Superexotic $K^{*+}D^{*+}K^{*+}$ bound state

TL;DR

This work investigates a highly exotic three-meson bound state, $K^{*+}D^{*+}K^{*+}$, with $I=rac{3}{2}$ and $J=3$, by first forming a bound $K^{*+}D^{*+}$ cluster in $I=1$, $J=2$ (binding about $68$ MeV) and then coupling a third $K^{*+}$ via a fixed center approximation to obtain a three-body bound state. The calculation employs a unitary, elastic-threshold–consistent FCA framework, incorporating loop functions $G_0$ and $G_C^{(i)}$, cluster form factors $F_C$, momentum cutoffs $q_{ ext{max}}$, and two-body amplitudes $t_1$, $t_2$ from the local hidden gauge approach; the $K^{*}K^{*}$ interaction in the same channel is repulsive but insufficient to prevent binding. The results indicate a bound state with binding around $100$ MeV and width about $10$ MeV, with a resonance at $ ilde{M} oughly 3626$ MeV, robust against variations in the repulsive channel and regulator choices. The predicted decay channel $K^{*+}D^{*+} o KD$ (leading to $K D K^*$) provides a practical path for experimental observation at LHCb/ALICE, highlighting the potential for discovering a new class of multimeson molecular states beyond conventional $qar q$ mesons.

Abstract

We study a system made from $K^{*+}D^{*+}K^{*+}$ with charge $3$, isospin $I=3/2$, spin $J=3$, and a quark content of $c\bar d \bar s u \bar s u$, which make it highly exotic relative to the standard $q\bar q$ structure of mesons. The interaction of the three body system is obtained starting from a cluster of $K^{*+}D^{*+}$ in $I=1$ and $J=2$, that in different works has been found bound, and adding to it an extra $K^{*+}$ with spin aligned with those of the vectors of the cluster. We find that the $K^* K^*$ interaction in $I=1$ and $J=2$ is repulsive, but its strength is small compared to that of $K^{*+}D^{*+}$ in $I=1$ and $J=2$, such that we find a three body state bound by about $100 \, \rm MeV$ with respect to the mass of a $K^{*+}$ and the $K^{*+} D^{*+}$ cluster. The width of the state, of about $10\, \rm MeV$, is much smaller than the binding, which facilitates its observation. We suggest to find that state by measuring the invariant mass of $K D K^*$, something feasible in present experimental facilities.

Figures (4)

• Figure 1: Amplitude $T$ of the three-body $(D^{*+}K^{*+})K^{*+}$ system as a function of the total center-of-mass energy. The black solid, red dashed, and blue dash-dotted lines denote $|T|$, $\mathrm{Re}(T)$, and $\mathrm{Im}(T)$, respectively. The vertical lines indicate the $(D^{*+}K^{*+})\,K^{*+}$ and $D^{*+} K^{*+} K^{*+}$ thresholds.
• Figure 2: Same as Fig. \ref{['Fig:fig1']} but with the $K^{*+}K^{*+}$ interaction switched off ($t_{2}=0$), illustrating the impact of the repulsive $K^{*+}K^{*+}$ force on the three-body amplitude.
• Figure 3: Same as Fig. \ref{['Fig:fig1']} but removing the momentum cut implemented through the $\Theta$ functions in Eq. \ref{['eq:5']}, showing the role of this cutoff in shaping the amplitude.
• Figure 4: Diagrams included in the calculation of the $K^{*+}K^{*+}\to K^{*+}K^{*+}$ potential.