Abstract
A coupled-channel approach including the ΛcD¯(*) and ηcp channels in addition to the Σc(*)D¯(*) and J/ψp channels, as required by unitarity and heavy quark spin symmetry (HQSS), is applied to the hidden-charm pentaquark Pc states, i.e., Pc(4312), Pc(4440) and Pc(4457), discovered by LHCb Collaboration. It is demonstrated that to obtain cutoff independent results, the one-pion exchange potential in the multichannel systems is to be supplemented with next-leading order counter terms responsible for the S-wave-to-D-wave transitions. We show that the experimental data for the J/ψp mass distributions are fully in line with the ΣcD¯ and ΣcD¯* hadronic molecular interpretation of the Pc(4312) and Pc(4440)/Pc(4457), respectively. A narrow Σc*D¯ molecule around 4.38 GeV is required by the HQSS with the evidence for its existence seen in the J/ψp spectrum. Moreover, we predict the line shapes for the elastic and inelastic channels.
Highlights
The observation of the Pc(4380) and Pc(4450) [1], as the first well established signals of pentaquarks, in 2015 builds a landmark in searching for the so-called exotic states allowed by quantum chromodynamics (QCD), i.e., the color neutral objects composed rather than a pair of quark and antiquark or three quarks
Since the one-dimensional fits to the mJ/ p distributions alone cannot distinguish broad Pc structures from background varying slowly with mJ/ p, a verification of the broad Pc(4380) observed in Ref. [1] awaits an full amplitude analysis of the new data
The molecular picture is of particular interest since all of the three narrow pentaquark states can be simultaneously interpreted as ⌃cD (⇤) bound states with help of heavy quark spin symmetry (HQSS)
Summary
The observation of the Pc(4380) and Pc(4450) [1], as the first well established signals of pentaquarks, in 2015 builds a landmark in searching for the so-called exotic states allowed by quantum chromodynamics (QCD), i.e., the color neutral objects composed rather than a pair of quark and antiquark (qq) or three quarks (qqq). When the OPE potentials are included together with the necessary next-leading order (NLO) S -D counter terms, only one of the two solutions present in purely contact potentials survives under the requirement of the renormalizability (regulatorbainedneJaprPreon=wde32⌃n−⇤ct)Da, ̄nwdbhoi12uc−nh,dsruesgstagpteeesc,ttsirvetehqlauyti.rtehWde eqbuyaalsntohtuesmhHonQwuSmtShb,aetirnsthotehfreethmiesPJe/cv(pi4d4me4na0cs)esafdnoidrstPtrhicbe(u4et4ix5oi7nst)easnrhcooeuunolddf 4.38 GeV. The width of this Pc(4380) is of the same order of the three narrow Pc states as a consequence of HQSS and di↵erent from the broad one reported by LHCb in 2015 [1]
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