TY - JOUR

T1 - Pion and Kaon electromagnetic masses in chiral perturbation theory

AU - Langacker, Paul

AU - Pagels, Heinz

PY - 1973

Y1 - 1973

N2 - We examine the electromagnetic self-energies of the ground-state mesons in chiral perturbation theory about SU(2) × SU(2) and SU(3) × SU(3), to leading order in the electromagnetic interaction. If ε is a measure of chiral breaking, then the leading-order corrections to the ground-state meson level splitting relative to the symmetry limit is εlnε. For the pion electromagnetic-mass difference expanded around the chiral SU(2) × SU(2) limit, all terms of O(μπ2lnμπ2) are calculated and are found to give only a 12% correction. For chiral SU(3) × SU(3) one has Dashen's sum rule μπ+2-μπ02=μK+2-μK02 in the symmetry limit. We explicitly calculate the leading correction to the symmetry limit and find that it is larger than the symmetric term, establishing the breakdown of chiral SU(3) × SU(3) perturbation theory in this application and the assumption on which the Dashen sum rule was based. We conjecture that these remarks are valid in the context of gauge models and suggest that the power-series expansions in α=fine-structure constant can fail in some gauge models, there being terms of the form αlnα.

AB - We examine the electromagnetic self-energies of the ground-state mesons in chiral perturbation theory about SU(2) × SU(2) and SU(3) × SU(3), to leading order in the electromagnetic interaction. If ε is a measure of chiral breaking, then the leading-order corrections to the ground-state meson level splitting relative to the symmetry limit is εlnε. For the pion electromagnetic-mass difference expanded around the chiral SU(2) × SU(2) limit, all terms of O(μπ2lnμπ2) are calculated and are found to give only a 12% correction. For chiral SU(3) × SU(3) one has Dashen's sum rule μπ+2-μπ02=μK+2-μK02 in the symmetry limit. We explicitly calculate the leading correction to the symmetry limit and find that it is larger than the symmetric term, establishing the breakdown of chiral SU(3) × SU(3) perturbation theory in this application and the assumption on which the Dashen sum rule was based. We conjecture that these remarks are valid in the context of gauge models and suggest that the power-series expansions in α=fine-structure constant can fail in some gauge models, there being terms of the form αlnα.

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U2 - 10.1103/PhysRevD.8.4620

DO - 10.1103/PhysRevD.8.4620

M3 - Article

AN - SCOPUS:0000705875

VL - 8

SP - 4620

EP - 4627

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 12

ER -