Revisiting the nature of the Pc pentaquarks

Abstract

A bstract The nature of the three narrow hidden-charm pentaquark P c states, i.e., P c (4312), P c (4440) and P c (4457), is under intense discussion since their discovery from the updated analysis of the process $$ {\Lambda}_b^0\to J/\psi {pK}^{-} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>Λ</mml:mi> <mml:mi>b</mml:mi> <mml:mn>0</mml:mn> </mml:msubsup> <mml:mo>→</mml:mo> <mml:mi>J</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ψ</mml:mi> <mml:msup> <mml:mi>pK</mml:mi> <mml:mo>−</mml:mo> </mml:msup> </mml:math> by LHCb. In this work we extend our previous coupled-channel approach [Phys. Rev. Lett. 124 , 072001 (2020)], in which the P c states are treated as $$ {\Sigma}_c^{\left(\ast \right)}{\overline{D}}^{\left(\ast \right)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>Σ</mml:mi> <mml:mi>c</mml:mi> <mml:mfenced> <mml:mo>∗</mml:mo> </mml:mfenced> </mml:msubsup> <mml:msup> <mml:mover> <mml:mi>D</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mfenced> <mml:mo>∗</mml:mo> </mml:mfenced> </mml:msup> </mml:math> molecules, by including the $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:msup> <mml:mover> <mml:mi>D</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mfenced> <mml:mo>∗</mml:mo> </mml:mfenced> </mml:msup> </mml:math> and η c p as explicit inelastic channels in addition to the J/ψp , as required by unitarity and heavy quark spin symmetry (HQSS), respectively. Since inelastic parameters are very badly constrained by the current data, three calculation schemes are considered: (a) scheme I with pure contact interactions between the elastic, i.e., $$ {\Sigma}_c^{\left(\ast \right)}{\overline{D}}^{\left(\ast \right)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>Σ</mml:mi> <mml:mi>c</mml:mi> <mml:mfenced> <mml:mo>∗</mml:mo> </mml:mfenced> </mml:msubsup> <mml:msup> <mml:mover> <mml:mi>D</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mfenced> <mml:mo>∗</mml:mo> </mml:mfenced> </mml:msup> </mml:math> , and inelastic channels and without the $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:msup> <mml:mover> <mml:mi>D</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mfenced> <mml:mo>∗</mml:mo> </mml:mfenced> </mml:msup> </mml:math> interactions, (b) scheme II, where the one-pion exchange (OPE) is added to scheme I, and (c) scheme III, where the $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:msup> <mml:mover> <mml:mi>D</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mfenced> <mml:mo>∗</mml:mo> </mml:mfenced> </mml:msup> </mml:math> interactions are included in addition. It is shown that to obtain cutoff independent results, OPE in the multichannel system is to be supplemented with S -wave-to- D -wave mixing contact terms. As a result, in line with our previous analysis, we demonstrate that the experimental data for the J/ψp invariant mass distribution are consistent with the interpretation of the P c (4312) and P c (4440)/ P c (4457) as $$ {\Lambda}_c\overline{D} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mover> <mml:mi>D</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> and $$ {\Sigma}_c{\overline{D}}^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Σ</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:msup> <mml:mover> <mml:mi>D</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> hadronic molecules, respectively, and that the data show clear evidence for a new narrow state, P c (4380), identified as a $$ {\Sigma}_c^{\ast}\overline{D} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>Σ</mml:mi> <mml:mi>c</mml:mi> <mml:mo>∗</mml:mo> </mml:msubsup> <mml:mover> <mml:mi>D</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> molecule, which should exist as a consequence of HQSS. While two statistically equally good solutions are found in scheme I, only one of these solutions with the quantum numbers of the P c (4440) and P c (4457) being J P = 3/2 − and 1/2 − , respectively, survives the requirement of regulator independence once the OPE is included. Moreover, we predict the line shapes in the elastic and inelastic channels and demonstrate that those related to the P c (4440) and the P c (4457) in the $$ {\Sigma}_c^{\left(\ast \right)}\overline{D} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>Σ</mml:mi> <mml:mi>c</mml:mi> <mml:mfenced> <mml:mo>∗</mml:mo> </mml:mfenced> </mml:msubsup> <mml:mover> <mml:mi>D</mml:mi>

Topics & Concepts