Bottomonium-like States Research Articles

Predicting hidden bottom molecular tetraquarks with a complex scaling method

In the present work, we perform a coupled-channel analysis of B(s)(*)B¯(s)(*) systems with the one-boson-exchange potentials. We first study the I(JPC)=1(1+−) BB¯*/B*B¯* system to describe the Zb(10610) and Zb(10650) particles as molecular states and determine the reasonable range of cutoff parameter Λ. Then, other B(s)(*)B¯(s)(*) combinations with different quantum numbers are systematically investigated. Some bound states and resonances appear in the isoscalar systems, while only several shallow bound states exist for isovector systems. Far away from the excited conventional P-wave bottomium, these predicted states can be easily identified as exotic particles both theoretically and experimentally. Moreover, the ηb(nS)/ϒ(nS) plus light mesons are the excellent final states to search for the bound states, while the BB¯*+H.c. and B*B¯* channels are suitable for the resonances. We highly recommend that the LHCb and Belle II Collaborations hunt for these bottomoniumlike states in the future. Published by the American Physical Society 2024

Status and Prospects of Exotic Hadrons at Belle II

In the past 20 years, many new hadrons that are difficult to explain within the conventional quark model have been discovered in the quarkonium region; these are called exotic hadrons. The Belle II experiment, as the next-generation B factory, provides a good platform for exploring them. The charmonium-like states can be produced at Belle II in several ways, such as B meson decays, initial-state radiation processes, two-photon collisions and double charmonium production. Bottomonium-like states can be produced directly in e + e − colliding energies at Belle II with low continuum backgrounds. Belle II plans to perform a high-statistics energy scan from the threshold up to the highest possible energy of 11.24 GeV to search for new Yb states with J PC = 1−−, Xb [the bottom counterpart of χ c1(3872), also known as X(3872)] and partners of Zb states. We give a mini-review on the status and prospects of exotic hadrons at Belle II.

Composite nature of Z_b states from data analysis

We use a near-threshold parameterization with explicit inclusion of the Castillejo–Dalitz–Dyson poles, which is more general than the effective range expansion, to study the bottomonium-like states Z_b(10610) and Z_b(10650). In terms of the partial-wave amplitude, we fit the event number distribution of B^{(*)}{bar{B}}^* system to the experimental data for these resonances from Belle Collaboration. The data could be described very well in our method, which supports the molecular interpretation. Then the relevant physical quantities are obtained, including the B^{(*)}bar{B}^* scattering length (a), effective range (r), and residue squared (gamma _s^2) of the pole in the complex plane. In particular, we find the compositeness can range from about 0.4 up to 1 for the B{bar{B}}^* (B^*{bar{B}}^*) component in the resonance Z_b(10610) (Z_b(10650)).

Production of bottomonium-like Zb states in e-h and ultraperipheral h-h collisions * *This project is supported by the National Natural Science Foundation of China (12065014, 11705076, 11747160), and by the Strategic Priority Research Program of Chinese Academy of Sciences, (XDB34030301). This work is partly Supported by HongLiu Support Funds for Excellent Youth Talents of Lanzhou University of Technology. We also

The photoproduction of the bottomonium-like states and via scattering is studied within an effective Lagrangian approach and the vector-meson-dominance model. The Regge model is employed to calculate the photoproduction of states via the t-channel with exchange. The numerical results show that the values of the total cross-sections of and can reach 0.09 nb and 0.02 nb, respectively, near the center-of-mass energy of 22 GeV. Experimental measurements and studies of the photoproduction of states near the energy region around GeV are suggested. Moreover, with the help of eSTARlight and STARlight programs, we have obtained the cross-sections and numbers of events for production in electron-ion collisions (EIC) and ultraperipheral collisions (UPCs). The results show that a considerable number of events can be produced in the relevant experiments on EICs and UPCs. We have also calculated the rates and kinematic distributions for in and collisions via EICs and UPCs. The results will provide an important reference for the RHIC, LHC, EIC-US, LHeC, and FCC experiments in searching for bottomonium-like states.

Insights into Zb(10610) and Zb(10650) from dipion transitions from ϒ(10860)

The dipion transitions $\Upsilon(10860)\to\pi^+\pi^-\Upsilon(nS)$ ($n=1,2,3$) 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 $\Upsilon(10860)\to\pi^+\pi^-\Upsilon(nS)$ final states ($n=1,2,3$). This is achieved by employing dispersion theory to account for the final state interaction of the $\pi\pi$ subsystem including its coupling to the $K\bar K$ 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 $\Upsilon(10860)\to\pi^+\pi^-\Upsilon(nS)$ channels achieved in this work provides additional strong support for the molecular interpretation of the $Z_b$ states.

Decoding the nature of Zcs(3985) and establishing the spectrum of charged heavy quarkoniumlike states in chiral effective field theory

We study the newly observed charmoniumlike state $Z_{cs}(3985)$ in the framework of chiral effective field theory. The interaction kernel of the $\bar{D}_sD^\ast/\bar{D}^\ast_sD$ system is calculated up to the next-to-leading order with the explicit chiral dynamics. With the fitted parameters extracted from the $Z_c(3900)$ data as inputs, the mass, width and event distributions of the $Z_{cs}(3985)$ are very consistent with the experimental measurements. Our studies strongly support the $Z_{cs}(3985)$ as the partner of the $Z_c(3900)$ in the SU(3)$_f$ symmetry and the $\bar{D}_sD^\ast/\bar{D}^\ast_sD$ molecular resonance with the same dynamical origin as the other charged heavy quarkoniumlike states. We precisely predict the resonance parameters of the unobserved states in $\bar{D}_s^\ast D^\ast$, $B^\ast_s \bar{B}/B_s\bar{B}^\ast$ and $B_s^\ast\bar{B}^\ast$ systems, and establish a complete spectrum of the charged charmoniumlike and bottomoniumlike states with the $I(J^P)$ quantum numbers $1(1^+)$ and $\frac{1}{2}(1^+)$, respectively.

Deciphering the charged heavy quarkoniumlike states in chiral effective field theory

We generalize the framework of chiral effective field theory to study the interactions of the isovector $D^\ast\bar{D}^{(\ast)}$ and $B^\ast\bar{B}^{(\ast)}$ systems up to the next-to-leading order, in which the long-, mid-, and short-range force contributions as well as the $S$-$D$ wave mixing are incorporated. Based on the Lippmann-Schwinger equation, we fit the invariant mass distributions of the elastic channels measured by the BESIII and Belle Collaborations. Our results indicate that the four charged charmoniumlike and bottomoniumlike states $Z_c(3900)$, $Z_c(4020)$ and $Z_b(10610)$, $Z_b(10650)$ can be well identified as the $D\bar{D}^{\ast},D^\ast\bar{D}^{\ast}$ and $B\bar{B}^{\ast},B^\ast\bar{B}^{\ast}$ molecular resonances. The bound state explanations are vetoed in our framework. Our study favors the $Z_c$ and $Z_b$ states are the twin partners under the heavy quark symmetry.

Exotic Hadrons with Heavy Quarks

We discuss a model-independent effective-field-theory-based approach to bottomonium-like states $$Z_{b}(10610)$$ and $$Z_{b}(10650)$$ and a prediction of the properties of their spin partners with the quantum numbers $$0^{++}$$ , $$1^{++}$$ , and $$2^{++}$$ .

Predictions of transitions * * Supported in part by the Fundamental Research Funds for the Central Universities (FRF-BR-19-001A), and by the National Natural Science Foundation of China (11975028)

We study the contributions of intermediate bottomonium-like states and the bottom meson loops in the heavy quark spin flip transitions . Depending on the constructive or destructive interferences between the -exchange and the bottom meson loops mechanisms, we predict two possible branching ratios for each process: BR or , and or . The contribution of the bottom meson loops is found to be considerably larger than that of the -exchange in the transitions, while its decay rates are not comparable to those of heavy quark spin conserved processes. We also predict the contribution of the charm meson loops in the branch fractions of .

Spin partners WbJ from the line shapes of the Zb(10610) and Zb(10650)

In a recent paper Phys.Rev. D98, 074023 (2018), the most up-to-date experimental data for all measured production and decay channels of the bottomonium-like states $Z_b(10610)$ and $Z_b(10650)$ were analysed in a field-theoretical coupled-channel approach which respects analyticity and unitarity and incorporates both the pion exchange as well as a short-ranged potential nonperturbatively. All parameters of the interaction were fixed directly from data, and pole positions for both $Z_b$ states were determined. In this work we employ the same approach to predict in a parameter-free way the pole positions and the line shapes in the elastic and inelastic channels of the (still to be discovered) spin partners of the $Z_b$ states. They are conventionally referred to as $W_{bJ}$'s with the quantum numbers $J^{PC}=J^{++}$ ($J=0,1,2$). It is demonstrated that the results of our most advanced pionful fit, which gives the best $\chi^2/{\rm d.o.f.}$ for the data in the $Z_b$ channels, are consistent with all $W_{bJ}$ states being above-threshold resonances which manifest themselves as well pronounced hump structures in the line shapes. On the contrary, in the pionless approach, all $W_{bJ}$'s are virtual states which can be seen as enhanced threshold cusps in the inelastic line shapes. Since the two above scenarios provide different imprints on the observables, the role of the one-pion exchange in the $B^{(*)}\bar{B}^{(*)}$ systems can be inferred from the once available experimental data directly.

Heavy quarkonia: the beauty and the beasts

New enhancements in the charmonium and bottomonium spectra observed since 2003 are very briefly reviewed. Special attention is paid to χc1(3872) (formerly X(3872)) owing to its remarkable proximity to the threshold, which allows modelling as a quasibound axial-vector state with a large admixture. In contrast, the interpretation of many other charmonium-like and bottomonium-like states is still very controversial and some may not even correspond to genuine resonances. Accordingly, several entries in the PDG tables have been wildly changing over the years. Three representative states are reviewed here as non-resonant enhancements due to threshold effects, viz. ψ(4260), ψ(4660), and ϒ(10580).

Remarks on the heavy-quark flavour symmetry for doubly heavy hadronic molecules

The possibility for a common effective field theory for hadronic molecules with different heavy-quark flavours is examined critically. It is argued that such a theory does not allow one to draw definite conclusions for doubly heavy molecules. In particular, it does not allow one to relate binding energies for the molecules in the c-quark and b-quark sectors with controlled uncertainties. Therefore, while this kind of reasoning does not preclude from employing heavy-quark spin symmetry for charmonium- and bottomonium-like states separately within a well established effective field theory framework, relations between different heavy-quark sectors can only be obtained using phenomenological approaches with uncontrolled uncertainties.

Line shapes of the Zb(10610) and Zb(10650) in the elastic and inelastic channels revisited

The most recent experimental data for all measured production and decay channels of the bottomonium-like states $Z_b(10610)$ and $Z_b(10650)$ are analysed simultaneously using solutions of the Lippmann-Schwinger equations which respect constraints from unitarity and analyticity. The interaction potential in the open-bottom channels $B^{(*)}\bar{B}^{*}+\mbox{c.c.}$ contains short-range interactions as well as one-pion exchange. It is found that the long-range interaction does not affect the line shapes as long as only $S$ waves are considered. Meanwhile, the line shapes can be visibly modified once $D$ waves, mediated by the strong tensor forces from the pion exchange potentials, are included. However, in the fit they get balanced largely by a momentum dependent contact term that appears to be needed also to render the results for the line shapes independent of the cut-off. The resulting line shapes are found to be insensitive to various higher-order interactions included to verify stability of the results. Both $Z_b$ states are found to be described by the poles located on the unphysical Riemann sheets in the vicinity of the corresponding thresholds. In particular, the $Z_b(10610)$ state is associated with a virtual state residing just below the $B\bar{B}^{*}/\bar B{B}^{*}$ threshold while the $Z_b(10650)$ state most likely is a shallow state located just above the $B^*\bar{B}^{*}$ threshold.

Production and absorption of exotic bottomoniumlike states in high energy heavy ion collisions

We investigate the production and absorption of $Z_b (10610)$ and $Z_b ^{\prime}(10650)$ states in a hadronic medium, via the processes $\bar{B}^{(*)} B^{(*)} \rightarrow \pi Z_b ^{(\prime)} $ and the corresponding inverses reactions. We use effective field Lagrangians based on an $SU(4)$-extension of the hidden gauge formalism to account for the couplings between light and heavy mesons, and a phenomenological Lagrangian involving the $ B^{\ast} B^{(\ast)} Z_b ^{(\prime)}$ vertices. The absorption cross sections are found to be much larger than the production ones.

Bottomonium-like states: Physics case for energy scan above the BB̄ threshold at Belle-II

The Belle-II experiment is expected to collect large data samples at the [Formula: see text] and [Formula: see text] resonances to study primarily [Formula: see text] and [Formula: see text] mesons. We discuss what other data above the [Formula: see text] threshold are of interest. We propose to perform a high-statistics energy scan from the [Formula: see text] threshold up to the highest possible energy, and to collect data at the [Formula: see text] and at higher mass states if they are found in the scan. We emphasize the interest in increasing the maximal energy from 11.24 GeV to 11.5–12 GeV in the future. These data are needed for the investigation of bottomonium and bottomonium-like states.

Energy Scan of the e^{+}e^{-}→h_{b}(nP)π^{+}π^{-} (n=1, 2) Cross Sections and Evidence for ϒ(11020) Decays into Charged Bottomoniumlike States.

Using data collected with the Belle detector at the KEKB asymmetric-energy e^{+}e^{-} collider, we measure the energy dependence of the e^{+}e^{-}→h_{b}(nP)π^{+}π^{-} (n=1, 2) cross sections from thresholds up to 11.02GeV. We find clear ϒ(10860) and ϒ(11020) peaks with little or no continuum contribution. We study the resonant substructure of the ϒ(11020)→h_{b}(nP)π^{+}π^{-} transitions and find evidence that they proceed entirely via the intermediate isovector states Z_{b}(10610) and Z_{b}(10650). The relative fraction of these states is loosely constrained by the current data: The hypothesis that only Z_{b}(10610) is produced is excluded at the level of 3.3 standard deviations, while the hypothesis that only Z_{b}(10650) is produced is not excluded at a significant level.

Effective field theory investigations of the XYZ puzzle

Quantum Chromodynamics, the theory of strong interactions, predicts several types of bound states. Among them are conventional mesons (qq̅) and baryons (qqq), which have been the only states observed in experiments for years. However, in the last decade, many states that do not fit this picture have been observed at B-factories (BaBar, Belle and CLEO), at τ-charm facilities (CLEO-c, BESIII) and also at proton-proton colliders (CDF, D0, LHCb, ATLAS, CMS). There is growing evidence that at least some of the new charmonium- and bottomonium-like states, the so-called XYZ mesons, are new forms of matter such as quark-gluon hybrids, mesonic molecules or different arrangements of tetraquarks, pentaquarks... Effective Field Theories (EFTs) have been constructed for heavy-quark-antiquark bound states, but a general study of the XYZ mesons within the same framework has not yet been done. The scope of this conference proceedings is to discuss the possibilities we have in developing novel EFTs that, characterizing the conventional quarkonium states, facilitate also the systematic and model-independent description of the new exotic matter, in particular, the hybrid mesons.

General considerations on the nature ofZb(10610)andZb(10650)from their pole positions

The nature of the bottomonium-like states $Z_b(10610)$ and $Z_b(10650)$ is studied by calculating the $B^{(*)}\overline B^{*}$ compositeness ($X$) in those resonances. We first consider uncoupled isovector $S$-wave scattering of $B^{(*)}\overline B^{*}$ within the framework of effective-range expansion (ERE). Expressions for the scattering length ($a$) and effective range ($r$) are derived exclusively in terms of the masses and widths of the two $Z_b$ states. We then develop compositeness within ERE for the resonance case and deduce the expression $X=1/\sqrt{2r/a-1}$, which is then applied to the systems of interest. Finally, the actual compositeness parameters are calculated in terms of resonance pole positions and their experimental branching ratios into $B^{(*)}\overline{B}^*$ by using the method of Ref.[1]. We find the values $X=0.66\pm 0.11$ and $0.51\pm 0.10$ for the $Z_b(10610)$ and $Z_b(10650)$, respectively. We also compare the ERE with Breit-Wigner and Flatt\'e parameterizations to discuss the applicability of the last two ones for near-threshold resonances with explicit examples.

X(3872),Xb, and theχb1(3P)state

We discuss the possible production and discovery channels in $e^+e^-$ and $pp$ machines of the $X_b$, the bottomonium counterpart of $X(3872)$ and the putative isoscalar analogue of the charged bottomonium-like states $Z_b$ discovered by Belle. We suggest that the $X_b$ may be close in mass to the bottomonium state $\chi_{b1}(3P)$, mixing with it and sharing its decay channels, just as $X(3872)$ is likely a mixture of a $\bar D D^*$ molecule and $\chi_{c1}(2P)$. Consequently, the experiments which reported observing $\chi_{b1}(3P)$ might have actually discovered the $X_b$, or a mixture of the two states.

Bottomonium Studies at Belle

Recent results on studies of bottomonium and bottomonium-like states at Belle are reported. The results are obtained with a 121.4 fb −1 data sample collected with the Belle detector in the vicinity of the ϒ(5 S ) resonance at the KEKB asymmetric-energy e + e − collider.