Pseudoscalar Meson and Charmed Baryon Scattering Lengths

Up to now many heavy hadrons have been discovered experimentally. Their inner structures and interactions attract much attention. Some of them are speculated to be possible new hadron states beyond the traditional quark model. For example, the newly discovered Zb states are treated as the B̄ (∗)B∗ molecular states [1, 2]. Many other molecular states, such as those composed of ΞcΞc, DD̄ ∗, are also proposed [3–8]. Whether there is attractive interaction between the particles is the most important condition to form molecular states. On the other hand, the hadron-hadron interaction may distort the conventional quark model spectrum through the coupled channel effects. For example, the bare charm-strange scalar meson lies around 2.4 GeV according to the quark model calculation. Experimentally the mass of the Ds0(2317) state was measured to be around 2.3 GeV. The attractive interaction between the D meson and kaon is essential to lower its mass through the coupling effect between the bare cs̄ state and the DK continuum [9]. There has been lots of research work on the strong interactions of the charmed or bottomed mesons, such as the lattice study, calculations with the chiral perturbation theory and so on [10–19]. The charmed triplet (B3̄), sextet (B6) and excited sextet (B ∗ 6) baryons are relatively stable particles. The pair from the ground and corresponding excited sextet form a degenerate doublet in the heavy quark spin symmetry limit. They interact with other particles through the exchange of the pseudoscalar mesons in the low energy effective field theory. It is very important to study the strong interaction between the lightest pseudoscalar meson (φ) and charmed baryon. A physical observable such as the scattering amplitude can be expanded order by order with the explicit power counting in the heavy baryon chiral perturbation theory (HBχPT). The inclusion of the nonanalytic corrections resulting from the loop diagrams would highly reduce the error of extraction in the lattice study [20, 21], which is one of the motivations of the present investigation. In this work, we shall study the pseudoscalar meson and charmed baryon scattering lengths to the third order with HBχPT. We include the interaction of B6 and B ∗ 6 explicitly for the φB3̄ scattering instead of absorbing their effects into the low energy constants (LECs) at higher order since the mass difference among the charmed baryons is small and the couplings between them can not be neglected. The situation is similar for the φB6 and φB ∗ 6 cases. We express the results as power series in ǫ = p/Λχ with the explicit power counting, where p represents the mass and momentum of pseudoscalar Goldstone bosons, the residual momentum of charmed baryons, the mass difference among charmed baryons, while Λχ is either the mass of charmed baryons or 4πf . This paper is organized as follows: in Sec. II, we list the HBχPT Lagrangians of the pseudoscalar mesons and charmed baryons, with which we get the expressions of the T -matrices at thresholds. In Sec. III, we estimate the LECs in the Lagrangians. We present the numerical results and discussions in Sec. IV. Sec. V is a short conclusion.