Open Flavor Thresholds Research Articles

Charmonium spectroscopy motivated by general features of pNRQCD

Mass spectrum of charmonium is computed in the framework of potential non-relativistic quantum chromodynamics. O(1/m) and O(1/m2) relativistic corrections to the Cornell potential and spin-dependent potential have been added, and is solved numerically. New experimentally observed and modified positive and negative parity states like ψ(4230), ψ(4260), ψ(4360), ψ(4390), ψ(4660), χc1(4140) and χc1(4274) near open-flavor threshold have also been studied. We explain them as admixtures of S-D wave states and P-wave states. Apart from these states, some other states like X(3915), χc1(3872), ψ(3770) and ψ(4160) have been identified as 23P0, 23P1, 13D1 and 23D1 states. Subsequently, the electromagnetic transition widths and γγ, e+e−, light hadron and γγγ decay widths of several states are calculated at various leading orders. All the calculated results are compared with experimental and results from various theoretical models.

Simple spectrum of cc¯cc¯ states in the dynamical diquark model

We develop the spectroscopy of $c\bar c c\bar c$ and other all-heavy tetraquark states in the dynamical diquark model. In the most minimal form of the model (e.g., each diquark appears only in the color-triplet combination; the non-orbital spin couplings connect only quarks within each diquark), the spectroscopy is extremely simple. Namely, the $S$-wave multiplets contain precisely 3 degenerate states ($0^{++}$, $1^{+-}$, $2^{++}$) and the 7 $P$-wave states satisfy an equal-spacing rule when the tensor coupling is negligible. When comparing numerically to the recent LHCb results, we find the best interpretation is assigning $X(6900)$ to the $2S$ multiplet, while a lower state suggested at about $6740$ MeV fits well with the members of the $1P$ multiplet. We also predict the location of other multiplets ($1S$, $1D$, etc.) and discuss the significance of the $cc$ open-flavor threshold.

Are the XYZ states unconventional states or conventional states with unconventional properties?

We discuss three possible scenarios for the interpretation of mesons containing a heavy quark and its antiquark near and above the first threshold for a decay into a pair of heavy mesons in a relative [Formula: see text]-wave. View I assumes that these thresholds force the quark potential to flatten which implies that while in these energy ranges molecular states may be formed, there should not be any quark–antiquark states above these thresholds. View II assumes that the main part of the interaction between two mesons is due to the poles which originate from the [Formula: see text] interaction. The properties of the [Formula: see text] mesons are strongly influenced by opening thresholds but the number of states is given by the quark model. In View III, both types of mesons are admitted also near and above the open flavor thresholds: [Formula: see text] mesons and dynamically generated mesons. Experimental consequences of these different views are discussed.

Radiative transitions between 0−+ and 1−− heavy quarkonia on the light front

We present calculations of radiative transitions between vector and pseudoscalar quarkonia in the light-front Hamiltonian approach. The valence sector light-front wavefunctions of heavy quarkonia are obtained from the Basis Light-Front Quantization (BLFQ) approach in a holographic basis. We study the transition form factor with both the traditional "good current" $J^+$ and the transverse current $\vec J_\perp$ (in particular, $J^R=J^x+i J^y$). This allows us to investigate the role of rotational symmetry by considering vector mesons with different magnetic projections ($m_j=0,\pm 1$). We use the $m_j=0$ state of the vector meson to obtain the transition form factor, since this procedure employs the dominant spin components of the light-front wavefunctions and is more robust in practical calculations. While the $m_j=\pm 1$ states are also examined, transition form factors depend on subdominant components of the light-front wavefunctions and are less robust. Transitions between states below the open-flavor thresholds are computed, including those for excited states. Comparisons are made with the experimental measurements as well as with Lattice QCD and quark model results. In addition, we apply the transverse current to calculate the decay constant of vector mesons where we obtain consistent results using either $m_j=0$ or $m_j=1$ light-front wavefunctions. This consistency provides evidence for features of rotational symmetry within the model.

Threshold effects in hadron spectrum: a new spectroscopy?

The exploration of energies above the open-flavor threshold in the meson spectra has led to the appearance of unexpected states difficult to accommodate in the naive picture of a bound state of a quark and an antiquark. Many of such states are located close to meson-meson thresholds, which suggests that molecular structures may be a relevant component in the total wave function of such resonances. In this work, the state of meson-meson molecules calculations is reviewed, using a nonrelativistic constituent quark model that has been applied to a wide range of hadronic observables, and therefore all model parameters are completely constrained. The model has been able to reproduce, among others, the properties of the X(3872), described as a mixture of cc and DD* states, or the spectrum of the P-wave charm-strange mesons, which are well reproduced only if DK and D*K structures are taken into account. We show that such constituent quark model, which is able to describe the ordinary heavy meson spectra, is also capable of providing a good description of many new states recently reported.

Diffractive charmonium spectrum in high energy collisions in the basis light-front quantization approach

Using the charmonium light-front wavefunctions obtained by diagonalizing an effective Hamiltonian with the one-gluon exchange interaction and a confining potential inspired by light-front holography in the basis light-front quantization formalism, we compute production of charmonium states in diffractive deep inelastic scattering and ultra-peripheral heavy ion collisions within the dipole picture. Our method allows us to predict yields of all vector charmonium states below the open flavor thresholds in high-energy deep inelastic scattering, proton–nucleus and ultra-peripheral heavy ion collisions, without introducing any new parameters in the light-front wavefunctions. The obtained charmonium cross section is in reasonable agreement with experimental data at HERA, RHIC and LHC. We observe that the cross-section ratio σΨ(2s)/σJ/Ψ reveals significant independence of model parameters.

Hadronic resonances enhanced by thresholds

We present a neat example of a meson--baryon system where the vicinity of two different thresholds enhances the binding of a hadronic resonance, a pentaquark. As a consequence the pattern of states may change when moving among different flavor sectors, what poses a warning on naive extrapolations to heavy flavor sectors based on systematic expansions. For this purpose we simultaneously analyze the $N\bar D$ and $NB$ two-hadron systems looking for possible bound states or resonances. When a resonance is controlled by a coupled-channel effect, going to a different flavor sector may enhance or diminish the binding. This effect may, for example, generate significant differences between the charmonium and bottomonium spectra above open-flavor thresholds or pentaquark states in the open-charm and open-bottom sectors.

Too many X’s, Y’s and Z’s?

Heavy meson spectroscopy above open flavor thresholds has become a challenge both from the experimental and theoretical points of view. Experimentally, several signals have been interpreted as meson resonances with unusual properties; theoretically, such signals may be identified with meson-meson molecules or compact multiquark structures. We analyze the influence of thresholds on heavy meson spectroscopy comparing different flavor sectors and quantum numbers. The validity of a quark-model picture above open-flavor thresholds would severely restrict the number of channels that may lodge multiquark structures as meson-meson molecules.

Light Quark Mass Dependence in Heavy Quarkonium Physics

The issue of chiral extrapolations in heavy quarkonium systems is discussed. We show that the light quark mass dependence of the properties of heavy quarkonia is not always suppressed. For quarkonia close to an open flavor threshold, even a nonanalytic chiral extrapolation is needed. Both these nontrivial facts are demonstrated to appear in the decay widths of the hindered M1 transitions between the first radially excited and ground state P-wave charmonia. The results at a pion mass of about 500 MeV could deviate from the value at the physical pion mass by a factor of two. Our findings show the necessity of performing chiral extrapolations for lattice simulations of heavy quarkonium systems. Furthermore, lattice calculations of these transitions would also provide a definite answer to the role of coupled-channel effects in heavy quarkonium physics due to virtual heavy mesons.

Too many Xʼs, Yʼs and Zʼs?

A large number of new states have been reported during the last few years in charmonium spectroscopy above the charmed meson production threshold. They have been called Xʼs, Yʼs, and Zʼs. We reflect on the influence of thresholds on heavy meson spectroscopy comparing different flavor sectors and quantum numbers. The validity of a quark-model picture above open-flavor thresholds would severely restrict the number of channels that may lodge meson–meson molecules.

Heavy quarkonium: progress, puzzles, and opportunities

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), χ c2(2P), $B_{c}^{+}$ , and η 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 $c\bar{c}$ , $b\bar{b}$ , and $b\bar{c}$ 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.

Peak shifts due toB(*)−B¯(*)rescattering inΥ(5S)dipion transitions

We study the energy distributions of dipion transitions {upsilon}(5S) to {upsilon}(1S,2S,3S){pi}{sup +}{pi}{sup -} in the final-state rescattering model. Since the {upsilon}(5S) is well above the open bottom thresholds, the dipion transitions are expected to mainly proceed through the real processes {upsilon}(5S){yields}B{sup (*)}B{sup (*)} and B{sup (*)}B{sup (*)}{yields}{upsilon}(1S,2S,3S){pi}{sup +}{pi}{sup -}. We find that the energy distributions of {upsilon}(1S,2S,3S){pi}{sup +}{pi}{sup -} markedly differ from that of {upsilon}(5S){yields}B{sup (*)}B{sup (*)}. In particular, the resonance peak will be pushed up by about 7-20 MeV for these dipion transitions relative to the main hadronic decay modes. These predictions can be used to test the final-state rescattering mechanism in hadronic transitions for heavy quarkonia above the open flavor thresholds.

Heavy quark fragmentation functions for D-wave quarkonium and charmed b-flavored mesons.

At the large transverse momentum region, the production of heavy-heavy bound-states such as charmonium, bottomonium, and $\bar bc$ mesons in high energy $e^+e^-$ and hadronic collisions is dominated by parton fragmentation. We calculate the heavy quark fragmentation functions into the D-wave quarkonium and $\bar bc$ mesons to leading order in the strong coupling constant and in the non-relativistic expansion. In the $\bar b c$ meson case, one set of its D-wave states is expected to lie below the open flavor threshold. The total fragmentation probability for a $\bar b$ antiquark to split into the D-wave $\bar b c$ mesons is about $2 \times 10^{-5}$, which implies that only 2\% of the total pseudo-scalar ground state $B_c$ comes from the cascades of these orbitally excited states.

Heavy-quark thresholds in Higgs-boson physics.

We perform a comprehensive study of the effects related to a heavy-quark threshold in the production and decay of a scalar or pseudoscalar Higgs particle. We study the QCD corrections to the decay mode into a quark-antiquark pair and also the mixing of a Higgs boson with quarkonium states, both below and above the open-flavor threshold, which can change the properties of the Higgs boson drastically. Numerical results for a Higgs boson of mass around 10 GeV, where the mixing with {ital b{ital b}} states has a great influence on the decay widths and branching ratios, are worked out in detail for the cases of the standard model and minimal supersymmetry. The production cross section of a Higgs particle can also be enhanced by mixing with a quarkonium. A possibility to search for a Higgs boson in the 10-GeV mass range via {tau}{sup +}{tau}{sup {minus}} decays in fixed-target {ital pp} experiments at the Fermilab Tevatron or Serpukhov UNK is suggested, and ways to enhance the signal-to-background ratio are discussed.