From Threshold Crossing to Wave-function Renormalization: Defining the Pion Mott Temperature in a Magnetic Field
Abstract
We investigate the dissociation of the neutral pion in hot magnetized quark matter within the two-flavor Nambu--Jona-Lasinio model. At zero magnetic field, the Mott temperature is conventionally determined by mπ0(TMott)=2M(TMott), above which a real pole ceases to exist. At finite magnetic field, Landau quantization replaces this single threshold by a hierarchy of quark--antiquark continua and generates multiple solutions of the pion pole equation, rendering a direct threshold-crossing criterion ambiguous since a real pion solution below the lowest nominal threshold always exists. We therefore propose to define the magnetic Mott temperature through the inflection point of the pion wave-function renormalization factor Zπ0(T,eB) of that lowest pole, corresponding to the fastest loss of its spectral function strength. The prescription reproduces the conventional Mott temperature as eB→ 0 and tracks the chiral pseudocritical temperature for both constant and magnetic-field-dependent couplings. Our results characterize pion dissociation in a magnetic field as a spectral crossover rather than a simple threshold crossing.
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BibTeX
@misc{avancini2026from,
title = {{From Threshold Crossing to Wave-function Renormalization: Defining the Pion Mott Temperature in a Magnetic Field}},
author = {Sidney S. Avancini and Maximo Coppola and Dyana C. Duarte and Ricardo L. S. Farias and Norberto N. Scoccola and William R. Tavares},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.31125},
eprint = {2608.31125},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.31125},
}
RIS
TY - UNPB
TI - From Threshold Crossing to Wave-function Renormalization: Defining the Pion Mott Temperature in a Magnetic Field
AU - Sidney S. Avancini
AU - Maximo Coppola
AU - Dyana C. Duarte
AU - Ricardo L. S. Farias
AU - Norberto N. Scoccola
AU - William R. Tavares
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.31125
UR - https://arxiv.org/abs/2608.31125
AB - We investigate the dissociation of the neutral pion in hot magnetized quark matter within the two-flavor Nambu--Jona-Lasinio model. At zero magnetic field, the Mott temperature is conventionally determined by m_π^0(T_Mott)=2M(T_Mott), above which a real pole ceases to exist. At finite magnetic field, Landau quantization replaces this single threshold by a hierarchy of quark--antiquark continua and generates multiple solutions of the pion pole equation, rendering a direct threshold-crossing criterion ambiguous since a real pion solution below the lowest nominal threshold always exists. We therefore propose to define the magnetic Mott temperature through the inflection point of the pion wave-function renormalization factor Z_π^0(T,eB) of that lowest pole, corresponding to the fastest loss of its spectral function strength. The prescription reproduces the conventional Mott temperature as eB→ 0 and tracks the chiral pseudocritical temperature for both constant and magnetic-field-dependent couplings. Our results characterize pion dissociation in a magnetic field as a spectral crossover rather than a simple threshold crossing.
ER -