Revisiting the U(1)-CP tension in QCD from a 1PI-action perspective
Abstract
We discuss the tension one encounters in trying to solve, simultaneously, the U(1) and strong-CP problems in QCD with light quarks and a small θ̅ angle within QCD itself. We do so by considering the low-energy expansion of a $1$PI effective action Γ, a functional of a properly chosen set of gauge-invariant (composite) operators. After enforcing Ward-identity constraints on Γ, we prove, under minor assumptions, that CP violation at small non-vanishing θ̅ can be avoided only if the anomaly-induced contribution to the pseudoscalar mass matrix is completely negligible when compared to its non-anomalous counterpart - that is, only if the U(1) problem is not solved. The topological susceptibility in QCD and a precise generalization of the one in pure Yang-Mills theory emerge as the most important players in establishing the above tension and in determining the corrections to various known results at leading order in θ̅.
Related
- Revisiting the Hubble tension with an inverse power-law early dark energy
- Revisiting the Hubble Tension with DESI DR2 Baryon Acoustic Oscillation Observations and Machine Learning Methods
- Viscous fingering at ultralow interfacial tension
- Preliminary results on hydro-chemo-mechanical response of Wharton's jelly undergoing tension
- Revisiting the Fokker-Planck approach and its relation to the sample’s real-space correlation function in single-grid X-ray dark-field imaging
BibTeX
@misc{vecchia2026revisiting,
title = {{Revisiting the $U(1)$-$CP$ tension in QCD from a 1PI-action perspective}},
author = {Paolo Di Vecchia and Francesco Sannino and Graham M. Shore and Gabriele Veneziano and Shimon Yankielowicz},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28253},
eprint = {2608.28253},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28253},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Revisiting the U(1)-CP tension in QCD from a 1PI-action perspective
AU - Paolo Di Vecchia
AU - Francesco Sannino
AU - Graham M. Shore
AU - Gabriele Veneziano
AU - Shimon Yankielowicz
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28253
UR - https://arxiv.org/abs/2608.28253
AB - We discuss the tension one encounters in trying to solve, simultaneously, the U(1) and strong-CP problems in QCD with light quarks and a small θ̅ angle within QCD itself. We do so by considering the low-energy expansion of a $1$PI effective action Γ, a functional of a properly chosen set of gauge-invariant (composite) operators. After enforcing Ward-identity constraints on Γ, we prove, under minor assumptions, that CP violation at small non-vanishing θ̅ can be avoided only if the anomaly-induced contribution to the pseudoscalar mass matrix is completely negligible when compared to its non-anomalous counterpart - that is, only if the U(1) problem is not solved. The topological susceptibility in QCD and a precise generalization of the one in pure Yang-Mills theory emerge as the most important players in establishing the above tension and in determining the corrections to various known results at leading order in θ̅.
ER -