Abstract
The $DD^{*}$ potentials are studied within the framework of heavy meson chiral effective field theory. We obtain the effective potentials of the $DD^{*}$ system up to $O(\epsilon^2)$ at the one-loop level. In addition to the one-pion exchange contribution, the contact and two-pion exchange interactions are also investigated in detail. Furthermore, we search for the possible molecular states by solving the Schr\"odinger equation with the potentials. We notice that the contact and two-pion exchange potentials are numerically non-negligible and important for the existence of a bound state. In our results, no bound state is found in the $I=1$ channel within a wide range of cutoff parameter, while there exists a bound state in the $I=0$ channel as the cutoff is near $m_\rho$ in our approach.
Highlights
Chiral effective field theory (ChEFT) is an effective field theory respecting the chiral symmetry of quantum chromodynamics (QCD) at low momenta
We investigated the DDÃ effective potentials in ChEFT using Weinberg’s scheme
With the effective potentials obtained in momentum space, we analyzed the contact, one-pion exchange (OPE), and two-pion exchange (TPE) contributions in detail
Summary
Chiral effective field theory (ChEFT) is an effective field theory respecting the chiral symmetry of quantum chromodynamics (QCD) at low momenta. The study of hadronic molecules with effective field theories was reviewed in Ref. There have been many studies of heavy meson systems using the one-boson-exchange model and effective field theories, as mentioned above. We investigate their higher-order effects in chiral effective field theory; we discuss the potential in coordinate space and search for the bound state by solving the Schrödinger equation. [75] to search for bound and resonant states, and they used pion and vector-meson exchange potentials which are constrained by heavy quark symmetry and chiral symmetry.
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