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

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

비만아 부모의 돌봄 경험: q 방법론

A golden age for heavy-quarkonium physics dawned a decade ago, initiated by the confluence of exciting advances in quantum chromodynamics (QCD) and an explosion of related experimental activity. The early years of this period were chronicled in the Quarkonium Working Group (QWG) CERN Yellow Report (YR) in 2004, which presented a comprehensive review of the status of the field at that time and provided specific recommendations for further progress. However, the broad spectrum of subsequent breakthroughs, surprises, and continuing puzzles could only be partially anticipated. Since the release of the YR, the BESII program concluded only to give birth to BESIII; the B-factories and CLEO-c flourished; quarkonium production and polarization measurements at HERA and the Tevatron matured; and heavy-ion collisions at RHIC have opened a window on the deconfinement regime. All these experiments leave legacies of quality, precision, and unsolved mysteries for quarkonium physics, and therefore beg for continuing investigations at BESIII, the LHC, RHIC, FAIR, the Super Flavor and/or Tau-Charm factories, JLab, the ILC, and beyond. The list of newly found conventional states expanded to include h(c)(1P), chi(c2)(2P), B-c(+), and eta(b)(1S). In addition, the unexpected and still-fascinating X(3872) has been joined by more than a dozen other charmonium- and bottomonium-like "XYZ" states that appear to lie outside the quark model. Many of these still need experimental confirmation. The plethora of new states unleashed a flood of theoretical investigations into new forms of matter such as quark-gluon hybrids, mesonic molecules, and tetraquarks. Measurements of the spectroscopy, decays, production, and in-medium behavior of c (c) over bar, b (b) over bar, and b (c) over bar bound states have been shown to validate some theoretical approaches to QCD and highlight lack of quantitative success for others. Lattice QCD has grown from a tool with computational possibilities to an industrial-strength effort now dependent more on insight and innovation than pure computational power. New effective field theories for the description of quarkonium in different regimes have been developed and brought to a high degree of sophistication, thus enabling precise and solid theoretical predictions. Many expected decays and transitions have either been measured with precision or for the first time, but the confusing patterns of decays, both above and below open-flavor thresholds, endure and have deepened. The intriguing details of quarkonium suppression in heavy-ion collisions that have emerged from RHIC have elevated the importance of separating hot- and cold-nuclear-matter effects in quark-gluon plasma studies. This review systematically addresses all these matters and concludes by prioritizing directions for ongoing and future efforts.

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Heavy quarkonium: progress, puzzles, and opportunities

We use the method of light-cone sum rules to study the electromagnetic transition of the ${\mathrm{\ensuremath{\Xi}}}_{cc}^{*++}$ into ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\gamma}$, whose decay width is estimated to be ${13.7}_{\ensuremath{-}7.9}^{+17.7}\text{ }\text{ }\mathrm{keV}$. This value is large enough for the ${\mathrm{\ensuremath{\Xi}}}_{cc}^{*++}$ to be observed in the ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\gamma}$ channel, and we propose to continually search for it in future LHCb and BelleII experiments.

Suggested search for doubly charmed baryons of $J^P=3/2^+$ via their electromagnetic transitions

With the heavy quark symmetry and spin rearrangement scheme, we study the strong decay behavior of the hidden-charm pentaquark states with ${J}^{P}={\frac{3}{2}}^{\ifmmode\pm\else\textpm\fi{}}$, ${\frac{5}{2}}^{\ifmmode\pm\else\textpm\fi{}}$ assuming they are molecular candidates composed of ${\overline{D}}^{(*)}$ and ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}$. We obtain several typical ratios of the partial decay widths of the hidden-charm pentaquarks. For the three S-wave ($\overline{D}{\mathrm{\ensuremath{\Sigma}}}_{c}^{*}$), (${\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$), and (${\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}^{*}$) molecular pentaquarks with ${J}^{P}={3/2}^{\ensuremath{-}}$, we have obtained the ratio of their $J/\ensuremath{\psi}N$ decay widths: $\mathrm{\ensuremath{\Gamma}}[(\overline{D}{\mathrm{\ensuremath{\Sigma}}}_{c}^{*})]:\mathrm{\ensuremath{\Gamma}}[({\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c})]:\mathrm{\ensuremath{\Gamma}}[({\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}^{*})]=2.7:1.0:5.4$, which may be useful to further test the possible molecular assignment of the ${P}_{c}$ states.

Strong decay patterns of the hidden-charm pentaquark states P c ( 4380 ) and P c ( 4450 )

Very recently, the LHCb Collaboration reported a fully charmed tetraquark state $X(6900)$ in the invariant mass spectrum of $J/\ensuremath{\psi}$ pairs. If one $J/\ensuremath{\psi}$ meson is replaced with a fully charmed baryon, we obtain a fully charmed pentaquark candidate. In this work, we perform a systematic study on the mass spectra of the $S$-wave fully heavy pentaquark $QQQQ\overline{Q}$ in the framework of the chromomagnetic interaction model. Based on our results in two different schemes, we further investigate the decay behaviors for them. We hope that our study will be helpful in searching for such types of exotic pentaquark states in experiments in the future.

Fully heavy pentaquarks

We investigate the ratio of the branching fractions of the molecular candidates decaying into the ground and radially excited states within the quark-interchange model. Our numerical results suggest that these molecular candidates are more likely to decay into the radially excited states than into ground states. In particular, the ratio $\mathrm{\ensuremath{\Gamma}}[{Z}_{c}(4430)\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\psi}(2S)]/\mathrm{\ensuremath{\Gamma}}[{Z}_{c}(4430)\ensuremath{\rightarrow}\ensuremath{\pi}J/\ensuremath{\psi}]\ensuremath{\sim}9.9$ is close to the experimental measurement, which supports the interpretation of ${Z}_{c}(4430)$ as the $\overline{D}{D}^{*}(2S)$ molecular state. The ratios of the branching fractions of ${Z}_{b}(10610)$ and ${Z}_{b}(10650)$ to $\ensuremath{\pi}\mathrm{\ensuremath{\Upsilon}}(2S,3S)$ and $\ensuremath{\pi}\mathrm{\ensuremath{\Upsilon}}(1S)$ agrees very well with the Belle Collaboration's measurement. We also predict the similar ratios for ${Z}_{c}(3900)$, ${Z}_{c}(4020)$, ${R}_{{Z}_{c}(3900)}\ensuremath{\approx}1.4$, and ${R}_{{Z}_{c}(4020)}\ensuremath{\approx}4.8$. Hopefully, the $\ensuremath{\pi}\ensuremath{\psi}(2S)$ mode and the ratios ${R}_{{Z}_{c}(3900)}$ and ${R}_{{Z}_{c}(4020)}$ will be measured by the BESIII and Belle collaborations in the near future, which shall be very helpful for understanding the underlying dynamics of these exotic states.

Resolving the puzzling decay patterns of charged Z c and Z b 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.

Xiang Liu

Papers

Suggested search for doubly charmed baryons of $J^P=3/2^+$ via their electromagnetic transitions

Strong decay patterns of the hidden-charm pentaquark states P c ( 4380 ) and P c ( 4450 )

Fully heavy pentaquarks

Resolving the puzzling decay patterns of charged Z c and Z b states

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