Light pseudoscalar meson and heavy meson scattering lengths to $\mathcal{O}(p^4)$ in heavy meson chiral perturbation theory

Abstract

We calculate the threshold $T$ matrices of the light pseudoscalar meson and heavy meson scattering to fourth order in heavy meson chiral perturbation theory. We determine the low-energy constants by fitting to the lattice QCD data points through both the perturbative and iterated methods and obtain the physical scattering lengths in both formalisms. The values of the scattering lengths tend to be convergent at fourth order for most of the channels in the perturbative method. The value of the scattering length for the channel $DK(I=0)$, which involves the bound state $D_{s0}^{\ast }(2317)$, is obtained correctly in the iterated method. Based on the heavy diquark-antiquark symmetry, we also estimate the meson and doubly charmed (bottom) baryon scattering lengths, and find that the bound states can be generated with high probability in the channels $\bar{K}{\Xi }_{cc}(I=0)$ and $\bar{K}{\Xi }_{bb}(I=0)$. We strongly urge the LHCb Collaboration to look for the very narrow $\bar{K}{\Xi }_{cc}$ state with $I{J}^P=0{\frac{1}{2}}^{-}$ through either the electromagnetic decay or the iso-spin violating strong decay ${\Omega }_{cc}\pi$.

arXiv comment21 pages, 3 figures, 12 tables

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Cited by in corpus (12)

• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Novel coupled channel framework connecting quark model and lattice QCD: an investigation on near-threshold $D_s$ states
• Studying the interaction between charm and light-flavor mesons
• Charm and Bottom Hadrons in Hot Hadronic Matter
• Two-Body Strong Decay of the 2P and 3P Charmonium states
• The investigations of the $P$-wave $B_s$ states combining quark model and lattice QCD in the coupled channel framework
• Masses and radiative decay widths of the $D_{s0}^{\ast }(2317)$ and $D_{s1}^{\prime }(2460)$ and their bottom analogs
• Phase shifts of the light pseudoscalar meson and heavy meson scattering in heavy meson chiral perturbation theory
• Investigating $S$-wave bound states composed of two pseudoscalar mesons
• Octet baryon and heavy meson interactions in chiral effective field theory
• Analysis of the hadronic molecules $DK$, $D^{\ast }K$, $D{K}^{\ast }$ and their bottom analogs with QCD sum rules
• Meson-baryon scattering lengths without annihilation diagrams to order $p^4$ in heavy baryon chiral perturbation theory