Binding of the three-hadron $D{D}^{\ast }K$ system from the lattice effective field theory

Abstract

We employ the nuclear lattice effective field theory (NLEFT), an efficient tool for nuclear ab initio calculations, to solve the asymmetric multihadron systems. We take the $D{D}^{\ast }K$ three-body system as an illustration to demonstrate the capability of the method. Here the two-body chiral interactions between $D$, $D^{\ast }$, and $K$ are regulated with a soft lattice regulator and calibrated with the binding energies of the $T_{cc}^{+}$, $D_{s0}^{\ast }(2317)$, and $D_{s1}(2460)$ molecular states. We then calculate the three-body binding energy using the NLEFT and analyze the systematic uncertainties due to the finite volume effects, the sliding cutoff, and the leading-order three-body forces. Even when the three-body interaction is repulsive (even as large as the infinite repulsive interaction), the three-body system has a bound state unambiguously with binding energy no larger than the $D_{s1}(2460)D$ threshold. To check the renormalization group invariance of our framework, we extract the first excited state. We find that when the ground state is fixed, the first excited states with various cutoffs coincide with each other when the cubic size goes larger. In addition, the standard angular momentum and parity projection technique is implemented for the quantum numbers of the ground and excited states. We find that both of them are $S$-wave states with quantum number $J^P=1^{-}$. Because the three-body state contains two charm quarks, it is easier to be detected in the Large Hadron Collider.

arXiv comment17 pages, 6 figures. Published in: Phys. Rev. D 111(2025)3, 036002

References in corpus (72)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Observation of a narrow charmonium-like state in exclusive B+ -> K+ pi+pi- J/psi decays
• Observation of a New Narrow Charmonium State in Exclusive B+-->K+ pi+pi- J/psi Decays
• Modern Theory of Nuclear Forces
• Chiral effective field theory and nuclear forces
• Hadronic molecules
• The hidden-charm pentaquark and tetraquark states
• Observation of $J/\psi p$ resonances consistent with pentaquark states in ${\Lambda }_b^0\to J/\psi K^{-}p$ decays
• The $XYZ$ states: experimental and theoretical status and perspectives
• Heavy-Quark QCD Exotica
• Phenomenology of Heavy Meson Chiral Lagrangians
• Observation of a narrow pentaquark state, $P_c(4312{)}^{+}$, and of two-peak structure of the $P_c(4450{)}^{+}$
• An updated review of the new hadron states
• Renormalization of the Three-Body System with Short-Range Interactions
• From low-momentum interactions to nuclear structure
• Observation of a Narrow Resonance of Mass 2.46 GeV/c^2 Decaying to D_s^*+ pi^0 and Confirmation of the D_sJ^* (2317) State
• Efimov Physics: a review
• Observation of structure in the $J/\psi$-pair mass spectrum
• Observation of an exotic narrow doubly charmed tetraquark
• Three-body forces: From cold atoms to nuclei
• Microscopic Clustering in Light Nuclei
• Study of the doubly charmed tetraquark $T_{cc}^{+}$
• Observed D_s(2317) and tentative D(2100-2300) as the charmed cousins of the light scalar nonet
• Structure and rotations of the Hoyle state
• Threshold cusps and triangle singularities in hadronic reactions
• Lattice simulations for few- and many-body systems
• Observation of the DsJ(2317) and DsJ(2457) in B decays
• Four-Quark Hadrons: an Updated Review
• Hybrid Mesons
• Interactions of Charmed Mesons with Light Pseudoscalar Mesons from Lattice QCD and Implications on the Nature of the D_{s0}^*(2317)
• Interactions between heavy mesons and Goldstone bosons from chiral dynamics
• Ab initio calculation of the spectrum and structure of ${}^{16}$O
• Model-independent evidence for $J/\psi p$ contributions to ${\Lambda }_b^0\to J/\psi p{K}^{-}$ decays
• Coupled-channel approach to $T_{cc}^{+}$ including three-body effects
• Charmed baryon strong decays in a chiral quark model
• Radiative and isospin-violating decays of Ds mesons in the hadrogenesis conjecture
• Lattice Simulations for Light Nuclei: Chiral Effective Field Theory at Leading Order
• Efimov States in Nuclear and Particle Physics
• Nuclear binding near a quantum phase transition
• New structures in the J/$\psi$J/$\psi$ mass spectrum in proton-proton collisions at $\sqrt{s}$ = 13 TeV
• Observation of an excess of di-charmonium events in the four-muon final state with the ATLAS detector
• Spectrum of three-body bound states in a finite volume
• A New Hadron Spectroscopy
• Heavy hadronic molecules with pion exchange and quark core couplings: a guide for practitioners
• Gluon flux-tube distribution and linear confinement in baryons
• Ab initio calculations of the isotopic dependence of nuclear clustering
• The $KD$, $\eta D_s$ interaction in finite volume and the nature of the $D_{s^{\ast }0}(2317)$ resonance
• Lattice chiral effective field theory with three-body interactions at next-to-next-to-leading order
• X(3872) in the molecular model
• Predicting another doubly charmed molecular resonance $T_{cc}^{\prime +}(3876)$
• Hyperon-nuclear interactions from SU(3) chiral effective field theory
• $DK$, $DDK$, and $DDDK$ molecules--understanding the nature of the $D_{s0}^{\ast }(2317)$
• $DDK$ system in finite volume
• Flux Tubes of Two- and Three-Quark System in Full QCD
• Ab initio nuclear thermodynamics
• Hyperon-nucleon interaction in chiral effective field theory at next-to-next-to-leading order
• $K^{\ast }$ mesons with hidden charm arising from $KX(3872)$ and $K{Z}_c(3900)$ dynamics
• The triton and three-nucleon force in nuclear lattice simulations
• Few-body systems consisting of mesons
• Three-particle bound states in a finite volume: unequal masses and higher partial waves
• Strangeness $S=-1$ hyperon-nucleon interactions: chiral effective field theory vs. lattice QCD
• Perturbative quantum Monte Carlo method for nuclear physics
• Bound state formation in the $DDK$ system
• Excited $K$ meson, $K_c(4180)$, with hidden charm as a $D\bar{D}K$ bound state
• Ab initio lattice results for Fermi polarons in two dimensions
• Double heavy tri-hadron bound state via delocalized $\pi$ bond
• Relativistic effects and three-body interactions in atomic nuclei
• Breaking and restoration of rotational symmetry on the lattice for bound state multiplets
• Fermion-dimer scattering using an impurity lattice Monte Carlo approach and the adiabatic projection method
• Impurity Lattice Monte Carlo for Hypernuclei
• Structure Factors for Hot Neutron Matter from Ab Initio Lattice Simulations with High-Fidelity Chiral Interactions
• Three-body molecules $\bar{D}{\bar{D}}^{\ast }{\Sigma }_c$- understanding the nature of $T_{cc}$, $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$

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