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Accessing the Wess-Zumino-Witten term using Lattice QCD
Abstract
The Wess-Zumino-Witten interaction in chiral perturbation theory is a manifestation of chiral anomalies. One of its consequences is the presence of a nonvanishing K K̅ → π+ π0 π- amplitude. We derive the finite-volume formalism that allows one to access this, and related, amplitudes, using the spectra of two and three particles in finite volumes, spectra that can be calculated using lattice QCD. Specifically, we present the formalism for the systems K K̅ + 3 π with I=0 and πK + ππK with I=1/2 and 3/2. In addition, we determine the threshold expansions for the 2↔ 3 and 3↔ 3 K matrices that enter the formalism, and calculate the leading order predictions from chiral perturbation theory for the coefficients that enter these expansions.
Related
- Revisiting the Wess-Zumino-Witten Term in Nuclear and Quark Matter under Magnetic Fields and Rotation
- Fractional Superfluid Vortices and Worldsheet Wess--Zumino--Witten Models in Two-Color QCD and Sp(2N) Gauge Theories
- The 1+1D 𝒩=2 Wess--Zumino model
- The Wess-Zumino Action of the Conformal Anomaly
- Lattice QCD calculation of the pion-nucleon coupling g̅0 induced by the QCD Θ-term
BibTeX
@misc{romerolopez2026accessing,
title = {{Accessing the Wess-Zumino-Witten term using Lattice QCD}},
author = {Fernando Romero-López and Stephen R. Sharpe},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05006},
eprint = {2609.05006},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05006},
}
RIS
TY - UNPB
TI - Accessing the Wess-Zumino-Witten term using Lattice QCD
AU - Fernando Romero-López
AU - Stephen R. Sharpe
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05006
UR - https://arxiv.org/abs/2609.05006
AB - The Wess-Zumino-Witten interaction in chiral perturbation theory is a manifestation of chiral anomalies. One of its consequences is the presence of a nonvanishing K K̅ → π^+ π^0 π^- amplitude. We derive the finite-volume formalism that allows one to access this, and related, amplitudes, using the spectra of two and three particles in finite volumes, spectra that can be calculated using lattice QCD. Specifically, we present the formalism for the systems K K̅ + 3 π with I=0 and πK + ππK with I=1/2 and 3/2. In addition, we determine the threshold expansions for the 2↔ 3 and 3↔ 3 K matrices that enter the formalism, and calculate the leading order predictions from chiral perturbation theory for the coefficients that enter these expansions.
ER -