Baryon mass splittings in chiral perturbation theory

Abstract

Baryon masses are calculated in chiral perturbation theory at the one-loop-O(p 3 ) level in the chiral expansion and to leading order in the heavy baryon expansion. Ultraviolet divergences occur requiring the introduction of counter-terms. Despite this neccessity, no knowledge of the counter terms is required to determine the violations to the Gell-Mann Okubo mass relation for the baryon octet or to the decuplet equal mass-spacing rule, as all divergences cancel exactly at this order. For the same reason all reference to an arbitrary scale µ is absent. Neither of these features continue to higher-powers in the chiral expansion. We also discuss critically the absolute neccessity of simultaneously going beyond the leading order heavy baryon expansion, if one goes beyond the one-loop-O(p 3 ) level. We point out that these corrections in 1/MB generate new divergences ∝ m 4 /M10. These divergences together with the divergences occuring in one-loop-O(p 4 ) graphs of chiral perturbation theory are taken care of by the same set of counter-terms. Because of these unknown counter-terms one cannot predict the baryon mass splittings at the one-loop-O(p 4 ) level. We point out another serious problem of going to the one-loop-O(p 4 ) level. When the decuplet is off its mass-shell there are additional πN ∆ and π∆∆ interaction terms. These interactions contribute not only to the divergent terms ∝ (m 4 /M10), but also to nonanalytic terms such as ∝ (m 4 /M10)ln(m/M10). Thus without a knowledge of the coupling constants appearing in these interactions one cannot carry out a consistent one-loop-O(p 4 ) level calculation.

Chiral symmetry and the nucleon’s vector strangeness form factors

“…The essential strategy of CHPT is to exploit the approximate SU(3) L × SU(3) R chiral symmetry of QCD for the three lightest flavors to relate one set of observables to another (accounting for loop effects), or to draw on one set of measured quantities to predict another. This approach has recently been employed to analyze of baryon octet and decuplet magnetic moments [42][43][44] and the nucleon's isovector charge radius [45]. As we illustrate below, this strategy breaks down in the flavor-singlet channel, rendering CHPT un-predictive for the nucleon's strangeness matrix elements.…”

Decuplet baryon masses in partially quenched chiral perturbation theory

“…The masses of the octet and decuplet baryons have been investigated considerably in χPT [33,41,45,46,47,48,49]. Here we calculate the masses of the decuplet baryons to NNLO in χPT.…”

Baryon chiral perturbation theory A.D. 1994

“…Second, the pion cloud contribution is attractive, i.e. it lowers the nucleon mass, and third, it vanishes in the chiral limit, i.e it has the expected chiral dimension of three (since it is a one-loop graph with insertions from the lowest order effective Lagrangian [36]. Here, I only wish to state that at present it is not known whether the scalar three-flavour sector (i.e.…”