Angular analysis of the $B^+\to\pi^+\mu^+\mu^-$ decay

This paper presents the first measurement of the angular distribution parameters, specifically the forward-backward asymmetry ($A_{\rm FB}$) and the flat term ($F_{H}$), for the $B^+\to\pi^+\mu^+\mu^-$ decay using LHCb data, finding results that are largely consistent with Standard Model predictions.

The Gist

The Cosmic Detective Story: Hunting for "Ghost Particles" in a B-Meson Decay

Imagine you are a detective trying to solve a mystery in a world where the rules of physics are the "laws of the land." Most of the time, these laws (the Standard Model) work perfectly. But physicists suspect there might be "ghosts" in the machine—invisible particles or forces that aren't in our rulebook but are secretly influencing how things move.

This paper, written by the massive LHCb collaboration at CERN, is a report on a high-stakes investigation into one specific, rare event: the decay of a particle called a $B^+$ meson.

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1. The Subject: The "Unstable Dancer"

Think of a $B^+$ meson as a highly energetic, unstable dancer performing a complex routine. Eventually, the dancer "breaks apart" (decays) into three smaller pieces: a pion ($\pi^+$) and two muons ($\mu^+$ and $\mu^-$).

Because this specific dance is incredibly rare—happening only about 8 times in every billion attempts—it is the perfect place to look for trouble. If a "ghost particle" (New Physics) is lurking around, it will nudge the pieces of the dance, changing the way they fly away from each other.

2. The Investigation: Measuring the "Dance Moves"

The scientists aren't just looking to see if the decay happens; they are looking at the geometry of the explosion. They focus on two specific "moves" in the dance:

• The Forward-Backward Asymmetry ($A_{FB}$): Imagine the two muons flying away from the center. Do they prefer to fly in the same direction, or do they prefer to fly in opposite directions? If they fly in a way that seems "lopsided" or biased, it’s a sign that an invisible force is pushing them.
• The Flatness ($F_H$): This measures how "spread out" the muons are. Are they flying out in a predictable, organized pattern, or is the distribution "flat" and chaotic?

3. The Tool: The World’s Most Powerful Microscope

To see this, they used the LHCb experiment, a giant detector at the Large Hadron Collider. Think of the LHC as a massive, high-speed particle smasher that creates billions of these "dancers" every second. The LHCb is like a high-speed, ultra-sensitive camera that captures the exact angle and speed of every tiny fragment flying off after the crash.

4. The Findings: "No Ghosts... Yet"

After analyzing a massive amount of data (equivalent to 9 femtobarns of collision energy), the scientists looked at their results:

• In the "High-Energy" zone: Everything looked exactly like the rulebook (the Standard Model) predicted. The "dance" was perfectly normal.
• In the "Low-Energy" zone: They saw a tiny bit of "wobble." The numbers didn't perfectly match the rulebook, but they weren't "weird" enough to call it a discovery. It was like seeing a shadow in the corner of your eye—it might be a ghost, or it might just be the way the light hit the wall.

In scientific terms, they say the results are "consistent with the Standard Model."

The Bottom Line

This paper is a "sanity check" for the universe. By proving that this specific decay follows the known rules of physics, they are narrowing down where the "ghosts" might be hiding. They haven't found the New Physics yet, but they have successfully mapped out the territory, telling future detectives: "Don't look for the ghosts here; keep searching elsewhere!"

Technical Summary

Technical Summary: Angular Analysis of the $B^+ \to \pi^+ \mu^+ \mu^-$ Decay

Title: Angular analysis of the $B^+ \to \pi^+ \mu^+ \mu^-$ decay
Collaboration: LHCb Collaboration
Date: April 23, 2026
Dataset: 9 fb⁻¹ of proton-proton collision data (LHC Run 1 and Run 2, 2011–2018)

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1. The Problem

The decay $B^+ \to \pi^+ \mu^+ \mu^-$ is a rare process mediated by a $b \to d$ flavour-changing neutral-current (FCNC) transition. In the Standard Model (SM), these transitions are forbidden at the tree level and occur only through loop diagrams (penguin and box diagrams). Because the $V_{td}$ element of the CKM matrix is small, the branching fraction is highly suppressed ($\mathcal{O}(10^{-8})$).

While previous studies by LHCb and other collaborations have measured the branching fraction and CP asymmetry, the angular distribution of this specific decay had never been measured. Measuring the angular observables is critical because they are sensitive to potential New Physics (NP) contributions—such as scalar, pseudoscalar, or tensor interactions—that could deviate from SM predictions even if the total decay rate remains consistent with the SM.

2. Methodology

The analysis focuses on two angular parameters that describe the differential decay rate:

• $A_{FB}$ (Forward-Backward Asymmetry): The asymmetry of the dimuon system.
• $F_H$ (Flat Term): A parameter characterizing the flatness of the $\cos \theta_\ell$ distribution.

Experimental Approach:

• Data Selection: The researchers used a dataset of 9 fb⁻¹ collected at center-of-mass energies of 7, 8, and 13 TeV. The analysis is split into two dimuon mass squared ($q^2$) intervals to avoid the narrow charmonium resonances ($J/\psi$ and $\psi(2S)$):
  • Low-$q^2$: $1.1 < q^2 < 6.0 \text{ GeV}^2/c^4$
  • High-$q^2$: $15.0 < q^2 < 22.0 \text{ GeV}^2/c^4$
• Signal Extraction: A simultaneous unbinned maximum-likelihood fit was performed on the $\pi^+ \mu^+ \mu^-$ invariant mass and the $\cos \theta_\ell$ angle.
• Background Modeling: The primary background is the misidentified $B^+ \to K^+ \mu^+ \mu^-$ decay (where a kaon is mistaken for a pion). Other backgrounds include combinatorial backgrounds and hadronic decays (e.g., $B^+ \to \pi^+ \pi^- \pi^+$).
• Statistical Method: Due to the small sample sizes and the physical boundary requirement ($|A_{FB}| \leq F_H/2$), the Feldman–Cousins approach was used to construct confidence intervals.
• Control Channels: $B^+ \to J/\psi \pi^+$ and $B^+ \to J/\psi K^+$ were used to validate the selection and modeling strategies.

3. Key Contributions

• First Measurement: This paper represents the first-ever measurement of the angular distribution ($A_{FB}$ and $F_H$) for the $B^+ \to \pi^+ \mu^+ \mu^-$ decay.
• Precision Modeling: The study provides a detailed treatment of angular efficiency using Legendre polynomials and accounts for complex systematic uncertainties, including $q^2$ spectrum dependence and detector resolution.
• Constraint on New Physics: By providing these measurements, the paper sets new constraints on the possible presence of non-SM tensor, scalar, and pseudoscalar couplings in $b \to d$ transitions.

4. Results

The measured values for the two $q^2$ regions are summarized below:

Region	$F_H$ (Value)	$F_H$ (68% CL Interval)	$A_{FB}$ (Value)	$A_{FB}$ (68% CL Interval)
Low-$q^2$	0.91	[0.60, 0.99]	0.27	[0.11, 0.42]
High-$q^2$	0.04	[0.00, 0.20]	0.02	[−0.02, 0.09]

• Low-$q^2$ Region: The results show a non-zero $A_{FB}$ and a large $F_H$. While these values are not consistent with the SM at the 95% confidence level, they remain consistent with the SM within the 99% confidence level.
• High-$q^2$ Region: The results are fully consistent with the SM within the 68% confidence level.

5. Significance

This measurement is a significant step in the global effort to find deviations from the Standard Model in rare B-decays. While the low-$q^2$ results show a slight tension with the SM (notably in the $A_{FB}$ and $F_H$ values), the statistical significance is not yet high enough to claim a discovery of New Physics. However, the results provide a vital benchmark for theoretical models and set the stage for future, higher-precision measurements with more data from the LHCb Upgrade.