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.
UR - http://www.scopus.com/inward/record.url?scp=0000705875&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0000705875&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.8.4620
DO - 10.1103/PhysRevD.8.4620
M3 - Article
AN - SCOPUS:0000705875
SN - 1550-7998
VL - 8
SP - 4620
EP - 4627
JO - Physical review D: Particles and fields
JF - Physical review D: Particles and fields
IS - 12
ER -