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Probing charmonium-like state X(3915)through meson photoproduction

Qing-Yong Lin1,2,3,∗ Xiang Liu1,4†,‡ and Hu-Shan Xu1,21Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS, Lanzhou 730000, China

2Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China3University of Chinese Academy of Sciences, Beijing, 100049, China

4School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China(Dated: October 19, 2018)

Inspired by the observation of charmonium-like stateX(3915), we explore the discovery potential of theX(3915) production via meson photoproduction process. By investigating theγp → J/ψωp process includingtheX(3915) signal and background contributions, we obtain the corresponding information of the cross section,the Dalitz plot and theJ/ψω invariant mass spectrum, which is helpful to further experimental study ofX(3915)via meson photoproduction.

PACS numbers: 14.40.Lb, 12.39.Fe, 13.60.Le

I. INTRODUCTION

X(3915) is a typical charmonium-like state, which wasfirstly observed in theJ/ψω invariant mass spectrum ofγγ→J/ψω. It’s mass and width areMX(3915) = (3915± 3(stat)±2(syst)) MeV andΓX(3915)= (17± 10(stat)± 3(syst)) MeV, re-spectively. SinceX(3915) comes from theγγ fusion process,eitherJP = 0+ or JP = 2+ is the possible spin-parity assign-ment to X(3915). Furthermore, Belle’s measurement givesΓX(3915)→γγ · BR(X(3915)→ J/ψω) = (61± 17(stat)± 8(syst))eV and (18± 5(stat)± 2(syst)) eV corresponding toJP = 0+

andJP = 2+, respectively [1].What is its inner structure is a crucial question to reveal the

property ofX(3915). In Ref. [2], X(3915) as the first radialexcitation ofχc0(1P) was proposed by the analysis of massspectrum and the study of its strong decay behavior. This con-ventional charmonium explanation toX(3915) was confirmedby the BaBar Collaboration, where BaBar carried out a spin-parity analysis ofX(3915), which supports theJP = 0+ as-signment due to theχc0(2P) resonance [3]. However,X(3915)as aχc0(2P) state brings us a new problem. Aχc0(2P) statedominantly decays intoDD [2]. Until now theX(3915) signalhas been missing in theDD invariant mass spectrum given byBelle [4] and BaBar [5] in γγ→ DD, where the charmonium-like stateZ(3930) was reported [4, 5], which is aχc2(2P) state.For solving this problem, the authors in Ref. [6] proposedthat theZ(3930) enhancement structure may contain two P-wave higher charmoniaχc0(2P) andχc2(2P). The numericalresult shows that this assumption is supported by the analysisof the DD invariant mass spectrum and the cosθ distributionof γγ → DD [6]. Thus, there does not exist any difficulty tothisχc0(2P) explanation toX(3915).

Just introduced in the above,X(3915) was only reported intheγγ fusion process. It is also natural to ask whetherX(3915)can be found in other processes. At present, according to theproduction mechanisms, all observed charmonium-like states

†corresponding author∗Electronic address:qylin@impcas.ac.cn‡Electronic address:xiangliu@lzu.edu.cn

reported in the past decade can be roughly categorized intofour groups, which correspond to theγγ fusion process, theB meson decay with the kaon emission, thee+e− annihila-tion, the hidden-charm dipion decays of higher charmoniaand charmonium-like states. In the past yeas, there are sometheoretical explorations of the production of charmonium-likestate by other processes different from the above four mech-anisms mentioned above. For example, Liu, Zhao and Closesuggesed thatZ(4430)± can be produced via the meson pho-toproduction processγp → Z(4430)+n → ψ′π+n [7]. Whilethe authors in Ref. [8] proposed to studyZ(4430)± by thenucleon-antinucleon scattering at the forthcoming PANDAexperiment. In Ref. [9], He and Liu discussed the discoverypotential of charmonium-like stateY(3940) by the meson pho-toproduction processγp→ Y(3940)p. Very recently, the pro-duction of the newly observed chargedZc(3900) by the pho-toproduction processγp→ Zc(3900)n was discussed [10]. Itis obvious that probing the production ofX(3915) by differentprocesses from theγγ fusion is an interesting research topic.

We notice theX(3915)→ J/ψω decay mode [1]. Sinceboth J/ψ andω in the final state of theX(3915)→ J/ψω de-cay are vector meson, we suppose that we can carry out thestudy of theX(3915) production via meson photoproduction.For further testing this idea, in this work we need to choosesuitable meson photoproduction process to study the produc-tion of X(3915) and discuss the discovery potential ofX(3915)through meson photoproduction. In the next section, we illus-trate the detailed consideration.

This paper is organized as follows. In Sec.I, we introducethe research status ofX(3915) and our motivation of studyingthe production ofX(3915) by meson photoproduction. Afterintroduction, we present the details of whole calculation.Andthe numerical result will be given in SectionsII andIII . Thelast section is a short summary.

II. THE PRODUCTION OF X(3915) VIA MESONPHOTOPRODUCTION

Under the assumption of vector meson dominance (VMD)[11–13], ω or J/ψ can interact with a photon. Thus, byexchanging a vector meson likeω or J/ψ, X(3915) can

2

be produced via the meson photoproduction processγp →X(3915)p, which is shown in Fig.1. As discussed in Refs.[14, 15] and references therein, the coupling ofω with the nu-cleons is obviously stronger than that ofJ/ψ interacting withthe nucleons. In addition, the mass of the exchangedJ/ψ is farlarger than that of the exchangedω meson. Thus, the contri-bution from Fig.1 (a) must be far larger than that from Fig.1(b), which makes us only consider the contribution from Fig.1 (a) in our study. Later, we will present the results of the totalcross section and differential cross section.

γ

p p

X(3915)

J/ψ

p1 p2

q

k1k2

ω

(a)

γ

p p

X(3915)

ω

p1 p2

q

k1k2

J/ψ

(b)

FIG. 1: Theγp → X(3915)p process with theω (a) andJ/ψ (b)meson exchanges.

For depicting the interaction of theω meson with the nu-cleons, we adopt the following effective Lagrangian [16]

LNNω = −gNNω

(

ΨγµΨφµ − κω

4mNΨσµνΨFµν

)

, (1)

whereΨ and φ denote the fields of the nucleon and theωmeson, respectively. We defineFµν = ∂µφν − ∂νφµ andσµν = i[γµ, γν]/2. For theppω vertex, there exist two strongcoupling constantsgNNω andκω. At present, these couplingconstants are not well determined. Different models and ap-proaches gave different theoretical estimates for these twocoupling constants [15]. In TableI, we list different combina-tions of thegNNω andκω values from different models. Addi-tionally, a monopole form factorFNNω(q2) = (Λ2

ω−m2ω)/(Λ2

ω−q2) is introduced to compensate the off-shell effect of the ex-changedω meson, where the cutoff Λω is set to be 1.2 GeV[17].

According to the VMD mechanism [11–13], the La-grangian describing the interaction between the photon andthe vector meson can be expressed as

LVγ = −em2

V

fVVµAµ, (2)

wheremV and fV are the mass and the decay constant of thevector mesonV, respectively. The decay constantfV can bedetermined by the decayV → e+e−, i.e.,

efV=

3ΓV→e+e−m2V

8α|k|3

1/2

, (3)

where|k| = (m2V−4m2

e)1/2/2 ≃ mV/2 is the three momentum ofelectron in the rest frame of the vector meson.α = e2/(4π) =

TABLE I: The theoretical values of the coupling constantsgNNω andκω.

Mechanism/Model gω κω

Paris [18, 19] 12.2 −0.12

Nijmegen [20] 12.5 +0.66

Bonn [21] 15.9 0

Pion photoproduction [22] 7 − 10.5 0

Nucleon EM form factors [23] 20.86± 0.25 −0.16± 0.01

QCD sum rule [24] 18± 8 0.8± 0.43P0 quark model [16] − −3/2

Light meson emission model [25]23± 3 0

14.6± 2.0 −3/2

1/137 is the fine-structure constant. ByΓJ/ψ→e+e− = 5.55±0.14± 0.02 keV [26] and Eq. (3), one obtainse/ fJ/ψ = 0.027.

Under the assignment of quantum numberJPC = 0++ toX(3915) [2, 3], the interaction ofX(3915) withJ/ψω can bedepicted by [27, 28]

〈J/ψ(k1)ω(ǫ2, k2)|X(3915)(ǫ1)〉 = gXJ/ψωTµνǫµ

1ǫν2 (4)

with

T µν = gµνk1 · k2 − kν1kµ2,

whereǫ1(ǫ2) is the polarization vector ofJ/ψ(ω). The cou-pling constantgXJ/ψω can be determined by the decay widthof X(3915)→ J/ψω, i.e.

Γ[

X → ψω]

=18π|p′|m2

X

|M[X → ψω]|2

=

(

gXψω

mX

)2 |p′|16π

[

m4ψ + 2M2

ψ(2m2ω − m2

X)

+(m2ω − m2

X)2]

, (5)

wherep′ = [(m2X − (mψ + mω)2)(m2

X − (mψ − mω)2)]1/2/(2mX)denotes the three momentum of the daughter mesons in theparent’s center of mass frame. At present, the decay widthof X(3915) → J/ψω has not been well determined in ex-periment. In order to discuss the production ofX(3915) viaphotoproduction process, we adopt several typical values ofthe decay width ofX(3915)→ J/ψω as input, i.e., we takeΓ(X → J/ψω) = 0.15, 1.7, 5.1 MeV1, which correspond

1 The lower and upper limits of theoretical two-photon decay width are 1 keVto 5.47 keV, respectively, which are from different model calculations [29–34]. Thus, by Belle’s measurementΓX(3915)→γγ · BR(X(3915)→ J/ψω) =(61± 17(stat)± 8(syst)) eV [1], we can obtain the corresponding range ofthe decay width ofX(3915)→ J/ψω, which is 0.19 ∼ 1 MeV. The typicalvalues ofX(3915)→ J/ψω taken in this work cover the above theoreticalrange.

3

dσ/d

t(nb/G

eV2 )

−t (GeV2)0.0 0.5 1.0 1.5 2.0 2.5 3.00

5

10

15

20

(12.2,-0.12) (12.5,0.66) (15.9,0.0)

dσ/d

t(nb/G

eV2 )

−t (GeV2)0.0 0.5 1.0 1.5 2.0 2.5 3.00

5

10

15

20 =0.15 MeV =1.70 MeV =5.10 MeV

(a) (b)

σ(n

b)

√

s (GeV)

4 6 8 10 12 14 16 18 200.1

1

10

(12.2,-0.12) (12.5,0.66) (15.9,0.0)

σ(n

b)

√

s (GeV)

4 6 8 10 12 14 16 18 200.01

0.1

1

10

=0.15 MeV =1.70 MeV =5.10 MeV

(c) (d)

FIG. 2: (Color online). The differential and total cross sections ofγp → X(3915)p dependent on−t and√

s, respectively. (a) and (c) are theresults of the differential and total cross sections withΓ(X(3915)→ J/ψω) = 5.1 MeV and several typical values of the coupling constants(gNNω, κω), respectively. (b) and (d) are the results of the differential and total cross sections with the fixed (gNNω, κω) = (15.9,0) and the typicalvalues of decay width of theX(3915)→ J/ψω decay, respectively.

to the coupling constantsgXJ/ψω = 0.118, 0.3956, 0.6852GeV−1, respectively.

With the Lagrangians given above, we obtain the transitionamplitude forγp→ X(3915)p shown in Fig.1

T f i =

(

efψ

gNNωgXψω

)

(gµνk1 · q − kν1qµ)−gνα + qνqα/m2

ω

q2 − m2ω

×u(p2)

(

γα +iκω2mN

σαβqβ

)

u(p1)ǫµγ

×FNNω(q2)FXψω(q2), (6)

where we also introduce a monopole form factorFXJ/ψω(q2) =(Λ2

X − m2ω)/(Λ2

X − q2) to describe the vertex with an off-shellω meson and takeΛX = mψ [7]. And then, the unpolarizeddifferential cross section reads as

dσdt=

164πs

1|k1cm|2

14

∑

pol

∣

∣

∣T f i

∣

∣

∣

2(7)

wherek1cm is the photon energy in the center of mass frameof the γp scattering.s = (k1 + p1)2 and t = (k2 − k1) = q2

denote the Mandelstam variables. Just indicated in Eq.7, thetotal cross section is proportional tog2

Xψω.In Fig. 2, we show the differential cross section ofγp →

X(3915)p dependent on−t, where two cases are considered:(1) We present the results corresponding to several (gNNω, κω)coupling constants. (2) We also list the results with threetypical decays widths ofX(3915)→ J/ψω. While the cor-responding dependence of the total cross section ofγp →X(3915)p on

√s is given in Fig. 2. We need to specify that

the differential cross section is calculated with the fixed value√s = 9.9 GeV.The results of differential cross section show that there is a

peak structure at low−t region, which increases rapidly nearthe threshold and then decreases slowly with the increase of−t. The line shape of the total cross section goes up veryrapidly near the threshold, and then increases slowly with theincrease of

√s.

4

III. THE BACKGROUND ANALYSIS AND DALITZ PLOT

In the above section, we discussed the production ofX(3915) via theγp→ X(3915)p process. For providing moreabundant information of the discovery potential ofX(3915)via the meson photoproduction, in the following we performthe background analysis and the Dalitz plot, where we notonly consider theX(3915) signal contribution but also includethe background contribution. SinceX(3915) can decay intoJ/ψω [1], we analyze theγp→ X(3915)p→ J/ψωp reactionin detail.

γJ/ψ X(3915)

ω

p p

q1k1

q2

J/ψ

ω

k2

k3p1 p2

FIG. 3: The processγp → X(3915)p → J/ψωp via theω mesonexchange.

As the main signal contribution, theγp → X(3915)p →J/ψωp reaction with theω exchange is described in Fig.3.Adopting the effective Lagrangian approach, we write out thetransition amplitude

T S ingalf i =

(

gNNωg2Xψω

efψ

)

u(p2)(γρ +iκω2mN

σρλq1λ)u(p1)

×(

gναk2 · k3 − k2αk3ν)(gµβk1 · q1 − k1βq1µ

)

×(−gβρ + qβ1qρ1/m

2ω)

q21 − m2

ω

ǫµγ ǫ∗νψ ǫ∗αω

(q22 − m2

X + imXΓX)

×

Λ2ω − m2

ω

Λ2ω − q2

1

Λ2X − m2

ω

Λ2X − q2

1

Λ2X − m2

X

Λ2X − q2

2

, (8)

where the cutoff is taken asΛX = mψ [35]. In Fig. 3, therelevant kinematic variables are marked.

The Pomeron contribution has been widely applied to thestudy of the diffractive transitions in Refs. [36–38]. Since thePomeron can mediate the long-distant interaction between aconfined quark and a nucleon and behaves like an isoscalarphoton withC = +1, the Pomeron exchange can mainly con-tribute to theγp → J/ψp → J/ψωp reaction, which providesthe background contribution. The concrete description of thisprocess is given in Fig.4.

To describe the Pomeron exchange process shown in Fig.4, we adopt the formula given in Refs. [7, 36, 37, 39]. ThePomeron-nucleon coupling can be expressed as

Fµ(t) =3β0(4m2

N − 2.8t)

(4m2N − t)(1− t/0.7)2

γµ = f (t)γµ, (9)

γ

p p

ω

J/ψ

p1

k3

k2

qP

p2

k1

(a)

k1

γ J/ψ

p

p

ω(b)

qs

qP

p1

qu

k3

k2

p2

FIG. 4: Theγp→ J/ψωp process through the Pomeron exchange.

wheret = q2P = (k1 − k2)2 is the the exchanged Pomeron mo-

mentum squared.β0 denotes the coupling constant between asingle Pomeron and a light constituent quark.

As suggested in Ref. [39], an on-shell approximation withthe gauge-fixing scheme is applied to depict theγVP vertex,where the equivalent vertex for theγψP interaction is writtenas

VγVP =2βc × 4µ2

0

(M2ψ − t)(2µ2

0 + M2ψ − t)

Tµανǫµγ ǫ

νψPα

= V(t)Tµανǫµγ ǫ

νψPα (10)

with

T µαν = (k1 + k2)αgµν − 2kν1gαµ + 2[

kµ1gαν

+kν2k2

2

(k1 · k2gαµ − kα1kµ2 − kµ1kα2)

−k2

1kµ2k2

2k1 · k2(k2

2gαν − kα2kν2)

+ (k1 − k2)αgµν. (11)

In Eq. (10), βc is the effective coupling constant between aPomeron and a charm quark withinJ/ψ, andµ0 is a cutoff inthe form factor related to the Pomeron.

Thus, we get the amplitudes of Fig.4 (a) and (b), i.e.,

T Pomeronf i (a) = gNNωFppω(q2

s) f (t)V(t)GP(s, t)T µρνǫµγ ǫ∗νψ ǫ∗αω

×u(p2)

(

γα +iκω2mN

σαβkβ

3

)

/qs + mN

q2s − m2

N

γρu(p1),

(12)

T Pomeronf i (b) = gNNωFppω(q2

u) f (t)V(t)GP(s, t)T µανǫµγ ǫ∗νψ ǫ∗αω

×u(p2)γρ/qu + mN

q2u − m2

N

(

γα +iκω2mN

σαβkβ

3

)

u(p1)

(13)

with GP(s, t) = −i(α′s)α(t)−1, which is related to the Pomerontrajectoryα(t) = 1+ ǫ + α′ t. The values of the parameters in-volved in the above amplitudes include:β2

0 = 4.0 GeV2, β2c =

0.8 GeV2, α′ = 0.25 GeV−2, ǫ = 0.08, andµ0 = 1.2 GeV.

5

To describe the effect of the off-shell intermediate nucleonas shown in Fig.4, a form factor for theppω vertex is con-sidered with the formFppω(q2) = (Λ2

ppω − m2N)/(Λ2

ppω − q2),whereq2 is the momentum of the intermediate nucleon. Later,we will discuss how to constrain the value of the cutoff Λppω.

With the amplitudes listed in Eq. (8) and Eqs. (12)-(13),we obtain the square of the total invariant transition amplitude

|M|2 =∑

∣

∣

∣

∣

T S ignalf i + T Pomeron

f i (a) + T Pomeronf i( b)

∣

∣

∣

∣

2. (14)

The corresponding total cross section of the processγp →J/ψωp is

dσ =m2

N

|k1 · p1||M|2

4(2π)4dΦ3(k1 + p1; p2, k2, k3), (15)

where then-body phase space is defined as [26]

dΦn(P; p1, ..., pn) = δ4(P −

n∑

i=1

pi)3

∏

i=1

d3pi

(2π)32Ei.

For numerically calculating the total cross section includingboth signal and background contributions, we use the FOWLcode. In Fig. 5 the total cross section of the Pomeron ex-change contributions forγp → J/ψωp is given with differenttypicalΛppω values (Λppω = 0.9, 1.0 and 1.1 GeV). Our cal-culation shows that the results are sensitive to the values of thecutoff. And the line shape of the total cross section dependenton√

s is monotonously increasing. We notice that there wereseveral experiments ofγp→ J/ψp, where the measured crosssection of this process is about 10nb [40, 41]. To some extend,the discussedγp → J/ψωp process is similar toγp → J/ψp.It is natural to assume that the cross section ofγp → J/ψωpshould be similar or even lower than that ofγp → J/ψp. Un-der this assumption, we can roughly constrain the cutoff tobeΛppω = 0.9 GeV, which will be applied to the followingdiscussions.

σ(n

b)

√

s (GeV)

2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.010-4

10-3

10-2

10-1

100

101

102

pp =0.9 GeV pp =1.0 GeV pp =1.1 GeV

FIG. 5: (color online). The total cross section ofγp→ J/ψωp fromthe Pomeron exchange. Here, we take different typical cutoff Λppω

as input.

In Fig. 6, we further present the total cross section ofγp → J/ψωp including the signal and background contribu-tions, which corresponds to Eqs. (14)-(15). By the compari-son of the typicalσω, σT andσPom, we find:

1. WhenΓ(X(3915)→ J/ψω) = 0.15 MeV, the corre-spondingσω is rather small. However,σω is larger thanσPom

around√

s = 5 GeV, which is close to the threshold of√

sof the γp → J/ψωp reaction. Since the decay width ofX(3915)→ J/ψω determines whether theX(3915) signal isburied by the background, the above analysis makes us obtainthe lower limit ofΓ(X(3915)→ J/ψω) if distinguishing theX(3915) signal from the background.

2. WhenΓ(X(3915)→ J/ψω) = 1.7 MeV and 5.1 MeV, thecorrespondingσT is dominated by theX(3915) signal contri-bution at

√s ≤ 8 and

√s ≤ 15 GeV, respectively (see Fig.6

for the detail). It means that theX(3915) signal can be easilyobserved if taking suitable

√s range.

σ(n

b)

√

s (GeV)

2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.010-6

10-5

10-4

10-3

10-2

10-1

100

101

Pom

( =0.15 MeV) T ( =0.15 MeV)

( =1.70 MeV) T ( =1.70 MeV)

( =5.10 MeV) T ( =5.10 MeV)

FIG. 6: (color online). The energy dependence of the total crosssections forγp → J/ψωp. Here, σPom and σω are the resultsonly considering the Pomeron exchange and theω exchange con-tributions, respectively, whileσT denotes the total cross section ofγp → J/ψωp. We also give the variations ofσω andσT to

√s cor-

responding to the typical valuesΓ(X(3915)→ J/ψω) = 0.15 MeV,Γ(X(3915)→ J/ψω) = 1.7 MeV andΓ(X(3915)→ J/ψω) = 5.1MeV.

Besides presenting the above study of the total cross sec-tion of γp → J/ψωp, we further carry out the analysis ofthe Dalitz plot, which can provide important information ofthe discovery potential ofX(3915) by photoproduction pro-cessγp → J/ψωp. In Fig. 7, the Dalitz plot and the corre-spondingJ/ψω mass spectrum with several typical values of√

s are listed. The numerical results indicate:1. For the case with typical valueΓ(X(3915)→ J/ψω) =

0.15 MeV, it is difficult to identifyX(3915) signal if only tak-ing 100 million collisions, since there is no enough signalevent. More collisions is helpful to the search for theX(3915)signal (see the first row in Fig.7). When performing a MonteCarlo simulation with 10 billion collisions, the signal event is5 events/0.02 GeV−2. We need to emphasize that the ideal

√s

range is around the threshold of theγp→ J/ψωp reaction.2. If Γ(X(3915)→ J/ψω) = 1.7 MeV, the signal ofX(3915)

6

with√

s = 9.9 GeV is more explicit than that with√

s = 5.9GeV. Then, with increasing

√s, the background contribution

becomes visible, which is the reason why there exists a hor-izontal band in Fig.7 (d) and (e). This phenomena is con-sistent with the result from Fig.6 since the cross sectionfrom the Pomeron exchange goes up continuously. The sit-uations corresponding toΓ(X(3915)→ J/ψω) = 1.7 MeVand Γ(X(3915) → J/ψω) = 5.1 MeV are similar to eachother. By theJ/ψω invariant mass spectrum, we estimate thatthe event ofX(3915) reaches up to around 200/0.02 GeV−2

at√

s = 16.9 GeV and with 100 million collisions, whenΓ(X(3915)→ J/ψω) = 5.1 MeV is adopted.

3. The comparison of the results listed in the second and thethird rows of Fig.7 indicates that larger value ofΓ(X(3915)→J/ψω) is more beneficial to the search forX(3915).

In the above discussion, the cutoff Λω for the ppω vertexwith off-shell ω meson is set to be 1.2 GeV as adopted in[17]. In the following, we further give the dependence of thesignal strength on the cutoff. In Fig. 8, we present the theΛω dependence of the cross section ofγp → J/ψωp fromthe signal contribution, where we takeΛω = 1.0 − 1.4 GeVwith step of 0.1 GeV. As shown in Fig.8, the line shape ofthe cross section are quite similar to that listed in Fig.2. Thecross section is 2.5 ∼ 13 nb corresponding toΛω = 1.0− 1.4GeV.

IV. SUMMARY

In this work, we explore the discovery potential ofcharmonium-like stateX(3915) by meson photoproduction.As a good candidate ofχ′c0(2P) [2], X(3915) was only ob-

served in theγγ fusion process [1]. Thus, searching for otherprocesses to investigateX(3915) is an interesting and impor-tant topic, which will be valuable to further deepen our under-standing ofX(3915).

Since the final state of the observedX(3915) decay con-tain two vector mesons, meson photoproduction process canbe suitable to studyX(3915). For quantitatively answeringwhetherX(3915) can be observed in meson photoproductionprocess, we study theγp → J/ψωp process by including theX(3915) signal and background contributions. Furthermore,the corresponding cross section and the analysis of the Dalitzplot are given, which provide abundant information to the ex-perimental study ofX(3915) by meson photoproduction.

Our study also shows that the experimental measurementof the decay width ofX(3915)→ J/ψω is a crucial input instudying the meson photoprodutionofX(3915). However, thiskey value is still absent in experiments. In this work, we con-sider several typical values ofΓ(X(3915)→ J/ψω) to discussthe discovery potential ofX(3915) by meson photoproduction.We expect further experiment of the hidden-charm decay ofX(3915). The following theoretical and experimental joint ef-fort will be helpful to probing charmonium-like stateX(3915)through meson photoproduction.

V. ACKNOWLEDGEMENTS

This project is supported by the National Natural Sci-ence Foundation of China under Grants No. 11222547, No.11175073, and No. 11035006, the Ministry of Education ofChina (SRFDP under Grant No. 20120211110002 and theFundamental Research Funds for the Central Universities),and the Fok Ying-Tong Education Foundation (No. 131006).

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FIG. 7: The Dalitz plot and the correspondingJ/ψω invariant mass spectrum for theγp → J/ψωp process. Here, the results listed in thefirst, the second and the third rows correspond to the typicalvalueΓ(X(3915)→ J/ψω) = 0.15 MeV, Γ(X(3915)→ J/ψω) = 1.7 MeV andΓ(X(3915)→ J/ψω) = 5.1 MeV, respectively.

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σ(n

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FIG. 8: (color online). The total cross section ofγp→ J/ψωp fromthe signal contribution dependent onΛω. Here, the partial decaywidth isΓ(X(3915)→ J/ψω) = 5.1 MeV and the coupling constantsare (gNNω, κω) = (15.9,0).

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