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Register a new user$Omega$ baryon spectrum and their decays in a constituent quark model
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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.
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In this work we calculate the mass spectrum of strangeonium up to the $3D$ multiplet within a nonrelativistic linear potential quark model. Furthermore, using the obtained wave functions, we also evaluate the strong decays of the strangeonium states with the $^3P_0$ model. Based on our successful explanations of the well established states $phi(1020)$, $phi(1680)$, $h_1(1415)$, $f_2(1525)$, and $phi_3(1850)$, we further discuss the possible assignments of strangeonium-like states from experiments by combining our theoretical results with the observations. It is found that some resonances, such as $f_2(2010)$ and $f_2(2150)$ listed by the Particle Data Group, and $X(2062)$ and $X(2500)$ newly observed by BESIII, may be interpreted as the strangeonium states. The possibility of $phi(2170)$ as a candidate for $phi(3S)$ or $phi(2D)$ cannot be excluded. We expect our results to provide useful references for looking for the missing $sbar{s}$ states in future experiments.
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We study the $f^+$ form factor for the semileptonic $bar B_sto K^+ell^-bar u_ell$ decay in a constituent quark model. The valence quark estimate is supplemented with the contribution from the $bar B^*$ pole that dominates the high $q^2$ region. We use a multiply-subtracted Omn`es dispersion relation to extend the quark model predictions from its region of applicability near $q^2_{rm max}=(M_{B_s}-M_K)^2sim 23.75$ GeV$^2$ to all $q^2$ values accessible in the physical decay. To better constrain the dependence of $f^+$ on $q^2$, we fit the subtraction constants to a combined input from previous light cone sum rule [Phys. Rev. D 78 (2008) 054015] and the present quark model results. From this analysis, we obtain $Gamma(bar B_sto K^+ell^-bar u_ell)=(5.45^{+0.83}_{-0.80})|V_{ub}|^2times 10^{-9},{rm MeV}$, which is about 20% higher than the prediction based only on QCD light cone sum rule estimates. Differences are much larger for the $f^+$ form factor in the region above $q^2=15$ GeV$^2$.
The vector meson $omega$-$phi$ mixing is studied in two alternative scenarios with different numbers of mixing angles, i.e., the one-mixing-angle scenario and the two-mixing-angle scenario, in both the octect-singlet mixing scheme and the quark flavor mixing scheme. Concerning the reproduction of experimental data and the $Q^2$ behavior of transition form factors, one-mixing-angle scenario in the quark flavor scheme performs better than that in the octet-singlet scheme, while the two-mixing-angle scenario works well for both mixing schemes. The difference between the two mixing angles in the octet-singlet scheme is bigger than that in the quark flavor scheme.
Isospin violating mixing of rho- and omega-mesons is reconsidered in terms of propagators. Its influence on various pairs of (rho^0,omega)-decays to the same final states is demonstrated. Some of them, (rho^0,omega)topi^+pi^- and (rho^0,omega)topi^0gamma, have been earlier discussed in the literature, others (e.g., (rho^0,omega)toetagamma and (rho^0,omega)to e^+e^-) are new in this context. Changes in partial widths for all the decay pairs are shown to be correlated. The set of present experimental data, though yet inconclusive, provides some limits for the direct (rhoomega)-coupling and indirectly supports enhancement of rho^0topi^0gamma in comparison with rho^{pm}topi^{pm}gamma, though not so large as in some previous estimates.
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