavour-changing neutral current (FCNC) at the quark level ($b \to d \ell^+ \ell^-$).

• Standard Model (SM) Context: In the SM, FCNCs are loop-suppressed. The $b \to d$ transition is further suppressed relative to the more common $b \to s$ transition by the ratio of CKM matrix elements $|V_{td}|^2/|V_{ts}|^2$.
• New Physics (NP) Potential: These decays are highly sensitive to New Physics. Deviations in branching fractions, CP asymmetries, or lepton flavour universality (LFU) could indicate physics beyond the SM.
• Current Status: While the muon counterpart ($B^+ \to \pi^+ \mu^+ \mu^-$) was observed by LHCb with a branching fraction of $(1.83 \pm 0.25) \times 10^{-8}$, the electron mode ($B^+ \to \pi^+ e^+ e^-$) had not been observed. Previous searches by Belle and Belle II only set an upper limit of $< 5.4 \times 10^{-8}$ (90% CL).

2. Methodology

Data Sample

• Experiment: LHCb detector at CERN.
• Dataset: Proton-proton collisions at center-of-mass energies $\sqrt{s} = 7, 8,$ and $13$ TeV.
• Integrated Luminosity: $9 \text{ fb}^{-1}$ (combining Run 1 and Run 2 data).

Event Reconstruction and Selection

• Trigger: Requires a high-energy electromagnetic calorimeter (ECAL) cluster associated with an electron candidate, followed by software triggers identifying displaced secondary vertices consistent with $b$-hadron decays.
• Candidate Selection:
  • Reconstructed from a charged hadron ($\pi^+$) and an oppositely charged electron pair ($e^+ e^-$).
  • Bremsstrahlung Recovery: Crucial for electrons, which lose energy via bremsstrahlung. The algorithm adds energy from ECAL clusters to the electron momentum. Candidates are split into two categories: HasBrem (clusters added) and NoBrem (no clusters).
  • Kinematic Cuts: Particles must have significant transverse momentum ($p_T$) and form a secondary vertex significantly displaced from the primary interaction vertex (PV).
• Background Suppression:
  • Misidentification: Stringent Particle Identification (PID) requirements using RICH, calorimeter, and muon system data to reject hadrons ($K, \pi$) misidentified as electrons.
  • Combinatorial Background: Suppressed using a Boosted Decision Tree (BDT) classifier trained on simulated signal and data sidebands.
  • Physical Backgrounds:
    • $B^+ \to K^+ e^+ e^-$ (where $K \to \pi$ mis-ID) is rejected via invariant mass vetoes.
    • Fully hadronic decays ($B^+ \to h^+ h^- h^+$) where two hadrons fake electrons are suppressed, particularly in the NoBrem category.
    • Semileptonic decays (e.g., $B^+ \to D^0 e^+ \nu_e$) are rejected using kinematic constraints (e.g., $m(\pi^+ e^-) > m_{D^0}$).

Analysis Strategy

• Normalization: The branching fraction is measured relative to the well-known mode $B^+ \to K^+ J/\psi (e^+ e^-)$.
• Fit Regions: The analysis is performed in two $q^2$ (dielectron mass squared) regions:
  1. Low-$q^2$: $[0.045, 6] \text{ GeV}^2/c^4$ (below charmonium resonances).
  2. High-$q^2$: $[15, 25] \text{ GeV}^2/c^4$ (above $\psi(2S)$).
• Statistical Model: An extended simultaneous maximum-likelihood fit is performed on the invariant mass distribution ($m(\pi^+ e^+ e^-)$) across eight categories (2 $q^2$ regions $\times$ 2 bremsstrahlung categories $\times$ 2 BDT output regions).
  • Signal: Modeled by a double-sided Crystal Ball function.
  • Backgrounds: Combinatorial background modeled by exponentials (low-$q^2$) or phase-space models (high-$q^2$); physical backgrounds constrained by simulation yields.

3. Key Contributions

• First Observation of $b \to d e^+ e^-$: This is the first evidence for the $B^+ \to \pi^+ e^+ e^-$ decay, establishing the existence of the $b \to d e^+ e^-$ quark-level transition.
• First Measurement of Branching Fraction: Provides the first quantitative measurement of the branching fraction for this specific channel.
• Methodological Rigor: Demonstrates advanced handling of bremsstrahlung recovery and misidentification backgrounds in electron modes, which are typically more challenging than muon modes due to photon conversions and hadron mis-ID.
• Validation of SM: The result serves as a critical test of Lepton Flavour Universality (LFU) by comparing the electron mode to the previously measured muon mode.

4. Results

Branching Fraction

The measured branching fraction is:
$$\mathcal{B}(B^+ \to \pi^+ e^+ e^-) = \left( 2.4^{+0.9}_{-0.8} \text{ (stat)} ^{+0.4}_{-0.2} \text{ (syst)} \right) \times 10^{-8}$$

Significance

• The signal excess has a statistical significance of $3.2\sigma$ (including systematic uncertainties).
• This constitutes "evidence" (typically defined as $>3\sigma$) but not yet "observation" ($>5\sigma$).

Differential Results

• Low-$q^2$ region: Significance of $3.2\sigma$.
• High-$q^2$ region: Significance of $0.8\sigma$. No signal observed; an upper limit is set: $\mathcal{B} < 1.25 \times 10^{-8}$ (90% CL).

Comparison with Standard Model

• The measured value is consistent with the SM prediction of $\mathcal{B}(B^+ \to \pi^+ \ell^+ \ell^-) = (2.04 \pm 0.21) \times 10^{-8}$.
• The ratio of electron to muon branching fractions is consistent with Lepton Flavour Universality within current uncertainties.

5. Significance

This paper represents a milestone in heavy flavour physics:

1. Completing the Picture: It confirms that the $b \to d$ transition occurs for electrons, matching the pattern seen in muons and validating the SM suppression mechanisms.
2. New Physics Constraints: By establishing a baseline measurement consistent with the SM, it constrains models of New Physics that might enhance $b \to d$ transitions or violate LFU specifically in the electron sector.
3. Future Prospects: The $3.2\sigma$ evidence suggests that with the full LHC Run 3 and Run 4 datasets (expected to increase luminosity significantly), this channel will likely reach the $5\sigma$ discovery threshold, allowing for precision tests of the CKM matrix and potential deviations from the SM.