TY - JOUR

T1 - Critical number of flavors in QED

AU - Bashir, A.

AU - Calcaneo-Roldan, C.

AU - Gutiérrez-Guerrero, L. X.

AU - Tejeda-Yeomans, M. E.

PY - 2011/2/11

Y1 - 2011/2/11

N2 - We demonstrate that in unquenched quantum electrodynamics (QED), chiral symmetry breaking ceases to exist above a critical number of fermion flavors Nf. This is a necessary and sufficient consequence of the fact that there exists a critical value of electromagnetic coupling α beyond which dynamical mass generation gets triggered. We employ a multiplicatively renormalizable photon propagator involving leading logarithms to all orders in α to illustrate this. We study the flavor and coupling dependence of the dynamically generated mass analytically as well as numerically. We also derive the scaling laws for the dynamical mass as a function of α and N f. Up to a multiplicative constant, these scaling laws are related through (α,αc)↔(1/Nf,1/Nfc). Calculation of the mass anomalous dimension γm shows that it is always greater than its value in the quenched case. We also evaluate the β function. The criticality plane is drawn in the (α,Nf) phase space which clearly depicts how larger Nf is required to restore chiral symmetry for an increasing interaction strength. © 2011 American Physical Society.

AB - We demonstrate that in unquenched quantum electrodynamics (QED), chiral symmetry breaking ceases to exist above a critical number of fermion flavors Nf. This is a necessary and sufficient consequence of the fact that there exists a critical value of electromagnetic coupling α beyond which dynamical mass generation gets triggered. We employ a multiplicatively renormalizable photon propagator involving leading logarithms to all orders in α to illustrate this. We study the flavor and coupling dependence of the dynamically generated mass analytically as well as numerically. We also derive the scaling laws for the dynamical mass as a function of α and N f. Up to a multiplicative constant, these scaling laws are related through (α,αc)↔(1/Nf,1/Nfc). Calculation of the mass anomalous dimension γm shows that it is always greater than its value in the quenched case. We also evaluate the β function. The criticality plane is drawn in the (α,Nf) phase space which clearly depicts how larger Nf is required to restore chiral symmetry for an increasing interaction strength. © 2011 American Physical Society.

U2 - 10.1103/PhysRevD.83.033003

DO - 10.1103/PhysRevD.83.033003

M3 - Article

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

ER -