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Register a new userEffect of $Z_b$ states on $Upsilon(3S)toUpsilon(1S)pipi$ decays
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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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We study the dipion transitions $Upsilon(4S) rightarrow Upsilon(nS) pi^+pi^-$ $(n=1,2)$. In particular, we consider the effects of the two intermediate bottomoniumlike exotic states $Z_b(10610)$ and $Z_b(10650)$ as well as bottom meson loops. The strong pion-pion final-state interactions, especially including channel coupling to $Kbar{K}$ in the $S$-wave, are taken into account model-independently by using dispersion theory. Based on a nonrelativistic effective field theory we find that the contribution from the bottom meson loops is comparable to those from the chiral contact terms and the $Z_b$-exchange terms. For the $Upsilon(4S) rightarrow Upsilon(2S) pi^+pi^-$ decay, the result shows that including the effects of the $Z_b$-exchange and the bottom meson loops can naturally reproduce the two-hump behavior of the $pipi$ mass spectra. Future angular distribution data are decisive for the identification of different production mechanisms. For the $Upsilon(4S) rightarrow Upsilon(1S) pi^+pi^-$ decay, we show that there is a narrow dip around 1 GeV in the $pipi$ invariant mass distribution, caused by the final-state interactions. The distribution is clearly different from that in similar transitions from lower $Upsilon$ states, and needs to be verified by future data with high statistics. Also we predict the decay width and the dikaon mass distribution of the $Upsilon(4S) rightarrow Upsilon(1S) K^+ K^-$ process.
The dipion transitions $Upsilon(2S,3S,4S) to Upsilon(1S,2S)pipi$ are systematically studied by considering the mechanisms of the hadronization of soft gluons, exchanging the bottomoniumlike $Z_b$ states, and the bottom-meson loops. The strong pion-pion final-state interaction, especially including the channel coupling to $Kbar{K}$ in the $S$-wave, is taken into account in a model-independent way using the dispersion theory. Through fitting to the available experimental data, we extract values of the transition chromopolarizabilities $|alpha_{Upsilon(mS)Upsilon(nS)}|$, which measure the chromoelectric couplings of the bottomonia with soft gluons. It is found that the $Z_b$ exchange has a slight impact on the extracted chromopolarizablity values, and the obtained $|alpha_{Upsilon(2S)Upsilon(1S)}|$ considering the $Z_b$ exchange is $(0.29pm 0.20)~text{GeV}^{-3}$. Our results could be useful in studying the interactions of bottomonium with light hadrons.
The dipion transitions $Upsilon(10860)topi^+pi^-Upsilon(nS)$ ($n=1,2,3$) are studied in the framework of a unitary and analytic coupled-channel formalism previously developed for analysing experimental data on the bottomoniumlike states $Z_b(10610)$ and $Z_b(10650)$ [Phys. Rev. D 98, 074023 (2018)] and predicting the properties of their spin partners [Phys. Rev. D 99, 094013 (2019)]. In this work we use a relatively simple but realistic version of this approach, where the scattering and production amplitudes are constructed employing only short-ranged interactions between the open- and hidden-flavour channels consistent with the constraints from heavy quark spin symmetry, for an extended analysis of the experimental line shapes. In particular, the transitions from the $Upsilon(10860)$ to the final states $pi pi h_b(mP)$ ($m=1,2$) and $pi B^{(*)}bar B^* $ already studied before, are now augmented by the $Upsilon(10860)topi^+pi^-Upsilon(nS)$ final states ($n=1,2,3$). This is achieved by employing dispersion theory to account for the final state interaction of the $pipi$ subsystem including its coupling to the $Kbar K$ channel. Fits to the two-dimensional Dalitz plots for the $pi^+pi^-Upsilon$ final states were performed. Two real subtraction constants are adjusted to achieve the best description of the Dalitz plot for each $Upsilon(nS)$ $(n=1,2,3)$ while all the parameters related to the properties of the $Z_b$s are kept fixed from the previous study. A good overall description of the data for all $Upsilon(10860)topi^+pi^-Upsilon(nS)$ channels achieved in this work provides additional strong support for the molecular interpretation of the $Z_b$ states.
We search for the $J^{PC}=0^{--}$ and $1^{+-}$ light tetraquark states with masses up to 2.46~GeV/$c^2$ in $Upsilon(1S)$ and $Upsilon(2S)$ decays with data samples of $(102pm 2)$ million and $(158pm 4)$ million events, respectively, collected with the Belle detector. No significant signals are observed in any of the studied production modes, and 90% credibility level (C.L.) upper limits on their branching fractions in $Upsilon(1S)$ and $Upsilon(2S)$ decays are obtained. The inclusive branching fractions of the $Upsilon(1S)$ and $Upsilon(2S)$ decays into final states with $f_1(1285)$ are measured to be ${cal B}(Upsilon(1S)to f_1(1285)+anything)=(46pm28({rm stat.})pm13({rm syst.}))times 10^{-4}$ and ${cal B}(Upsilon(2S)to f_1(1285)+anything)=(22pm15({rm stat.})pm6.3({rm syst.}))times 10^{-4}$. The measured $chi_{b2} to J/psi + anything$ branching fraction is measured to be $(1.50pm0.34({rm stat.})pm0.22({rm syst.}))times 10^{-3}$, and 90% C.L. upper limits for the $chi_{b0,b1} to J/psi + anything$ branching fractions are found to be $2.3times 10^{-3}$ and $1.1times 10^{-3}$, respectively. For ${cal B}(chi_{b1} to omega + anything)$, the branching fraction is measured to be $(4.9pm1.3({rm stat.})pm0.6({rm syst.}))times 10^{-2}$. %($<3.68times 10^{-2}$ at 90% C.L.). All results reported here are the first measurements for these modes.
The branching fractions of the $Upsilon(1S)$ inclusive decays into final states with a $J/psi$ or a $psi(2S)$ are measured with improved precision to be $BR(Upsilon(1S)to J/psi + {rm anything})=(5.25pm 0.13(mathrm{stat.})pm 0.25(mathrm{syst.}))times 10^{-4}$ and $BR(Upsilon(1S)to psi(2S) + {rm anything})=(1.23pm 0.17(mathrm{stat.})pm 0.11(mathrm{syst.}))times 10^{-4}$. The first search for $Upsilon(1S)$ decays into $XYZ$ states that decay into a $J/psi$ or a $psi(2S)$ plus one or two charged tracks yields no significant signals for $XYZ$ states in any of the examined decay modes, and upper limits on their production rates in $Upsilon(1S)$ inclusive decays are determined.
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