Baryon masses at second order in large-$N$ chiral perturbation theory

Paulo F. Bedaque; Markus A. Luty

doi:10.1103/PhysRevD.54.2317

paper

Baryon masses at second order in large- $N$ chiral perturbation theory

arXiv:hep-ph/9510453 · doi:10.1103/PhysRevD.54.2317

Abstract

We consider flavor breaking in the the octet and decuplet baryon masses at second order in large- $N$ chiral perturbation theory, where $N$ is the number of QCD colors. We assume that $1/ N \sim 1/ N_{F} \sim m_{s} /Λ ≫ m_{u, d} /Λ, α_{E M}$ , where $N_{F}$ is the number of light quark flavors, and $m_{u, d, s} /Λ$ are the parameters controlling $S U (N_{F})$ flavor breaking in chiral perturbation theory. We consistently include non-analytic contributions to the baryon masses at orders $m_{q}^{3/2}$ , $m_{q}^{2} ln m_{q}$ , and $(m_{q} ln m_{q}) / N$ . The $m_{q}^{3/2}$ corrections are small for the relations that follow from $S U (N_{F})$ symmetry alone, but the corrections to the large- $N$ relations are large and have the wrong sign. Chiral power-counting and large- $N$ consistency allow a 2-loop contribution at order $m_{q}^{2} ln m_{q}$ , and a non-trivial explicit calculation is required to show that this contribution vanishes. At second order in the expansion, there are eight relations that are non-trivial consequences of the $1/ N$ expansion, all of which are well satisfied within the experimental errors. The average deviation at this order is $7 \MeV$ for the $\De I = 0$ mass differences and $0.35 \MeV$ for the $\De I \ne 0$ mass differences, consistent with the expectation that the error is of order $1/ N^{2} \sim 10%$ .

19 pages, 2 uuencoded ps figs, uses revtex

Baryon masses at second order in large- $N$ chiral perturbation theory

Abstract

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Cited by in corpus (14)

Baryon masses at second order in large-N chiral perturbation theory

Abstract

References in corpus (14)

Cited by in corpus (14)

Baryon masses at second order in large- $N$ chiral perturbation theory