Eur. Phys. J. C (2016) 76:142
DOI 10.1140/epjc/s10052-016-3983-2
Regular Article - Theoretical Physics
Analysis of the
1
2
±
pentaquark states in the
diquark–diquark–antiquark model with QCD sum rules
Zhi-Gang Wang
a
Department of Physics, North China Electric Power University, Baoding 071003, People’s Republic of China
Received: 25 December 2015 / Accepted: 25 February 2016 / Published online: 14 March 2016
© The Author(s) 2016. This article is published with open access at Springerlink.com
Abstract In this article, we construct both the axial
vector-diquark–axialvector-diquark–antiquark type and the
axialvector-diquark–scalar-diquark–antiquark type interpo-
lating currents, then calculate the contributions of the vac-
uum condensates up to dimension 10 in the operator prod-
uct expansion, and we study the masses and pole residues
of the J
P
=
1
2
±
hidden-charm pentaquark states with the
QCD sum rules in a systematic way. In calculations, we use
the formula μ =
M
2
P
− (2M
c
)
2
to determine the energy
scales of the QCD spectral densities. We take into account
the SU(3) breaking effects of the light quarks, and we obtain
the masses of the hidden-charm pentaquark states with the
strangeness S = 0, −1, −2, −3, which can be confronted
with the experimental data in the future.
1 Introduction
Recently, the LHCb collaboration studied the
0
b
→
J/ψ K
−
p decays, and one observed two pentaquark can-
didates P
c
(4380) and P
c
(4450) in the J/ψ p mass spectrum
with the significances of more than 9 σ [1]. The measured
masses and widths are M
P
c
(4380)
= 4380 ± 8 ± 29 MeV,
M
P
c
(4450)
= 4449.8 ± 1.7 ± 2.5MeV,
P
c
(4380)
= 205 ±
18±86 MeV, and
P
c
(4450)
= 39±5±19 MeV, respectively.
The decays P
c
(4380) → J/ψ p take place through the rel-
ative S-wave channel, while the decays P
c
(4450) → J /ψ p
take place through the relative P-wave channel, the decays
P
c
(4380) → J /ψ p are kinematically favored and P
c
(4380)
has larger width. The preferred spin-parities of P
c
(4380) and
P
c
(4450) are J
P
=
3
2
−
and
5
2
+
, respectively. There have
been several attempted assignments, such as
c
¯
D
∗
,
∗
c
¯
D
∗
,
χ
c1
p, J/ψ N (1440), and the J /ψ N(1520) molecule-like
pentaquark states [2–11] (or not the molecular pentaquark
states [12]), the diquark–diquark–antiquark type pentaquark
a
e-mail: zgwang@aliyun.com
states [13–22], the diquark–triquark type pentaquark states
[23], re-scattering effects [24–27], etc.
The quarks have color SU(3) symmetry; we can con-
struct the pentaquark configurations according to the routine
quark → diquark → pentaquark,
(3 ⊗ 3) ⊗ (3 ⊗ 3) ⊗
3
= (
3 ⊕ 6) ⊗ (3 ⊕ 6) ⊗ 3 = 3 ⊗ 3 ⊗ 3 ⊕···=1 ⊕···,
(1)
where 1, 3 (
3), and 6 denote the color singlet, triplet
(antitriplet), and sextet, respectively. The diquarks q
T
j
Cq
k
have five structures in Dirac spinor space, where C = Cγ
5
,
C, Cγ
μ
γ
5
, Cγ
μ
, and Cσ
μν
for the scalar, pseudoscalar, vec-
tor, axialvector, and tensor diquarks, respectively, and the j
and k are color indices. The attractive interactions of one-
gluon exchange favor formation of the diquarks in color
antitriplet
3
c
, flavor antitriplet 3
f
, and spin singlet 1
s
[28,29],
while the favored configurations are the scalar (Cγ
5
) and
axialvector (Cγ
μ
) diquark states [30–32]. The calculations
based on the QCD sum rules indicate that the heavy-light
scalar and axialvector diquark states have almost degener-
ate masses [30,31], while the masses of the light axialvector
diquark states lie (150–200) MeV above that of the light
scalar-diquark states [32], if they have the same quark con-
stituents.
In Refs. [19,20], we choose the light scalar diquark
and heavy axialvector diquark (or heavy scalar diquark) as
the basic constituents, construct both the scalar-diquark–
axialvector-diquark–antiquark type and scalar-diquark–
scalar-diquark–antiquark type interpolating currents, which
are supposed to couple potentially to the lowest pentaquark
states according to the light scalar-diquark constituent [32],
then calculate the contributions of the vacuum condensates
up to dimension 10 in the operator product expansion and
study the masses and pole residues of J
P
=
3
2
−
,
5
2
+
, and
1
2
±
hidden-charm pentaquark states with the QCD sum rules. The
numerical results favor assigning P
c
(4380) and P
c
(4450)
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