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Volume Dependence of the Pion Mass in the Quark-Meson-Model

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arxiv hep-ph/0408116 v2 pith:M5RZIXZR submitted 2004-08-09 hep-ph

J. Braun (1) , B. Klein (1) , H.-J. Pirner (1 , 2) ((1) University of Heidelberg , (2) Max-Planck-Institut fuer Kernphysik , Heidelberg) This is my paper · ORCID
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keywords volumefinitepionchiralmassdependenceequationsflow
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We consider the quark-meson-model in a finite three-dimensional volume using the Schwinger proper-time renormalization group. We derive and solve the flow equations for finite volume in local potential approximation. In order to break chiral symmetry in the finite volume, we introduce a small current quark mass. The corresponding effective meson potential breaks chiral O(4) symmetry explicitly, depending on sigma and pion fields separately. We calculate the volume dependence of the pion mass and of the pion decay constant with the renormalization group flow equations and compare with recent results from chiral perturbation theory in a finite volume.

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Cited by 2 Pith papers

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  1. Dynamical quark mass and finite volume effects in the Dyson-Schwinger Equations

    hep-ph 2025-08 conditional novelty 4.0 of 10

    In a Dyson-Schwinger model with spherical finite-volume corrections and magnetic-field-dependent coupling, constituent quark masses fall by about 30-40% as the fireball radius shrinks from infinity to 2 fm.

  2. Finite size effects on the phase diagram and the baryon fluctuations via momentum space constraints

    hep-ph 2024-12 conditional novelty 4.0 of 10

    Finite-volume momentum-space constraints in a mean-field quark-meson model shift the critical endpoint significantly for L<10 fm and displace baryon fluctuation signals, with the shift direction depending on the chose...

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