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Chiral anomaly: From vacuum to Columbia plot

Giacosa, Francesco B. [Jan Kochanowski Univ., Kielce (Poland); Goethe Univ., Frankfurt (Germany)] (ORCID:0000000272909366)·Kovács, Győző [Univ. of Wroclaw (Poland); HUN-REN Wigner Research Centre for Physics, Budapest (Hungary)] (ORCID:0000000305703621)·Kovács, Péter [HUN-REN Wigner Research Centre for Physics, Budapest (Hungary)] (ORCID:0000000337357620)·Pisarski, Robert D. [Brookhaven National Laboratory (BNL), Upton, NY (United States)] (ORCID:0000000278624759)·Rennecke, Fabian [Justus Liebig Univ., Giessen (Germany); Helmholtz Research Academy Hesse for FAIR (HFHF), Giessen (Germany)] (ORCID:000000031448677X)
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Abstract

Here, 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.

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73 NUCLEAR PHYSICS AND RADIATION PHYSICSChiral anomalyChiral modelsColumbia plotPolydeterminanteLSM

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Giacosa, Francesco B. [Jan Kochanowski Univ., Kielce (Poland); Goethe Univ., Frankfurt (Germany)] (ORCID:0000000272909366), Kovács, Győző [Univ. of Wroclaw (Poland); HUN-REN Wigner Research Centre for Physics, Budapest (Hungary)] (ORCID:0000000305703621), Kovács, Péter [HUN-REN Wigner Research Centre for Physics, Budapest (Hungary)] (ORCID:0000000337357620), Pisarski, Robert D. [Brookhaven National Laboratory (BNL), Upton, NY (United States)] (ORCID:0000000278624759), Rennecke, Fabian [Justus Liebig Univ., Giessen (Germany); Helmholtz Research Academy Hesse for FAIR (HFHF), Giessen (Germany)] (ORCID:000000031448677X). 2026-02-23. Chiral anomaly: From vacuum to Columbia plot. https://doi.org/10.1016/j.jspc.2026.100327

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