Conventional Quark Model Research Articles

Two-Body Hadronic Weak Decays of Bottomed Hadrons

The structure of light diquarks plays a crucial role in formation of exotic hadrons beyond the conventional quark model, especially with regard to the line shapes of bottomed hadron decays. We study the two-body hadronic weak decays of bottomed baryons and bottomed mesons to probe the light diquark structure and to pin down the quark–quark correlations in the diquark picture. It is found that the light diquark does not favor a compact structure. For instance, the isoscalar diquark [ud] in Λb0 can be easily split and rearranged to form Σc(*)D¯(*) via the color-suppressed transition. This provides a hint that the hidden charm pentaquark states produced in Λb0 decays could be the Σc(*)D¯(*) hadronic molecular candidates. This quantitative study resolves the apparent conflicts between the production mechanism and the molecular nature of these Pc states observed in experiment.

Status and Prospects of Exotic Hadrons at Belle II

In the past 20 years, many new hadrons that are difficult to explain within the conventional quark model have been discovered in the quarkonium region; these are called exotic hadrons. The Belle II experiment, as the next-generation B factory, provides a good platform for exploring them. The charmonium-like states can be produced at Belle II in several ways, such as B meson decays, initial-state radiation processes, two-photon collisions and double charmonium production. Bottomonium-like states can be produced directly in e + e − colliding energies at Belle II with low continuum backgrounds. Belle II plans to perform a high-statistics energy scan from the threshold up to the highest possible energy of 11.24 GeV to search for new Yb states with J PC = 1−−, Xb [the bottom counterpart of χ c1(3872), also known as X(3872)] and partners of Zb states. We give a mini-review on the status and prospects of exotic hadrons at Belle II.

Modifications on the Properties of \(D^*_{s0}\)(2317) as Four-quark State in Thermal Medium

Since the low mass of $D^*_{s0}(2317)$ has still been a problem to the conventional quark model, one can consider other options regarding as multi-quark system. Therefore we investigate the scalar open-charm state $D^*_{s0}(2317)$ by Thermal QCD Sum Rules (TQCDSR) method using the two-point correlation function together with contributions of the non-perturbative condensates up to dimension six. Deriving and numerically analyzing thermal mass and pole residue sum rules, we accomplish the effects on the properties of $D^*_{s0}(2317)$ resonance in hot medium. Our numerical evaluations indicate that the variations in mass and pole residue values are stable through the growing temperature up to $T\cong100~\mathrm{MeV}$, but they begin to fall after this point. At critical temperature, the values of mass and pole residue change up to $91\%, 70\% $ of their values in vacuum in the molecular scenario and $ 91\%, 69\% $ in the diquark-antidiquark scenario. Our results does not give any definite information as to whether $D^*_{s0}(2317)$ resonance has molecular or diquark-antidiquark structure since they are very close to each other to differentiate them. Besides, we predict the hadronic parameters of the bottom partner of the $D^*_{s0}(2317)$ resonance in both molecular and diquark-antidiquark pictures. This bound state is worth investigating in future experiments. Also the detailed search of hot medium effects on the hadronic parameters of open-charm meson $D^*_{s0}(2317)$ and the bottom partner could have some implications to define the QCD phase diagram obtained from heavy-ion collision experiments. Moreover these results can be useful in distinguishing conventional quark model mesons from exotica.

Mixing angles between the tetraquark states with two heavy quarks within QCD sum rules

LHCb Collaboration has recently announced the observation of a doubly charmed tetraquark $T_{cc \bar{u} \bar{d}}^+$ state with spin parity $J^P = 1^+$. This exotic state can be explained as a molecular state with small binding energy. According to conventional quark model, both $D^+ D^{0\ast}$ and $(D^0 D^{+\ast})$ multiquark states are expected to have the same mass and flavor in the exact $SU(3)$ symmetry. However, since the quark masses are different, $SU(3) (SU(2))$ symmetry is violated, hence, the mass and flavor eigenstates do not coincide. The mass eigenstates can be represented as a linear combination of the flavor eigenstates, which is characterized by the mixing angle $\theta$. In the present work, the possible mixing angles between the $T_{cc}$ states are calculated. Moreover, the analysis are extended for all the possible tetraquarks scenarios with two heavy and two light quarks within the molecular picture although those states have not been observed yet. Our prediction on mixing angle between doubly charmed tetraquark states shows that $SU(3)$ symmetry breaking is around $7\%$ maximally.

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 $D_{s0}(2590)$.

On leptonic width of X(4260)

New measurements on cross sections in e^+e^-rightarrow J/psi pi ^+pi ^-, h_cpi ^+pi ^-, D^0D^{*-}pi ^++c.c., psi (2S)pi ^+pi ^-, omega chi _{c0} and J/psi eta channels have been carried out by BESIII, Belle and BABAR experiments, as well as in the D_s^{*+}D_s^{*-} channel. We perform extensive numerical analyses by combining all these data available, together with those in D^+D^{*-}+c.c. and D^{*+}D^{*-} channels. Though the latter show no evident peak around sqrt{s}=4.230 GeV, the missing X(4260) is explained as that it is concealed by the interference effects of the well established charmonia psi (4040), psi (4160) and psi (4415). Our analyses reveal that the leptonic decay width of X(4260) ranges from mathcal {O}(10^2) eV to mathcal {O}(1) keV, and hence it is probably explained in the conventional quark model picture. That is, the X(4260) may well be interpreted as a mixture of 4^3S_1 and 3^3D_1 (2^3D_1) states.

Mixing angles between the tetraquark states with two heavy quarks within QCDsum rules

LHCb collaboration has recently announced the observation of a doubly charmed tetraquark $T_{cc \bar{u} \bar{d}}^+$ state with spin parity $J^P = 1^+$. This exotic state can be explained as a molecular state with small binding energy. According to conventional quark model, both $D^+ D^{0\ast}$ and $(D^0 D^{+\ast})$ multiquark states are expected to have the same mass and flavor in the exact $SU(3)$ symmetry. However, since the quark masses are different, $SU(3) (SU(2))$ symmetry is violated; hence, the mass and flavor eigenstates do not coincide. The mass eigenstates can be represented as a linear combination of the flavor eigenstates, which is characterized by the mixing angle $\theta$. In the present work, the possible mixing angles between the $T_{cc}$ states are calculated. Moreover, the analyses are extended for all the possible tetraquarks scenarios with two heavy and two light quarks within the molecular picture although those states have not been observed yet. Our prediction on mixing angle between doubly charmed tetraquark states shows that $SU(3)$ symmetry breaking is around $7\%$ maximally.

Trimeson bound state BBB* via a delocalized π bond

During the last decades, numerous exotic states which cannot be explained by the conventional quark model have been observed in experiment. Some of them can be understood as two-body hadronic molecules, such as the famous $X(3872)$, analogous to deuteron in nuclear physics. Along the same line, the existence of the triton leaves an open question whether there is a bound state formed by three hadrons. Since, for a given potential, a system with large reduced masses is more easier to form a bound state, we study the $BBB^{\ast}$ system with the one-pion exchange potential as an exploratory step by solving the three-body Schr\"odinger Equation. We predict that a tri-meson molecular state for the $BBB^{\ast}$ system is probably existent as long as the molecular states of its two-body subsystem $BB^*$ exist.

Double heavy tri-hadron bound state via delocalized π bond**Supported by the DFG (TR110) and the NSFC (11621131001) through funds provided to the Sino-German CRC 110 “Symmetries and the Emergence of Structure in QCD”. The work of UGM was also supported by the Chinese Academy of Sciences (CAS) President’s International Fellowship Initiative (PIFI) (2018DM0034) and by VolkswagenStiftung (93562)

The number of exotic candidates that are beyond the conventional quark model has increased dramatically over recent decades. Some of these can be viewed as analogues of the deuteron. Similarly, the existence of the triton indicates that bound states formed by three hadrons could also exist. To illustrate this possibility, we study the DD*K and systems using the Born-Oppenheimer approximation. To leading order, only one-pion exchange potentials are considered. This means that the three constituents share one virtual pion. This is similar to the role of the delocalized π bond for the formation of benzene in chemistry. After solving the Schrödinger equation, we find two three-body DD*K and bound states with masses and , respectively. The masses of their and analogues are and , respectively. From the experimental side, the bound state could be found by analyzing the current world data on the process, by focusing on the J/ψ π K channel.

Recent empirical developments in the study and understanding of XYZ states

Exotic hadronic states beyond the conventional quark model (called charmoniumlike/bottomoniumlike states or XYZ particles) have been searched for and many candidates were proposed including glueballs, hybrids, multi-quark states, hadron molecules, etc. Dramatic progress was made in the study of the exotic states after the running of the two B -factories, i.e., Belle at KEK and BaBar at SLAC. In my review report, I present the most recent results on the study of the XYZ states from the BESIII, Belle, BaBar, LHCb, CMS experiments, etc., including (1) X states: the observation of the X(3872) in e + e − → γX (3872) at around 4.26 GeV; searches for the X b state; (2) Y states including the updated results for the Y (4008), Y (4260), Y (4360), Y (4660), etc; (3) Z states including the observations of the Z (4430), Z 1 (4050), Z 2 (4250), Z c (3900), Z c (4020), Z c (4200); the evidence for the Z c (4050) ± → π ± ψ (2 S ); search for the Z cs in e + e − → K + K − J/ψ .

Overview of the status/results in the exotics sector

Many exotic hadronic states beyond the conventional quark model (called char-moniumlike/bottomoniumlike states or XYZ particles) were found in the B -factories or energy scans of the cross sections of e + e − annhilation into conventional quarkonia and light hadrons. Their nature properties were proposed including glueballs, hybrids, multi-quark states, hadron molecules, etc. Dramatic progress was made in the study of the them after the running of the B -factories. In this report, I present the most recent results on the XYZ results from Belle experiment.

Employing spin symmetry to disentangle different models for theXYZstates

In order to test different models proposed for some states discovered recently in the charmonium mass range that do not fit into the pattern predicted by the conventional quark model, we derive predictions for the spectrum within the hadro-charmonium picture, the tetraquark picture as well as the hadronic molecular approach. We exploit heavy quark spin symmetry for the hadro-charmonium and hadronic molecule scenarios. The patterns that emerge from the different models turn out to be quite distinct. For example, only within the hadro-charmonium picture a pseudoscalar state emerges that is lighter than the $Y(4260)$. Possible discovery channels of these additional states are discussed.

Observation of Structures in the J/ψϕ Mass Spectrum at CMS

Observation of charmonium like new states since 2003, which do not fit into conventional quark model renewed the interest in exotic states. Many models like meson molecule, tetraquark, and quark-gluon hybrid are proposed to explain the observed charmonium spectroscopy. The observation of Y(3940)[1] near the J/ψω threshold motivated the searches for similar structures near J/ψϕ threshold. In this proceeding, we summarize the recent developments on the observation of a peaking structure in the J/ψϕ mass spectrum from B± → J/ψϕK± decay.

Strong and radiative decays of the D s0 * (2317) and Ds1(2460)

Since their discovery in 2003, the open charm states D * s0 and D s1(2460) provide a challenge to the conventional quark model. In recent years, theoretical evidence has been accumulated for both states in favor of a predominantly DK and D*K molecular nature, respectively. However, a direct experimental proof of this hypothesis still needs to be found. Since radiative decays are generally believed to be sensitive to the inner structure of the decaying particles, we study in this work the radiative and strong decays of both the D * s0 (2317) and D s1(2460), as well as of their counterparts in the bottom sector. While the strong decays are indeed strongly enhanced for molecular states, the radiative decays are of similar order of magnitude in different pictures. Thus, the experimental observable that allows one to conclusively quantify the molecular components of the D * s0 (2317) and D s1(2460) is the hadronic width, and not the radiative one, in contradistinction to common belief. We also find that radiative decays of the sibling states in the bottom sector are significantly more frequent than the hadronic ones. Based on this, we identify their most promising discovery channels.

Few-Body Systems Composed of Heavy Quarks

Within the past 10 years many new hadrons states were observed experimentally, some of which do not fit into the conventional quark model. This work is about the few-body systems composed of heavy quarks, including the charmonium-like states and some loosely bound states.

Proton spin in a light-cone chiral quark model

We discuss the spin structure of the proton in a light-cone treatment of the chiral quark model. Based on the fact that the quark helicity ($\ensuremath{\Delta}q$) measured in polarized deep inelastic scattering experiments is actually the quark spin defined in the light-cone formalism rather than the quark spin ($\ensuremath{\Delta}{q}_{QM}$) defined in the conventional quark model (or in the rest frame of the nucleon), we calculate the $x$ dependence of the polarized quark distribution functions $\ensuremath{\Delta}q(x)$, and the polarized structure functions ${g}_{1}(x)$. Special attention is focused on the Melosh-Wigner rotation due to the transversal motions of quarks inside the nucleon and Melosh-Wigner rotation effects on the bare quark input. It is shown that our results match the experimental data well.

Hadron resonances with coexistence of different natures

We discuss coexistence/mixing of different natures of hadronic composite (molecule) and elementary (quark-intrinsic) ones in hadron resonances. The discussions here are based on our previous publications on the origin of hadron resonances \cite{Hyodo:2008xr}, exotic $\bar D$ meson-nucleons as hadronic composites containing one anti-heavy quark \cite{Yamaguchi:2011xb}, and the study of $a_1$ as a typical example to show explicitly the mixing of the two different natures \cite{Nagahiro:2011jn}. In all cases, interactions are derived from the chiral dynamics of the light flavor sector. These interactions generate in various cases hadronic composite/molecule states, serving varieties of structure beyond the conventional quark model.

Implications to assignments of and

Possible assignments of $D_{s1}(2700)^\pm$ and $D_{sJ}(2860)$ in the conventional quark model are analyzed. The study indicates that both the orbitally excited $c\bar s$ and the radially excited $c\bar s$ are possible. Some implications to these assignments are explored. If $D_{s1}(2700)^\pm$ and $D_{sJ}(2860)$ are the orbitally excited D-wave $1^- (j^P={3\over 2}^-)$ and $3^- (j^P={5\over 2}^-)$, respectively, another orbitally excited D-wave $2^-$ $D_s$, $D_{s2}(2800)$, is expected. If $D_{s1}(2700)^\pm$ and $D_{sJ}(2860)$ are the first radially excited $1^- (j^P={1\over 2}^-)$ and $0^+ (j^P={1\over 2}^+)$, respectively, other two radially excited $0^- D^\prime_s(2582)$ and $1^+ D^\prime_{s1}(2973)$ are expected. $D_{s2}(2800)$ and $D^\prime_{s1}(2973)$ are mixing states. The chiral doubling relation may exist in radially excited $D_s$, the splitting between the parity partners(the $(0^-,1^-)$ and the $(0^+,1^+)$) is $\approx 280$ MeV.

Implications of Heavy-Quark Spin Symmetry on Heavy-Meson Hadronic Molecules

In recent years, many heavy mesons and charmonia were observed which do not fit in the conventional quark model expectations. Some of them are proposed to be hadronic molecules. Here we investigate the consequences of heavy-quark spin symmetry on these heavy-meson hadronic molecules. Heavy-quark spin symmetry enables us to predict new heavy-meson molecules and provides us with a method to test heavy-meson molecule assumptions of some newly observed states. In particular, we predict an eta_{c};{'}f_{0}(980) bound state as the spin-doublet partner of the Y(4660) proposed as a psi;{'}f_{0}(980) bound state with a mass of 4616_{-6};{+5} MeV and the prominent decay mode eta_{c};{'}pipi. The width is predicted to be Gamma(eta_{c};{'}pipi) = 60 +/- 30 MeV. The pi;{+}pi;{-} invariant mass spectrum and the line shape are calculated. We suggest searching for this state in B;{+/-} --> eta_{c};{'}K;{+/-}pi;{+}pi;{-}, whose branching fraction is expected to be large.

The [formula omitted] splitting in constituent quark models

In this Letter we present a solution to describe simultaneously the light isoscalar and isovector vector mesons in constituent quark models. In Ref. [J. Vijande, F. Fernández, A. Valcarce, J. Phys. G 31 (2005) 481] the qq¯ spectrum was studied in a generalized constituent quark model constrained by the NN phenomenology and the baryon spectrum. An overall good fit to the available experimental data was obtained. A major problem of this description was the relative position of the vector ω and ρ mesons. The present results improve the description of the isoscalar meson spectroscopy. They should serve as a step forward in distinguishing conventional quark model mesons from exotic states.