[論文レビュー] Chiral anomaly: from vacuum to Columbia plot

Giacosa, Francesco, Győző Kovács+3 more|arXiv (Cornell University)|Jan 7, 2026

Quantum Chromodynamics and Particle Interactions被引用数 0

ひとこと要約

The paper analyzes how different U(1)A anomaly terms in the extended linear sigma model (eLSM) affect vacuum phenomenology and the finite-temperature Columbia plot, including a novel polydeterminant extension to link anomalous interactions across meson multiplets.

ABSTRACT

We use a low-energy effective approach, the extended linear sigma model, to study realizations of the $U(1)_A$ anomaly with different operators, linear and quadratic in the 't Hooft determinant. After discussing the parameterization in agreement with vacuum's phenomenology, we investigate the influence of these different anomaly terms on the Columbia plot: the square of the 't Hooft determinant favors a cross-over for small quark masses. Finally, we also discuss the extension of the 't Hooft determinant to cases in which different mesonic multiplets interact with each other. Novel chiral anomalous interaction terms involving excited (pseudo)scalar states, pseudovector, and pseudotensor mesons are expressed via a mathematical extension of the determinant, denoted as a polydeterminant.

研究の動機と目的

• Investigate how various anomaly terms (determinant and its squares) realize the U(1)A anomaly in the eLSM.
• Parameterize anomaly couplings to reproduce vacuum hadron phenomenology.
• Assess how anomaly terms modify the Columbia plot at nonzero temperature and quark masses.
• Introduce and discuss the polydeterminant extension as a way to couple multiple meson multiplets and glueball states.

提案手法

• Use the extended linear sigma model (eLSM) with (axial-)vector mesons to implement anomaly terms.
• Consider the standard ’t Hooft determinant and its square, plus alternative Q=2 terms, in the Lagrangian.
• Define an effective anomaly coupling xi_eff that combines multiple anomaly terms and condensate factors.
• Fit model parameters to vacuum meson masses and decays from PDG to ensure vacuum phenomenology compatibility.
• Solve field equations at nonzero temperature to map the Columbia plot as a function of explicit symmetry-breaking parameters h_N and h_S.
• Generalize the determinant to a polydeterminant to model interactions among different meson multiplets and potential extensions to excited states.

Figure 1: The different parameter sets in the parameters subspace spanned by the $\xi_{1}$ , $\xi_{1}^{1}$ , and $\xi_{2}^{\mathrm{gen}}=\xi_{2},\xi_{2}^{\pm}$ are aligned on the $F(\phi_{N},\phi_{S})$ surface $\xi_{1}+\alpha\,\xi_{1}^{1}+\beta\,\xi_{2}^{\mathrm{gen}}=\bar{\xi}_{\mathrm{eff}}$ deter

実験結果

リサーチクエスチョン

• RQ1 How do different U(1)A anomaly terms (determinant, determinant squared, and their variants) influence vacuum hadron phenomenology in the eLSM?
• RQ2 What is the impact of these anomaly terms on the order and structure of the finite-temperature chiral phase transition as depicted by the Columbia plot?
• RQ3 Can the effective anomaly coupling provide a robust description across parameter sets despite individual term differences?
• RQ4 How does the polydeterminant extend anomalous interactions to interactions among multiple meson multiplets and glueball states?

主な発見

• The square of the ’t Hooft determinant strengthens the crossover region in the Columbia plot for small quark masses.
• Changing the balance of anomaly terms (e.g., introducing xi2) shifts the position of first-order regions and can shrink or remove them depending on parameter choices.
• The effective anomaly coupling xi_eff helps relate different anomaly terms and remains approximately constant across parametrizations, making vacuum fits compatible across setups.
• Varying xi1 and xi2 can move the model between scenarios with persistent first-order regions and scenarios resembling anomaly-free (or reduced-anomaly) cases, illustrating the sensitivity of the Columbia plot to anomaly structure.
• A polydeterminant framework is proposed to extend anomaly terms to interactions among distinct meson multiplets and glueball states, enabling new anomalous interaction possibilities.

Figure 2: The Columbia plot in the plane of the normalized explicit symmetry breaking parameters with parameters including $\xi_{1}$ (left), $\xi_{2}$ (right), and both (center).