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Register a new userA periodic table for the excited Nucleon and Delta spectrum in a relativistic chiral quark model
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E.M. Tursunov
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A possibility of the construction of a periodic table for the excited baryon spectrum is shown in the frame of a relativistic chiral quark model based on selection rules derived from the one-pion exchange mechanism. It is shown that all the $N^*$ and $Delta^*$ resonances appearing in the $pi N$ scattering data and strongly coupling to the $pi N$ channel are identified with the orbital configurations $(1S_{1/2})^2(nlj)$. Baryon resonances corresponding to the orbital configuration with two valence quarks in excited states couple strongly to the $pi pi N$-channel, but not to the $pi N$ channel. At low energy scale up to 2000 MeV, the obtained numerical estimations for the SU(2) baryon states (up to and including F-wave $N^*$ and $Delta^*$ resonances) within the schematic periodic table are mostly consistent with the experimental data. It is argued that due-to the overestimation of the ground state N(939) and Roper resonance N(1440) almost by the same amount and that the Roper resonance is a radial excitation of the N(939), the lowering mechanism for the both baryon states must be the same. The same mechanism is expected in the $Delta$ sector. At higher energies, where the experimental data are poor, we can extend our model schematically and predict seven new $N^*$ and four $Delta^*$ resonances with larger spin values.
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The spectrum of the SU(2) flavor baryons is studied in the frame of a relativistic chiral quark potential model based on the one-pion and one-gluon exchange mechanisms. It is argued that the N* and Delta* resonances strongly coupled to the pi-N channel are identified with the orbital configurations $(1S_{1/2})^2(nlj)$ with a single valence quark in the excited state (nlj). With the obtained selection rules based on the chiral constraint, we show that it is possible to construct a schematic periodic table of baryon resonances, consistent with the experimental data and yielding no missing resonances. A new original method for the treatment of the center of mass problem is suggested, which is based on the separation of the three-quark Dirac Hamiltonian into the parts, corresponding to the Jacobi coordinates. The numerical estimations for the energy positions of the Nucleon and Delta baryons (up to and including F-wave resonances), obtained within the field-theoretical framework by using time ordered perturbation theory, yield an overall good description of the experimental data at the level of the relativized CQM of S. Capstick and W. Roberts without any fitting parameters. The Delta(1232) is well reproduced. However, N g. s. and most of the radially excited baryon resonances (including Roper) are overestimated. Contrary, the first band of the orbitally excited baryon resonances with a negative parity are underestimated. At the same time, the second band of the orbitally excited Delta* states with the negative parity are mostly overestimated, while the N* states are close to the experimental boxes. The positive parity baryon resonances with J=5/2, 7/2 are close to the experimental data. At higher energies, where the experimental data are poor, we can extend our model schematically and predict an existence of seven N* and four Delta* new states with larger spin values.
A convergence of the valence quark self-energies in the 1S, 2S, $1P_{1/2}$, $1P_{3/2}$ orbits induced by pion and gluon field configurations, is shown in the frame of a relativistic chiral quark model. It is shown that in order to reach a convergence, one needs to include contribution of the intermediate quark and anti-quark states with the total momentum up to $j=25/2$. It is argued that a restriction to the lowest mode when estimating the self-energy is not good approximation.
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 strong decays of charm-strange baryons up to N=2 shell are studied in a chiral quark model. The theoretical predictions for the well determined charm-strange baryons, $Xi_c^*(2645)$, $Xi_c(2790)$ and $Xi_c(2815)$, are in good agreement with the experimental data. This model is also extended to analyze the strong decays of the other newly observed charm-strange baryons $Xi_c(2930)$, $Xi_c(2980)$, $Xi_c(3055)$, $Xi_c(3080)$ and $Xi_c(3123)$. Our predictions are given as follows. (i) $Xi_c(2930)$ might be the first $P$-wave excitation of $Xi_c$ with $J^P=1/2^-$, favors the $|Xi_c ^2P_lambda 1/2^->$ or $|Xi_c ^4P_lambda 1/2^->$ state. (ii) $Xi_c(2980)$ might correspond to two overlapping $P$-wave states $|Xi_c ^2P_rho 1/2^->$ and $|Xi_c ^2P_rho 3/2^->$, respectively. The $Xi_c(2980)$ observed in the $Lambda_c^+bar{K}pi$ final state is most likely to be the $|Xi_c ^2P_rho 1/2^->$ state, while the narrower resonance with a mass $msimeq 2.97$ GeV observed in the $Xi_c^*(2645)pi$ channel favors to be assigned to the $|Xi_c ^2P_rho 3/2^->$ state. (iii) $Xi_c(3080)$ favors to be classified as the $|Xi_c S_{rhorho} 1/2^+>$ state, i.e., the first radial excitation (2S) of $Xi_c$. (iv) $Xi_c(3055)$ is most likely to be the first $D$-wave excitation of $Xi_c$ with $J^P=3/2^+$, favors the $|Xi_c ^2D_{lambdalambda} 3/2^+>$ state. (v) $Xi_c(3123)$ might be assigned to the $|Xi_c ^4D_{lambdalambda} 3/2^+>$, $|Xi_c ^4D_{lambdalambda} 5/2^+>$, or $|Xi_c ^2D_{rhorho} 5/2^+>$ state. As a by-product, we calculate the strong decays of the bottom baryons $Sigma_b^{pm}$, $Sigma_b^{*pm}$ and $Xi_b^*$, which are in good agreement with the recent observations as well.
Using the newly measured masses of $B_c(1S)$ and $B_c(2S)$ from the CMS Collaboration and the $1S$ hyperfine splitting determined from the lattice QCD as constrains, we calculate the $B_c$ mass spectrum up to the $6S$ multiplet with a nonrelativistic linear potential model. Furthermore, using the wave functions from this model we calculate the radiative transitions between the $B_c$ states within a constituent quark model. For the higher mass $B_c$ states lying above $DB$ threshold, we also evaluate the Okubo-Zweig-Iizuka (OZI) allowed two-body strong decays with the $^{3}P_{0}$ model. Our study indicates that besides there are large potentials for the observations of the low-lying $B_c$ states below the $DB$ threshold via their radiative transitions, some higher mass $B_c$ states, such as $B_c(2^3P_2)$, $B_c(2^3D_1)$, $B_c(3^3D_1)$, $B_c(4^3P_0)$, and the $1F$-wave $B_c$ states, might be first observed in their dominant strong decay channels $DB$, $DB^*$ or $D^*B$ at the LHC for their relatively narrow widths.
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