Light baryon static properties in dispersive approach

Abstract

We extend our dispersive analyses on meson static properties to those of light baryons. The formalism treats the dispersion relation, which a baryonic correlation function obeys, as an inverse problem, solve for the involved spectral density with available operator-product-expansion (OPE) inputs directly, and extract baryon static properties from the spectral density. We observe that the simultaneous implementation of the chiral-even and chiral-odd dispersive constraints unambiguously determines baryon masses and pole residues. A common set of quark and gluon condensates, which appear in OPE factorization and are universal, is found to accommodate the masses of a $ρ$ meson, a proton and a $Δ(1232)$ baryon. The advantage of our approach over the conventional handling of QCD sum rules is advocated. This work encourages broad applications of our nonperturbative analytical method to baryon systems.

Figures (6)

• Figure 1: Dependencies of $\rho(s)$ on $s$ for $\Lambda = 2\; \text{GeV}^2$ and $N=13$ (dashed line), $N=15,16,17$ (solid lines) and $N=19$ (dotted line).
• Figure 2: Dependence of the $\rho$ meson mass $M_\rho$ on $\Lambda$. The specific $N$ is taken for each $\Lambda$ that minimizes the Frechet distance in Eq. (\ref{['fre']}).
• Figure 3: Proton masses $M_P$ and pole residues $\lambda_P$ derived from the chiral-even dispersion relation (dots) and the chiral-odd dispersion relation (squares) for $\Lambda=2$ GeV$^2$, 3 GeV$^2$ and 4 GeV$^2$ from top to bottom.
• Figure 4: Dependencies of the proton mass $M_P$ and pole residue $\lambda_P$ on $\Lambda$.
• Figure 5: Dependence of the proton mass $M_P$ on the Borel mass $M_B$ in conventional QCD sum rules with the inputs in Eq. (\ref{['newpND']}).