Direct Detection of Dark Baryons Naturally Suppressed by $\mathcal{H}$-parity

We identify symmetries in a broad class of vector-like confining dark sectors that forbid the leading electromagnetic moments that would ordinarily mediate dark baryon scattering with the Standard Model. The absence of these operators implies dark baryon dark matter has much smaller cross sections for elastic scattering off nuclei, leading to suppressed direct detection signals. In the confined description, we identify an ``$\mathcal{H}$-parity'' symmetry that exists in any dark sector with dark quarks transforming under a vector-like representation of a new confining SU($N_c$) gauge theory as well as a vector-like representation of the electroweak group SU(2)$_L$. The parity is independent of $N_c$ and $N_f$, though it is essential that the dark quarks are neutral under hypercharge. This parity forbids dark hadron electric and magnetic dipole moments, charge radius, and anapole moment, while permitting dimension-7 operators that include polarizability, electroweak loop-induced interactions, as well as lower dimensional electromagnetic $\textit{transition}$ moments between different neutral dark baryon states. We work out an explicit example, $N_c=N_f=3$, that is the most minimal theory with fermionic dark baryons. In this specific model, we use the non-relativistic quark model to show the magnetic dipole moment and charge radius vanish while the transition moments are non-zero, consistent with $\mathcal{H}$-parity. We discuss the implications of a suppressed direct detection signal, emphasizing that this broad class of models provide a well-motivated target for future colliders.