We propose a practical parametrization for the line shapes of near-threshold states compatible with all requirements of unitarity and analyticity. The coupled-channel system underlying the proposed ...parametrization includes bare poles and an arbitrary number of elastic and inelastic channels treated fully nonperturbatively. The resulting formulas are general enough to be used for a simultaneous analysis of the data in all available production and decay channels of the (system of) state(s) under consideration for a quite wide class of reactions. As an example, we fit the experimental data currently available for several decay channels for the charged Z super((')) sub(b) states in the spectrum of bottomonia and find a good overall description of the data. We find the present data to be consistent with the Z sub(b)(10610) as a virtual state and with the Z sub(b)(10650) as a resonance, both residing very close to the BB* and B*B* threshold, respectively.
Numerous quarkonium(like) states lying near S-wave thresholds are observed experimentally. We propose a self-consistent approach to these near-threshold states compatible with unitarity and ...analyticity. The underlying coupled-channel system includes a bare pole and an arbitrary number of elastic and inelastic channels treated fully nonperturbatively. The resulting analytical parametrization is ideally suited for a combined analysis of the data available in various channels that is exemplified by an excellent overall description of the data for the charged Z(b)(10610) and Z(b)(10650) states.
A
bstract
Model estimates are obtained for the influence of Coulomb effects on the ratio of the cross sections for the production of charged and neutral
B
B
¯
and
B
*
B
¯
*
pairs in
e
+
e
−
...annihilation. It is shown that the difference between the masses of charged and neutral mesons obtained under the assumption that this ratio is constant on a scale of the order of the beam energy spread can differ from the true one by
δM
∼ 0
.
03 MeV at the energy of Υ(5
S
) and by
δM ∼
0
.
4 MeV at the energy of Υ(4
S
). Thus, the errors given in the PDG for the difference between the masses of charged and neutral
B
mesons, based on the results obtained at the energy of Υ(4
S
), are strongly underestimated. Similar measurements at the energy of Υ(5
S
) will have an order of magnitude smaller systematic shift for the mass difference. This circumstance should be taken into account when planning future experiments at the
B
factory in KEK.
We review recent results on bottomonium(-like) states from e+e- colliders. They include energy scan of the e+e- annihilation cross sections into (nS)π+ π- and hb(nP)π+π- final states, studies of ...transitions from (4S) resonance with emission of η meson and update of (5S) → B(*)π analysis from Belle.
A
bstract
Model estimates are obtained for the influence of Coulomb effects on the ratio of the cross sections for the production of charged and neutral
B
$$ \overline{B} $$
B
¯
and
B
*
$$ ...\overline{B} $$
B
¯
*
pairs in
e
+
e
−
annihilation. It is shown that the difference between the masses of charged and neutral mesons obtained under the assumption that this ratio is constant on a scale of the order of the beam energy spread can differ from the true one by
δM
∼ 0
.
03 MeV at the energy of Υ(5
S
) and by
δM ∼
0
.
4 MeV at the energy of Υ(4
S
). Thus, the errors given in the PDG for the difference between the masses of charged and neutral
B
mesons, based on the results obtained at the energy of Υ(4
S
), are strongly underestimated. Similar measurements at the energy of Υ(5
S
) will have an order of magnitude smaller systematic shift for the mass difference. This circumstance should be taken into account when planning future experiments at the
B
factory in KEK.
The dipion transitions Υ(10860)→π+π−Υ(nS) (n=1, 2, 3) are studied in the framework of a unitary and analytic coupled-channel formalism previously developed for analyzing experimental data on the ...bottomoniumlike states Zb(10610) and Zb(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-flavor 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 Υ(10860) to the final states ππhb(mP) (m=1, 2) and πB(*)¯B∗ already studied before, are now augmented by the Υ(10860)→π+π−Υ(nS) final states (n=1, 2, 3). This is achieved by employing dispersion theory to account for the final state interaction of the ππ subsystem including its coupling to the K¯K channel. Fits to the two-dimensional Dalitz plots for the π+π−Υ final states were performed. Two real subtraction constants are adjusted to achieve the best description of the Dalitz plot for each Υ(nS) (n=1, 2, 3) while all the parameters related to the properties of the Zbs are kept fixed from the previous study. A good overall description of the data for all Υ(10860)→π+π−Υ(nS) channels achieved in this work provides additional strong support for the molecular interpretation of the Zb states.
In the last decade many states in the spectrum of charmonium and bottomonium have been observed experimentally above the lowest open-flavour threshold. Most of these states reside in the vicinity of ...strong thresholds and show properties that cannot be captured by simple quark models. Description and understanding of such exotic states is a challenge for the phenomenology of strong interactions, since it requires building adequate theoretical tools and approaches. In this work, a practical parametrisation for the line shapes of near threshold resonance(s) is derived in the framework of a coupled-channel model which includes an arbitrary number of elastic and inelastic channels as well as of bare pole terms. Parameters of the distribution have a direct relation to phenomenology and the resulting analytical parametrisation is therefore ideally suited to harvest the full information content provided by the measurements and to establish a link between the experimental data and their theoretical interpretation.
A practical parametrisation for the line shapes of near threshold resonance(s) is derived in the framework of a coupled-channel model which includes an arbitrary number of elastic and inelastic ...channels as well as a bare pole term. The parameters have a direct relation to phenomenology and can be employed to study the nature of the near-threshold states. The resulting analytical parametrisation is therefore ideally suited to investigate the full information content provided by the measurements and to establish a link between the experimental data and their theoretical interpretation
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