Abstract
We have systematically investigated the decuplet (T) to octet (B) baryon (Trightarrow Bgamma ) transition magnetic moments to the next-to-next-to-leading order and electric quadruple moments to the next-to-leading order in the framework of the heavy baryon chiral perturbation theory. Our calculation includes the contributions from both the intermediate decuplet and octet baryon states in the loops. Throughout our calculation, we have adopted the small-scale scheme and have not considered the 1/M recoiling corrections directly. We count the octet and decuplet baryon mass splitting delta , the small momenta p, and the pion mass m_{phi } as the same order small-scale parameter, which was denoted as epsilon . Our results for the transition magnetic moments show reasonably good convergence of the chiral expansion. The analytical expressions may be useful to the chiral extrapolation of the lattice simulations of the decuplet electromagnetic properties.
Highlights
The electromagnetic property of the baryons has been an important topic in both theory and experiment
In order to study the convergence of the chiral expansion, we show the numerical results at each order for the transition magnetic moments: μ +→pγ = −6.68 × (1 − 0.33 − 0.15) = −3.50, μ 0→nγ = −6.68 × (1 − 0.33 − 0.15) = −3.50, μ ∗+→ +γ = 6.68 × (1 − 0.52 + 0.19) = 4.46, μ ∗0→ 0γ = −3.34 × (1 − 0.57 + 0.27) = −2.34, μ ∗0→ γ = 5.78 × (1 − 0.38 + 0.01) = 3.62, μ ∗−→ −γ = 0.32 × (0 + 1 − 1.65) = −0.21, μ ∗0→ 0γ = 6.68 × (1 − 0.52 + 0.32) = 5.38, Page 11 of 19 66
We have systematically studied the decuplet to octet baryon transition magnetic moments up to the next-to-next-to-leading order in the framework of the heavy baryon chiral perturbation theory
Summary
The electromagnetic property of the baryons has been an important topic in both theory and experiment. One of the first successes of the constituent quark model was the prediction of the (1232) → N γ transition magnetic moment [37]. [47], the authors studied the magnetic moments of (1232) → N γ transition with the relativistic quark models improved by chiral corrections. Quark model is rather successful in predicting the internal structure of the baryons, the (1232) → N γ transition magnetic moment is generally underestimated by 25% in the constituent quark model. The decuplet baryon nearly entirely decays into the Goldstone boson and octet. [53,54], where the mass splitting between the octet and decuplet baryon is treated to be the same order as the masses of pseudo-Goldstone bosons.
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