Doubly-strange hidden-charm pentaquarks from the Fermi statistics of the light-quark cloud

Abstract

We extend the baryo-charmonium picture of pentaquarks – a color-octet

core bonded to a color-octet light-quark cloud – to the doubly-strange sector

$$c\bar{c} ssq$$ c c ¯ s s q

. The mass splittings are set entirely by the light cloud, so the only new inputs are the strange–strange couplings

$$J^{ss}$$ J ss

, fixed by a second application of the chromomagnetic scaling, and an additive strange-mass increment taken from the observed

$$P_c\!\rightarrow \!P_{cs}$$ P c → P cs

shift. We obtain two negative-parity triplets, one produced with a kaon and one with an antiproton, the lowest kaon-associated

$$\tfrac{1}{2}^{-}$$ 1 2 -

state near 4.60 GeV and the antiproton-associated triplet some 120 MeV below. The robust, distinctive prediction is that the upper two kaon-associated states form a near-degenerate doublet, in sharp contrast to the well-separated triplets of the lighter sectors – a sparse, fixed-spacing pattern that sets the scheme apart from the molecular and diquark alternatives. The internal splittings follow without adjustment from the measured

$$P_c$$ P c

and

$$P_{cs}$$ P cs

spectra; the absolute scale relies on the additive strange-mass ansatz, the main assumption of the extrapolation. The predicted masses agree with recent molecular coupled-channel and QCD sum-rule results.