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Register a new userRe-Study on the wave functions of $Upsilon(nS)$ states in LFQM and the radiative decays of $Upsilon(nS)to eta_b+gamma$
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The Light-front quark model (LFQM) has been applied to calculate the transition matrix elements of heavy hadron decays. However, it is noted that using the traditional wave functions of the LFQM given in literature, the theoretically determined decay constants of the $Upsilon(nS)$ obviously contradict to the data. It implies that the wave functions must be modified. Keeping the orthogonality among the $nS$ states and fitting their decay constants we obtain a series of the wave functions for $Upsilon(nS)$. Based on these wave functions and by analogy to the hydrogen atom, we suggest a modified analytical form for the $Upsilon(nS)$ wave functions. By use of the modified wave functions, the obtained decay constants are close to the experimental data. Then we calculate the rates of radiative decays of $Upsilon(nS)to eta_b+gamma$. Our predictions are consistent with the experimental data on decays $Upsilon(3S)to eta_b+gamma$ within the theoretical and experimental errors.
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Based on previous studies that support the vector-vector molecular structure of the $f_2(1270)$, $f_2(1525)$, $bar{K}^{*,0}_2(1430)$, $f_0(1370)$ and $f_0(1710)$ resonances, we make predictions for $psi (2S)$ decay into $omega(phi) f_2(1270)$, $omega(phi) f_2(1525)$, $K^{*0}(892) bar{K}^{*,0}_2(1430)$ and radiative decay of $Upsilon (1S),Upsilon (2S), psi (2S)$ into $gamma f_2(1270)$, $gamma f_2(1525)$, $gamma f_0(1370)$, $gamma f_0(1710)$. Agreement with experimental data is found for three available ratios, without using free parameters, and predictions are done for other cases.
The hyperfine splittings in heavy quarkonia are studied in a model-independent way using the experimental data on di-electron widths. Relativistic correlations are taken into account together with the smearing of the spin-spin interaction. The radius of smearing is fixed by the known $J/psi-eta_c(1S)$ and $psi(2S)-eta_c(2S)$ splittings and appears to be small, $r_{ss} cong 0.06$ fm. Nevertheless, even with such a small radius an essential suppression of the hyperfine splittings ($sim 50%)$ is observed in bottomonium. For the $nS~ bbar b$ states $(n=1,2,...,6)$ we predict the values (in MeV) 28, 12, 10, 6, 6, and 3, respectively. For the $3S$ and $4S$ charmonium states the splittings 16(2) MeV and 12(4) MeV are obtained.
Applying the nonrelativistic quantum chromodynamics factorization formalism to the $Upsilon(1S,2S,3S)$ hadroproduction, a complete analysis on the polarization parameters $lambda_{theta}$, $lambda_{thetaphi}$, $lambda_{phi}$ for the production are presented at QCD next-to-leading order. With the long-distance matrix elements extracted from experimental data for the production rate and polarization parameter $lambda_{theta}$ of $Upsilon$ hadroproduction, our results provide a good description for the measured parameters $lambda_{thetaphi}$ and $lambda_{phi}$ in both the helicity and the Collins-Soper frames. In our calculations the frame invariant parameter $tilde{lambda}$ is consistent in the two frames. Finally, it is pointed out that there are discrepancies for $tilde{lambda}$ between available experimental data and corresponding theoretical predictions.
We estimate the $Upsilon$, $eta_b$ and $B^*$ meson mass shifts in symmetric nuclear matter. The interest is, whether the strengths of the bottomonium-(nuclear matter) and charmonium-(nuclear matter) interactions are similar or different. This is because, each ($J/Psi,Upsilon$) and ($eta_c,eta_b$) meson group is usually assumed to have very similar properties based on the heavy charm and bottom quark masses. The estimate for the $Upsilon$ is made using an SU(5) effective Lagrangian and the anomalous coupling one, by studying the $BB$, $BB^*$, and $B^*B^*$ meson loop contributions for the self-energy. As for the $eta_b$, we include the $BB^*$ and $B^*B^*$ meson loop contributions in the self-energy. The in-medium masses of the $B$ and $B^*$ mesons appearing in the self-energy are calculated by the quark-meson coupling model. An analysis on the $BB$, $BB^*$, and $B^*B^*$ meson loops in the $Upsilon$ mass shift is made by comparing with the corresponding $DD, DD^*$, and $D^*D^*$ meson loops for the $J/Psi$ mass shift. Our prediction for the $eta_b$ mass shift is made including only the lowest order $BB^*$ meson loop. The $Upsilon$ mass shift, with including only the $BB$ loop, is predicted to be -16 to -22 MeV at the nuclear matter saturation density using the $Upsilon BB$ coupling constant determined by the vector meson dominance model with the experimental data, while the $eta_b$ mass shift is predicted to be -75 to -82 MeV with the SU(5) universal coupling constant determined by the $Upsilon BB$ coupling constant. Our results show an appreciable difference between the bottomonium-(nuclear matter) and charmonium-(nuclear matter) interaction strengths. We also study the $Upsilon$ and $eta_b$ mass shifts in a heavy quark (heavy meson) symmetry limit.
Within the framework of dispersion theory, we analyze the dipion transitions between the lightest $Upsilon$ states, $Upsilon(nS) rightarrow Upsilon(mS) pipi$ with $m < n leq 3$. In particular, we consider the possible effects of two intermediate bottomoniumlike exotic states $Z_b(10610)$ and $Z_b(10650)$. The $pipi$ rescattering effects are taken into account in a model-independent way using dispersion theory. We confirm that matching the dispersive representation to the leading chiral amplitude alone cannot reproduce the peculiar two-peak $pipi$ mass spectrum of the decay $Upsilon(3S) rightarrow Upsilon(1S) pipi$. The existence of the bottomoniumlike $Z_b$ states can naturally explain this anomaly. We also point out the necessity of a proper extraction of the coupling strengths for the $Z_b$ states to $Upsilon(nS)pi$, which is only possible if a Flatte-like parametrization is used in the data analysis for the $Z_b$ states.
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