New precise measurement of the $e^+e^- \rightarrow π^+π^-(γ)$ cross section with BABAR

The BABAR collaboration presents preliminary results from a new blind analysis of 460 fb⁻¹ of data, confirming consistency with their 2009 measurement of the $e^+e^- \rightarrow \pi^+\pi^-(\gamma)$ cross section to improve the precision of the muon anomalous magnetic moment prediction.

The Gist

Imagine the universe as a giant, complex machine, and one of its most important dials is the muon. A muon is a tiny particle, like a heavier cousin of the electron, that spins around like a top. Physicists have a very precise prediction for how fast this top should spin, based on the laws of physics they know. However, when they actually measure the spin in the lab, it spins slightly differently than expected. This tiny difference is called the "anomalous magnetic moment," and it's a huge mystery.

The paper you provided is about a team of scientists (the BABAR collaboration) trying to solve a piece of this puzzle. Here is how they did it, explained simply:

The Problem: A Noisy Room

To understand why the muon's spin is off, scientists need to calculate a specific contribution called "hadronic vacuum polarization." Think of this as trying to hear a whisper in a very noisy room. The "noise" comes from the fact that empty space isn't actually empty; it's bubbling with temporary particles popping in and out of existence.

The biggest source of this noise comes from a specific interaction where an electron and a positron (a particle of antimatter) collide and turn into a pair of pions (another type of particle). To get a clear picture of the muon's spin, scientists need to measure exactly how often this collision happens.

The Old vs. The New Measurement

The BABAR experiment, which ran from 1999 to 2008, previously measured this collision in 2009. But they wanted to be even more sure. So, they went back to their data vaults and looked at twice as much information (460 units of data, compared to the 232 they had before).

The Old Way (2009):
Imagine trying to sort a pile of red and blue marbles. In 2009, the scientists used a special "magnet" (called Particle Identification) to separate the red marbles (pions) from the blue ones (muons). However, this magnet wasn't perfect; it sometimes got confused, and that confusion was the biggest source of error in their results.

The New Way (2025):
In this new study, the scientists decided to throw away the "magnet" entirely. Instead, they looked at the dance moves of the particles.

• They analyzed the angle at which the particles flew apart after the collision.
• Just like you can tell a dancer is doing a waltz versus a tango by their footwork, the scientists could tell if they were looking at pions or muons based purely on the angles of their paths.
• They used a computer "blindfold" (a technique called blinding) so they wouldn't accidentally bias the results while they were working. They only took the blindfold off at the very end.

The Results: A Perfect Match

After doing all this complex math and angle-checking, they compared their new results with the old 2009 results.

• The Verdict: The two measurements matched almost perfectly.
• Why it matters: This is like if you measured the height of a building with a ruler in 2009, and then used a laser scanner in 2025, and both gave you the exact same number. It proves that the measurement is solid and reliable.

The Big Picture

By combining their old and new data, the BABAR team has created the most precise measurement ever of this specific particle interaction from a single experiment.

This doesn't solve the entire mystery of the muon's spin yet, but it removes a major source of doubt. It tells the rest of the physics community: "We are very confident in this number." Now, other scientists can use this precise number to see if the remaining difference between the theory and the experiment is truly a sign of new, unknown physics, or just a calculation error.

In short: The scientists took a second, more careful look at an old experiment using a clever new trick (watching the angles instead of using a magnet). The new look confirmed the old look, giving the scientific community a much stronger foundation to investigate the mysteries of the universe.

Technical Summary

Technical Summary: New Precise Measurement of the $e^+e^- \to \pi^+\pi^-(\gamma)$ Cross Section with BABAR

Problem and Motivation
The anomalous magnetic moment of the muon, $a_\mu$, is a critical observable for testing the Standard Model, with its predicted value dominated by uncertainties in the hadronic vacuum polarization (HVP) contribution. Current dispersive predictions for the HVP contribution to $a_\mu$, derived from $e^+e^- \to \text{hadrons}$ cross-section measurements, exhibit significant tensions with one another (notably between KLOE and CMD-3 results at the $\rho$ meson peak) and with direct experimental measurements and lattice QCD calculations. The $e^+e^- \to \pi^+\pi^-$ channel provides the largest input to this dispersion integral. The BABAR collaboration previously published a measurement of this cross section in 2009 using 232 fb$^{-1}$ of data. This paper presents a new, independent analysis utilizing approximately 460 fb$^{-1}$ of data (twice the previous statistics) to resolve discrepancies and improve precision.

Methodology
The new analysis employs a "blind" procedure with an independent channel separation method distinct from the 2009 study. Key methodological shifts include:

• Data Sample: Utilization of 460 fb$^{-1}$ of data collected at the $\Upsilon(4S)$ resonance and off-resonance, compared to the 232 fb$^{-1}$ used previously.
• Channel Separation: Unlike the 2009 analysis, which relied on Particle Identification (PID) to distinguish pions from muons (requiring $p > 1$ GeV/c), this study removes strict PID requirements. Instead, it utilizes an angular fit based on the absolute value of the cosine of the angle between the negative charge track and the Initial State Radiation (ISR) photon in the two-track center-of-mass frame ($|\cos \theta^*|$).
• Kinematic Fits: Events undergo kinematic fits assuming Next-to-Leading Order (NLO) radiation, performed twice under both muon and pion mass hypotheses.
• Background Subtraction: Signal and background processes are separated using a two-dimensional $\chi^2$ selection ($\chi^2_{LA}$ vs. $\chi^2_{SA}$) optimized with Boosted Decision Trees (BDTs), retaining over 98% of the signal. Remaining backgrounds ($\pi\pi\gamma$, $\mu\mu\gamma$, $KK\gamma$, and $ee\gamma$) are subtracted using templates derived from corrected Monte Carlo (MC) simulations or data-enriched samples (specifically for $ee\gamma$).
• Blinding: Both the $\mu\mu\gamma$ and $\pi\pi\gamma$ mass spectra are blinded using unique multiplicative factors until the final steps. Trigger and tracking corrections are similarly blinded.
• Luminosity Determination: The effective ISR luminosity is derived from the unfolded $\mu\mu\gamma$ spectrum, validated against QED predictions. The ratio of the $\pi\pi\gamma$ to $\mu\mu\gamma$ spectra is used to calculate the bare cross section, canceling common systematic effects related to ISR photon efficiency, luminosity, and vacuum polarization.

Key Results

• Consistency with QED: The ratio of the dimuon data spectrum to the QED prediction is found to be flat across the full mass range, yielding a value of $0.9955 \pm 0.0035_{\text{stat}} \pm 0.0030_{\text{syst}} \pm 0.0033_{\gamma\text{ISR}} \pm 0.0043_{\text{lumi}}$. This validates the separation procedure and the efficiency corrections.
• Cross Section Measurement: The measured $e^+e^- \to \pi^+\pi^-(\gamma)$ cross section is presented as a function of reduced energy $\sqrt{s'}$. The results are consistent with the 2009 BABAR measurement across most of the range from threshold to 1.4 GeV, with deviations observed only at higher energies.
• Contribution to $a_\mu$:
  • Below 0.5 GeV: $(58.0 \pm 5.5_{\text{stat}} \pm 1.7_{\text{syst}}) \times 10^{-10}$.
  • Between 0.5 and 1.4 GeV: $(456.2 \pm 2.2_{\text{stat}} \pm 1.7_{\text{syst}}) \times 10^{-10}$.
  • These values are in excellent agreement with the 2009 results ($57.6 \pm 0.6 \pm 0.6$ and $455.6 \pm 2.1 \pm 2.6$, respectively).
• Combined Precision: When combined with the 2009 study from threshold to 1.8 GeV, the two analyses yield a value of $(514.4 \pm 2.5) \times 10^{-10}$, representing the most precise measurement of the $\pi\pi$ contribution to $a_\mu$ from a single experiment.

Significance and Claims
The paper claims that the new analysis demonstrates the robustness of the BABAR measurements through the consistency of two independent analyses using different separation techniques and doubled statistics. By removing the reliance on PID (the dominant systematic uncertainty in the 2009 analysis) and replacing it with an angular fit, the study mitigates specific systematic errors. While the new measurement does not improve the precision at low energies due to the statistical dominance of dimuon events in those regions, it improves the systematic uncertainty in the higher energy range. The primary significance lies in the confirmation of the previous BABAR results and the provision of the most precise single-experiment determination of the $\pi\pi$ contribution to the muon anomalous magnetic moment to date.