Chiral restoration at finite T under the magnetic field with the meson-loop corrections

Journal Article · Sun May 01 00:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.096009· OSTI ID:21541658

Nam, Seung-il ^[1]; Kao, Chung-Wen ^[2]

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1. Research Institute for Basic Sciences, Korea Aerospace University, Goyang 412-791 (Korea, Republic of)
2. Department of Physics, Chung-Yuan Christian University, Chung-Li 32023, Taiwan (China)

We investigate the (partial) chiral restoration at finite temperature (T) under the strong external magnetic field B=B{sub 0}z-circumflex of the SU(2) light-flavor QCD matter. To this end, we employ the instanton-liquid QCD vacuum configuration accompanied with the linear Schwinger method for inducing the magnetic field. The Harrington-Shepard caloron solution is used to modify the instanton parameters, i.e. the average instanton size ({rho}) and interinstanton distance (R), as functions of T. In addition, we include the meson-loop corrections as the large-N{sub c} corrections because they are critical for reproducing the universal chiral-restoration pattern. We present the numerical results for the constituent-quark mass as well as chiral condensate, which signal the spontaneous breakdown of chiral-symmetry (SB{chi}S), as functions of T and B{sub 0}. From our results we observe that the strengths of those chiral order parameters are enhanced with respect to B{sub 0} due to the magnetic-catalysis effect. We also find that there appears a region where the u and d-quark constituent masses coincide with each other at eB{sub 0{approx_equal}}(7-9)m{sub {pi}}{sup 2}, even in the presence of the explicit isospin breaking (m{sub u{ne}}m{sub d}). The critical T for the chiral restoration T{sub c} tends to shift to the higher temperature in the presence of the B{sub 0} for the chiral limit but keeps almost stationary for the physical quark mass case. The strength of the isospin breaking between the quark condensates is also explored in detail by defining the ratio R{identical_to}(<iu{sup {dagger}u}>-<id{sup {dagger}d}>)/(<iu{sup {dagger}u}>+<id{sup {dagger}d}>), which indicates the competition between the explicitly isospin-breaking effect and magnetic-catalysis effect. We also compute the pion weak-decay constant F{sub {pi}} and pion mass m{sub {pi}} below T{sub c}, varying the strength of the magnetic field, showing correct partial chiral-restoration behaviors. Besides we find that the changes for the F{sub {pi}} and m{sub {pi}} due to the magnetic field is relatively small, in comparison to those caused by the finite T effect.

• OSTI ID: 21541658
• Journal Information: Physical Review. D, Particles Fields, Vol. 83, Issue 9; Other Information: DOI: 10.1103/PhysRevD.83.096009; (c) 2011 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BREAKDOWN
CHIRAL SYMMETRY
CHIRALITY
COMPARATIVE EVALUATIONS
COMPUTERIZED SIMULATION
CONDENSATES
CONFIGURATION
CORRECTIONS
D QUARKS
FLAVOR MODEL
ISOSPIN
MAGNETIC FIELDS
MASS
ORDER PARAMETERS
PARTICLE DECAY
PIONS
QUANTUM CHROMODYNAMICS
QUARK CONDENSATION
SCHWINGER VARIATIONAL METHOD
BOSONS
CALCULATION METHODS
COMPOSITE MODELS
DECAY
DIMENSIONLESS NUMBERS
ELEMENTARY PARTICLES
EVALUATION
FERMIONS
FIELD THEORIES
HADRONS
MATHEMATICAL MODELS
MESONS
PARTICLE MODELS
PARTICLE PROPERTIES
PSEUDOSCALAR MESONS
QUANTUM FIELD THEORY
QUARK MODEL
QUARKS
SIMULATION
SYMMETRY
VARIATIONAL METHODS