Magnetic Moments and Radiative Transitions of the $T_{cc}(3875)^+$ and its partner states

Abstract: We systematically investigate the magnetic moments (MMs) and radiative decay widths of S-wave doubly heavy tetraquark states based on chromomagnetic interaction (CMI). They provide a complementary probe to distinguish compact from molecule structures in addition to the mass spectrum and strong decay properties. Using the CMI eigenvectors, we compute the MMs and M1 transition rates for the tetraquarks in the compact configuration. We predict the MM of the observed $T_{cc}(3875)<sup>+$ with $I(J<sup>P)=0(1<sup>+)$ to be 0.45 $μ<em>N$ when treating it as a compact tetraquark state, whereas the MM of the $0(1^+)$ $DD<sup>*$ molecule is about $-0.07\,μ_N$. Five radiative transition channels related to the $T</em>{cc}(3875)<sup>+$ are identified with widths ranging from $6.07$ keV to $306.37$ keV. Our results show that the MMs of the $J<sup>P=1<sup>+$ $bc\bar{q}\bar{q}<sup>\prime$ ($q/q<sup>\prime=u,d,s$) and $J<sup>P=1<sup>+$ $QQ\bar{n}\bar{s}$ ($Q=b,c; n=u,d$) states are influenced by the diquark-spin mixing. Through the analyses of radiative transitions between different tetraquark states, we find that such processes in the $QQ\bar{n}\bar{n}<sup>\prime$, $QQ\bar{s}\bar{s}$, and $bc\bar{n}\bar{s}$ cases may serve to reveal the tetraquark structures of the initial or final states. We also define the magnetic coupling matrices characterizing the MMs of the tetraquark system with $J<sup>P=1<sup>+$, with which the range of MM can be constrained. The present study provides a valuable reference point for the search of exotic states in future particle physics experiments.