There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

The hidden-charm pentaquark and tetraquark states

A large number of experimental discoveries especially in the heavy quarkonium sector that did not at all fit to the expectations of the until then very successful quark model led to a renaissance of hadron spectroscopy Among various explanations of the internal structure of these excitations, hadronic molecules, being analogues of light nuclei, play a unique role since for those predictions can be made with controlled uncertainty We review experimental evidences of various candidates of hadronic molecules, and methods of identifying such structures Nonrelativistic effective field theories are the suitable framework for studying hadronic molecules, and are discussed in both the continuum and finite volumes Also pertinent lattice QCD results are presented Further, we discuss the production mechanisms and decays of hadronic molecules, and comment on the reliability of certain assertions often made in the literature

Hadronic molecules

Pentaquark and Tetraquark states

The LHCb Collaboration at the Large Hadron Collider at CERN discovered two pentaquark states P_{c}(4380) and P_{c}(4450). These two hidden-charm states are interpreted as the loosely bound Σ_{c}(2455)D^{*} and Σ_{c}^{*}(2520)D^{*} molecular states in the boson exchange interaction model, which provides an explanation for why the experimental width of P_{c}(4450) is much narrower than that of P_{c}(4380). The discovery of the new resonances P_{c}(4380) and P_{c}(4450), indeed, opens a new page for hadron physics. The partners of P_{c}(4380) and P_{c}(4450) should be pursued in future experiments.

Identifying exotic hidden-charm pentaquarks

On March 26th, 2019, at the Rencontres de Moriond QCD conference, the LHCb Collaboration reported the observation of three new pentaquarks, namely $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$, which are consistent with the loosely bound molecular hidden-charm pentaquark states composed of an S-wave charmed baryon $\Sigma_c$ and an S-wave anti-charmed meson ($\bar{D}, \bar{D}^*$). In this work, we present a direct calculation by the one-boson-exchange (OBE) model and demonstrate explicitly that the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ do correspond to the loosely bound $\Sigma_c\bar{D}$ with $(I=1/2,J^P=1/2^-)$, $\Sigma_c\bar{D}^*$ with $(I=1/2,J^P=1/2^-)$ and $\Sigma_c\bar{D}^*$ with $(I=1/2,J^P=3/2^-)$, respectively.

Strong LHCb evidence for supporting the existence of hidden-charm molecular pentaquarks

Hidden-charm molecular pentaquarks and their charm-strange partners

The magnetic moment of a baryon state is an equally important dynamical observable as its mass, which encodes crucial information of its underlying structure. According to the different color-flavor structure, we have calculated the magnetic moments of the hidden-charm pentaquark states with the isospin $(I,{I}_{3})=(\frac{1}{2},\frac{1}{2})$ and ${J}^{P}={\frac{1}{2}}^{\ifmmode\pm\else\textpm\fi{}}$, ${\frac{3}{2}}^{\ifmmode\pm\else\textpm\fi{}}$, ${\frac{5}{2}}^{\ifmmode\pm\else\textpm\fi{}}$, ${\frac{7}{2}}^{+}$ in the molecular model, the diquark-triquark model, and the diquark-diquark-antiquark model, respectively. Although a good description for the pentaquark mass spectrum and decay patterns has been obtained in all three models, different color-flavor structures lead to different magnetic moments, which can be used to pin down their inner structures and distinguish various models.

Magnetic moments of the hidden-charm pentaquark states

In this work, we explore a systematic investigation on $S$-wave interactions between a doubly charmed baryon ${\mathrm{\ensuremath{\Xi}}}_{cc}(3621)$ and a charmed meson in a $T$ doublet $({D}_{1},{D}_{2}^{*})$. We first analyze the possibility for forming ${\mathrm{\ensuremath{\Xi}}}_{cc}{D}_{1}/{\mathrm{\ensuremath{\Xi}}}_{cc}{D}_{2}^{*}$ bound states with the heavy quark spin symmetry. Then, we further perform a dynamical study on the ${\mathrm{\ensuremath{\Xi}}}_{cc}{D}_{1}/{\mathrm{\ensuremath{\Xi}}}_{cc}{D}_{2}^{*}$ interactions within a one-boson-exchange model by considering both the $S\ensuremath{-}D$ wave mixing and coupled channel effect. Finally, our numerical results conform the proposals from the heavy quark spin symmetry analysis: the ${\mathrm{\ensuremath{\Xi}}}_{cc}{D}_{1}$ systems with $I({J}^{P})=0(1/{2}^{+},3/{2}^{+})$ and the ${\mathrm{\ensuremath{\Xi}}}_{cc}{D}_{2}^{*}$ systems with $I({J}^{P})=0(3/{2}^{+},5/{2}^{+})$ can possibly be loose triple-charm molecular pentaquarks. Meanwhile, we also extend our model to the ${\mathrm{\ensuremath{\Xi}}}_{cc}{\overline{D}}_{1}$ and ${\mathrm{\ensuremath{\Xi}}}_{cc}{\overline{D}}_{2}^{*}$ systems, and our results indicate the isoscalars of ${\mathrm{\ensuremath{\Xi}}}_{cc}{\overline{D}}_{1}$ and ${\mathrm{\ensuremath{\Xi}}}_{cc}{\overline{D}}_{2}^{*}$ can be possible molecular candidates.

Rui Chen

Papers

Identifying exotic hidden-charm pentaquarks

Strong LHCb evidence for supporting the existence of hidden-charm molecular pentaquarks

Hidden-charm molecular pentaquarks and their charm-strange partners

Magnetic moments of the hidden-charm pentaquark states

Possible triple-charm molecular pentaquarks from Ξ c c D 1 /Ξ c c D 2 * interactions