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

Abstract

Abstract We extend the baryo-charmonium picture of pentaquarks – a color-octet $$c\bar{c}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>c</mml:mi> <mml:mover> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math> core bonded to a color-octet light-quark cloud – to the doubly-strange sector $$c\bar{c} ssq$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>c</mml:mi> <mml:mover> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mi>s</mml:mi> <mml:mi>s</mml:mi> <mml:mi>q</mml:mi> </mml:mrow> </mml:math> . The mass splittings are set entirely by the light cloud, so the only new inputs are the strange–strange couplings $$J^{ss}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>J</mml:mi> <mml:mrow> <mml:mi>ss</mml:mi> </mml:mrow> </mml:msup> </mml:math> , fixed by a second application of the chromomagnetic scaling, and an additive strange-mass increment taken from the observed $$P_c\!\rightarrow \!P_{cs}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mspace/> <mml:mo>→</mml:mo> <mml:mspace/> <mml:msub> <mml:mi>P</mml:mi> <mml:mrow> <mml:mi>cs</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> shift. We obtain two negative-parity triplets, one produced with a kaon and one with an antiproton, the lowest kaon-associated $$\tfrac{1}{2}^{-}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mstyle> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mstyle> <mml:mo>-</mml:mo> </mml:msup> </mml:math> 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 $$P_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> and $$P_{cs}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>P</mml:mi> <mml:mrow> <mml:mi>cs</mml:mi> </mml:mrow> </mml:msub> </mml:math> 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.