scholarly journals Two-flavor chiral perturbation theory at nonzero isospin: pion condensation at zero temperature

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Prabal Adhikari ◽  
Jens O. Andersen ◽  
Patrick Kneschke
Keyword(s):  
Perturbation Theory ◽  
Equation Of State ◽  
Condensed Phase ◽  
Chiral Perturbation Theory ◽  
Chemical Potential ◽  
Tree Level ◽  
Zero Temperature ◽  
Leading Order ◽  
Chiral Perturbation ◽  
Pion Condensation

Abstract In this paper, we calculate the equation of state of two-flavor finite isospin chiral perturbation theory at next-to-leading order in the pion-condensed phase at zero temperature. We show that the transition from the vacuum phase to a Bose-condensed phase is of second order. While the tree-level result has been known for some time, surprisingly quantum effects have not yet been incorporated into the equation of state.  We find that the corrections to the quantities we compute, namely the isospin density, pressure, and equation of state, increase with increasing isospin chemical potential. We compare our results to recent lattice simulations of 2 + 1 flavor QCD with physical quark masses. The agreement with the lattice results is generally good and improves somewhat as we go from leading order to next-to-leading order in $$\chi $$χPT.

scholarly journals Quark and pion condensates at finite isospin density in chiral perturbation theory

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Prabal Adhikari ◽  
Jens O. Andersen
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Chemical Potential ◽  
Chiral Condensate ◽  
Zero Temperature ◽  
Leading Order ◽  
Chiral Perturbation ◽  
Pion Condensate ◽  
Independent Analysis ◽  
Model Independent

AbstractIn this paper, we consider two-flavor QCD at zero temperature and finite isospin chemical potential $$\mu _I$$ μ I using a model-independent analysis within chiral perturbation theory at next-to-leading order. We calculate the effective potential, the chiral condensate and the pion condensate in the pion-condensed phase at both zero and nonzero pionic source. We compare our finite pionic source results for the chiral condensate and the pion condensate with recent (2+1)-flavor lattice QCD results. Agreement with lattice results generally improves as one goes from leading order to next-to-leading order.

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

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Prabal Adhikari ◽  
Jens O. Andersen ◽  
Martin A. Mojahed
Keyword(s):  
Phase Diagram ◽  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Chemical Potential ◽  
Low Energy ◽  
Leading Order ◽  
Loop Order ◽  
Chiral Perturbation ◽  
Model Calculations ◽  
Symmetric Phase

AbstractWe consider two-flavor chiral perturbation theory ($$\chi $$ χ PT) at finite isospin chemical potential $$\mu _I$$ μ I and finite temperature T. We calculate the effective potential and the quark and pion condensates as functions of T and $$\mu _I$$ μ I 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 $$\mu _I$$ μ I –T plane. Numerically, we find that the transition to the pion-condensed phase is second order in the region of validity of $$\chi $$ χ 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 $$\mu _I$$ μ I and find that $$\chi $$ χ PT seems to be converging very well.

scholarly journals Chiral perturbation theory and nucleon–pion-state contaminations in lattice QCD

2017 ◽  
Vol 32 (15) ◽  
pp. 1730011 ◽  
Author(s):  
Oliver Bär
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Distribution Functions ◽  
Leading Order ◽  
Chiral Perturbation ◽  
Parton Distribution Functions ◽  
Physical Point ◽  
Source Sink ◽  
The Impact ◽  
Quark Momentum

Multiparticle states with additional pions are expected to be a non-negligible source of excited-state contamination in lattice simulations at the physical point. It is shown that baryon chiral perturbation theory can be employed to calculate the contamination due to two-particle nucleon–pion-states in various nucleon observables. Leading order results are presented for the nucleon axial, tensor and scalar charge and three Mellin moments of parton distribution functions (quark momentum fraction, helicity and transversity moment). Taking into account phenomenological results for the charges and moments the impact of the nucleon–pion-states on lattice estimates for these observables can be estimated. The nucleon–pion-state contribution results in an overestimation of all charges and moments obtained with the plateau method. The overestimation is at the 5–10% level for source-sink separations of about 2 fm. The source-sink separations accessible in contemporary lattice simulations are found to be too small for chiral perturbation theory to be directly applicable.

scholarly journals ON THE CHIRAL PERTURBATION THEORY FOR TWO-FLAVOR TWO-COLOR QCD AT FINITE CHEMICAL POTENTIAL

2006 ◽  
Vol 21 (07) ◽  
pp. 559-569 ◽  
Author(s):  
TOMÁŠ BRAUNER
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Chemical Potential ◽  
Effective Theory ◽  
Einstein Condensation ◽  
Chiral Perturbation ◽  
Physical Content ◽  
Chemical Potentials ◽  
Bose Einstein ◽  
Quark Flavors

We construct the chiral perturbation theory for two-color QCD with two quark flavors as an effective theory on the SO(6)/SO(5) coset space. This formulation turns out to be particularly useful for extracting the physical content of the theory when finite baryon and isospin chemical potentials are introduced, and Bose–Einstein condensation sets on.

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