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Register a new userUniversal Constituent-Quark Model for Baryons
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We present a relativistic constituent-quark model that covers all known baryons from the nucleon up to $Omega_{bbb}$. The corresponding invariant mass operator includes a linear confinement and a hyperfine interaction based on effective degrees of freedom. The model provides for a unified description of practically all baryon spectra in good agreement with present phenomenology and it can tentatively be employed for the relativistic treatment of all kinds of baryon reactions. Predictions of states still missing in the phenomenological data base, especially in the lesser explored heavy-flavor sectors of charm and bottom baryons, should be important especially for future experiments in these areas.
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In this work, we study the mass spectrum of the $Omega_{ccc}$ and $Omega_{bbb}$ baryons up to the $N=2$ shell within a nonrelativistic constituent quark model (NRCQM). The model parameters are adopted from the determinations by fitting the charmonium and bottomonium spectra in our previous works. The masses of the $Omega_{ccc}$ and $Omega_{bbb}$ baryon states predicted in present work reasonably agree with the results obtained with the Lattice QCD calculations. Furthermore, to provide more knowledge of the $Omega_{ccc}$ and $Omega_{bbb}$ states, we evaluate their radiative decays with the available masses and wave functions from the potential model.
We calculate the matrix elements of the color-spin interaction for all possible multi-quark states of tribaryons in flavor SU(3) broken case. For that purpose, we construct the flavor$otimes$color$otimes$spin wave functions of the tribaryons, which are taken to be antisymmetric to satisfy the Pauli exclusion principle. Furthermore, we analyze the diquark structure of the tribaryon configurations using the symmetric and antisymmetric basis set of flavor, color and spin states.
Constituent quark masses can be determined quite well from experimental data in several ways and one can obtain fairly accurate values for all six $m_q$. The strong quark-meson coupling $g=2pi /sqrt{3}$ arises from the quark-level linear $sigma$ model, whereas $e$ and $sintheta_w$ arise from weak interactions when the heavy $M_W$ and $M_Z$ are regarded as resonances in analogy with the strong KSFR relation. The Higgs boson mass, tied to null expectation value of charged Higgs components, is found to be around 317 GeV. Finally, the experimental CPV phase angle $delta$ and the three CKM angles $Theta_c, Theta_2, Theta_3$ are successfully deduced from the 6 constituent quark masses following Fritzschs approach.
Combining the recent developments of the observations of $Omega$ sates we calculate the $Omega$ spectrum up to the $N=2$ shell within a nonrelativistic constituent quark potential model. Furthermore, the strong and radiative decay properties for the $Omega$ resonances within the $N=2$ shell are evaluated by using the masses and wave functions obtained from the potential model. It is found that the newly observed $Omega(2012)$ resonance is most likely to be the spin-parity $J^P=3/2^-$ $1P$-wave state $Omega(1^{2}P_{3/2^{-}})$, it also has a large potential to be observed in the $Omega(1672)gamma$ channel. Our calculation shows that the 1$P$-, 1$D$-, and 2$S$-wave $Omega$ baryons have a relatively narrow decay width of less than 50 MeV. Based on the obtained decay properties and mass spectrum, we further suggest optimum channels and mass regions to find the missing $Omega$ resonances via the strong and/or radiative decay processes.
The recently discovered $P_c(4380)^+$ and $P_c(4450)^+$ states at LHCb have masses close to the $bar DSigma_c^*$ and $bar D^*Sigma_c$ thresholds, respectively, which suggest that they may have significant meson-baryon molecular components. We analyze these states in the framework of a constituent quark model which has been applied to a wide range of hadronic observables, being the model parameters, therefore, completely constrained. The $P_c(4380)^+$ and $P_c(4450)^+$ are studied as molecular states composed by charmed baryons and open charm mesons. Several bound states with the proper binding energy are found in the $bar DSigma_c^*$ and $bar D^*Sigma_c$ channels. We discuss the possible assignments of these states from their decay widths. Moreover, two more states are predicted, associated with the $bar DSigma_c$ and $bar D^* Sigma_c^*$ thresholds.
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