Strong LHCb evidence supporting the existence of the hidden-charm molecular pentaquarks
Rui Chen Zhi-Feng Sun Xiang Liu Shi-Lin Zhu









xiangliu@lzu.edu.cn

zhusl@pku.edu.cn


^1School of Physical
Science and Technology, Lanzhou University, Lanzhou 730000, China

^2Research Center for Hadron and CSR Physics, Lanzhou University
and Institute of Modern Physics of CAS, Lanzhou 730000, China

^3 School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China

^4Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

^5Center of High Energy Physics, Peking University, Beijing
100871, China


On March 26th, 2019, at the Rencontres de Moriond QCD conference,
the LHCb Collaboration reported the observation of three new
pentaquarks, namely P_c(4312), P_c(4440) and P_c(4457), which
are consistent with the loosely bound molecular hidden-charm
pentaquark states composed of an S-wave charmed baryon Σ_c
and an S-wave anti-charmed meson (D̅, D̅^*). In this
work, we present a direct calculation by the one-boson-exchange
(OBE) model and demonstrate explicitly that the P_c(4312),
P_c(4440) and P_c(4457) do correspond to the loosely bound
Σ_cD̅ with (I=1/2,J^P=1/2^-), Σ_cD̅^* with
(I=1/2,J^P=1/2^-) and Σ_cD̅^* with
(I=1/2,J^P=3/2^-), respectively. 






12.39.Pn, 14.40.Lb, 14.40.Rt



Strong LHCb evidence supporting the existence of the hidden-charm molecular pentaquarks
    Shi-Lin Zhu^3,4,5
    Received ; accepted 
=======================================================================================



Introduction:—Finding the multiquark matter is an extremely
important issue of hadron physics, which is full of challenge and
opportunity not only for theorists but also for experimentalists. In
the past sixteen years, a series of observations of the
charmoniumlike XYZ states and two P_c states have inspired
extensive investigations of the hidden-charm tetraquarks and
pentaquarks, which enlarge our knowledge of the multiquark matter
(see review articles <cit.> for
more details).

Focusing on hidden-charm pentaquark, we must mention the predictions
for the existence of the molecular type pentaquark
<cit.>
before LHCb's observation <cit.>. In 2015, LHCb
announced the observation of two hidden-charm pentaquarks
P_c(4380) and P_c(4450) in the J/ψ p invariant mass
spectrum of Λ_b→ J/ψ K p <cit.>. This
observation had stimulated extensive discussions on decoding their
inner structures based on different configurations, which include
the loosely bound molecular baryon-meson state
<cit.> and tightly bound
pentaquark state
<cit.>. The
experimental data in 2015 was unable to distinguish them.

Exploring the novel multiquark matter continues. Very recently, the
LHCb Collaboration once again brought us surprise. On March 26th,
2019, at the Rencontres de Moriond QCD conference, the LHCb
Collaboration reported the observation of three new pentaquarks
<cit.>. By analyzing the J/ψ p invariant mass
spectrum, a new pentaquark named as the P_c(4312) was discovered
with 7.3σ significance. And LHCb updated analysis further
indicates that the P_c(4450) reported previously by LHCb
<cit.> contains two narrow subpeaks, P_c(4440) and
P_c(4457), which have 5.4σ significance. Their resonance parameters
include  <cit.> shown in Fig. <ref>.


    P_c(4312)^+:  {[ m=4311.9±0.7^+6.8_-0.6  MeV;    Γ=9.8±2.7^+3.7_-4.5  MeV ]. ,
    
    P_c(4440)^+:  {[ m=4440.3±1.3^+4.1_-4.7  MeV;  Γ=20.6±4.9^+8.7_-10.1  MeV ]. ,
    
    P_c(4457)^+:  {[ m=4457.3±1.3^+0.6_-4.1  MeV;    Γ=6.4±2.0^+5.7_-1.9  MeV ]. .

Since these three pentaquarks are observed in the J/ψ p
invariant mass spectrum, they have definite isospin quantum number
I=1/2. We notice that the P_c(4312)^+ is just below the
Σ_c^+D̅^0 threshold, while the masses of the
P_c(4440)^+ and P_c(4457)^+ are slightly lower than the
Σ_c^+D̅^*0 threshold (see Fig. <ref>).






By borrowing the experience of studying nuclear force, the OBE model
was developed to investigate these observed charmoniumlike XYZ
states
<cit.>.
Later, in 2011, we applied the OBE model to study the
Σ_cD̅ and Σ_cD̅^* interactions
<cit.>. Although the treatment of the Σ_cD̅
and Σ_cD̅^* systems in Ref. <cit.> was quite
simple and straightforward, the existence of the Σ_cD̅
and Σ_cD̅^* molecular hidden-charm pentaquark was
predicted clearly, which has become one of the pioneering papers
exploring the molecular hidden-charm pentaquarks.


Until now, the OBE model has been greatly improved compared with the
situation in 2011 (see review <cit.>), which stimulates
us to include the coupled-channel effect and S-D wave mixing in the
calculation. Especially, the new observations of three pentaquarks
announced by LHCb makes the study of the hidden-charm molecular
pentaquarks enter upon a new era with higher precision.

In this letter, we will present a precise investigation of the
Σ_cD̅ and Σ_cD̅^* systems, from which the
readers can learn why this baryon-meson configuration of the
hidden-charm pentaquark <cit.> is connected with the
LHCb new measurement <cit.>. For the Σ_cD̅ and
Σ_cD̅^* systems, there are only three molecular states
with isospin I=1/2. The newly observed P_c(4312)^+ corresponds
to the Σ_cD̅ with I(J^P)=1/2(1/2^-), while the
P_c(4440)^+ and P_c(4457)^+ can be identified as the
Σ_cD̅ molecular states with I(J^P)=1/2(1/2^-) and
1/2(3/2^-) respectively. The updated LHCb measurement
<cit.> confirms the existence of molecular hidden-charm
pentaquarks composed of an S-wave charmed baryon and an S-wave
anti-charmed meson
<cit.>,
which shall become a milestone in the exploration of the multiquark
hadronic matter.


Reproducing three pentaquarks:—In the framework of the OBE
model, a key point is the deduction of the effective potentials for
the hadronic molecular systems. Considering the coupled channel
effect and S-D wave mixing, we may list the corresponding channel
contributions to the Σ_cD̅ system with J^P=1/2^-, two
Σ_cD̅^* systems with J^P=1/2^-,3/2^- and the
Σ_c^*D̅ system with J^P=3/2^-, which can be
categorized into two groups

    [                                                                                               1/2^-:                                Σ_cD̅|^2𝕊_1/2⟩,
         Σ_c^*D̅|^4𝔻_1/2⟩,
         Σ_cD̅^*|^2𝕊_1/2/^4𝔻_1/2⟩,;                                                             Σ_c^*D̅^*|^2𝕊_1/2/
        ^4𝔻_1/2/^6𝔻_1/2⟩,;                                                                                               3/2^-: Σ_cD̅^*|^4𝕊_3/2/
              ^2𝔻_3/2/^4𝔻_3/2⟩,
          Σ_c^*D̅^*|^4𝕊_3/2/^2𝔻_3/2/
         ^4𝔻_3/2/^6𝔻_3/2⟩. ]

The involved flavor wave functions |I,I_3⟩ are

    [ |1/2,1/2⟩ =
         √(2/3)|Σ_c^(*)++D^(*)-⟩
         -1/√(3)|Σ_c^(*)+D̅^(*)0⟩; |1/2,-1/2⟩ =
         1/√(3)|Σ_c^(*)+D^(*)-⟩
         -√(2/3)|Σ_c^(*)0D̅^(*)0⟩ ].

In order to calculate the effective potentials of the hidden-charm
molecular baryons, we need to utilize the effective Lagrangian
describing the interactions of the charmed or anti-charmed
baryon/meson with the light mesons. The Lagrangian depicting the
interaction of the ground state charmed baryons with the light
mesons can be constructed according to the chiral symmetry, the
heavy quark symmetry and the hidden local symmetry
<cit.>, while the one for the S-wave pseudoscalar and
vector charmed mesons according to the chiral symmetry and the heavy
quark symmetry
<cit.>.
Here we list the Lagrangians in the following

    ℒ_H   =    g_S⟨H̅_aσ H_b⟩
      +ig⟨H̅_aγ_μA_ab^μγ_5H_b⟩
          -iβ⟨H̅_av_μ(𝒱_ab^μ-ρ_ab^μ)
      H_b⟩
      +iλ⟨H̅_aσ_μνF^μν(ρ)H_b⟩,
    ℒ_𝒮   =   l_S⟨𝒮̅_μσ𝒮^μ⟩
    -3/2g_1ε^μνλκv_κ⟨𝒮̅_μ
    A_ν𝒮_λ⟩⟩
          
    +iβ_S⟨𝒮̅_μv_α(𝒱_ab^α
    -ρ_ab^α)
    𝒮^μ⟩+λ_S⟨𝒮̅_μF^μν(ρ)
    𝒮_ν⟩.

Here, the following definitions are used, i.e., H=
[𝒫̃^*μγ_μ-𝒫̃γ_5]1-
v/2, 𝒮_μ=
-√(1/3)(γ_μ+v_μ)γ^5ℬ_6
       +ℬ_6μ^*, H̅=γ_0H^†γ_0,
𝒮̅_μ=𝒮_μ^†γ_0,
A_μ=1/2(ξ^†∂_μξ-ξ∂_μξ^†)=i/f_π∂_μℙ+…, 𝒱_μ=
1/2(ξ^†∂_μξ-ξ∂_μξ^†)
=i/2f_π^2[ℙ,∂_μℙ]+…,
ξ=exp(iℙ/f_π),
ρ^μ=ig_V𝕍^μ/√(2), and
F^μν(ρ)=∂^μρ^ν-∂^νρ^μ
+[ρ^μ,ρ^ν]. And 𝒫̃ and
𝒫̃^* satisy
𝒫̃=(D̅^0, D^-)^T, 𝒫̃^*=(D̅^*0, D^*-)^T.
Note that the SU(3) chiral symmetry is considered to construct the
Lagrangians. However, for convenience, we only show the first two
lines and columns in the above matrices, since we do not consider,
in this letter, the strange case which corresponds to the third line
and column. Thus, the ℬ_3, ℬ_6 and
ℬ_6^* are defined as

    ℙ   =   ([  π^0/√(2)+η/√(6)              π^+;              π^- -π^0/√(2)+η/√(6) ]),  ℬ_6^(*) = ([     Σ_c^(*)++ Σ_c^(*)+/√(2); Σ_c^(*)+/√(2)      Σ_c^(*)0 ]),
    𝕍   =   ([  ρ^0/√(2)+ω/√(2)              ρ^+;              ρ^- -ρ^0/√(2)+ω/√(2) ]).


With the above preparation, we consider the t-channel Feynman
diagrams to deduce the effective potentials, where the Breit
approximation 𝒱_E(q) =
          -ℳ/
          √(∏_i2M_i∏_f2M_f)
is needed to relate the t-channel scattering amplitudes
ℳ to the potentials 𝒱_E(q) in the
momentum space. The Fourier transformation is performed to obtain
the potentials in the coordinate space. Besides, the monopole form
factor ℱ(q^2,m_E^2)= (Λ^2-m_E^2)/(Λ^2-q^2)
is introduced for compensating the off shell effect of the exchanged
meson and describing the structure effect of every interaction
vertex. According to the experience of the deuteron and interaction between the proton and neutron, cutoff Λ in the form factor is taken around 1 GeV, which is widely used to test whether a loose molecular state exists or not.

In the OBE model, The general expressions of the potentials in the coordinate
space for the discussed systems include scalar, pseudoscalar, and vector mesons exchanges part, i.e.,
 

    V^ij(r)=V_π/η^ij(r)+V_ρ/ω^ij(r)+V_σ^ij(r),

according to the mass difference of exchanged mesons, π, σ/η, and ρ/ω exchanges contribute in long, intermediate, and short range.
For J=1/2, i,j=1,2,3,4 corresponds to the channels
Σ_cD̅,  Σ_c^*D̅,  Σ_cD̅^*,
 Σ_c^*D̅^*, while for J=3/2, i,j=1,2 corresponds to
Σ_cD̅^*,  Σ_c^*D̅^*. For convenience, we
define the following expressions

    Y(Λ,m,r)    =   1/4π r(e^-mr-e^-Λ r)-Λ^2-m^2/8πΛe^-Λ r,
    𝒴^ij_Λ m_a   =   𝒟_ijY(Λ,m_σ,r),
    𝒵^ij_Λ m_a   =   (ℰ_ij∇^2+ℱ_ijr∂/∂ r1/r∂/∂ r)Y(Λ,m_a,r),
    𝒵^' ij_Λ
    m_a   =   (2ℰ_ij∇^2-ℱ_ijr∂/∂
    r1/r∂/∂ r)Y(Λ,m_a,r),

where the matrices 𝒟_ij,ℰ_ij correspond to
the spin-spin operators and ℱ_ij to the tensor
operator, e.g., for the process
Σ_cD̅^*→Σ_cD̅^*,

    𝒟=ϵ_2·ϵ_4^†,  ℰ=σ·(iϵ_2×ϵ_4^†),  ℱ=S(r̂,σ,
         iϵ_2×ϵ_4^†).

In a numerical calculation, these operators should be sandwiched
between the discussed spin-orbit wave functions, all of the
operators will be replaced by serials of nonzero matrix elements,
for example, for Σ_cD̅^*→Σ_cD̅^* with
J^P=1/2^-, ⟨Σ_cD̅^*(1/2^-)|ℰ|Σ_cD̅^*(1/2^-)⟩
=([ -2  0;  0  1 ]). The
subpotentials now can be written as

    V^11   =   -AY(Λ,m_σ,r)
           -𝒢B/2Y(Λ,m_ρ,r)-B/4Y(Λ,m_ω,r),
    
    V^12   =   A/√(3)𝒴_Λ_3 m_σ3
           +𝒢B/2√(3)𝒴^12_Λ_3,m_ρ3
           +B/4√(3)𝒴^12_Λ_3,m_ω3,
    
    V^13   =   𝒢C/3𝒵^13_Λ_4,m_π4
            +C/18𝒵^13_Λ_4,m_η4
            +2𝒢D/9𝒵^'13_Λ_4,m_ρ4
          
            +D/9𝒵^'13_Λ_4,m_ω4,
    
    V^14   =   𝒢C/2√(3)𝒵^14_Λ_5,m_π5
            +C/12√(3)𝒵^14_Λ_5,m_η5
            +𝒢D/3√(3)𝒵^'14_Λ_5,m_ρ5
          
            +D/6√(3)𝒵^'14_Λ_5,m_ω5,
    
    V^22   =   -A𝒴^11_Λ,m_σ
           -𝒢B/2𝒴^22_Λ,m_ρ
           -B/4𝒴^22_Λ,m_ω,
    
    V^23   =   𝒢C/2√(3)𝒵^23_Λ_0,m_π0
        +C/12√(3)𝒵^23_Λ_0,m_η0
        -𝒢D/3√(3)𝒵^'23_Λ_0,m_ρ0
          
        -D/6√(3)𝒵^'23_Λ_0,m_ω0,
    
    V^24   =   𝒢C/2𝒵^24_Λ_1,m_π1
        +C/12𝒵^24_Λ_1,m_η1
        -𝒢D/3𝒵^'24_Λ_1,m_ρ1
          
        -D/6𝒵^' 24_Λ_1,m_ω1,
    
    V^33   =   -A𝒴^33_Λ,m_σ
         +𝒢C/3𝒵^33_Λ,m_π
         +C/18𝒵^33_Λ,m_η
        -𝒢B/2𝒴^33_Λ,m_ρ
          -2𝒢D/9𝒵^'33_Λ,m_ρ
        -B/4𝒴^33_Λ,m_ω
        -D/9𝒵^'33_Λ,m_ω,
    
    V^34   =   A/√(3)𝒴^34_Λ_2,m_σ2
        +√(3)𝒢C/6𝒵^34_Λ_2,m_π2
        +√(3)C/36𝒵^34_Λ_2,m_η2
          
            +𝒢B/2√(3)𝒴^34_Λ_2,m_ρ2
            -𝒢D/3√(3)𝒵^'34_Λ_2,m_ρ2
            +B/4√(3)𝒴^34_Λ_2,m_ω2
          -D/6√(3)𝒵^' 34_Λ_2,m_ω2,
    
    V^44   =    -A𝒴^44_Λ,m_σ
           -𝒢C/2𝒵^44_Λ,m_π
           -C/12𝒵^44_Λ,m_η
           -𝒢B/2𝒴^44_Λ,m_ρ
          +𝒢D/3𝒵^'44_Λ,m_ρ
           -B/4𝒴^44_Λ,m_ω
           +D/6𝒵^'44_Λ,m_ω.

Here, A=l_Sg_S, B=ββ_Sg_V^2, C=gg_1/f_π^2,
D=λλ_Sg_V^2, 𝒢 is the isospin factor,
which is taken as -1 for the isospin 1/2 system (for the isospin
3/2 system 𝒢=1/2). The variables in these functions
are defined as Λ_b^2 =Λ^2-q_b^2,
m_b^2=m^2-q_b^2, with b=0,1,...,5, and q_i^2s are the
functions of the masses of the charmed mesons and baryons whose
values are q_0=35.60 MeV, q_1=61.41 MeV, q_2=25.08 MeV,
q_3=97.38 MeV, q_4=60.53 MeV, q_5=35.45 MeV.

The values of the coupling constants are taken from
<cit.>,
g_S=0.76,g=0.59,β=0.9,l_S=6.2,g_1=0.94,β_S=-1.74,
λ=0.56 GeV^-1, λ_S=-3.31 GeV^-1, and g_V=5.9. Here, the coupling constants for the pion exchange g and g_1 are determined from the experiment data, Γ(D^*→ Dπ) and Γ(Σ_c^(*)→Λ_cπ) <cit.>. For the scalar and vector mesons exchanges, the coupling constants are estimated in the quark model, where the average of the coupling vertex is simultaneously calculated, at hadron level and at quark level, and the heavy quark does not couple to the light mesons. The signs are fixed with the help of the quark model.

Finally, the binding energies for the Σ_cD̅ and
Σ_cD̅^* systems can be evaluated by solving the
Schrödinger equation. In Fig. <ref>, we present
the bound state masses for the coupled channel
Σ_c^(*)D̅^(*) systems with I=1/2 which depends on
the cutoff Λ. As the cutoff increases, the binding energy of
all the systems becomes deeper and deeper.

For the J^P=1/2^- case, we can reproduce the masses of the
P_c(4312) and P_c(4440) with a very reasonable cutoff value
Λ=1.04 GeV. The binding energies for these systems are
-8.00 MeV and -19.27 MeV, respectively.
Their corresponding root-mean-square (RMS) radii are 1.22 fm and 0.88 fm, respectively.
For the P_c(4312), the
Σ_cD̅ channel is dominant, the probabilities of the
Σ_cD̅, Σ_cD̅^*, and Σ_c^*D̅^*
components are around 84%, 12%, and 4%, respectively. The
P_c(4440) is mainly composed of the S-wave Σ_cD̅^*
component with the probability over 94%.

For the I(J^P)=1/2(3/2^-) case, as shown in Fig. <ref>,
the mass of the P_c(4457) is also reproduced with Λ=1.32
GeV. Here, its binding energy and RMS radius are -4.38 MeV and 1.61 fm, respectively. The coupled-channel effect plays an important role,
since the probabilities of the Σ_cD̅^* and
Σ_c^*D̅^* components are around 75% and 25%,
respectively.

With the same value of the cutoff as that of P_c(4457), we find
another bound state of the quantum number I(J^P)=1/2(3/2^-),
which locates below the Σ_c^*D̅ threshold with a binding
energy E=-6.20 MeV and RMS radius r_RMS=1.40 fm. The dominant channel is the
Σ_c^*D̅(^4S_3/2) with a probability over 87%. This
state can be identified with the P_c^+(4380) observed in 2015 also
by LHCb collaboration <cit.>, although the recent LHCb
measurement doesn't give any information of such a particle. We hope
the further experiments can provide a more precise measurement and
confirm the existence of this state.



From the above discussion, we see that the three resonances
P_c^+(4312), P_c^+(4440), P_c^+(4457) are naturally
interpreted within the loosely bound Σ_cD̅ and
Σ_cD̅^* molecule picture. For the Σ_c
D̅^(*) systems, there are only three molecular states with
isospin 1/2, i.e., Σ_c D̅ corresponding to the lower
peak P_c(4312)^+, and Σ_c D̅^* to the higher peaks
P_c(4440) and P_c(4457). Within the hidden-charm molecular
assignment, we can easily understand why the two higher peaks are
very close to each other, and the mass difference between the two
higher peaks and the lowest P_c^+(4312) peak is around 140 MeV
which is approximately the mass difference of the D and D^*
mesons.





More predictions:— Besides explaining the three
particles P_c(4312), P_c(4440) and P_c(4457), we
further investigate the possible existence of the
Σ_c^(*)D̅^(*) with
(I=3/2,J^P=1/2^-/3/2^-). In Table
<ref>, we collect the corresponding bound state
solutions. However, when the bound state solutions emerge, the
corresponding cutoffs are around 2∼ 4 GeV and quite large for
all these systems. The past experience indicates that such a large
cutoff value sometimes points to the non-existence of the molecular
states. Consequently, we cannot give a clear conclusion whether the
Σ_c^(*)D̅^(*) systems with isospin 3/2 exist or
not.








In the experimental process Λ_b→ J/ψ p K, all the
P_c states are produced by the weak decay of Λ_b^0. With
the assignment that the P_c(4312) and P_c(4440)/P_c(4457) are
the Σ_cD̅ and Σ_cD̅^* molecules,
respectively, these states can transit to the final J/ψ p by
exchanging a S-wave charmed meson, and the J/ψ and p
reside in a S wave.

The molecular systems Σ_c^(*)D̅^(*) with
(I=3/2,J^P=1/2^-/3/2^-), if they should
exist, can not decay into J/ψ p due to the isospin
conservation. A possible decay mode is J/ψΔ(1232) for
both J=1/2 and 3/2, which will be helpful for future
experimental search.



Summary:—Very recently, LHCb reported the observation of
three new pentaquarks P_c(4312)^+, P_c(4440)^+ and P_c(4457)^+
in the J/ψ p invariant mass spectrum of Λ_b→ J/ψ p
K <cit.>, which benefitted from large data samples
collected at LHC Run 1 and Run 2. This new discovery further opens
the mysterious Pandora's box of exploring exotic multiquark states.
This new LHCb observation the first time confirmed the existence of
the baryon-meson configuration molecular hidden-charm pentaquarks in
experiment, which should become a milestone of the exploration of
the multiquark hadronic matter. In this work, we have performed a
phenomenological study to decode the inner structure of the newly
observed P_c(4312), P_c(4440) and P_c(4457) based on the OBE
model after the inclusion of the coupled-channel effect and S-D wave
mixing. The consistence of the LHCb new observation with the
hidden-charm molecular pentaquarks with the baryon-meson
configuration is clearly demonstrated.


In this work, we have also studied the interaction of the
Σ^*_cD̅ system in the framework of the OBE model, and
found the existence of a Σ^*_cD̅ molecular hidden-charm
pentaquark with I(J^P)=1/2(3/2^-), which has a mass 4379.11 MeV.
This predicted Σ^*_cD̅ molecular hidden-charm pentaquark
may correspond to the P_c(4380) reported by LHCb in 2015
<cit.>. However, the talk at the Rencontres de Moriond
QCD conference <cit.> did not mention P_c(4380). After
checking the new experimental data released by LHCb <cit.>,
one may notice the evidence of the accumulation of events around
4380 MeV in the J/ψ p invariant mass spectrum. Moreover, we
have also studied the possible existence of the hidden-charm
molecular pentaquarks with isospin I=3/2, which are the isospin
partners of the newly observed P_c(4312)^+, P_c(4440)^+ and
P_c(4457)^+. These states should also be searched for at LHCb. The
past sixteen years has been the golden age of the search of the
exotic hadrons. 






§ ACKNOWLEDGMENTS


This project is supported by the National Natural Science Foundation
of China under Grants No. 11705069 and No. 11575008, and National Key
Basic Research Program of China (Grant No. 2015CB856700). R.C. is also supported by the National Postdoctoral Program for Innovative Talent. X.L. is also supported
by the National Program for Support of Top-notch Young Professionals
and the China National Funds for Distinguished Young Scientists
under Grant No. 11825503.


99


Chen:2016qju
H. X. Chen, W. Chen, X. Liu and S. L. Zhu, The hidden-charm
pentaquark and tetraquark states, Phys. Rept.  639, 1 (2016)






Liu:2013waa
X. Liu, An overview of XYZ new particles, Chin. Sci. Bull.59, 3815 (2014)






Guo:2017jvc
  F. K. Guo, C. Hanhart, U. G. Meiner, Q. Wang, Q. Zhao and B. S. Zou,
  Hadronic molecules,
  Rev. Mod. Phys.  90, no. 1, 015004 (2018)
  
  
  
  


 
Wu:2010jy
J. J. Wu, R. Molina, E. Oset and B. S. Zou, Prediction of narrow
N^* and Λ^* resonances with hidden charm above 4 GeV,
Phys. Rev. Lett.  105, 232001 (2010)







Yang:2011wz
Z. C. Yang, Z. F. Sun, J. He, X. Liu and S. L. Zhu, The possible
hidden-charm molecular baryons composed of anti-charmed meson and
charmed baryon, Chin. Phys. C 36, 6 (2012)









Wang:2011rga
W. L. Wang, F. Huang, Z. Y. Zhang and B. S. Zou, Σ_c D̅
and Λ_c D̅ states in a chiral quark model, Phys. Rev.C 84, 015203 (2011)









Wu:2012md
J. J. Wu, T.-S. H. Lee and B. S. Zou, Nucleon Resonances with Hidden
Charm in Coupled-Channel Models, Phys. Rev. C 85, 044002
(2012)






Li:2014gra
  X. Q. Li and X. Liu,
  A possible global group structure for exotic states,
  Eur. Phys. J. C 74, no. 12, 3198 (2014)
  
  
  
  






Aaij:2015tga
R. Aaij et al. [LHCb Collaboration], Observation of J/ψ
Resonances Consistent with Pentaquark States in
Λ_b^0→ J/ψ K^-p Decays, Phys. Rev. Lett.115, 072001 (2015)






Chen:2015loa
R. Chen, X. Liu, X. Q. Li and S. L. Zhu, Identifying exotic
hidden-charm pentaquarks, Phys. Rev. Lett.  115, 132002
(2015)






Chen:2015moa
H. X. Chen, W. Chen, X. Liu, T. G. Steele and S. L. Zhu, Towards
exotic hidden-charm pentaquarks in QCD, Phys. Rev. Lett.  115, 172001 (2015)






Karliner:2015ina
M. Karliner and J. L. Rosner, New Exotic Meson and Baryon Resonances
from Doubly-Heavy Hadronic Molecules, Phys. Rev. Lett.  115, no. 12, 122001 (2015)






Maiani:2015vwa
L. Maiani, A. D. Polosa and V. Riquer, The New Pentaquarks in the
Diquark Model, Phys. Lett. B 749, 289 (2015)






Anisovich:2015cia
V. V. Anisovich, M. A. Matveev, J. Nyiri, A. V. Sarantsev and
A. N. Semenova, Pentaquarks and resonances in the pJ/ψ
spectrum, arXiv:1507.07652 [hep-ph].




Lebed:2015tna
R. F. Lebed, The Pentaquark Candidates in the Dynamical Diquark
Picture, Phys. Lett. B 749, 454 (2015)






Wang:2015ava
  Z. G. Wang and T. Huang,
  Analysis of the 1/2^± pentaquark states in the diquark model with QCD sum rules,
  Eur. Phys. J. C 76, no. 1, 43 (2016)
  
  
  
  


LHCbtalk
Tomasz Skwarnicki on behalf of the LHCb collaboration, Hadron
spectroscopy and exotic states at LHCb, talk given at Moriond QCD
2019, http://moriond.in2p3.fr/2019/QCD/Program.html.



Aaij:2019vzc
  R. Aaij et al. [LHCb Collaboration],
  Observation of a narrow pentaquark state, P_c(4312)^+, and of two-peak structure of the P_c(4450)^+,
  Phys. Rev. Lett. 122, 222001 (2019).
  
  



Liu:2007bf
  X. Liu, Y. R. Liu, W. Z. Deng and S. L. Zhu,
  Is Z^+(4430) a loosely bound molecular state?,
  Phys. Rev. D 77, 034003 (2008)
  
  
  
  


Liu:2008xz
  X. Liu, Y. R. Liu, W. Z. Deng and S. L. Zhu,
  Z^+(4430) as a D_1^' D^* (D_1 D^*) molecular state,
  Phys. Rev. D 77, 094015 (2008)
  
  
  
  


Liu:2008fh
  Y. R. Liu, X. Liu, W. Z. Deng and S. L. Zhu,
  Is X(3872) Really a Molecular State?,
  Eur. Phys. J. C 56, 63 (2008)
  
  
  
  



Liu:2008tn
  X. Liu, Z. G. Luo, Y. R. Liu and S. L. Zhu,
  X(3872) and Other Possible Heavy Molecular States,”
  Eur. Phys. J. C 61, 411 (2009)
  
  
  
  

  
Liu:2009ei
  X. Liu and S. L. Zhu,
  Y(4143) is probably a molecular partner of Y(3930),”
  Phys. Rev. D 80, 017502 (2009)
  Erratum: [Phys. Rev. D 85, 019902 (2012)]
 
  
  
  


Close:2009ag
  F. Close and C. Downum,
  On the possibility of Deeply Bound Hadronic Molecules from single Pion Exchange,
  Phys. Rev. Lett.  102, 242003 (2009)
  
  
  
  




Liu:2011xc
Y. R. Liu and M. Oka, Λ_c N bound states revisited, Phys.Rev. D 85, 014015 (2012)







Yan:1992gz
T. M. Yan, H. Y. Cheng, C. Y. Cheung, G. L. Lin, Y. C. Lin and
H. L. Yu, Heavy quark symmetry and chiral dynamics, Phys. Rev.  D
46, 1148 (1992) [Erratum-ibid.  D 55, 5851 (1997)].



Wise:1992hn
M. B. Wise, Chiral perturbation theory for hadrons containing a
heavy quark, Phys. Rev.  D 45, R2188 (1992).



Burdman:1992gh
G. Burdman and J. F. Donoghue, Union of chiral and heavy quark
symmetries, Phys. Lett.  B 280, 287 (1992).



Casalbuoni:1996pg
R. Casalbuoni, A. Deandrea, N. Di Bartolomeo, R. Gatto, F. Feruglio
and G. Nardulli, Phenomenology of heavy meson chiral Lagrangians,
Phys. Rept.  281, 145 (1997)




Falk:1992cx
A. F. Falk and M. E. Luke, Strong decays of excited heavy mesons in
chiral perturbation theory, Phys. Lett.  B 292, 119 (1992)




Tanabashi:2018oca
  M. Tanabashi et al. [Particle Data Group],
  Review of Particle Physics,
  Phys. Rev. D 98, 030001 (2018).
 
  
  



