Production of $\mathrm{\Lambda }\mathrm{\Lambda }$ and $\overline{\mathrm{\Lambda }n}$ in central Pb + Pb collisions at $\sqrt{s_{\mathit{NN}}}=2.76$ TeV within a covariant coalescence model

We study the production of $\mathrm{\Lambda }\mathrm{\Lambda }$ and $\overline{\mathrm{\Lambda }n}$ exotic states in central $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s_{\mathit{NN}}}=2.76$ TeV at the CERN Large Hadron Collider (LHC) via both hadron and quark coalescence within a covariant coalescence model with a blast-wave-like parametrization for the phase-space configurations of constituent particles at freeze-out. In the hadron coalescence, the two states are considered as molecular states while they are considered as six-quark states in the quark coalescence. For $\overline{\mathrm{\Lambda }n}$, we find that the yields of both molecular and six-quark states are much larger than the experimental upper-limits. For $\mathrm{\Lambda }\mathrm{\Lambda }$, while the molecule-state yield is much larger than the experimental upper limits, the six-quark-state yield could be lower than the upper limits. The higher molecule-state yields are mainly due to the large contribution of short-lived strong resonance decays into (anti-)nucleons and (anti-)$\mathrm{\Lambda }$ which can significantly enhance the molecule-state yields of $\mathrm{\Lambda }\mathrm{\Lambda }$ and $\overline{\mathrm{\Lambda }n}$ via hadron coalescence. Our results suggest that the current experimental measurement at the LHC cannot exclude the existence of the $\mathrm{\Lambda }\mathrm{\Lambda }$ as an exotic six-quark state, and if $\mathrm{\Lambda }\mathrm{\Lambda }$ is a six-quark state, it is then on the brink of being discovered.

Figure 1

The yields of (a) $\overline{\mathrm{\Lambda }n}$ and (b) $\mathrm{\Lambda }\mathrm{\Lambda }$ versus root-mean-square radii through hadron coalescence and quark coalescence. The diamonds indicate the yield with binding energy $E_{\text{bind}}=1$ MeV in the hadron coalescence while the stars represent the yield with a radius obtained from the harmonic-oscillator frequency $w_s$ (see text for the details) in the quark coalescence. The dash-dotted lines are predictions from the thermal model [9].

Figure 2

Transverse momentum distributions of hadrons in central $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s_{\mathit{NN}}}=2.76\mathrm{TeV}$. The experimental results (stars) are taken from ALICE measurement [32, 36, 37, 38]. The solid lines are from the quark coalescence model. The results of protons have been multiplied by a factor of 10.

Figure 3

Comparison between experimental upper limits and theoretical calculations for the yields of (a) $\overline{\mathrm{\Lambda }n}$ and (b) $\mathrm{\Lambda }\mathrm{\Lambda }$. A preferred branching ratio of $64\%$ [41] is used for $\mathrm{\Lambda }\mathrm{\Lambda }\to \mathrm{\Lambda }p{\pi }^{-}$ and $54\%$ [42] for $\overline{\mathrm{\Lambda }n}\to \overline{d}{\pi }^{+}$. The experimental results are taken from the ALICE measurement [9]. The olive-shaded regions and the orange bands are predictions of molecular states and multiquark states from hadron coalescence and quark coalescence, respectively.

Figure 4

Comparison between experiment upper limits under the assumption of the lifetime of a free $\mathrm{\Lambda }$ and theoretical calculations for the yields of (a) $\overline{\mathrm{\Lambda }n}$ and (b) $\mathrm{\Lambda }\mathrm{\Lambda }$. The dashed lines represent the molecular states from hadron coalescence with a binding energy $E_{\text{bind}}=1$ MeV and the bands correspond to multiquark states from quark coalescence with $r_{\text{rms}}=0.5\sim 5$ fm.