PrecisionSM: an annotated database for low-energy $e^+e^-$ hadronic cross sections

This paper presents PrecisionSM, a curated database developed within the STRONG2020 and RMCL2 initiatives that compiles annotated low-energy $e^+e^-$ hadronic cross-section data to support precise Standard Model tests via the muon anomalous magnetic moment, currently featuring dominant channels like $2\pi$, $3\pi$, and $\pi^0\gamma$ with plans for further expansion.

The Gist

Imagine the universe is a giant, incredibly complex machine, and the Standard Model is the instruction manual physicists have written to explain how every part of that machine works. For decades, this manual has been spot-on. But recently, a specific part of the machine—the muon (a tiny, heavy cousin of the electron)—started behaving in a way the manual didn't quite predict. It's wobbling slightly more than it should.

This wobble is called the anomalous magnetic moment (or $a_\mu$). Physicists are trying to figure out: Is the manual wrong? Or are we just missing a few pages?

The Problem: A Messy Library

To check the manual, scientists need to calculate a specific number based on how muons interact with other particles. To do this, they need to look at data from billions of past experiments where electrons and positrons smashed together to create bursts of other particles (hadrons).

Think of this data as a massive, chaotic library.

• The books (experimental papers) are scattered all over the world.
• Some are written in different languages (different formats).
• Some have torn pages (missing details about how they handled "radiative corrections," which are like accounting for the static electricity that messes up the measurements).
• Some books even contradict each other! (For example, a recent experiment called CMD-3 found results that didn't match older books, causing a huge debate).

Trying to calculate the muon's wobble using this messy library is like trying to bake a perfect cake by reading recipes from 50 different cookbooks, some of which are written in pencil, some are missing the sugar measurements, and some say "add a pinch of salt" while others say "add a cup."

The Solution: PrecisionSM

Enter PrecisionSM. Think of this not as a new book, but as a super-organized, annotated library catalog created by a team of librarians (the authors of this paper).

Here is what PrecisionSM does, using simple analogies:

1. The Master List: It gathers every single "recipe" (experiment) ever published for low-energy particle collisions. Instead of hunting through dusty archives, you go to one website.
2. The "Annotated" Part: This is the magic. For every experiment listed, the team adds sticky notes. These notes explain:
   • How did they handle the static electricity? (Radiative corrections).
   • What tools did they use? (Monte Carlo generators).
   • Are there any errors?
   • Where can I find the raw data? (Links to HEPData).
3. The Interactive Dashboard: It's not just a list; it's a dashboard. You can click a button to see a graph that instantly combines all these recipes to show you the current best estimate of the muon's wobble. It's like having a smart kitchen scale that automatically adjusts the recipe based on which cookbooks you trust most.

Why Does This Matter?

Right now, there is a "tension" (a disagreement) in the physics world.

• Group A uses the old library (dispersive approach) and says the muon's wobble proves there is new physics (new particles or forces we haven't discovered yet).
• Group B uses a supercomputer simulation (Lattice QCD) and says the manual is actually correct, and the wobble is just what we expected.

The PrecisionSM database is the referee. By cleaning up the data, fixing the "sticky notes," and making sure everyone is comparing apples to apples, it helps scientists decide who is right.

The Big Picture

The authors of this paper are part of a global team (STRONG2020) working to tidy up this library. They have already organized the data for the most important "ingredient" (the two-pion channel) and are working on the rest.

In short: PrecisionSM is a digital tool that turns a chaotic pile of confusing scientific papers into a clear, reliable map. This map helps physicists finally solve the mystery of the wobbling muon, which could either confirm our current understanding of the universe or reveal that there is a whole new layer of reality waiting to be discovered.

Technical Summary

1. Problem Statement

The paper addresses a critical discrepancy in Particle Physics regarding the muon anomalous magnetic moment ($a_\mu$).

• The Tension: There is a significant tension between the experimental measurement of $a_\mu$ (from Fermilab) and the theoretical prediction based on the Standard Model (SM).
• The Discrepancy Source: The theoretical prediction relies heavily on the hadronic vacuum polarization (HVP) contribution. The "data-driven dispersive approach" calculates this using an integral over low-energy $e^+e^- \to \text{hadrons}$ cross-sections.
• Recent Conflicts:
  • In 2020, the dispersive approach showed a $3.7\sigma$ tension with experiment.
  • In 2021, Lattice QCD calculations suggested a value closer to experiment, reducing the tension to $2.2\sigma$ but creating a new tension with the dispersive approach.
  • In 2023, the CMD-3 collaboration released new $e^+e^- \to \pi^+\pi^-$ cross-section data that disagreed with previous measurements used in the 2020 dispersive evaluation, further complicating the picture.
• The Need: To resolve these discrepancies and improve the precision of the dispersive approach, there is an urgent need for a centralized, annotated, and verified repository of all existing low-energy hadronic cross-section data, including details on radiative corrections and systematic treatments.

2. Methodology

The authors developed PrecisionSM, a specialized annotated database, through a structured workflow involving community collaboration:

• Organizational Framework: The project was initiated under the STRONG2020 European Union project (specifically the JRA3-PrecisionSM activity) and is now maintained by the RadioMonteCarLow2 (RMCL2) Working Group. This group unites experimentalists and theorists to study radiative corrections and Monte Carlo generators.
• Data Collection Strategy:
  1. Expert Consultation: A list of relevant experimental measurements was compiled based on expert input and existing reviews (e.g., Muon $g-2$ Theory Initiative reports).
  2. Channel Prioritization: The database initially focused on the dominant $2\pi$ ($\pi^+\pi^-$) channel, which contributes the most to the HVP integral, followed by $3\pi$ and $\pi^0\gamma$ channels.
• Validation and Curation Process:
  • Expert Point-of-Contact: The team contacts experimental collaborations to identify a specific expert.
  • HEPData Submission: The expert submits the raw data to the public repository HEPData.
  • Cross-Reference Validation: A reviewer validates the HEPData entry against the published paper on INSPIRE-HEP to ensure data integrity and correct metadata.
  • Annotation: The database links the HEPData tables to INSPIRE-HEP papers and adds specific "details" regarding:
    • Energy ranges.
    • Treatment of radiative corrections (crucial for "undressed" cross-sections).
    • Monte Carlo generators used.
    • Experimental techniques and systematic errors.
• Technical Implementation:
  • The database is hosted on a custom website (https://precision-sm.github.io) generated by Nikola.
  • It provides responsive plots that allow users to visualize data directly from HEPData tables, including error bars calculated with covariance matrices where available.

3. Key Contributions

• PrecisionSM Database: The creation of the first comprehensive, annotated database specifically for low-energy $e^+e^-$ hadronic cross sections.
• Standardization of Metadata: Unlike standard data repositories, PrecisionSM explicitly annotates the treatment of radiative corrections and the specific Monte Carlo generators used by each experiment. This is vital for comparing "bare" cross-sections ($\sigma_0$) without double-counting vacuum polarization effects.
• Integration of Tools: The platform links directly to INSPIRE-HEP (theory/paper context) and HEPData (raw data), and provides user-friendly tools to generate plots and calculate contributions to the $a_\mu$ integral (Eq. 1 in the paper).
• Community Collaboration: It establishes a formal workflow for experimental collaborations to submit, validate, and annotate their data for the global theoretical community.

4. Results

• Current Status: The database currently contains over 60 entries covering three hadronic channels:
  • $e^+e^- \to \pi^+\pi^-$ (dominant channel).
  • $e^+e^- \to \pi^+\pi^-\pi^0$ ($3\pi$).
  • $e^+e^- \to \pi^0\gamma$.
• Data Coverage: It includes historical data from major experiments (e.g., BESIII, BaBar, CLEO, KLOE, CMD-2, CMD-3, SND, VEPP-2M) spanning from the 1960s to 2024.
• Visualization: The paper presents examples of responsive plots generated from the database, including a plot evaluating the contribution of the $2\pi$ channel to the $a_\mu$ integral for experiments covering the 0.6–0.88 GeV range.
• CMD-3 Context: The database is designed to accommodate and facilitate the comparison of the controversial CMD-3 results with previous measurements to resolve the current tensions.

5. Significance

• Resolving the $a_\mu$ Crisis: By providing a unified, annotated source of truth for cross-section data, PrecisionSM enables independent groups to re-evaluate the dispersive calculation of $a_\mu$ with greater transparency. This is essential for determining whether the tension with experiment is due to new physics or inconsistencies in the input data.
• Bridging Theory and Experiment: The database serves as a critical interface between experimentalists (who provide the data) and theorists (who calculate $a_\mu$ and lattice QCD comparisons), ensuring that theoretical inputs are "undressed" and consistent.
• Future-Proofing: As the Fermilab Muon $g-2$ experiment reaches unprecedented precision (124 ppb) and Lattice QCD improves, the ability to quickly access and validate specific experimental inputs becomes paramount. PrecisionSM provides the infrastructure to support these high-precision tests of the Standard Model.
• Community Standard: It sets a new standard for data curation in hadronic physics, moving beyond simple data dumps to annotated, context-rich repositories that include methodological details (radiative corrections) often lost in raw data files.