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

We investigate the electromagnetic polarizabilities of singly heavy mesons and doubly heavy baryons within the framework of heavy hadron chiral perturbation theory up to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi mathvariant="script">O</a:mi> <a:mo stretchy="false">(</a:mo> <a:msup> <a:mrow> <a:mi>p</a:mi> </a:mrow> <a:mrow> <a:mn>3</a:mn> </a:mrow> </a:msup> <a:mo stretchy="false">)</a:mo> </a:mrow> </a:math> . We estimate the low-energy constants using the nonrelativistic constituent quark model. A striking prediction of our study is the giant electric polarizabilities of the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msup> <f:mi>D</f:mi> <f:mo>*</f:mo> </f:msup> </f:math> mesons: <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msub> <h:mi>α</h:mi> <h:mi>E</h:mi> </h:msub> <h:mo stretchy="false">(</h:mo> <h:msup> <h:mover accent="true"> <h:mi>D</h:mi> <h:mo stretchy="false">¯</h:mo> </h:mover> <h:mrow> <h:mo>*</h:mo> <h:mn>0</h:mn> </h:mrow> </h:msup> <h:mo stretchy="false">)</h:mo> <h:mo>≈</h:mo> <h:mn>294</h:mn> <h:mo>×</h:mo> <h:msup> <h:mn>10</h:mn> <h:mrow> <h:mo>−</h:mo> <h:mn>4</h:mn> </h:mrow> </h:msup> <h:mtext> </h:mtext> <h:mtext> </h:mtext> <h:msup> <h:mrow> <h:mi>fm</h:mi> </h:mrow> <h:mn>3</h:mn> </h:msup> </h:math> and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:msub> <n:mi>α</n:mi> <n:mi>E</n:mi> </n:msub> <n:mo stretchy="false">(</n:mo> <n:msup> <n:mi>D</n:mi> <n:mrow> <n:mo>*</n:mo> <n:mo>−</n:mo> </n:mrow> </n:msup> <n:mo stretchy="false">)</n:mo> <n:mo>≈</n:mo> <n:mspace linebreak="goodbreak"/> <n:mn>1.42</n:mn> <n:mi>–</n:mi> <n:mn>64.5</n:mn> <n:mi mathvariant="normal">i</n:mi> <n:mo>×</n:mo> <n:msup> <n:mn>10</n:mn> <n:mrow> <n:mo>−</n:mo> <n:mn>4</n:mn> </n:mrow> </n:msup> <n:mtext> </n:mtext> <n:mtext> </n:mtext> <n:msup> <n:mrow> <n:mi>fm</n:mi> </n:mrow> <n:mn>3</n:mn> </n:msup> </n:math> . These anomalously large values arise from the near-degenerate mass between <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:msup> <t:mi>D</t:mi> <t:mo>*</t:mo> </t:msup> </t:math> and <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:mi>D</v:mi> <v:mi>π</v:mi> </v:math> , 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 <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:mi>b</x:mi> <x:mi>c</x:mi> <x:mi>q</x:mi> </x:math> system differs markedly from <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:mi>c</z:mi> <z:mi>c</z:mi> <z:mi>q</z:mi> </z:math> and <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:mi>b</bb:mi> <bb:mi>b</bb:mi> <bb:mi>q</bb:mi> </bb:math> 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.