Condensates and pressure of two-flavor chiral perturbation theory at nonzero isospin and temperature

2020/10/31 by Prabal Adhikari, Jens O. Andersen, Martin A. Mojahed
Physics and Astronomy · #Chiral perturbation theory #High-Energy Particle Collisions Research #Isospin #Lattice (music) #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Phase diagram #Phase transition #Pion #Pulsars and Gravitational Waves Research #Quantum Chromodynamics and Particle Interactions #hep-ph #nucl-th

paper · pdf · doi:10.1140/epjc/s10052-021-08948-6

published as Eur. Phys. J. C 80, 173 (2021) · 11 pages and 6 figures, LaTeX; typos corrected, references added

openalex created_date 2020/10/29 · openalex publication_date 2021/02/01 · arxiv created 2021/02/21 · arxiv updated 2021/02/26 · openalex updated_date 2026/08/05

Abstract

Abstract We consider two-flavor chiral perturbation theory ( χ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>χ</mml:mi> </mml:math> PT) at finite isospin chemical potential μ _I <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>μ</mml:mi> <mml:mi>I</mml:mi> </mml:msub> </mml:math> and finite temperature T . We calculate the effective potential and the quark and pion condensates as functions of T and μ _I <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>μ</mml:mi> <mml:mi>I</mml:mi> </mml:msub> </mml:math> to next-to-leading order in the low-energy expansion in the presence of a pionic source. We map out the phase diagram in the μ _I <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>μ</mml:mi> <mml:mi>I</mml:mi> </mml:msub> </mml:math> – T plane. Numerically, we find that the transition to the pion-condensed phase is second order in the region of validity of χ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>χ</mml:mi> </mml:math> PT, which is in agreement with model calculations and lattice simulations. Finally, we calculate the pressure to two-loop order in the symmetric phase for nonzero μ _I <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>μ</mml:mi> <mml:mi>I</mml:mi> </mml:msub> </mml:math> and find that χ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>χ</mml:mi> </mml:math> PT seems to be converging very well.

Citations

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