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

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

This is a review paper about neutrino mass and mixing and flavour model building strategies based on discrete family symmetry. After a pedagogical introduction and overview of the whole of neutrino physics, we focus on the PMNS mixing matrix and the latest global fits following the Daya Bay and RENO experiments which measure the reactor angle. We then describe the simple bimaximal, tri-bimaximal and golden ratio patterns of lepton mixing and the deviations required for a non-zero reactor angle, with solar or atmospheric mixing sum rules resulting from charged lepton corrections or residual trimaximal mixing. The different types of see-saw mechanism are then reviewed as well as the sequential dominance mechanism. We then give a mini-review of finite group theory, which may be used as a discrete family symmetry broken by flavons either completely, or with different subgroups preserved in the neutrino and charged lepton sectors. These two approaches are then reviewed in detail in separate chapters including mechanisms for flavon vacuum alignment and different model building strategies that have been proposed to generate the reactor angle. We then briefly review grand unified theories (GUTs) and how they may be combined with discrete family symmetry to describe all quark and lepton masses and mixing. Finally, we discuss three model examples which combine an SU(5) GUT with the discrete family symmetries A₄, S₄ and Δ(96).

https://iopscience.iop.org/article/10.1088/0034-4885/76/5/056201/pdf

Neutrino Mass and Mixing with Discrete Symmetry

We present distance measurements to 71 high redshift type Ia supernovae discovered during the first year of the 5-year Supernova Legacy Survey (SNLS). These events were detected and their multi-color light-curves measured using the MegaPrime/MegaCam instrument at the Canada-France-Hawaii Telescope (CFHT), by repeatedly imaging four one-square degree fields in four bands. Follow-up spectroscopy was performed at the VLT, Gemini and Keck telescopes to confirm the nature of the supernovae and to measure their redshift. With this data set, we have built a Hubble diagram extending to z = 1, with all distance measurements involving at least two bands. Systematic uncertainties are evaluated making use of the multiband photometry obtained at CFHT. Cosmological fits to this first year SNLS Hubble diagram give the following results: {Omega}{sub M} = 0.263 {+-} 0.042 (stat) {+-} 0.032 (sys) for a flat {Lambda}CDM model; and w = -1.023 {+-} 0.090 (stat) {+-} 0.054 (sys) for a flat cosmology with constant equation of state w when combined with the constraint from the recent Sloan Digital Sky Survey measurement of baryon acoustic oscillations.

The Supernova Legacy Survey: Measurement of Omega_m, Omega_l and w from the First Year Data Set

We construct models of leptons based on S
 4 family symmetry combined with a generalised CP symmetry H
 CP
  We show how the flavon potential can spontaneously break the symmetry S
 4 ⋊ H
 CP
 down to $ {Z_2}\times H_{CP}^v $
 in the neutrino sector, where the choice of preserved CP symmetry $ H_{CP}^v $
 is controlled by free (real) parameters in the flavon potential We propose two realistic models of this kind, one at the effective level and one at the renormalisable level Both models predict trimaximal lepton mixing with CP being either fully preserved or maximally broken, with the intermediate possibility forbidden by the structure of the models

Spontaneous CP violation from vacuum alignment in S 4 models of leptons

We construct models of leptons based on $S_4$ family symmetry combined with a generalised CP symmetry $H_{CP}$. We show how the flavon potential can spontaneously break the symmetry $S_4 \rtimes H_{CP}$ down to $Z_2 \times H^{\nu}_{CP}$ in the neutrino sector, where the choice of preserved CP symmetry $H^{\nu}_{CP}$ is controlled by free (real) parameters in the flavon potential. We propose two realistic models of this kind, one at the effective level and one at the renormalisable level. Both models predict trimaximal lepton mixing with CP being either fully preserved or maximally broken, with the intermediate possibility forbidden by the structure of the models.

Spontaneous CP violation from vacuum alignment in $S_4$ models of leptons

We present a comprehensive analysis of neutrino mass and lepton mixing in theories with ${A}_{5}$ modular symmetry. We construct the weight 2, weight 4, and weight 6 modular forms of level 5 in terms of Dedekind eta-functions and Klein forms, and their decomposition into irreducible representation of ${A}_{5}$. We construct all the simplest models based on ${A}_{5}$ modular symmetry, including scenarios of models with and without flavons in the charged lepton sectors. For each case, the neutrino masses can be generated through either the Weinberg operator or the type I seesaw mechanism. We perform an exhaustive numerical analysis, organizing our results in an extensive set of figures and tables.

Neutrino mass and mixing with A 5 modular symmetry

In this work, we have investigated whether $Y(4260)$ and ${Z}_{2}^{+}(4250)$ could be ${D}_{1}D$ or ${D}_{0}{D}^{*}$ molecules in the framework of meson exchange model. The off-diagonal interaction induced by $\ensuremath{\pi}$ exchange plays a dominant role. The $\ensuremath{\sigma}$ exchange has been taken into account, which leads to diagonal interaction. The contribution of $\ensuremath{\sigma}$ exchange is not favorable to the formation of the molecular state with ${I}^{G}({J}^{PC})={0}^{\ensuremath{-}}({1}^{--})$; however, it is beneficial to the binding of the molecule with ${I}^{G}({J}^{P})={1}^{\ensuremath{-}}({1}^{\ensuremath{-}})$. Light vector meson exchange leads to diagonal interaction as well. For ${Z}_{2}^{+}(4250)$, the contribution from $\ensuremath{\rho}$ and $\ensuremath{\omega}$ exchange almost cancels each other. For the currently allowed values of the effective coupling constants and a reasonable cutoff $\ensuremath{\Lambda}$ in the range 1--2 GeV, we find that $Y(4260)$ could be accommodated as a ${D}_{1}D$ and ${D}_{0}{D}^{*}$ molecule, whereas the interpretation of ${Z}_{2}^{+}(4250)$ as a ${D}_{1}D$ or ${D}_{0}{D}^{*}$ molecule is disfavored. The bottom analog of $Y(4260)$ and ${Z}_{2}^{+}(4250)$ may exist, and the most promising channels to discover them are ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\Upsilon}$ and ${\ensuremath{\pi}}^{+}{\ensuremath{\chi}}_{b1}$, respectively.

Are Y ( 4260 ) and Z 2 + ( 4250 ) D 1 D or D 0 D * hadronic molecules?

In the modular symmetry approach to neutrino models, the flavour symmetry emerges as a finite subgroup ΓN of the modular symmetry, broken by the vacuum expec- tation value (VEV) of a modulus field τ. If the VEV of the modulus τ takes some special value, a residual subgroup of ΓN would be preserved. We derive the fixed points τS = i, τST = (−1 + i
 $$ \sqrt{3} $$
 )/2, τTS = (1 + i
 $$ \sqrt{3} $$
 )/2, τT = i∞ in the fundamental domain which are in-variant under the modular transformations indicated. We then generalise these fixed points to τf = γτS, γτST, γτTS and γτT in the upper half complex plane, and show that it is suffi-cient to consider γ ∈ ΓN. Focussing on level N = 4, corresponding to the flavour group S4, we consider all the resulting triplet modular forms at these fixed points up to weight 6. We then apply the results to lepton mixing, with different residual subgroups in the charged lepton sector and each of the right-handed neutrinos sectors. In the minimal case of two right-handed neutrinos, we find three phenomenologically viable cases in which the light neutrino mass matrix only depends on three free parameters, and the lepton mixing takes the trimaximal TM1 pattern for two examples. One of these cases corresponds to a new Littlest Modular Seesaw based on CSD(n) with n = 1 + $$ \sqrt{6} $$
 ≈ 3.45, intermediate between CSD(3) and CSD(4). Finally, we generalize the results to examples with three right-handed neutrinos, also considering the level N = 3 case, corresponding to A4 flavour symmetry.

/pdf/modular-s-4-and-a-4-symmetries-and-their-fixed-points-new-14myb98hcd.pdf

Gui-Jun Ding

Papers

Spontaneous CP violation from vacuum alignment in S 4 models of leptons

Spontaneous CP violation from vacuum alignment in $S_4$ models of leptons

Neutrino mass and mixing with A 5 modular symmetry

Are Y ( 4260 ) and Z 2 + ( 4250 ) D 1 D or D 0 D * hadronic molecules?

Modular S 4 and A 4 symmetries and their fixed points: new predictive examples of lepton mixing