Pions swell in the heat express

Original: "A large size of the pion-like excitations in the stringy fluid above $$T_{ch}$$ is model independent and required by current algebra"
· L. Ya. Glozman
arXiv:2608.04563v1 · 2026-08-05 · CC BY 4.0 · 1 min
Above a critical temperature, pions lose mass and become enormous.

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Ordinary ice turns into water at zero degrees. And matter at nuclear density, quark-gluon plasma, undergoes something similar at about 155 MeV (roughly two trillion degrees). Only here, it's not a crystal lattice that melts, but the so-called quark condensate — the vacuum sea that gives particles their mass. Above this threshold, quarks become massless but remain confined in color singlets, as if tethered by gluonic strings.

155 MeV is the energy at which a cubic femtometer of space stops telling left from right.

In such a hot medium, pions, the lightest composite particles, begin to swell rapidly. The reason is the Pauli principle: thermal quarks fill all the low-energy levels, leaving no room for the condensate to form. Without the condensate, the pion has nothing to lean on, and its size grows. In the limit of zero quark mass, the pion becomes infinitely large. This is not a hypothesis but a direct consequence of current algebra.

Huge pions easily collide with each other — hence the collectivity observed in experiments: particles move as a single fluid with a very small mean free path. Lattice calculations confirm that above 3T_{ch}, pion peaks in correlators disappear — likely because the particle no longer fits in the simulation box.

Original abstract

as written by the authors arXiv:2608.04563v1

Multiple lattice evidences support the existence of a confining but chirally symmetric stringy fluid regime of QCD above the chiral symmetry restoration temperature at T_{ch} ~ 155 MeV. This regime is characterized by an approximate chiral spin symmetry and its extensions which means that the propagating excitations represent the chirally symmetric quarks connected into color singlets by the chromoelectric string. Clear \pi,\pi' peaks above T_{ch} were extracted on the lattice from the spatial and temporal correlators, which become broader with temperature and disappear roughly at $$3T_{ch}$$. The meson-like excitations above T_{ch} were studied within the manifestly confining and chirally symmetric model. It has been demonstrated that the chiral symmetry restoration in the confining regime happens because of Pauli blocking of the levels, required for the existence of the quark condensate, by the thermal quark excitation. The same Pauli blocking leads to a huge swelling of the low-spin mesons above T_{ch} which become infinitely large in the chiral limit. This property should be crucial for the explanation of the high collectivity and a very small mean-free path of the constituents above $$T_{ch}$$ seen experimentally. Here we demonstrate that the swelling of pions above T_{ch} is a model-independent effect required by current algebra.

In the chiral limit (when the quark mass is exactly zero), the pion becomes infinitely large, yet it remains a bound state, the gluonic string does not break.

In Vernor Vinge's novel "A Fire Upon the Deep," faster-than-light communication works through "zones of thought," where the properties of space change — much like temperature switches the regimes of the QCD vacuum.

Scientists
Ludwig BoltzmannRudolf ClausiusEmmy NoetherWolfgang PauliEnrico FermiPaul Dirac
Concepts
critical point Phase transition gluon Standard Modelsecond law of thermodynamicsNoether's theoremspin–statistics theoremFermi's golden ruleCPT theoremCurie's law