Analyzing doubly heavy tetra- and penta-quark states by variational method

Abstract

Motivated by the very recent observations of hidden charm pentaquarks Pc(4312) + , Pc(4440) + and Pc(4457) + of the LHCb Collaboration, we systematically study the spectra of the doublyheavy (with or without charm/bottom numbers) pentaquarks and tetraquarks in non-relativistic constituent quark model. The model independent variational method is employed to solve the Schrödinger equation, where the test functions adopted are symmetric for the light quarks. In our study, the Pc(4312) + may be assigned as the ground state with spin-parity 1 2 − or 3 2 − , while the Pc(4440) + and Pc(4457) + may be assigned as the excited states with 1 2 − , which might all belong to the sextet with scc = 1 and s = 3 2 . It is notable that our working framework is quite similar to that of Hydrogen molecule, but with different potential structure. We also classify these pentaquarks and tetraquarks in light of the heavy quark symmetry and their decay properties are analyzed. Several promising channels for the observation of doubly-heavy pentaquarks and doubly-heavy tetraquarks in experiment are proposed.

Molecular interpretation of the Pc(4440) and Pc(4457) sta

“…With its unambiguous prediction of quantum numbers, our model is also quite different from most compact pentaquark scenarios, which typically allow for states with many possible quantum numbers, specifically 1=2 − , 3=2 − , and 5=2 − for S-wave states, and 1=2 þ , 3=2 þ , 5=2 þ , and 7=2 þ for P-waves [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. (Although we note that some pentaquark scenarios predict a restricted spectrum, in particular, models which incorporate the coupling to mesonbaryon pairs [49], or which include additional dynamical assumptions [50].…”

Production of Pc states from Λb decay

“…Very recently, the LHCb Collaboration updated its analysis of the J=ψp invariant mass spectroscopy of Λ b → KJ=ψp and found three pentaquark states, which are P þ c ð4312Þ, P þ c ð4440Þ, and P þ c ð4457Þ [33]. After the new observation, some interpretation has been proposed immediately in the molecular [34][35][36][37][38][39][40][41][42][43][44][45][46][47] and pentaquark scenarios [48][49][50][51][52][53][54]. In addition, by fitting the LHCb data around 4312 MeV with the amplitudes satisfying the general principles of S-matrix theory, P c ð4312Þ is assigned as a virtual state resulting from the weak interactions ofD and Σ c [55].…”

Interpretation of the LHCb Pc States as Hadronic Molecules and Hints of a Narrow Pc(4380)

“…At the same time, the broad P c (4380) loses its sig-nificance (whose existence needs to be verified in a complete amplitude analysis that is under way). A cornucopia of theoretical interpretations followed these new discoveries, including models of hadronic molecules , compact pentaquark states [39][40][41][42][43][44] and hadrocharmonia [45]. An amplitude analysis was performed in Ref.…”