Electromagnetic polarizabilities of the triplet hadrons in heavy hadron chiral perturbation theory

TL;DR

The paper develops a systematic heavy-hadron chiral perturbation theory framework to compute electromagnetic polarizabilities of singly heavy mesons and doubly heavy baryons up to $\mathcal{O}(p^3)$. By estimating low-energy constants with a non-relativistic constituent quark model and exploiting heavy-quark spin-flavor symmetry (HDAS), it reveals pion-loop dominance and striking threshold effects, notably a giant electric polarizability for $D^*$ mesons driven by the near-degeneracy $\Delta\approx m_{\pi}$. For doubly heavy baryons, polarizabilities sensitively depend on heavy-flavor content, with $bcq$ systems showing unique channel mixings due to a low-lying scalar diquark state, and a consistent HDAS limit connects the meson and baryon sectors. The results provide essential theoretical benchmarks for lattice QCD and future experimental investigations of heavy-hadron structure, highlighting the long-range pion cloud as a key driver of electromagnetic response.

Abstract

We investigate the electromagnetic polarizabilities of singly heavy mesons and doubly heavy baryons within the framework of heavy hadron chiral perturbation theory up to $\mathcal{O}(p^3)$. We estimate the low-energy constants using the non-relativistic constituent quark model. A striking prediction of our study is the giant electric polarizabilities of the $D^*$ mesons: $α_E(\bar{D}^{*0}) \approx 291.4 \times 10^{-4} \text{fm}^3$ and $α_E(D^{*-}) \approx -0.4-64.4 i \times 10^{-4} \text{fm}^3$. These anomalously large values arise from the near-degenerate mass between $D^*$ and $D π$, which are orders of magnitude larger than those of their bottom counterparts. This kinematic coincidence induces a pronounced cusp structure in the chiral loops, reflecting the long-range dynamics of a pion cloud. For doubly heavy baryons, polarizabilities depend strongly on heavy-flavor composition: the $bcq$ system differs markedly from $ccq$ and $bbq$ due to mixing with scalar heavy-diquark states. Using heavy diquark-antiquark symmetry (HDAS), we unify the chiral dynamics of singly heavy mesons and doubly heavy baryons in the heavy-quark limit. The pion-loop contributions dominate the electromagnetic structure of heavy hadrons and provide essential benchmarks for future lattice QCD simulations.

Figures (2)

• Figure 1: The Born and loop diagrams contribute to the electromagnetic polarizabilities of pseudoscalar mesons (spin-${1}/{2}$ baryons) up to $\mathcal{O}(p^3)$. The solid dots denote the $\mathcal{L}_{H\gamma}^{(2)}$ ($\mathcal{L}_{B\phi}^{(2)}$) vertices. The single and double lines represent the pseudoscalar mesons (spin-${1}/{2}$ baryons) and vector mesons (spin-${3}/{2}$ baryons), respectively. Crossed diagrams are not shown.
• Figure 2: The Born and loop diagrams contribute to the electromagnetic polarizabilities of vector mesons (spin-${3}/{2}$ baryons) up to $\mathcal{O}(p^3)$. The notations are the same as those in Fig. \ref{['fig:spin0']}.