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Register a new userCharmonium states in QCD-inspired quark potential model using Gaussian expansion method
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We investigate the mass spectrum and electromagnetic processes of charmonium system with the nonperturbative treatment for the spin-dependent potentials, comparing the pure scalar and scalar-vector mixing linear confining potentials. It is revealed that the scalar-vector mixing confinement would be important for reproducing the mass spectrum and decay widths, and therein the vector component is predicted to be around 22%. With the state wave functions obtained via the full-potential Hamiltonian, the long-standing discrepancy in M1 radiative transitions of $J/psi$ and $psi^{prime}$ are alleviated spontaneously. This work also intends to provide an inspection and suggestion for the possible $cbar{c}$ among the copious higher charmonium-like states. Particularly, the newly observed X(4160) and X(4350) are found in the charmonium family mass spectrum as $M(2^1D_2)= 4164.9$ MeV and $M(3^3P_2)= 4352.4$ MeV, which strongly favor the $J^{PC}=2^{-+}, 2^{++}$ assignments respectively. The corresponding radiative transitions, leptonic and two-photon decay widths have been also predicted theoretically for the further experimental search.
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We have studied the dominant radiative transitions of the charmonium $S$- and $P$-wave states within the CCQM. The gauge invariant leading-order transition amplitudes have been expressed by using either the conventional Lorentz structures, or the helicity amplitudes, where it was effective. The renormalization couplings of the charmonium states have been strictly fixed by the compositeness conditions that excludes the constituent degrees of freedom from the space of physical states. We use the basic model parameters for the constituent c-quark mass $m_c=1.80$ GeV and the global infrared cutoff $lambda=0.181$ GeV. We additionally introduce only one adjustable parameter $varrho>0$ common for the the charmonium states $eta_c({}^1!S_0)$, $J/psi({}^3!S_1)$, $chi_{c0}({^{3}}!P_{0})$, $chi_{c1}({^{3}}!P_{1})$, $h_c({^{1}}!P_{1})$, and $chi_{c2}({^{3}}!P_{2})$ to describe the quark distribution inside the hadron. This parameter describes the ratio between the charmonium size and its physical mass. The optimal value $varrho=0.485$ has been fixed by fitting the latest data for the partial widths of the one-photon radiative decays of the triplet $chi_{cJ}({^{3}}!P_{J}),~J={0,1,2}$. Then, we calculate corresponding fractional widths for states $J/psi({}^3!S_1)$ and $h_c({^{1}}!P_{1})$. Estimated results are in good agreement with the latest data. By using the fraction data from PDG2020 and our estimated partial decay width for $h_c({^{1}}!P_{1})$ we recalculate the theoretical full width $Gamma^{rm theor}_{h_c} simeq ( 0.57 pm 0.12 )$ MeV in comparison with latest data $Gamma^{rm exp}_{h_c} simeq (0.7pm 0.4)$ MeV. We also repeated our calculations by gradually decreasing the global cutoff parameter and revealed that the results do not change for any $lambda<0.181$ GeV up to the deconfinement limit.
In recent years, more and more exotic hadronic states have been discovered successively. Many of them can be explained as hadronic molecules, such as $D_{s0}^*(2317)$, $X(3872)$, and $P_c$ pentaquark states. Analogous to the formation of nuclei, we study three-body hadronic molecules with the Gaussian expansion method and predict the existence of the $DDK$, $Xi_{cc}Xi_{cc}bar{K}$, and $BBbar{K}$ bound states, which are likely to be found in the current and updated facilities.
We investigate how the derivative expansion in the HAL QCD method works to extract physical observables, using a separable potential in quantum mechanics, which is solvable but highly non-local in the coordinate system. We consider three cases for inputs to determine the HAL QCD potential in the derivative expansion, (1) energy eigenfunctions (2) time-dependent wave functions as solutions to the time dependent Schrodinger equation with some boundary conditions (3) time-dependent wave function made by a linear combination of finite number of eigenfunctions at low energy to mimic the finite volume effect. We have found that, for all three cases, the potentials provide reasonable scattering phase shifts even at the leading order of the derivative expansion, and they give more accurate results as the order of the expansion increases. By comparing the above results with those from the formal derivative expansion for the separable potential, we conclude that the derivative expansion is not a way to obtain the potential but a method to extract physical observables such as phase shifts and binding energies, and that the scattering phase shifts from the derivative expansion in the HAL QCD method converge to the exact ones much faster than those from the formal derivative expansion of the separable potential.
We present a unified approach to the thermodynamics of hadron-quark-gluon matter at finite temperatures on the basis of a quark cluster expansion in the form of a generalized Beth-Uhlenbeck approach with a generic ansatz for the hadronic phase shifts that fulfills the Levinson theorem. The change in the composition of the system from a hadron resonance gas to a quark-gluon plasma takes place in the narrow temperature interval of $150 - 185$ MeV where the Mott dissociation of hadrons is triggered by the dropping quark mass as a result of the restoration of chiral symmetry. The deconfinement of quark and gluon degrees of freedom is regulated by the Polyakov loop variable that signals the breaking of the $Z(3)$ center symmetry of the color $SU(3)$ group of QCD. We suggest a Polyakov-loop quark-gluon plasma model with $mathcal{O}(alpha_s)$ virial correction and solve the stationarity condition of the thermodynamic potential (gap equation) for the Polyakov loop. The resulting pressure is in excellent agreement with lattice QCD simulations up to high temperatures.
In the past years there has been a revival of hadron spectroscopy. Many interesting new hadron states were discovered experimentally, some of which do not fit easily into the quark model. This situation motivated a vigorous theoretical activity. This is a rapidly evolving field with enormous amount of new experimental information. In the present report we include and discuss data which were released very recently. The present review is the first one written from the perspective of QCD sum rules (QCDSR), where we present the main steps of concrete calculations and compare the results with other approaches and with experimental data.
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