Comment on "$\sigma$-meson: Four-quark versus two-quark components and decay width in a Bethe-Salpeter approach"

B. Blankleider; A. N. Kvinikhidze

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arXiv · 2102.05818

Comment on "$\sigma$-meson: Four-quark versus two-quark components and decay width in a Bethe-Salpeter approach"

B. Blankleider·A. N. Kvinikhidze

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Abstract

In a recent paper by N. Santowsky et al. [Phys. Rev. D 102, 056014 (2020)], covariant coupled equations were derived to describe a tetraquark in terms of a mix of four-quark states $2q 2\bar{q}$ and two-quark states $q\bar{q}$. These equations were expressed in terms of vertices describing the disintegration of a tetraquark into identical two-meson states, into a diquark-antidiquark pair, and into a quark-antiquark pair. We show that these equations are inconsistent as they imply a $q\bar{q}$ Bethe-Salpeter kernel that is $q\bar{q}$-reducible.

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B. Blankleider, A. N. Kvinikhidze. 2021-02-11. Comment on "$\sigma$-meson: Four-quark versus two-quark components and decay width in a Bethe-Salpeter approach". https://arxiv.org/abs/2102.05818

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