E(1420) meson as aKK¯π molecule
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Abstract
In this article an experimental summary of the E(1420) meson with ${\mathit{J}}^{\mathit{P}\mathit{C}}$=${1}^{++}$ is presented and it is argued that the E(1420) is not explained by QCD in terms of being a fundamental arrangement of quarks and gluons. We then develop a final-state rescattering mechanism based on one-particle-exchange Born terms. We sum these Born terms through a Fredholm integral equation and obtain a Fredholm determinant which shows an enhancement at the E(1420) with ${\mathit{J}}^{\mathit{P}\mathit{C}}$=${1}^{++}$. The subsequent sum of Born terms is analogous to a \ensuremath{\pi} orbiting in a p wave around an s-wave KK\ifmmode\bar\else\textasciimacron\fi{} system. This represents the first example of a molecular state which is bound by color-singlet particle exchanges, as opposed to work by Weinstein and Isgur, which uses color forces to bind their molecule. A phenomenological analysis of all the latest KK\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\pi} data arising from hadroproduction argues that the molecular picture for the E(1420) is consistent. We show that if the molecular nature for the E(1420) is generated by the above final-state Born terms, an exotic ${\mathit{K}}^{+}$K${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{0}$${\mathit{K}}^{+}$ ${\mathit{J}}^{\mathit{P}}$=${0}^{\mathrm{\ensuremath{-}}}$ molecule must exist at the KK\ifmmode\bar\else\textasciimacron\fi{}K threshold.
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