Why static bound-state calculations of tetraquarks should be met with scepticism

Abstract

Recent experimental signals have led to a revival of tetraquarks, the hypothetical $q^2{\bar{q}}^2$ hadronic states proposed by Jaffe in 1976 to explain the light scalar mesons. Mesonic structures with exotic quantum numbers have indeed been observed recently, though a controversy persists whether these are true resonances and not merely kinematical threshold enhancements, or otherwise states not of a true $q^2{\bar{q}}^2$ nature. Moreover, puzzling non-exotic mesons are also often claimed to have a tetraquark configuration. However, the corresponding model calculations are practically always carried out in pure and static bound-state approaches, ignoring completely the coupling to asymptotic two-meson states and unitarity, especially the dynamical effects thereof. In this short paper we argue that such static predictions of real tetraquark masses are highly unreliable and provide little evidence of the very existence of such states.

arXiv comment8 pages, 1 table, plain LaTeX; version 2: some additions in text and references, title slightly changed, version accepted for publication in Chinese Physics C (5 pages in cpc-hepnp style)

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• Tetraquark operators in lattice QCD and exotic flavour states in the charm sector
• Importance of meson-meson and of diquark-antidiquark creation operators for a $\bar{b}\bar{b}ud$ tetraquark
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• Unitary model analysis of $f_0(500)$ pole positions by continuously varying $m_{\pi }$: comparison with discrete lattice predictions