Explaining the Many Threshold Structures in the Heavy-Quark Hadron Spectrum

Abstract

Tremendous progress has been made experimentally in the hadron spectrum containing heavy quarks in the last two decades. It is surprising that many resonant structures are around thresholds of a pair of heavy hadrons. There should be a threshold cusp at any $S$-wave threshold. By constructing a nonrelativistic effective field theory with open channels, we discuss the generalities of threshold behavior, and offer an explanation of the abundance of near-threshold peaks in the heavy quarkonium regime. We show that the threshold cusp can show up as a peak only for channels with attractive interaction, and the width of the cusp is inversely proportional to the reduced mass relevant for the threshold. We argue that there should be threshold structures at any threshold of a pair of heavy-quark and heavy-antiquark hadrons, which have attractive interaction at threshold, in the invariant mass distribution of a heavy quarkonium and light hadrons that couple to that open-flavor hadron pair. The structure becomes more pronounced if there is a near-threshold pole. Predictions of the possible pairs are also given for the ground state heavy hadrons. Precisely measuring the threshold structures will play an important role in revealing the heavy-hadron interactions, and thus understanding the puzzling hidden-charm and hidden-bottom structures.

Title changed, version to appear in Phys. Rev. Lett.; 8 pages, 2 figures

References in corpus (9)

• Multiquark Resonances
• Pentaquark and Tetraquark states
• Observation of a narrow pentaquark state, $P_c(4312{)}^{+}$, and of two-peak structure of the $P_c(4450{)}^{+}$
• Exotics: Heavy Pentaquarks and Tetraquarks
• Observation of a near-threshold structure in the $K^{+}$ recoil-mass spectra in $e^{+}{e}^{-}\to K^{+}(D_s^{-}{D}^{\ast 0}+D_s^{\ast -}{D}^0)$
• Interpretation of the LHCb $P_c$ States as Hadronic Molecules and Hints of a Narrow $P_c(4380)$
• $Z_b$ and $Z_c$ Exotic States as Coupled Channel Cusps
• Could the near-threshold $XYZ$ states be simply kinematic effects?
• How Resonances can synchronise with Thresholds

Cited by in corpus (73)

• An updated review of the new hadron states
• A survey of heavy-heavy hadronic molecules
• Probing the long-range structure of the $T_{cc}^{+}$ with the strong and electromagnetic decays
• Revisiting the nature of the $P_c$ pentaquarks
• Hadronic molecules in B decays
• Subleading contributions to the decay width of the $T_{cc}^{+}$ tetraquark
• Coupled-channel effects of the ${\Sigma }_c^{(\ast )}{\bar{D}}^{(\ast )}$-${\Lambda }_c(2595)\bar{D}$ system and molecular nature of the $P_c$ pentaquark states from one-boson exchange model
• $P_c(4312{)}^{+}$, $P_c(4380{)}^{+}$, and $P_c(4457{)}^{+}$ as double triangle cusps
• Higher mass spectra of the fully-charmed and fully-bottom tetraquarks
• The double thresholds distort the lineshapes of the $P_{\psi s}^{\Lambda }(4338{)}^0$ resonance
• Establishing the heavy quark spin and light flavor molecular multiplets of the $X(3872)$, $Z_c(3900)$ and $X(3960)$
• Building up the spectrum of pentaquark states as hadronic molecules
• Pole determination of $P_{\psi s}^{\Lambda }(4338)$ and possible $P_{\psi s}^{\Lambda }(4255)$ in $B^{-}\to J/\psi \Lambda \bar{p}$
• Tetraquarks in large-$N_c$ QCD
• Implications of the $Z_{cs}(3985)$ and $Z_{cs}(4000)$ as two different states
• A combined analysis of the $Z_c(3900)$ and the $Z_{cs}(3985)$ exotic states
• Hidden and doubly heavy molecular states from interactions $D_{(s)}^{(\ast )}{\bar{D}}_s^{(\ast )}$/$B_{(s)}^{(\ast )}{\bar{B}}_s^{(\ast )}$ and $D_{(s)}^{(\ast )}{D}_s^{(\ast )}$/$B_{(s)}^{(\ast )}{B}_s^{(\ast )}$
• Heavy Flavour Physics and CP Violation at LHCb: a Ten-Year Review
• Correlation of the hidden-charm molecular tetraquarks and the charmoniumlike structures existing in the $B\to XYZ+K$
• Prediction of a narrow exotic hadronic state with quantum numbers $J^{PC}=0^{--}$
• Heavy- and light-flavor symmetry partners of the $T_{cc}^{+}(3875)$, the $X(3872)$ and the $X(3960)$ from light-meson exchange saturation
• Fully-charm and -bottom pentaquarks in a Lattice-QCD inspired quark model
• Anticharmed strange pentaquarks from the one-boson-exchange model
• Understanding the $0^{++}$ and $2^{++}$ charmonium(-like) states near 3.9 GeV
• Decay behaviors of the fully-bottom and fully-charm tetraquark states
• Spectrum of the molecular tetraquarks: Unraveling the $T_{cs0}(2900)$ and $T_{c\bar{s}0}^a(2900)$
• Search for a $D\bar{D}$ bound state in the ${\Lambda }_b\to \Lambda D\bar{D}$ process
• Triply-heavy tetraquarks in an extended relativized quark model
• Predicting isovector charmonium-like states from X(3872) properties
• Threshold effects as the origin of $Z_{cs}(4000)$, $Z_{cs}(4220)$ and $X(4700)$ observed in $B^{+}\to J/\psi \varphi K^{+}$
• Improved understanding of the peaking phenomenon existing in the new di-$J/\psi$ invariant mass spectrum from the CMS Collaboration
• Precise determination of the pole position of the exotic $Z_c(3900)$
• Classifying near-threshold enhancement using deep neural network
• Virtual states in the coupled-channel problems with an improved complex scaling method
• Production of $Z_{cs}$ in $B$ and $B_s$ decay
• $P_{cc}^N$ states in a unitarized coupled-channel approach
• $Z_{cs}$ states from the $D_s^{\ast }{\bar{D}}^{\ast }$ and $J/\psi K^{\ast }$ coupled channels: Signal in $B^{+}\to J/\psi \varphi K^{+}$ decay
• $P$-wave charmonium contribution to hidden-charm states from reanalysis of lattice QCD data
• $\sigma$ exchange in the one-boson exchange model involving the ground state octet baryons
• Towards a precision determination of the $X(6200)$ parameters from data
• Shedding light on the $X(3930)$ and $X(3960)$ states with the $B^{-}\to K^{-}J/\psi \omega$ reaction
• On the structure in the $\Lambda N$ cross section at the $\Sigma N$ threshold
• Hadronic molecular states with the quark contents $bc\bar{s}\bar{q}$, $b\bar{c}s\bar{q}$, and $b\bar{c}\bar{s}q$
• Study of exotic hadrons with machine learning
• Is two-poles' $\Lambda (1405)$ one state or two?
• Bottomonium-like tetraquarks in a chiral quark model
• Substructure of Multiquark Hadrons (Snowmass 2021 White Paper)
• Molecular pentaquark states with open charm and bottom flavors
• $X$ structures in $B^{+}\to J/\psi \varphi K^{+}$ as one-loop and double-triangle threshold cusps
• The $X(6900)$ peak could be a molecular state
• Production of pentaquarks with hidden charm and double strangeness in ${\Xi }_b$ and ${\Omega }_b$ decays
• Molecular states in $D_s^{(\ast )+}{\Xi }_c^{{(}^{\prime },\ast )}$ systems
• $X$ and $Z_{cs}$ in $B^{+}\to J/\psi \varphi K^{+}$ as $s$-wave threshold cusps and alternative spin-parity assignments to $X(4274)$ and $X(4500)$
• Two-pion exchange for coupled-channel scattering of two heavy mesons
• How does the $X(3872)$ show up in $e^{+}{e}^{-}$ collisions: dip versus peak
• Role of the short-range dynamics in the formation of $D^{(\ast )}{\bar{D}}^{(\ast )}/B^{(\ast )}{\bar{B}}^{(\ast )}$ hadronic molecules
• $P_c(4457)$ interpreted as a $J^P=1/2^{+}$ state by ${\bar{D}}^0{\Lambda }_c^{+}(2595)$-${\pi }^0{P}_c(4312)$ interaction
• Classification of Coupled-Channel Near-Threshold Structures
• Search for hidden-charm tetraquark with strangeness in $e^{+}{e}^{-}\to K^{+}{D}_s^{\ast -}{D}^{\ast 0}+c.c.$
• Effective range expansion with a long-range force
• Pole analysis for the $D^{\ast }\bar{K}$-$D\overline{K^{\ast }}$ coupled-channel system
• Closed-channel parameters of Feshbach resonances
• Coupled-channel analysis of the near-threshold $e^{+}{e}^{-}\to N\bar{N}$ cross sections
• Hints of the $J^{PC}=0^{--}$ and $1^{--}$ $K^{\ast }{\bar{K}}_1(1270)$ Molecules in the $J/\psi \to \varphi \eta {\eta }^{\prime }$ Decay
• Possible ${\Sigma }_c^{\ast }\bar{\Sigma }$ molecular states
• Revisit the $Z_c(4025)$ structure observed by BESIII in the $e^{+}{e}^{-}\to (D^{\ast }{\bar{D}}^{\ast }{)}^{\pm ,0}{\pi }^{\mp ,0}$ reactions at $\sqrt{s}=4.26$ GeV
• Hunting for the heavy quark spin symmetry partner of $Z_{cs}$
• Low-energy $N\varphi$ scattering from a pole-enhanced triangle diagram
• Interactions of the Pseudoscalar Meson Octet and the Baryon Decuplet in the Continuum and a Finite Volume
• Hadronic molecules and multiquark states
• $P_c(4312{)}^{+}$ and $P_c(4337{)}^{+}$ as interfering ${\Sigma }_c\bar{D}$ and ${\Lambda }_c{\bar{D}}^{\ast }$ threshold cusps
• Role of the short-range dynamics in simultaneous interpretation of $P_{cs}$ pentaqurks via ${\Xi }_c^{(\prime ,\ast )}{\bar{D}}^{(\ast )}$ molecules
• Decoding the near-threshold $X_{0,1}(4140)$ and $X_1(4685)$ states via OZI-suppressed coupled-channel scattering