Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules

Chiral symmetry and its spontaneous breaking play an important role both in the light hadron and heavy hadron systems. The chiral perturbation theory ($\chi$PT) is the low energy effective field theory of the Quantum Chromodynamics. In this work, we shall review the investigations on the chiral corrections to the properties of the heavy mesons and baryons within the framework of $\chi$PT. We will also review the scatterings of the light pseudoscalar mesons and heavy hadrons, through which many new resonances such as the $D_{s0}^{\ast }\left(2317\right)$ could be understood.

Moreover, many new hadron states were observed experimentally in the past decades. A large group of these states is near-threshold resonances, such as the charged charmoniumlike $Z_c$ and $Z_{cs}$ states, bottomoniumlike $Z_b$ states, hidden-charm pentaquark $P_c$ and $P_{cs}$ states and the doubly charmed $T_{cc}$ state, etc. They are very good candidates of the loosely bound molecular states composed of a pair of charmed (bottom) hadrons, which are very similar to the loosely bound deuteron. The modern nuclear force was built upon the chiral effective field theory ($\chi$EFT), which is the extension of the $\chi$PT to the systems with two matter fields. The long-range and medium-long-range interactions between two nucleons arise from the single- and double-pion exchange respectively, which are well constrained by the chiral symmetry and its spontaneous breaking. The short-distance interactions can be described by the low energy constants. Such a framework works very well for the nucleon–nucleon scattering and nuclei. In this work, we will perform an extensive review of the progress on the heavy hadronic molecular states within the framework of $\chi$EFT. We shall emphasize that the same chiral dynamics not only govern the nuclei and forms the deuteron, but also dictates the shallow bound states or resonances composed of two heavy hadrons.