Baryon masses at second order in large-{ital N} chiral perturbation theory
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
We consider flavor breaking in the octet and decuplet baryon masses at second order in large-{ital N} chiral perturbation theory, where {ital N} is the number of QCD colors. We assume that 1/{ital N}{approximately}1/{ital N}{sub {ital F}}{approximately}{ital m}{sub {ital s}}/{Lambda}{gt}{ital m}{sub {ital u},{ital d}}/{Lambda},{alpha}{sub EM}, where {ital N}{sub {ital F}} is the number of light quark flavors, and {ital m}{sub {ital u},{ital d},{ital s}}/{Lambda} are the parameters controlling SU({ital N}{sub {ital F}}) flavor breaking in chiral perturbation theory. We consistently include nonanalytic contributions to the baryon masses at orders {ital m}{sub {ital q}}{sup 3/2}, {ital m}{sup 2}{sub {ital q}}ln{ital m}{sub {ital q}}, and ({ital m}{sub {ital q}}ln{ital m}{sub {ital q}})/{ital N}. The {ital m}{sub {ital q}}{sup 3/2} corrections are small for the relations that follow from SU({ital N}{sub {ital F}}) symmetry alone, but the corrections to the large-{ital N} relations are large and have the wrong sign. Chiral power counting and large-{ital N} consistency allow a two-loop contribution at order {ital m}{sup 2}{sub {ital q}}ln{ital m}{sub {ital q}}, and a nontrivial explicit calculation is required to show that this contribution vanishes. At second order in the expansion, there are eight relations that are nontrivial consequences of the 1/{ital N} expansion, all of which are well satisfied within the experimental errors. The average deviation at this order is 7 MeV for the {Delta}{ital I}=0 mass differences and 0.35 MeV for the {Delta}{ital I}{ne}0 mass differences, consistent with the expectation that the error is of order 1/{ital N}{sup 2}{approximately}10{percent}. {copyright} {ital 1996 The American Physical Society.}
- Research Organization:
- Massachusetts Institute of Technology
- DOE Contract Number:
- AC02-76ER03069
- OSTI ID:
- 286439
- Journal Information:
- Physical Review, D, Journal Name: Physical Review, D Journal Issue: 3 Vol. 54; ISSN PRVDAQ; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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