Electromagnetic polarizabilities of the spin-$\frac{3}{2}$ baryons in heavy baryon chiral perturbation theory

TL;DR

This work computes the electromagnetic polarizabilities of spin-$\frac{3}{2}$ baryons within heavy-baryon chiral perturbation theory up to $\mathcal{O}(p^3)$ in two sectors: light-flavor decuplet and singly heavy sextet. By analyzing the spin-averaged forward Compton tensor and employing detailed chiral Lagrangians, the authors separate and evaluate tree-level (seagull and M1-transition) and loop contributions, with long-range pion and kaon cloud effects found to be substantial, especially in the electric polarizabilities. They determine key low-energy constants from strong and electromagnetic decays and lattice inputs, revealing that $\alpha_E$ for $\Delta^{+}$ and $\Delta^{0}$ are notably large (around $17\times10^{-4}$ fm$^3$), while magnetic polarisabilities are strongly influenced by M1 transitions and can change sign. For singly heavy baryons, $\alpha_E$ is comparable to spin-$\frac{1}{2}$ partners, but $\beta_M$ exhibits both positive and negative values due to competing contributions, with heavy-quark symmetry guiding the relations between sectors. The results provide analytic expressions suitable for chiral extrapolations in lattice QCD and offer predictions that can be refined with future data and lattice efforts.

Abstract

We employ Heavy Baryon Chiral Perturbation Theory (HB$χ$PT), a non-relativistic effective field theory that treats baryons as heavy static sources, to calculate the electromagnetic polarizabilities of spin-3/2 baryons in two sectors: the light-flavor decuplet baryons and singly heavy sextet baryons. We derive the analytical expressions up to $\mathcal{O}\left(p^3\right)$. Our results indicate that the long-range chiral corrections provide substantial contributions to the polarizabilities. In addition, magnetic dipole (M1) transitions of the baryons can significantly affect the magnetic polarizabilities and may even reverse their signs. For the decuplet baryons, the $Δ^+$ and $Δ^0$ exhibit the largest electric polarizabilities. Their values, $α_E(Δ^+) = (17.5 \pm 9.5)\times 10^{-4} \, \mathrm{fm}^3$ and $α_E(Δ^0) = (17.0 \pm 9.3)\times 10^{-4} \, \mathrm{fm}^3$, significantly exceed those typically observed for nucleons. Meanwhile, the electric polarizabilities of spin-3/2 singly heavy baryons are comparable to those of their spin-1/2 partners.

Figures (1)

• Figure 1: The Born and loop diagrams contribute to the electromagnetic polarizabilities up to $\mathcal{O}\left(p^3\right)$. The solid dots denote the $\mathcal{L}_{\mathcal{T}/\mathcal{N} \phi }^{(2)}$ and $\mathcal{L}_{\mathcal{B} \phi }^{(2)}$ vertices. The single and double lines represent the spin-$\frac{3}{2}$ and spin-$\frac{1}{2}$ baryons, respectively. Crossed diagrams are not shown.