3P0 Model Research Articles

The assignments of the bottom mesons within the screened potential model and 3P0 model

In this work, we calculate the mass spectrum of the bottom mesons with a modified nonrelativistic quark model by involving the screening effect, and explore their strong decay properties within the 3P0 model. Our results suggest that the [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] could be reasonably assigned as the [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], respectively. The more precise measurements of the excited bottom mesons are crucial to confirm these assignments.

Analysis of the charmonium-like states X*(3860), X(3872), X(3915), X(3930) and X(3940) according to their strong decay behaviors**Supported by the Fundamental Research Funds for the Central Universities (2016MS133)

Inspired by the newly observed state X*(3860), we analyze the strong decay behaviors of some charmonium-like states, X*(3860), X(3872), X(3915), X(3930) and X(3940), with the 3P0 model. We carry out our work based on the hypothesis that all of these states are charmonium systems. Our analysis indicates that, as a 0++ charmonium state, X*(3860) can reproduce the experimental data. As for X(3872), it can tentatively be interpreted as the mixture of a system and a molecular state. If we consider X(3940) as a 31S0 state, its total width in the present work is much lower than the experimental result. Thus, the 31S0 charmonium state seems not to be a good candidate for X(3940). Furthermore, our analysis implies that it is reasonable to assign X(3915) and X(3930) to be the same state, 2++. However, combining our analysis with that in Refs.[, ], we speculate that X(3915)/X(3930) might also be the mixture of a system and a molecular state.

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.

Study of radially excited Ds(21S0) and Ds(3P)**Supported by National Natural Science Foundation of China (11475111)

The unobserved JP = 0− radial excitation Ds(21S0) is anticipated to have mass 2650 MeV (denoted as Ds(2650)). Study of hadronic production is an important way to identify highly excited states. We study hadronic production of Ds(2650) from higher excited resonances in a 3P0 model. Relevant hadronic partial decay widths are found to be very small, which implies it is difficult to observe Ds(2650) in hadronic decays of higher excited resonances. Hadronic decay widths of radially excited Ds(3P) have also been estimated. The total decay widths of four Ds(3P) are large, but the branching ratios in the Ds(2650)η channel are very small, which implies that it seems impossible to observe Ds(2650) in hadronic decays of Ds(3P). The dominant decay channels of the four Ds(3P) have been pointed out, and D1(2420), D1(2430), , D(2550), D(2600), (11D2)D(2750) and are possible to observe in hadronic production from Ds(3P).

The Ds1(2536)+ Decay Widths in the C3P0 Model

The Fock-Tani representation is a field theory formalism appropriated for the simultaneous treatment of composite particles and their constituents. The 3P0 model is a typical decay model which considers only OZI-allowed strong decays. The model considers a quark-antiquark pair created with the vacuum quantum numbers in the presence of the initial state meson. It is described as the non-relativistic limit of the pair creation Hamiltonian. Applying the Fock-Tani transformation to the microscopic Hamiltonian of the pair creation produces the characteristic expansion in powers of the wavefunction, where the 3P0 model is the lowest order in the expansion. The corrected 3P0 model (C3P0) is obtained from higher orders in the expansion, by the introduction of the bound state kernel [Formula: see text], called the bound state correction. The goal of this work is to study the application of the 3P0 model and C3P0 model in detail for the strange charmed meson sector ([Formula: see text] meson). In particular, we shall calculate the decay amplitudes and decay rates of the [Formula: see text].

Direct pion emission in D*+ → D+π decays**Supported by National Natural Science Foundation of China (11375128)

The QCD multipole expansion (QCDME) is based on quantum field theory and has been extensively applied to study transitions among ϒ and ψ family members. As it refers to non-perturbative QCD, however, it has only a certain application range. Even though it successfully explains the transition data among members of the ϒ (ψ) family, as Eichten indicates, beyond the production threshold of mediate states it fails to match data by several orders of magnitude. In this work, by studying a simple decay mode D*→ D + π0, where a pion may be emitted before D* transitions into D, we analyze the contribution of QCD multipole expansion. As the Dπ portal is open, the dominant contribution is an OZI-allowed process where a light quark-pair is excited out from vacuum, and its contribution can be evaluated by the 3P0 model. Since direct pion emission is OZI-suppressed and violates isospin conservation, its contribution must be much smaller than the dominant one. By a careful calculation, we estimate that the QCDME contribution should be 3–4 orders smaller than the dominant contribution and this result can offer a quantitative interpretation for Eichten's statement.

Role of pentaquark components inϕmeson production proton-antiproton annihilation reactions

The pentaquark component is included in the proton wave functions to study phi meson production proton-antiproton annihilation reactions. With all possible configurations of the uuds subsystem proposed for describing the strangeness spin and magnetic moment of the proton, we estimate the branching ratios of the annihilation reactions at rest proton-antiproton to phi + X (X=pi, eta, rho, omega) from atomic proton-antiproton S- and P-wave states by using effective quark line diagrams incorporating the 3P0 model. The best agreement of theoretical prediction with the experimental data is found when the pentaquark configuration of the proton wave function takes the flavor-spin symmetry, [4]_FS [22]_F [22]_S.

Differences Between The 3P0 and C3P0 model in the Charming Strange Sector

The goal of this work is to establish a comparison between the very well studied 3P0 model and a bound-state corrected version, the C3P0 model, obtained from applying the Fock-Tani transformation to the 3P0 model, in the context of the charmed-strange meson sector (DSJ meson). In particular, we shall calculate the decay amplitudes and decay rates of the Ds1 (2460)+ → D*s+π0 and Ds1 (2536)+ → D*(2010)+K0, showing the differences between the two models.

In-medium decay widths of hidden and open charm vector mesons in a field theoretic model for composite hadrons

We calculate the decay widths of the charmonium states, J/ψ, ψ(3686) and ψ(3770), to [Formula: see text] pairs, as well as the decay width of D* → Dπ, in isospin asymmetric strange hadronic matter, using a field theoretical model for composite hadrons with quark constituents. For this purpose, we use the quark–antiquark pair creation term of the free Dirac Hamiltonian written in terms of the constituent quark field operators, and use explicit charmonium, D, [Formula: see text], D* and π states to evaluate the matrix elements for the charmonium as well as D* decay amplitudes. The medium modifications of the partial decay widths of charmonium to [Formula: see text] pair, arising from the mass modifications of the [Formula: see text] and the charmonium states calculated in a chiral effective model, are also included. The results of the present investigations are then compared with the decay widths computed earlier, in a model using light quark pair creation in 3P0 state. As in 3P0 model, the decay amplitude in the present model is multiplied with a strength parameter for the light quark pair creation, which is fitted from the observed vacuum decay width. The effects of the isospin asymmetry, the strangeness fraction of the hadronic matter on the masses of the charmonium states and [Formula: see text] mesons and hence on the decay widths, have also been studied. The isospin asymmetry effect is observed to be dominant for high densities, leading to appreciable difference in the decay channels of the charmonium to D+ D- and [Formula: see text] pairs. The decay width of D* → Dπ in the hadronic matter has also been calculated within the composite quark model in the present work, accounting for the medium modifications of the D and D* masses. The density modifications of the charmonium states and D(D*) mesons, which are observed to be appreciable at high densities, will be of relevance in the compressed baryonic matter (CBM) experiments at the future facility of FAIR, GSI, where charmed hadrons will be produced by annihilation of antiprotons on nuclei. The interactions of the charmonium states and D(D*) with the nuclear medium could lead to the possibility of the formation of exotic bound states of the nuclei with the (excited) charmonium states as well as with D(D*) mesons.

Higher mass bottomonia

We show the results of a quark model calculation of the bottomonium spectrum with self energy corrections due to the coupling to the meson-meson continuum. The bare masses used in the calculation are computed within the relativized quark model by Godfrey and Isgur. We also give results for the open-bottom strong decay amplitudes of higher bottomonia in a 3P0 model.

Angular momentum coefficients for meson strong decay and unquenched quark models

In most meson strong decay and unquenched (coupled-channel) quark models, the pair-creation operator is a scalar product of vectors in the spin and spatial degrees of freedom. While differing in the spatial part, most models have the same spin part, which creates a qq* pair coupled to spin triplet, with the spins of the initial quarks as spectators. This is a basic assumption of the 3P0 model, and is well-known to arise also in the flux tube model, starting from the strong coupling expansion of lattice QCD. In this article the same structure is shown to emerge in the Cornell model, in the dominant contributions of a more general microscopic decay model, and in the pseudoscalar-meson emission model. A solution is obtained for arbitrary matrix elements in these ``non-flip, triplet'' models, expressed as a weighted sum over spatial matrix elements. The coefficients in the expansion, which involve the spin degrees of freedom and the associated angular momentum algebra, are model-independent. Tables of the angular momentum coefficients are presented which can be used in future calculations, avoiding tedious Clebsch-Gordan sums. The symmetry and orthogonality properties of the coefficients are discussed, as well as their application to transitions involving hybrid mesons and states of mixed spin. New selection rules are derived, and existing ones generalised. The coefficients lead to model-independent relations among decay amplitudes and widths which can be tested in experiment and lattice QCD. They can also be used to explain how mass shifts in the unquenched quark model do not spoil successful predictions of the ordinary (quenched) quark model.

Strong decays of χcJ(2P) and χcJ(3P)

In the framework of the chiral quark model, the mass spectrum of χcJ (J = 0, 1, 2, n = 1, 2, 3) is studied with the Gaussian expansion method. Using the wave functions obtained in the study of mass spectrum, the open charm two-body strong decay widths of these states are calculated by using the 3P0 model. The results show that the masses of χcJ(1P) and χc2(2P) are consistent with the experimental data. But the strong decay width of χc2(2P) is three times that of the experimental value. The decay width of χc1(2P) is sensitive to its mass. In the quark-antiquark picture, the width is about 385 MeV. However, if the channel coupling effects shift its mass to 3872 MeV, its decay width will be around 1 MeV. The possibility of assigning the state X(3872) as χc1(2P) cannot be excluded. To assign X(3915) as χc0(2P) is disfavored, due to the unmatching of decay channel. For the χcJ(3P) states, no states have been assigned. The possible candidates of χc0(3P) are X(4160) and X(4140). Their masses are close to the theoretical ones. The experimental branching ratio of X(4160), \(\Gamma (X(4160) \to D\bar D)/\Gamma (X(4160) \to D*\bar D*) < 0.09\) is compatible with that of χc0(3P), 0.07. However the broad decay width of X(4160) cannot be explained by the open charm two-body decay. To assign X(4140) as χc0(3P) is also possible, due to the compatibility of the total decay width, the further measurement of decay modes of X(4140) are expected to justify the assignment.

WHY X(3915) IS SO NARROW AS A χc0(2P) STATE?

New resonance X(3915) was identified as the charmonium χc0(2P) by BaBar Collaboration, but there still seems an open question of this assignment: why its full width is so narrow? To answer this question, we calculate the Okubo–Zweig–Iizuka (OZI)-allowed strong decays [Formula: see text], where X(3915) is assigned as a χc0(2P) state, and estimate its full width in the cooperating framework of 3P0 model and the Bethe–Salpeter (BS) method using the Mandelstam formalism, during which nonperturbative quantum chromodynamics (QCD) effects of the hadronic matrix elements are well-considered by overlapping integral over the relativistic Salpeter wave functions of the initial and final states. We find the node structure of χc0(2P) wave function resulting in the narrow width of X(3915) and show the dependence of the decay width on the variation of the initial mass of X(3915). We point out that the rate of [Formula: see text] is crucial to confirm whether X(3915) is the χc0(2P) state or not.

Mixing between the 23S1 and 13D1 Ds

Mixing between the 23S1 and 13D1 Ds is studied within the 3P0 model. If mixing between these two 1− states exists, D*s1(2700)± and D*sJ(2860)± could be interpreted as the two orthogonal mixed states with mixing angle θ≈−80° in the case of a special β for each meson. However, in the case of a universal β for all mesons, D*s1(2700)± could be interpreted as the mixed state of 23S1 and 13D1 with mixing angle 12° < θ < 21° but D*sJ(2860)± seems difficult to interpret as the orthogonal partner of D*s1(2700)±.

HEAVY DIQUARK SYMMETRY CONSTRAINTS FOR STRONG DECAYS

The heavy diquark symmetry (HDS) of doubly heavy baryons (DHBs) provides new insights into the spectroscopy of these hadrons. We derive the consequences of this symmetry for the mass spectra and the decay widths of DHBs. We compare these symmetry constraints to results from a nonrelativistic quark model for the mass spectra and results from the 3P0 model for strong decays. The quark model we implement was not constructed with these symmetries and contains interactions which explicitly break HDS. Nevertheless these symmetries emerge. We argue that the 3P0 model and any other model for strong transitions which employs a spectator assumption explicitly respects HDS. We also explore the possibility of treating the strange quark as a heavy quark and apply these ideas to Ξ, Ξc and Ξb baryons.

Radial excitation states of η and η′ in the chiral quark model

A chiral quark model is applied to calculate the spectra of pseudoscalar mesons η and η′. By analyzing the obtained spectra, we find that the mesons η′(21S0), η(41S0), η′(31S0) and η′(41S0) are the possible candidates of η(1760), X(1835), X(2120) and X(2370). The strong decay widths of these pseudoscalars to all the possible two-body decay channels are calculated within the framework of the 3P0 model. Although the total width of η′(21S0) is compatible with the BES Collaboration's experimental value for η(1760), the partial decay width to ωω is too small, which is not consistent with the BES result. If X(1835) is interpreted as η(41S0), the total decay width is compatible with the experimental data, and the main decay modes will be πa0(980) and πa0(1450), which needs to be checked experimentally. The assignment of X(2120) and X(2370) to η′(31S0) and η′(41S0) is disfavored in the present calculation because of the incompatibility of the decay widths.

OZI-ALLOWED TWO BODY ϒ DECAYS IN THE 3P0 MODEL WITH THE RELATIVISTIC WAVE FUNCTIONS

We combine the Bethe–Salpeter method with the 3P0 model to describe OZI-allowed two body meson decays. In this combined method, the relativistic wave functions defined in the Salpeter equation show up in the decay amplitude of the 3P0 model automatically. We apply the method to OZI-allowed ϒ( 4S, 5S, 6S ) two body decays. The results are roughly consistent with the experimental data and the predictions of ϒ( 6S ) decays are given.

J/ψ DECAY IN THE C3P0 MODEL

The Fock-Tani representation, is a field theoretic formalism to treat problems involving both composite particles and their constituents. The application of the Fock-Tani transformation to a pair creation Hamiltonian produces the characteristic expansion in powers of the wave function. In lowest order of this expansion, we obtain the model known in the literature: the 3P0 model. In higher orders, the Corrected 3P0 model (C3P0) is obtained by introducing the bound state kernel. In this work, we use the C3P0 model to calculate the J/ψ decay rates in the following channels: ρ π, ω η, ω η′, K*+ K-, [Formula: see text], ϕ η, ϕ η′. We consider that the J/ψ is a mixture given by [Formula: see text].

DECAY PROCESS OF THE CHARMED MESON $D_{2}^{\ast}\,(2460)$ IN THE C3P0 Model

The Fock-Tani formalism is a successful mapping technique that has been used in hadron physics to describe hadron interaction and decay. In this one can obtain the 3P0 model with bound state corrections. In this work we applay this technique for [Formula: see text] decay, where the amplitude and its respective decay rates are evaluated.

C3P0 MODEL FOR CHARMED MESONS DECAY

The successful mapping technique, Fock–Tani formalism, has produced a corrected 3P0 model ( C 3P0 model), which retains the basic aspects of the 3P0 predictions with the inclusion of bound-state corrections. The model is applied for charmed mesons decay. The amplitude and its respective decay rates are evaluated.