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Related Experiment Video

Updated: May 29, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Lattice QCD and the timelike pion form factor.

Harvey B Meyer¹

¹Institut für Kernphysik, Johannes Gutenberg Universität Mainz, Germany.

Physical Review Letters

|September 10, 2011

Summary

We developed a new formula to calculate the pion form factor using lattice quantum chromodynamics (QCD). This method accurately determines two-pion contributions to vacuum polarization, crucial for muon anomalous magnetic moment calculations.

Area of Science:

* Theoretical particle physics
* Quantum chromodynamics (QCD)
* Hadron physics

Background:

* The pion form factor is essential for understanding vacuum polarization.
* Accurate calculations are needed to reduce theoretical uncertainty in the anomalous magnetic moment of the muon.
* Determining spectral functions typically requires analytic continuation, which is mathematically complex.

Purpose of the Study:

* To present a novel formula for calculating the pion form factor in the timelike region.
* To enable precise lattice QCD calculations of the pion form factor.
* To provide a method for determining spectral functions without analytic continuation.

Main Methods:

* Development of a new formula applicable to lattice QCD.

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* Focus on the timelike region for the pion form factor (2m(π) ≤ √(s) ≤ 4m(π)).

* Utilizing Euclidean observables to determine spectral functions.

Main Results:

* A formula is presented for calculating the pion form factor in a specific timelike kinematic regime.
* The formula quantifies the contribution of two-pion states to vacuum polarization.
* This approach avoids explicit analytic continuation for spectral function determination.

Conclusions:

* The presented formula offers a significant advancement in lattice QCD calculations.
* It provides a pathway to more accurate determination of the muon anomalous magnetic moment.
* This work represents a rare instance of determining a spectral function from Euclidean data without analytic continuation.