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

Through the spin rearrangement scheme in the heavy quark limit, we have performed a comprehensive investigation of the decay pattern and production mechanism of the hidden beauty dimeson states, which are either composed of a $P$-wave bottom meson and an $S$-wave bottom meson or two $S$-wave bottom mesons. We further extend the corresponding formula to discuss the decay behavior of some charmonium-like states by combining the experimental information with our numerical results. The typical ratios presented in this work can be measured by future experiments like BESIII, Belle, LHCb and the forthcoming BelleII, which shall provide important clues to the inner structures of the exotic states.

Strong decays of the $XYZ$ states

In the framework of the one-boson-exchange model, we explore whether the intermediate- and short-range forces from $\ensuremath{\sigma}/\ensuremath{\omega}$ exchange can be strong enough to bind heavy molecular states. ${\mathrm{\ensuremath{\Lambda}}}_{c}D(\overline{D})$ and ${\mathrm{\ensuremath{\Lambda}}}_{c}{\mathrm{\ensuremath{\Lambda}}}_{c}({\overline{\mathrm{\ensuremath{\Lambda}}}}_{c})$ systems have been studied and compared. We find that the force from $\ensuremath{\sigma}$ exchange is attractive and dominant, whereas the $\ensuremath{\omega}$-exchange force is not. As a consequence, the S-wave ${\mathrm{\ensuremath{\Lambda}}}_{c}D$, ${\mathrm{\ensuremath{\Lambda}}}_{c}{\mathrm{\ensuremath{\Lambda}}}_{c}$, and ${\mathrm{\ensuremath{\Lambda}}}_{c}{\overline{\mathrm{\ensuremath{\Lambda}}}}_{c}$ can be possible molecular candidates. We further indicate that a one hadron-hadron system with more light quarks $(u,d)$ can be easier to form than a bound state. As a by-product, by studying the heavy-quark mass dependence for the ${\mathrm{\ensuremath{\Lambda}}}_{c}D(\overline{D})$-like and ${\mathrm{\ensuremath{\Lambda}}}_{c}{\mathrm{\ensuremath{\Lambda}}}_{c}({\overline{\mathrm{\ensuremath{\Lambda}}}}_{c})$-like systems, we find that the charm/bottom sector can easily accommodate molecular states. Finally, the ${\mathrm{\ensuremath{\Lambda}}}_{c}N(\overline{N})$ and ${\mathrm{\ensuremath{\Lambda}}}_{b}N(\overline{N})$ systems are investigated. Our results indicate that they are also likely to form bound states. By including one-$\ensuremath{\pi}$-exchange forces, providing additional attraction when coupled channels are included, we expect many molecular states in heavy-quark sectors.

Heavy molecules and one-σ /ω -exchange model

Inspired by the newly observed two charged bottomoniumlike states, we consider the possible contribution from the intermediate ${Z}_{b}(10610)$ and ${Z}_{b}(10650)$ states to the $\ensuremath{\Upsilon}(5S)\ensuremath{\rightarrow}\ensuremath{\Upsilon}(2S){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decay process, which naturally explains Belle's previous observation of the anomalous $\ensuremath{\Upsilon}(2S){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ production near the peak of $\ensuremath{\Upsilon}(5S)$ at $\sqrt{s}=10.87\text{ }\text{ }\mathrm{GeV}$ [K. F. Chen et al. (Belle Collaboration), Phys. Rev. Lett. 100, 112001 (2008)]. The resulting $d\ensuremath{\Gamma}(\ensuremath{\Upsilon}(5S)\ensuremath{\rightarrow}\ensuremath{\Upsilon}(2S){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})/d{m}_{{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}}$ and $d\ensuremath{\Gamma}(\ensuremath{\Upsilon}(5S)\ensuremath{\rightarrow}\ensuremath{\Upsilon}(2S){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})/d\mathrm{cos}﻿\ensuremath{\theta}$ distributions agree with Belle's measurement after inclusion of these ${Z}_{b}$ states. This formalism also reproduces the Belle observation of the double-peak structure and its reflection in the $\ensuremath{\Upsilon}(2S){\ensuremath{\pi}}^{+}$ invariant mass spectrum of the $\ensuremath{\Upsilon}(5S)\ensuremath{\rightarrow}\ensuremath{\Upsilon}(2S){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decay.

Charged bottomoniumlike states Z b ( 10610 ) and Z b ( 10650 ) and the Υ ( 5 S ) → Υ ( 2 S ) π + π − decay

Based on the fact that the long expected pen- taquark which possesses the exotic quantum numbers of B = 1 and S = 1 was not experimentally found, although exotic states of XY Z have been observed recently, we con- jecture that the heavy flavors may play an important role in stabilizing the hadronic structures beyond the traditional q ¯ q

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A possible global group structure for exotic states

The ${P}_{c}(4312)$, ${P}_{c}(4440)$, and ${P}_{c}(4457)$ observed by the LHCb collaboration are very likely to be $S$-wave ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{(*)}$ molecular candidates due to their near threshold character. In this work, we study the hidden-charm decay modes of these ${P}_{c}$ states, ${P}_{c}\ensuremath{\rightarrow}J/\ensuremath{\psi}p({\ensuremath{\eta}}_{c}p)$, using a quark interchange model. The decay mechanism for the ${P}_{c}\ensuremath{\rightarrow}J/\ensuremath{\psi}p({\ensuremath{\eta}}_{c}p)$ processes arises from the quark-quark interactions, where all parameters are determined by the mass spectra of mesons. We present our results in two scenarios. In scenario I, we perform the dynamical calculations and treat the ${P}_{c}$ states as pure ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{(*)}$ molecules. In scenario II, after considering the coupled channel effect between different flavor configurations ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{\overline{D}}^{(*)}$, we calculate these partial decay widths again. The decay patterns in these two scenarios can help us to explore the molecular assignment and the inner flavor configurations for the ${P}_{c}$ states. In particular, the decay widths of $\mathrm{\ensuremath{\Gamma}}({P}_{c}(4312)\ensuremath{\rightarrow}{\ensuremath{\eta}}_{c}p)$ are comparable to the $J/\ensuremath{\psi}p$ decay widths in both of these two scenarios. Future experiments like LHCb may confirm the existence of the ${P}_{c}(4312)$ in the ${\ensuremath{\eta}}_{c}p$ channel.

Xiang Liu

Papers

Strong decays of the $XYZ$ states

Heavy molecules and one-σ /ω -exchange model

Charged bottomoniumlike states Z b ( 10610 ) and Z b ( 10650 ) and the Υ ( 5 S ) → Υ ( 2 S ) π + π − decay

A possible global group structure for exotic states

Probing hidden-charm decay properties of P c states in a molecular scenario