Hadro-quarkonia dynamics and Z b states
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ELEMENTARY PARTICLES AND FIELDS Theory
Hadro–Quarkonia Dynamics and Zb States∗ I. V. Danilkin, V. D. Orlovsky**, and Yu. A. Simonov Institute for Theoretical and Experimental Physics, Moscow, Russia Received April 3, 2012
Abstract—Dynamics of hadro–quarkonium system is formulated, based on the channel coupling of a ¯ to heavy–light mesons (Q¯ ¯ light hadron (h) and heavy quarkonium (QQ) q, Qq). Equations for hadro– quarkonium amplitudes and resonance positions are written explicitly, and numerically calculated for the special case of πΥ(nS) (n = 1, 2, 3). It is also shown that the recently observed by Belle two peaks Zb (10610) and Zb (10650) are in agreement with the proposed theory. It is demonstrated that theory predicts peaks at the BB ∗ , B ∗ B ∗ thresholds in all available πΥ(nS) channels. DOI: 10.1134/S1063778813090044
1. INTRODUCTION It was found in experiment [1–4] that resonances may appear in the system of a hadron and heavy quarkonium, which may be called hadro– quarkonium, see [5] for a review. On theoretical side the prevalent approaches associate hadro–quarkonia with molecular or four-quark (4q) states [6–16]. In the first case hadro–quarkonia are weakly bound states of two heavy–light mesons of the closest threshold with interaction tuned to produce loosely bound or virtual states, and in the 4q state thresholds cannot be easily connected with 4q. However, it will be argued that channel coupling (CC) near thresholds may play the dominant role in hadro–quarkonium dynamics, as was shown for heavy quarkonia in our previous papers [17, 18]. It was shown there that strong CC, calculated basically without fitting pa¯∗ c) pole exactly to the DD rameters, shifts the 23 P1 (c¯ threshold. In this way the X(3872) phenomenon was explained using only one parameter Mω , which was fixed in previous studies [19–22], and universal input: the string tension σ, the current (pole) quark masses, and the strong coupling αs (q). Recently Mω was found from the first principles in QCD [23]. It was shown there that Mω can be calculated as the matrix element of the operator σr, where σ is the string tension and r is the length of the string. The decay width of ψ(3770) is reproduced in this way and corresponds to Mω ≈ 0.8 GeV.
Recently in a series of papers [19, 20] the CC methods have been successfully applied to the transitions in systems containing heavy quarkonia and pions or η meson and in this way the main features of experimental pionic spectra in reactions X → Xππ, were explained, together with kaonic and η-meson final states [21, 22]. As will be shown below, the strong interaction of pions with Υ(nS) mesons produces charged Z-type resonances. Below we extend the formalism of CC developed in [17, 18] to the case of ¯ a hadron h = π, φ, η, ρ, ω, ... interacting with the QQ state. We study the interaction and possible poles of hadro–quarkonium amplitudes in the formalism of [17]. We assume that the most important interaction in hadro–quarkonium is due to interme¯ (e.g., diate states of heavy–light mesons (Q¯ q )(Qq) ∗ ∗ ∗
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