Revisiting the nature of the Pc pentaquarks

• Published in: The journal of high energy physics Vol. 2021; no. 8
• Main Authors: Du, Meng-Lin, Baru, Vadim, Guo, Feng-Kun, Hanhart, Christoph, Meißner, Ulf-G., Oller, José A., Wang, Qian
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 27-08-2021; Springer Nature B.V
• Subjects: Channels; Classical and Quantum Gravitation; Elementary Particles; High energy physics; Laboratories; Mass distribution; Mathematical analysis; Physics; Physics and Astronomy; Pions; Quantum Field Theories; Quantum Field Theory; Quantum numbers; Quantum Physics; Quarks; Regular Article - Theoretical Physics; Relativity Theory; S waves; String Theory; Theoretical physics; QCD Phenomenology; Non-perturbative renormalization
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2021)157

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
Λ
b
0
→
J
/
ψ
pK
−
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
Σ
c
∗
D
¯
∗
molecules, by including the
Λ
c
D
¯
∗
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.,
Σ
c
∗
D
¯
∗
, and inelastic channels and without the
Λ
c
D
¯
∗
interactions, (b) scheme II, where the one-pion exchange (OPE) is added to scheme I, and (c) scheme III, where the
Λ
c
D
¯
∗
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
Λ
c
D
¯
and
Σ
c
D
¯
∗
hadronic molecules, respectively, and that the data show clear evidence for a new narrow state,
P
c
(4380), identified as a
Σ
c
∗
D
¯
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
Σ
c
∗
D
¯
and
η
c
p
mass distributions from
Λ
b
0
→
Σ
c
∗
D
¯
K
−
and
Λ
b
0
→
η
c
pK
−
will shed light on the quantum numbers of those states, once the data are available. We also investigate possible pentaquark signals in the
Λ
c
D
¯
∗
final states.