Unquenched Quark Model Research Articles

Charmonia in an unquenched quark model

In this work, we study the charmonium spectrum within an unquenched quark model including coupled-channel effects. In couple-channel calculations, we include all of the opened charmed meson channels with the once-subtracted method, meanwhile we adopt a suppressed factor to soften the hard vertices given by the P03 model in the high momentum region. We obtain a good description of both the masses and widths for the well-established states in the charmonium spectrum. Furthermore, we give predictions for the higher S-, P-, and D-wave charmonium states up to mass region of ∼5.0 GeV. The magnitude of mass shifts due to the coupled-channel effects is estimated to be about 10s MeV. Although many decay channels are opened for the higher charmonium states, they are relatively narrow states. Their widths scatter in the range of ∼10s–100 MeV. Many charmoniumlike states, such as χc1(4274), χc0(3915), χc0(4500), χc0(4700), X(4160), X(4350), Y(4500), and ψ(4660)/Y(4710), can be accommodated by the charmonium spectrum when the unquenched coupled-channel effects are carefully considered. Published by the American Physical Society 2024

Unified unquenched quark model for heavy-light mesons with chiral dynamics

In this work, an unquenched quark model is proposed for describing the heavy-light mesons by taking into account the coupled-channel effects induced by chiral dynamics. After including a relativistic correction term for the strong transition amplitudes, both the mass spectra and decay widths of the observed heavy-light mesons can be successfully described simultaneously in a unified framework, several long-standing puzzles related to the small masses and broad widths are overcome naturally. We also provide valuable guidance in searching new heavy-light mesons by the detailed predictions of their masses, widths, and branching ratios. The success of the unquenched quark model presented in this work indicates it may be an important step for understanding the hadron spectrum. Published by the American Physical Society 2024

Light quarkonium and charmonium mass shifts in an unquenched quark model* *Supported by the National Natural Science Foundation of China (12205125, 11847145, 12205249, 11865019), and the Natural Science Foundation of Jiangsu Province, China (BK20221166)

The unquenched quark model for the light quarkonium and charmonium states is explored in this study. The quark-pair creation operator in the model, which combines the two-quark and four-quark components, is modified by considering the effects of the created quark pair's energy. Furthermore, the separation between the created quark pair and valence quark pair is modified. All the wave functions, including those for the mesons and the relative motion between two mesons, are obtained by solving the corresponding Schrödinger equation using the Gaussian expansion method. The aim of this study is to find a new set of parameters that can accurately describe the mass spectrum of low-lying light quarkonium and charmonium states. Moreover, certain exotic states, such as , can be described well in the unquenched quark model.

Charmonium mass shifts in an unquenched quark model

Charmonium mass shifts in an unquenched quark model

Charmonium spectrum in an unquenched quark model

The effects of virtual light quark pairs on the charmonium spectrum are studied. Pair creation is modelled with a ``$^{3}P_{0}$" vertex and intermediate states are summed up to 2S excitations. Quark model parameters are obtained by fitting to 12 well-known charmonium states, allowing for feedback between the decaying particle and the induced mass shifts. Both of these technical steps are new and improve agreement with the experimental spectrum. In general, the masses receive small shifts once model parameters are refit. This is true in almost cases except the $\chi_{cJ}(2P)$ multiplet, which experiences upwards mass shifts of order 150 MeV, has the ordering of the multiplet rearranged, and pushes the erstwhile $c\bar{c}$ ${2}^3P_1$ state well above $D^*\bar{D}$ threshold--observations that clarify the nature of the enigmatic $X(3872)$

Ds0(2590) as a dominant cs¯ state with a small D*K component

The recently discovered $D_{s0}(2590)$ state by the LHCb collaboration was regarded as the first excited state of $^1S_{0}$ charmed-strange meson. Its mass is, however, lower than the Godfrey-Isgur quark model prediction by about 80 MeV. In this work, we take into account the $D^{\ast}K$ contribution to the bare $c\bar{s}$ state, and show that the coupled-channel interaction induces an 88 MeV shift with respect to the conventional quark model $c\bar{s}$ state, which is much closer to the experimental mass. Our study shows that in addition to $S$-wave, $P$-wave coupled-channel interactions also play a role for hadrons located close to two-hadron thresholds. We further scrutinize the unquenched quark model results with a model independent approach. It is shown that the two-body $D^*K$ decay width is proportional to the weight of the $D^*K$ component. To saturate the experimental total decay width with the $D^*K$ partial decay width we need a weight of about 60\% while to reproduce the unquenched quark model result a weight of about 5\% is needed. Therefore, we encourage future experimental studies on the two-body $D^*K$ partial decay of $D_{s0}(2590)$.

Where are 3P and higher P -wave states in the charmonium family?

How to hunt for higher $P$-wave states of charmonium is still an open topic when $2P$ charmonia were identified. {In this work, we present an unquenched quark model calculation to illustrate the spectroscopy behavior of these $3P$, $4P$ and $5P$ states in charmonium family.} For the $3P$ charmonia, the predicted masses are around 4.2 GeV and their two-body open-charm decay behaviors were given, by which we propose that searching for these $3P$ states via their open-charm decay channels from $\gamma\gamma$ fusion and $B$ decay can be accessible at future experiment like LHCb and Belle II. We continue to calculate the masses of these $4P$ and $5P$ charmonia. Combing with these calculated results of higher $P$-wave states of charmonium, we find that the coupled-channel effect becomes more obvious with increasing the radial quantum number, which can be understood well by the modified Godfrey-Isgur model with screened potential.

The exotic hadron states in quenched and unquenched quark models

In the last two decades, a large number of exotic hadron states have been observed in experiments, which arouses great attention in the hadron physics community. In this short review, we briefly summarize progresses of our group on several exotic hadron states. Two approaches, quenched and unquenched quark models, are adopted in the calculation. The channel coupling effects, the multiquark states couple to open channels and the quark-antiquark states couple to meson-meson states, are emphasized. X(3872) is showed to be a mixture state of and in the unquenched quark model. X(2900) can be explained as a resonance state with the quantum numbers in both the quark delocalization color screening model and the chiral quark model. The reported state X(6900) can be explained as a compact resonance state with in both two quark models, and several fully heavy tetraquark states are predicated. The possible hidden-charm pentaquarks are systematically investigated in QDCSM, and seven resonance states are obtained in the corresponding baryon-meson scattering process, among which the with , with and are consistent with the experimental report of P c (4312), P c (4440), and P c (4457), respectively. More experimental data on exotic hadron states are vital for understanding exotic hadron states in quark models.

Predicting a new resonance as charmed-strange baryonic analog of Ds0*(2317)

By an unquenched quark model, we predict a charmed-strange baryon state, namely, the $\Omega_{c0}^d(1P,1/2^-)$. Its mass is predicted to be 2945 MeV, which is below the $\Xi_c\bar{K}$ threshold due to the nontrivial coupled-channel effect. So the $\Omega_{c0}^d(1P,1/2^-)$ state could be regraded as the analog of the charmed-strange meson $D_{s0}^*(2317)$. It is a good opportunity for the running Belle II experiment to search for this state in the $\Omega_c^{(*)}\gamma$ mass spectrum experiment in the future.

Possibility of charmoniumlike state X(3915) as χc0(2P) state

In this work, we seriously discuss whether $X(3915)$ can be treated as a $\chi_{c0}(2P)$ state. Based on an unquenched quark model, we give the mass spectrum of the $\chi_{cJ}(2P)$ states, where there are no free input parameters in our calculation. Our result shows that the mass gap between $\chi_{c0}(2P)$ and $\chi_{c2}(2P)$ can reach 13 MeV, which can reproduce the mass difference between $Z(3930)$ and $X(3915)$. Additionally, the calculated masses of $\chi_{c0}(2P)$ and $\chi_{c2}(2P)$ are consistent with experimental values of $X(3915)$ and $Z(3930)$, respectively. Besides, giving the mass spectrum analysis to support $X(3915)$ as $\chi_{c0}(2P)$, we also calculate the width of $\chi_{c0}(2P)$ with the same framework, which is also consistent with the experimental data of $X(3915)$. Thus, the possibility of charmoniumlike state $X(3915)$ as $\chi_{c0}(2P)$ state is further enforced.

X(3872) in an unquenched quark model

In this paper, we calculate mass and probability fractions of meson-meson components of $X(3872)$ in an unquenched quark model. Different from most of other unquenched quark models, the quark pairs creation operator from $^3P_0$ is modified by considering effects of the created quark pair energy and separation between the created quark pair and the valence quark-pair. In the calculation, all the wavefunctions of mesons and the relative motion between two mesons are obtained by solving the corresponding Schr\"{o}dinger equation with the help of gaussian expansion method. The multi-channel coupling of quark-antiquark state with possible meson-meson states are performed. The results show that the $X(3872)$ can be described as a mixing state of dominant charmonium state (70\%) and meson-meson components (30\%).

χb(3P) multiplet revisited: Hyperfine mass splitting and radiative transitions

Invoked by the recent CMS observation regarding candidates of the $\chi_b(3P)$ multiplet, we analyze the ultrafine and mass splittings among $3P$ multiplet in our unquenched quark model (UQM) studies. The mass difference of $\chi_{b2}$ and $\chi_{b1}$ in $3P$ multiplet measured by CMS collaboration ($10.6 \pm 0.64 \pm 0.17$ MeV) is very close to our theoretical prediction ($12$ MeV). Our corresponding mass splitting of $\chi_{b1}$ and $\chi_{b0}$ enables us to predict more precisely the mass of $\chi_{b0}(3P)$ to be ($10490\pm 3$) MeV. Moreover, we predict ratios of the radiative decays of $\chi_{bJ}(nP)$ candidates, both in UQM and quark potential model. Our predicted relative branching fraction of $\chi_{b0}(3P)\to\Upsilon(3S)\gamma$ is one order of magnitude smaller than $\chi_{b2}(3P)$, this naturally explains the non-observation of $\chi_{b0}(3P)$ in recent CMS search. We hope these results might provide useful references for forthcoming experimental searches.

Baryon Masses and Strangeness Suppression in the Unquenched Quark Model

We discuss the latest applications of the Unquenched Quark Model (UQM) to the calculation of baryon observables. In particular, we focus on strangeness suppression effects in baryon-meson electro-production in the UQM formalism. We also briefly discuss our results of the mass shifts of ground-state octet and decuplet baryons due to the coupling to the meson-baryon continuum.

Electromagnetic and weak decays of baryons in the unquenched quark model

In this contribution, we discuss the electromagnetic and weak decays of baryons in the unquenched quark model and show that the observed discrepancies between the experimental data and the predictions of the constituent quark model can be accounted for in large part by the effects of sea quarks. Finally, the obtained results are discussed in terms of flavor-symmetry breaking.

Light-meson masses in an unquenched quark model

We perform a coupled-channels calculation of the masses of light mesons with the quantum numbers $I{J}^{P=\ensuremath{-}}$, $(I,J)=0$, 1, by including $q\overline{q}$ and $(q\overline{q}{)}^{2}$ components in a nonrelativistic chiral quark model. The coupling between two- and four-quark configurations is realized through a $^{3}{P}_{0}$ quark-pair creation model. With the usual form of this operator, the mass shifts are large and negative, an outcome which raises serious issues of validity for the quenched quark model. Herein, therefore, we introduce some improvements of the $^{3}{P}_{0}$ operator in order to reduce the size of the mass shifts. By introducing two simple factors, physically well motivated, the coupling between $q\overline{q}$ and $(q\overline{q}{)}^{2}$ components is weakened, producing mass shifts that are around 10%--20% of hadron bare masses.

Contribution of sea quarks to the electromagnetic decay of decuplet baryons

In this work, we study briefly the electromagnetic dipole transitions from decuplet to octet S-wave baryons, where the current experimental data for the radiative decay width shows that these values are approximately two times larger than the predictions of the constituent quark model. The main aim is to solve this problem with the approach of effective degrees of freedom for quarks in the quark model, considering also the sea quarks, obtaining the valence and the sea quarks contributions. In order to do this, an unquenched quark model has been considered where the effects of the quark-antiquark pairs are incorporated as a perturbation with the quantum numbers of vacuum in the wave function for baryons as baryonmeson intermediate coupled states with the quantum numbers of the initial baryon through the 3P0 model. Also, an extended expression has been obtained to the Ml electromagnetic transition that gives a closer value to the actual experimental data due to the sea quark core contribution.

Self-energies of octet and decuplet baryons due to the coupling to the baryon-meson continuum

We present an unquenched quark model calculation of the mass shifts of ground-state octet and decuplet baryons due to the coupling to the meson-baryon continuum. All ground-state baryons and pseudoscalar mesons are included in our calculation as intermediate states. The $q\bar{q}$ pair creation effects are taken explicitly into account through a microscopic, QCD-inspired, quark-antiquark pair creation mechanism.

The non-perturbative unquenched quark model

In recent years states in the quarkonium spectrum not expected in the naive quark model have appeared and created a lot of interest. In the theoretical side the study of the effect of meson-meson thresholds in the spectrum have been performed in different approximations. In a quark model framework, and in the spirit of the Cornell model, when a meson-meson threshold is included, the coupling to all the quark-antiquark states have to be considered. In practice only the closest states are included perturbatively. In this contribution we will present a framework in which we couple quark-antiquark states with meson-meson states non-perturbatively, taking into account effectively the coupling to all quark-antiquark states. The method will be applied to the study of the X (3872) and a comparison with the perturbative calculation will be performed.

Strangeness suppression in the unquenched quark model

In this contribution, we discuss the strangeness suppression in the proton in the framework of the unquenched quark model. The theoretical results are in good agreement with the values extracted from CERN and JLab experiments.

The unquenched quark model

In this contribution, we briefly analyze the formalism of the unquenched quark model (UQM) and its application to the description of several observables of hadrons. In the UQM, the effects of charges sea pairs are introduced explicitly into the quark model through a QCD- inspired 3P0 pair-creation mechanism. We present our description of flavour asymmetry and strangeness in the proton when baryon-meson components are included. In the meson sector, the charmonium and bottomonium spectra with self-energy corrections due to the coupling to the meson-meson components.