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

The quark model was formulated in 1964 to classify mesons as bound states made of a quark-antiquark pair, and baryons as bound states made of three quarks. For a long time all known mesons and baryons could be classified within this scheme. Quantum Chromodynamics (QCD), however, in principle also allows the existence of more complex structures, generically called exotic hadrons or simply exotics. These include four-quark hadrons (tetraquarks and hadronic molecules), five-quark hadrons (pentaquarks) and states with active gluonic degrees of freedom (hybrids), and even states of pure glue (glueballs). Exotic hadrons have been systematically searched for in numerous experiments for many years. Remarkably, in the past fifteen years, many new hadrons that do not exhibit the expected properties of ordinary (not exotic) hadrons have been discovered in the quarkonium spectrum. These hadrons are collectively known as $XYZ$ states. Some of them, like the charged states, are undoubtedly exotic. Parallel to the experimental progress, the last decades have also witnessed an enormous theoretical effort to reach a theoretical understanding of the $XYZ$ states. Theoretical approaches include not only phenomenological extensions of the quark model to exotics, but also modern non-relativistic effective field theories and lattice QCD calculations. The present work aims at reviewing the rapid progress in the field of exotic $XYZ$ hadrons over the past few years both in experiments and theory. It concludes with a summary on future prospects and challenges.

The $XYZ$ states: experimental and theoretical status and perspectives

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

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.

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

Rui Chen1∗ and Xiang Liu2,3,4† Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, and Frontier Science Center for Rare Isotopes, Lanzhou University, Lanzhou 730000, China School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS, Lanzhou 730000, China (Dated: January 20, 2022)

Mass behavior of hidden-charm open-strange pentaquarks inspired by the established 
Pc
 molecular states

In this work, we study the $T\bar{T}$-type molecular systems systematically via one pion exchange model, where $T$ denotes the narrow $J^P=1^+$ $D_1$ meson or $2^+$ $D_2^*$ meson and $\bar{T}$ is its antiparticle. With the effective potentials, we try to find the bound state solutions of the corresponding systems, which provide crucial information of whether there exist the $T\bar{T}$-type molecular states. According to our analysis, we predict some $T\bar{T}$-type molecular states which may be accessible at future experiments like LHCb and forthcoming BelleII.

/pdf/predictions-of-the-hidden-charm-molecular-states-with-four-2wczip7mvc.pdf

Predictions of the hidden-charm molecular states with four-quark component

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Papers

Identifying exotic hidden-charm pentaquarks

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

Mass behavior of hidden-charm open-strange pentaquarks inspired by the established Pc molecular states

Predictions of the hidden-charm molecular states with four-quark component