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[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

The hidden-charm pentaquark and tetraquark states

Pentaquark and Tetraquark states

The past seventeen years have witnessed tremendous progress on the experimental and theoretical explorations of the multiquark states. The hidden-charm and hidden-bottom multiquark systems were reviewed extensively in [Phys. Rept. 639 (2016) 1-121]. In this article, we shall update the experimental and theoretical efforts on the hidden heavy flavor multiquark systems in the past three years. Especially the LHCb collaboration not only confirmed the existence of the hidden-charm pentaquarks but also provided strong evidence of the molecular picture. Besides the well-known $XYZ$ and $P_c$ states, we shall discuss more interesting tetraquark and pentaquark systems either with one, two, three or even four heavy quarks. Some very intriguing states include the fully heavy exotic tetraquark states $QQ\bar Q\bar Q$ and doubly heavy tetraquark states $QQ\bar q \bar q$, where $Q$ is a heavy quark. The $QQ\bar Q\bar Q$ states may be produced at LHC while the $QQ\bar q \bar q$ system may be searched for at BelleII and LHCb. Moreover, we shall pay special attention to various theoretical schemes. We shall emphasize the model-independent predictions of various models which are truly/closely related to Quantum Chromodynamics (QCD). There have also accumulated many lattice QCD simulations through multiple channel scattering on the lattice in recent years, which provide deep insights into the underlying structure/dynamics of the $XYZ$ states. In terms of the recent $P_c$ states, the lattice simulations of the charmed baryon and anti-charmed meson scattering are badly needed. We shall also discuss some important states which may be searched for at BESIII, BelleII and LHCb in the coming years.

In this work, we employ the heavy hadron chiral perturbation theory to calculate the ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{(*)}$ potentials to the next-to-leading order. The contact, the one-pion exchange, and the two-pion exchange interactions are all included in the calculation along with the mass splittings between the heavy quark spin symmetry partner states. Our result shows that neglecting the heavy quark symmetry violation effect may be misleading to predict the potentials between the charmed hadrons. We perform numerical analysis with three scenarios. In the first scenario, we relate the low-energy constants (LECs) in the contact terms of ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{(*)}$ to those of nucleon systems and reproduce the ${P}_{c}(4312)$ and ${P}_{c}(4440)$ as loosely bound states. In the second scenario, we vary the unknown LECs and find a small parameter region in which ${P}_{c}(4312)$, ${P}_{c}(4440)$ and ${P}_{c}(4457)$ can coexist as molecular states. In the third scenario, we include the coupled-channel effect on the basis of scenario II and notice that the three ${P}_{c}$ states can be reproduced as molecular states simultaneously in a large region of parameters. Our analytical results can be used for the chiral extrapolations in lattice QCD. With the lattice QCD results in the future as inputs, the identification of the ${P}_{c}$ states and predictions for other systems would be more reliable.

Hidden charm pentaquark states and Σ c D ¯ ( * ) interaction in chiral perturbation theory

We calculate the effective potentials of the ${\mathrm{\ensuremath{\Xi}}}_{c}{\overline{D}}^{(*)}$, ${\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}}{\overline{D}}^{(*)}$, and ${\mathrm{\ensuremath{\Xi}}}_{c}^{*}{\overline{D}}^{(*)}$ system s with the chiral effective field theory up to the next-to-leading order. We simultaneously consider the short-, intermediate-, and long-range interactions. With the newly observed ${P}_{c}$ spectra as inputs, we construct the quark-level contact Lagrangians to relate the low energy constants to those of ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{(*)}$ with the help of the quark model. Our calculation indicates there are seven bound states in the $I=0$ strange hidden charm $[{\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}}{\overline{D}}^{(*)}{]}_{J}(J=\frac{1}{2},\frac{3}{2})$ and $[{\mathrm{\ensuremath{\Xi}}}_{c}^{*}{\overline{D}}^{(*)}{]}_{J}(J=\frac{1}{2},\frac{3}{2},\frac{5}{2})$ systems. Our analyses also disfavor the ${\mathrm{\ensuremath{\Lambda}}}_{c}{\overline{D}}^{(*)}$ bound states. However, we obtain three new hadronic molecules in the isoscalar $[{\mathrm{\ensuremath{\Xi}}}_{c}{\overline{D}}^{(*)}{]}_{J}(J=\frac{1}{2},\frac{3}{2})$ systems. The masses of $[{\mathrm{\ensuremath{\Xi}}}_{c}\overline{D}{]}_{1/2}$, $[{\mathrm{\ensuremath{\Xi}}}_{c}{\overline{D}}^{*}{]}_{1/2}$, and $[{\mathrm{\ensuremath{\Xi}}}_{c}{\overline{D}}^{*}{]}_{3/2}$ are predicted to be ${4319.4}_{\ensuremath{-}3.0}^{+2.8}\text{ }\text{ }\mathrm{MeV}$, ${4456.9}_{\ensuremath{-}3.3}^{+3.2}\text{ }\text{ }\mathrm{MeV}$, and ${4463.0}_{\ensuremath{-}3.0}^{+2.8}\text{ }\text{ }\mathrm{MeV}$, respectively. We also notice the one-eta-exchange influence is rather feeble. Binding solutions in the $I=1$ channels are nonexistent. We hope the future analyses at LHCb can seek for these new ${P}_{cs}\mathrm{s}$ in the $J\ensuremath{\psi}\mathrm{\ensuremath{\Lambda}}$ final states, especially near the thresholds of ${\mathrm{\ensuremath{\Xi}}}_{c}{\overline{D}}^{(*)}$.

Spectrum of the strange hidden charm molecular pentaquarks in chiral effective field theory

The newly observed Pc(4312), Pc(4440) and Pc(4457) at the LHCb experiment are very close to the $$ {\varSigma}_c\overline{D} $$
 and $$ {\varSigma}_c{\overline{D}}^{\ast } $$
 thresholds. In this work, we perform a systematic study and give a complete picture on the interactions between the $$ {\varSigma}_c^{\left(\ast \right)} $$
 and $$ {\overline{D}}^{\left(\ast \right)} $$
 systems in the framework of heavy hadron chiral effective field theory, where the short-range contact interaction, long-range one-pion-exchange contribution, and intermediate-range two-pion-exchange loop diagrams are all considered. We first investigate the three Pc states without and with considering the Λc contribution in the loop diagrams. It is difficult to simultaneously reproduce the three Pcs unless the Λc is included. The coupling between the $$ {\varSigma}_c^{\left(\ast \right)}{\overline{D}}^{\left(\ast \right)} $$
 and $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$
 channels is crucial for the formation of these Pcs. Our calculation supports the Pc(4312), Pc(4440) and Pc(4457) to be the S-wave hidden-charm $$ {\left[{\varSigma}_c\overline{D}\right]}_{J=1/2}^{I=1/2},{\left[{\varSigma}_c{\overline{D}}^{\ast}\right]}_{J=1/2}^{I=1/2} $$
 and $$ {\left[{\varSigma}_c{\overline{D}}^{\ast}\right]}_{J=3/2}^{I=1/2} $$
 molecular pentaquarks, respectively. Our calculation disfavors the spin assignment $$ {J}^P=\frac{1^{-}}{2} $$
 for Pc(4457) and $$ {J}^P=\frac{3^{-}}{2} $$
 for Pc(4440), because the excessively enhanced spin-spin interaction is unreasonable in the present case. We obtain the complete mass spectra of the $$ {\left[{\varSigma}_c^{\left(\ast \right)}{\overline{D}}^{\left(\ast \right)}\right]}_J $$
 systems with the fixed low energy constants. Our result indicates the existence of the $$ {\left[{\varSigma}_c^{\ast }{\overline{D}}^{\ast}\right]}_J\left(J=\frac{1}{2},\frac{3}{2},\frac{5}{2}\right) $$
 hadronic molecules. The previously reported Pc(4380) might be a deeper bound one. Additionally, we also study the hidden-bottom $$ {\varSigma}_b^{\left(\ast \right)}{B}^{\left(\ast \right)} $$
 systems, and predict seven bound molecular states, which could serve as a guidance for future experiments. Furthermore, we also examine the heavy quark symmetry breaking effect in the hidden-charm and hidden-bottom systems by taking into account the mass splittings in the propagators of the intermediate states. As expected, the heavy quark symmetry in the bottom cases is better than that in the charmed sectors. We notice that the heavy quark symmetry in the $$ {\varSigma}_c\overline{D} $$
 and $$ {\varSigma}_c^{\ast}\overline{D} $$
 systems is much worse for some fortuitous reasons. The heavy quark symmetry breaking effect is nonnegligible in predicting the effective potentials between the charmed hadrons.

/pdf/hidden-charm-and-hidden-bottom-molecular-pentaquarks-in-2eu85opq0s.pdf

Hidden-charm and hidden-bottom molecular pentaquarks in chiral effective field theory

Recently, for the first time, the BESIII Collaboration reported the strange hidden charm tetraquark states ${Z}_{cs}(3985{)}^{\ensuremath{-}}$ in the ${K}^{+}$ recoil-mass spectrum near the ${D}_{s}^{\ensuremath{-}}{D}^{*0}/{D}_{s}^{*\ensuremath{-}}{D}^{0}$ mass thresholds in the processes of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{+}({D}_{s}^{\ensuremath{-}}{D}^{*0}+{D}_{s}^{*\ensuremath{-}}{D}^{0})$ at $\sqrt{s}=4.681\text{ }\text{ }\mathrm{GeV}$ (M. Ablikim et al., arXiv:2011.07855). The significance was estimated to be $5.3\ensuremath{\sigma}$. We show that the newly observed ${Z}_{cs}(3985{)}^{\ensuremath{-}}$ state is the $U$-spin partner of ${Z}_{c}(3900{)}^{\ensuremath{-}}$ as a resonance within coupled-channel calculation in the ${\mathrm{SU}(3)}_{F}$ symmetry and heavy quark spin symmetry (HQSS). In the ${\mathrm{SU}(3)}_{F}$ symmetry, we introduce the ${G}_{U/V}$ parity to construct the flavor wave functions of the ${Z}_{cs}$ states. In a unified framework, we consider the $J/\ensuremath{\psi}\ensuremath{\pi}(K)$, ${\overline{D}}_{(s)}{D}^{*}/{\overline{D}}_{(s)}^{*}D$ coupled-channel effect with the contact interaction. With the masses and widths of ${Z}_{c}(3900)$ and ${Z}_{c}(4020)$, we determine all the unknown coupling constants. We obtain mass and width of ${Z}_{cs}(3985)$ in good agreement with the experimental results, which strongly support the ${Z}_{cs}$ states as the $U/V$-spin partner states of the charged ${Z}_{c}(3900)$. We also calculate the ratio of the partial decay widths of ${Z}_{cs}(3985)$, which implies that the ${\overline{D}}_{s}{D}^{*}/{\overline{D}}_{s}^{*}D$ decay modes are dominant. We also predict the ${Z}_{cs}^{\ensuremath{'}}$ states with a mass around 4130 MeV and width around 30 MeV, which are the $U/V$-spin partner states of the charged ${Z}_{c}(4020)$ and HQSS partner states of the ${Z}_{cs}(3985)$. In the hidden bottom sector, we predict the strange tetraquark states ${Z}_{bs}$ and ${Z}_{bs}^{\ensuremath{'}}$ with a mass around 10700 and 10750 MeV, which are the $U/V$-spin partner states of ${Z}_{b}(10610{)}^{\ifmmode\pm\else\textpm\fi{}}$ and ${Z}_{b}(10650{)}^{\ifmmode\pm\else\textpm\fi{}}$, respectively.

Z c s (3985 ) - as the U -spin partner of Z c (3900 )- and implication of other states in the SU (3 ) F symmetry and heavy quark symmetry

The $D{D}^{*}$ potentials are studied within the framework of heavy meson chiral effective field theory. We obtain the effective potentials of the $D{D}^{*}$ system up to $O({\ensuremath{\epsilon}}^{2})$ at the one-loop level. In addition to the one-pion exchange contribution, the contact and two-pion exchange interactions are also investigated in detail. Furthermore, we search for the possible molecular states by solving the Schr\"odinger equation with the potentials. We notice that the contact and two-pion exchange potentials are numerically non-negligible and important for the existence of a bound state. In our results, no bound state is found in the $I=0$ channel within a wide range of the cutoff parameter, while there exists a bound state in the $I=1$ channel as the cutoff is near ${m}_{\ensuremath{\rho}}$ in our approach.

Bo Wang

Papers

Hidden charm pentaquark states and Σ c D ¯ ( * ) interaction in chiral perturbation theory

Spectrum of the strange hidden charm molecular pentaquarks in chiral effective field theory

Hidden-charm and hidden-bottom molecular pentaquarks in chiral effective field theory

Z c s (3985 ) - as the U -spin partner of Z c (3900 )- and implication of other states in the SU (3 ) F symmetry and heavy quark symmetry

D D * potentials in chiral effective field theory and possible molecular states