Decuplet Baryon Masses in Partially Quenched Chiral Perturbation Theory

Abstract

The masses of the spin-3/2 baryons are calculated to next-to-next-to-leading order in heavy baryon chiral perturbation theory and partially quenched heavy baryon chiral perturbation theory. The calculation is performed for three light flavors in the isospin limit. These results are necessary for extrapolating QCD and partially quenched QCD lattice calculations of the decuplet baryon masses.

Figures (4)

• Figure 1: One loop graphs which give contributions to $M_{T_i}^{(3/2)}$. The single, double and dashed lines correspond to octet baryons, decuplet baryons and mesons, respectively. The filled squares denote the axial coupling given in Eq. (\ref{['eq:leadlag']}).
• Figure 2: One-loop graphs which give contributions to $M_{T_i}^{(2)}$. Single, double and dashed lines correspond to octet baryons, decuplet baryons and mesons, respectively. The filled squares and filled circles denote axial couplings and insertions of ${\mathcal{M}_+}$ given in Eq. (\ref{['eq:leadlag']}). The empty squares denote insertions of fixed $1/M_B$ operators from Eq. (\ref{['eq:fixed']}), and the empty circles denote two-baryon-axial couplings defined in Eq. (\ref{['eq:hdo']}).
• Figure 3: In addition to the one-loop diagrams in Fig. \ref{['fig:NLO']}, $M_{T_i}^{(3/2)}$ also receives contributions from the singlet (hairpins) in PQ$\chi$PT. Single and doubles line correspond to $\mathbf {240}$-baryons and $\mathbf {138}$-baryons respectively. The crossed dashed line denotes a hairpin propagator. The filled squares denote the axial coupling given in Eq. (\ref{['eq:leadlagPQ']}).
• Figure 4: In addition to the one-loop diagrams in Fig. \ref{['fig:NNLO']}, $M_{T_i}^2$ also receives contributions from the singlet (hairpins) in PQ$\chi$PT. Single and double lines correspond to $\mathbf {240}$-baryons and $\mathbf {138}$-baryons respectively. The crossed dashed line denotes a hairpin insertion. Filled squares denote the axial coupling given in Eq. (\ref{['eq:leadlagPQ']}). Filled circles denote a coupling to ${\mathcal{M}_+}$ given in Eq. (\ref{['eq:leadlagPQ']}). Empty squares and empty circles denote insertions of fixed $1/M_B$ operators given in Eq. (\ref{['eq:fixedPQ']}), and insertions of a two-baryon-two-axial coupling given in Eq. (\ref{['eq:hdoPQ']}) respectively.