Light- and heavy-quark symmetries and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Y</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>4230</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Y</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>4360</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Y</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>4500</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Y</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>4620</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>4630</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> resonances

Abstract

The heavy hadron spectrum is constrained by symmetries, of which two of the most important ones are heavy-quark spin and SU(3)-flavor symmetries. Here we argue that in the molecular picture the $Y(4230)$ [or $Y(4260)$], the $Y(4360)$, and the recently discovered $Y(4500)$ and $Y(4620)$ vectorlike resonances are linked by these two symmetries. By formulating a contact-range effective field theory for the $D{\overline{D}}_{1}$ and ${D}_{s}{\overline{D}}_{s1}$ family of $S$- and $P$-wave charmed meson-antimeson systems, we find that if the $Y(4230)$ were to be a pure $D{\overline{D}}_{1}$ molecular state, there would be a ${D}^{*}{\overline{D}}_{1}$ partner with a mass similar to the $Y(4360)$, a ${D}_{s}{\overline{D}}_{s1}$ partner with a mass close to the $Y(4500)$, and three $J=1$, 2 ${D}_{s}^{*}{\overline{D}}_{s1}$ and $J=3$ ${D}_{s}^{*}{\overline{D}}_{s2}^{*}$ bound states with a mass in the vicinity of 4630 MeV, of which the first one ($J=1$) might correspond with the $Y(4620)$. The previous predictions can in turn be improved by modifying the assumptions we have used to build the effective field theory. In particular, if we consider the closeness of the ${D}^{*}{\overline{D}}_{1}\text{\ensuremath{-}}{D}^{*}{\overline{D}}_{2}^{*}$ and ${D}_{s}^{*}{\overline{D}}_{s1}\text{\ensuremath{-}}{D}_{s}^{*}{\overline{D}}_{s2}^{*}$ thresholds and include the related coupled channel dynamics, we predict a $J=2$ positive $C$-parity state with a mass around 4650 MeV. This hidden-strange and hidden-charm state might in turn be identified with the $X(4630)$ that has been discovered during the past year by the LHCb in the $J/\ensuremath{\psi}\ensuremath{\phi}$ invariant mass distribution.

Topics & Concepts