Physics Letters B 699 (2011) 341–344

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Novel charmonium-like structures in the J/ψφ and J/ψω invariant mass spectra

Xiang Liu a,b,∗, Zhi-Gang Luo c, Shi-Lin Zhu c,∗a School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, Chinab Research Center for Hadron and CSR Physics, Lanzhou University & Institute of Modern Physics of CAS, Lanzhou 730000, Chinac Department of Physics and State Key Laboratory of Nuclear Physics and Technology Peking University, Beijing 100871, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 17 December 2010Received in revised form 30 March 2011Accepted 13 April 2011Available online 16 April 2011Editor: W. Haxton

Keywords:Charmonium-like stateMolecular charmoniumHeavy meson chiral perturbation theoryOne boson exchange model

Stimulated by the new evidence of Y (4274) observed in the J/ψφ invariant mass spectrum, we firstpropose the charmonium-like state Y (4274) as the S-wave Ds Ds0(2317) + h.c. molecular state withJ P = 0−, which is supported well by dynamics study of the system composed of the pseudoscalar andscalar charmed mesons. The S-wave D D0(2400) + h.c. molecular charmonium appears as the molecularpartner of Y (4274), which is in accord with the enhancement structure appearing at 4.2 GeV in theJ/ψω invariant mass spectrum from B decays. Our study shows that the enhancement structures,i.e., the newly observed Y (4274) and the previously announced Y (4140)/Y (3930) in the J/ψφ andJ/ψω invariant mass spectra, can be understood well under the uniform framework of the molecularcharmonium, which can be tested by future experiments.

© 2011 Elsevier B.V. All rights reserved.

Very recently the CDF Collaboration [1] studied the J/ψφ in-variant mass spectrum in the B → J/ψφK channel based onthe sample of pp collision data with an integrated luminosity of6 fb−1. Besides confirming the previous Y (4140) state [2], CDFalso reported the observation of an explicit enhancement struc-ture with 3.1σ significance in the J/ψφ invariant mass spec-trum, which is of mass M = 4274.4±8.4

−6.7(stat) MeV and width Γ =32.3+21.9

−15.3(stat) MeV [1]. We will refer to this new structure by thename Y (4274) in this Letter.

The appearance of Y (4274) in the J/ψφ invariant mass spec-trum not only makes the charmonium-like family abundant, butalso raises our interest in exploring the origin of enhancementstructures in the J/ψφ invariant mass spectrum and revealingthe relation between Y (4274) and Y (4140), which will be help-ful to improve our knowledge of the underlying properties ofcharmonium-like state.

The previous observation of Y (4140) has stimulated great inter-est among theorists, especially when associating it with Y (3930)

reported by the Belle Collaboration [3] and confirmed by the BaBarCollaboration [4]. Both Y (4140) and Y (3930) were observed in themass spectrum of J/ψ + light vector meson in B meson decay

B → K +{ J/ψ φ ⇒ Y (4140)

J/ψ ω ⇒ Y (3930).

* Corresponding authors.E-mail addresses: xiangliu@lzu.edu.cn (X. Liu), zhusl@pku.edu.cn (S.-L. Zhu).

0370-2693/$ – see front matter © 2011 Elsevier B.V. All rights reserved.doi:10.1016/j.physletb.2011.04.024

Generally in the weak decays of B meson, the cc pair creationmainly results from the color-octet mechanism. Furthermore, acolor-octet qq pair is easily popped out by a gluon. Thus, c andc capture q and q respectively to form a pair of charmed mesons.By this mechanism, a pair of the charm-strange mesons with thelow momentum easily interact with each other and even formthe molecular charmonium. Additionally, Y (4140) and Y (3930) areclose to the thresholds of D∗

s D∗s and D∗ D∗ respectively, and satisfy

an almost exact mass relation

MY (4140) − 2MD∗s≈ MY (3930) − 2MD∗ . (1)

The mass difference between Y (4140) and Y (3930) is approx-imately equal to that between φ and ω mesons: MY (4140) −MY (3930) ∼ Mφ −Mω . The peculiarity of B → K (cc) and the similar-ity between Y (4140) and Y (3930) provoke an uniform molecularcharmonium picture to reveal the underlying structure of Y (4140)

and Y (3930) [5,6]. Applying D∗s D∗

s and D∗ D∗ molecular structuresto explain Y (4140) and Y (3930) respectively not only solves along-standing puzzle of the structure of Y (3930), but also opensa window to investigate the hadron dynamics of exotic state be-yond the conventional qq and qqq states. A series of research workrelated with Y (4140) were carried out later [5–19].

In Fig. 1, we present the comparison between the experimentaldata [1] and the thresholds of the charmed-strange meson pairs.Y (4274) is just below the threshold of Ds Ds0(2317) similar to thesituation of Y (4140), which stimulates us to deduce naturally thatY (4274) enhancement results from an S-wave Ds Ds0(2317) + h.c.molecular system Y ss with the flavor wave function

342 X. Liu et al. / Physics Letters B 699 (2011) 341–344

Fig. 1. The mass difference �M = m(μ+μ− K + K −) − m(μ+μ−) distribution (his-togram) for events in the B+ mass window [1]. Besides Y (4140), one explicitenhancement appears around 4274 MeV. Here, the purple dashed line is the back-ground from the three-body phase space. The blue solid line is the fitting resultwith resonance parameters of Y (4140) and Y (4270) resonances in Ref. [1]. The ver-tical red dashed lines denote the thresholds of D∗

s D∗s , Ds Ds0(2317), Ds D ′

s1(2460),D∗

s Ds0(2317), Ds Ds1(2536), Ds Ds2(2573), D∗s D ′

s1(2460) and D∗s Ds1(2536). (For in-

terpretation of the references to color in this figure legend, the reader is referred tothe web version of this Letter.)

∣∣Y ss⟩ = 1√2

[∣∣D+s D−

s0

⟩ + ∣∣D−s D+

s0

⟩]. (2)

The C parity of the isoscalar Y (4274) is positive due to theY (4274) → J/ψφ decay mode observed by CDF. As the cousinof Y ss , Y uu/dd is of the flavor wave function∣∣Y uu/dd⟩ = 1

2

[∣∣D00 D0⟩ + ∣∣D0

0 D0⟩ + ∣∣D−0 D+⟩ + ∣∣D+

0 D−⟩]. (3)

For such S-wave pseudoscalar–scalar systems, their quantum num-ber must be J P = 0− . Performing dynamical investigations of Y ss

and Y uu/dd can answer whether there exist Y ss and Y uu/dd molec-ular systems, which is one of the main tasks of this Letter. What ismore important is that understanding the underlying structure ofY (4274) will be helpful for revealing the properties of Y (4140)

[5,6] taking into account the similarities between Y (4274) andY (4140).

Using the effective Lagrangian in the heavy meson chiral per-turbation theory (HMχPT) [20,21] and the method developed inliterature [23], we obtain the effective potentials of Y ss and Y uu/dd

states [24]

Vsseff (r) = V Direct

φ (r) + 2

3V Cross

η (r), (4)

Vuu/ddeff (r) = 3

2V Direct

ρ (r) + 1

2V Direct

ω (r) + V Directσ (r)

+ 3

2V Cross

π (r) + 1

6V Cross

η (r). (5)

Here, the subscript of the sub-potential denotes the exchangedlight meson. The general expressions of the sub-potentials corre-sponding to the pseudoscalar, sigma and vector meson exchangesare

V DirectV (r) = −ββ ′

2g2

V Y (Λ,q0 = 0,mV , r), (6)

V Directσ (r) = −gσ g′

σ Y (Λ,q0 = 0,mσ , r), (7)

V CrossP (r) = h2q0

′2

f 2Y(Λ,q′

0,mP , r), (8)

π

Fig. 2. (Color online.) The potentials of Y ss (right-side diagram) and Y uu/dd (left-sidediagram) with typical value Λ = 1 GeV. Here, we take β = 0.9, β ′ = 1, gσ = g′

σ =−0.76, h = −0.56 ± 0.28 following Refs. [21,22].

where fπ = 132 MeV and gV = mρ/ fπ = 5.8. gV , h, β(′) , g(′)σ are

the parameters in the effective Lagrangian, which describe the in-teraction of the heavy flavor mesons with the light mesons [21].q′

0 is taken as mDs0 − mDs and mD0 − mD for Y ss and Y uu/dd , re-spectively. And the Y function is

Y (Λ,κ,m, r)

=⎧⎨⎩

if |κ | � m, − 14πr (e−ζ1r − e−ζ2r) + 1

8π

ζ 22 −ζ 2

1ζ2

e−ζ2r

otherwise, − 14πr (cos(ζ ′

1r) − e−ζ2r) + 18π

ζ 22 +ζ ′2

1ζ2

e−ζ2r

with ζ1 = √m2 − κ2, ζ ′

1 = √κ2 − m2 and ζ2 = √

Λ2 − κ2. Λ is thecutoff to cure the singularity of the effective potential.

In Fig. 2, one presents the line shapes of the potentials listedin Eqs. (4) and (5). For Y ss , the exchange potential of the φ me-son can be ignored compared with that of the η meson. The totaleffective potential of Y ss is dominated by the η exchange poten-tial. For Y uu/dd , the π meson plays an important role especiallyin the range of r > 5 GeV−1 since the exchange potentials of ρ ,ω, σ and η decay exponentially with r. The behavior of the po-tential depicted in Fig. 2 indicates that we only need to considerthe η meson exchange potential for Y ss and the π meson exchangepotential for Y uu/dd when finding the bound state solution by solv-ing Schrödinger equation. Furthermore, whether there exist boundstate solutions for Y ss and Y uu/dd systems is closely related to thecorresponding strengths of the Ds0(2317)Dsη and D0(2400)Dπcouplings.

In Fig. 3, we show the variation of the numerical result of thebound state solutions for Y ss with the values of h and Λ, whichindicates that there indeed exists a Ds0(2317)Ds + h.c. molecu-lar charmonium corresponding to newly observed enhancementY (4274). Our numerical results overlap with the mass difference(∼ −11 MeV) between Y (4274) and the threshold of Ds0(2317)Ds .The corresponding cutoff Λ lies in a reasonable range which isexpected to be around 1–3 GeV. We also find that the larger |h|values make the corresponding Λ become smaller, i.e., Λ tends tobe around 1 GeV, which is fully consistent with the expected be-havior of the potential of the S-wave Ds0(2317)Ds + h.c. system.

Besides supporting the assignment of Y (4274) as the S-waveDs0(2317)Ds + h.c. molecular state, our dynamical calculation alsoprovides a novel approach to extract the h parameter, which en-codes the important information of the Ds0(2317)Dsη interactionand the underlying properties of Ds0(2317) [25]. This couplingcannot be extracted experimentally since the Ds0(2317) → Dsη

X. Liu et al. / Physics Letters B 699 (2011) 341–344 343

Fig. 3. The obtained bound state solutions of Y ss system dependent on h valuesand Λ. Here, we also compare our result with the mass difference (red dashedline) between Y (4274) and the threshold of Ds0(2317)Ds . (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version ofthis Letter.)

Fig. 4. The J/ψω invariant mass spectrum in the B → J/ψωK decay announced bythe Belle Collaboration [3] and the BaBar Collaboration [4]. Here, the vertical bluedashed line denotes the threshold of D0(2400)D . The red dotted line is the fittingresult. (For interpretation of the references to color in this figure legend, the readeris referred to the web version of this Letter.)

decay is forbidden kinematically. Our result indicates that the|h| value corresponding to the binding energy of the S-waveDs0(2317)Ds + h.c. system consistent with mass difference(∼ −11 MeV) is in the range 1.2–1.5 associated with reasonableΛ value, which can be confirmed by further theoretical study.

We extend the same formalism to the Y uu/dd system, whereinput parameter h for the D0(2400)Dπ coupling is constrainedby the decay width of the D0(2400) → Dπ to be h = −0.56 ±0.2 [21]. The binding energy of the Y uu/dd system is −9.85,−10.11, −10.23, −10.30, −10.34, −10.38, −10.42 MeV corre-sponding to the typical value of Λ = 0.9, 1.0, 1.1, 1.2, 1.3, 1.4,1.5 GeV, where the bound state solution of the Y uu/dd system isinsensitive to Λ, which indicates the existence of the molecularcousin of the S-wave Ds0(2317)Ds + h.c. molecular state, i.e., anS-wave D0(2400)D + h.c. molecular charmonium. Thus, finding theevidence of S-wave D0(2400)D + h.c. molecular charmonium canprovide important support to the assignment of Y (4274) as anS-wave Ds0(2317)Ds + h.c. molecular state. The important hidden-charm decay mode of the S-wave D0(2400)D +h.c. molecular char-monium is J/ψω, which is the same as in the case of Y (3930)

[3,4].From the published experimental data of the J/ψω invariant

mass spectrum [3,4], we indeed notice an enhancement structurearound 4.2 GeV just below the threshold of the D0(2400)D pair asillustrated in Fig. 4, which is amazingly consistent with our pre-diction of the S-wave D0(2400)D + h.c. molecular charmonium.

We expect further high-statistics measurement from future ex-periments to test our prediction of the S-wave D0(2400)D + h.c.molecular charmonium.

The S-wave Ds0(2317)Ds/D0(2400)D molecular state withspin–parity J P = 0− does not couple to the D D/Ds Ds chan-nels, which is strictly forbidden by the conservation of the parityand angular momentum. In addition, the S-wave Ds0(2317)Ds/

D0(2400)D molecular state may couple to the D∗ D/D∗s Ds and

D∗ D∗/D∗s D∗

s via P-wave, which is expected to be suppressed com-pared to the S-wave mode. Due to the above reasons, the coupled-channel effect on the S-wave Ds0(2317)Ds/D0(2400)D molecularstate may be weak, which is ignored in this work.

As an S-wave Ds0(2317)Ds + h.c. molecular charmonium withJ P = 0− , the decay modes of Y (4274) include the hidden-charmdecay mode J/ψ φ observed by CDF [1], the two-body P-waveopen-charm decays Ds D∗

s + h.c. and D∗s D∗

s , the radiative decayD∗

s Dsγ + h.c., and the iso-spin violating three-body strong decay

Ds Dsπ0 via the η–π0 mixing mechanism [2,3]. Similarly Y uu/dd

can decay into J/ψ ω, D D∗ + h.c., D∗ D∗ , D Dπ , D∗ Dγ + h.c. etc.After figuring out the underlying structure of Y (4274) and pre-

dicting its molecular cousin, we notice that there exist two eventclusters around the ranges of �M ∼ 1.27 GeV and 1.4 < �M <

1.5 GeV marked by yellow and pink in Fig. 1, if we focus on theremaining CDF’s data corresponding to �M > 1.24 GeV. If thesetwo event clusters are confirmed by future experiments, we mightalso try to understand them under the same framework of themolecular charmonium. Basing on the present low-statistic data[1], we speculate that the structure appearing at �M ∼ 1.27 is re-lated to the Ds D ′

s1(2460) or D∗s Ds0(2317) system. The other one in

the range 1.4 < �M < 1.5 GeV may result from the Ds Ds1(2536),Ds Ds2(2573), D∗

s D ′s1(2460) and D∗

s Ds1(2536) systems since theevent cluster in the range 1.4 < �M < 1.5 GeV just overlaps withthe corresponding thresholds (see Fig. 1 for more details). Onemay recall the similar situation before finding the evidence ofY (4274) by CDF [1]. The CDF’s data with an integrated luminos-ity of 2.7 fb−1 reported in Ref. [2] only displayed the event clusterat 4.27 GeV besides the evidence of Y (4140). Confirming the abovespeculation by further experimental study of J/ψφ invariant massspectrum from B decay will not only test the molecular charmo-nium assignments of Y (4140) and Y (4274), but also improve ourunderstanding of the line shapes appearing at hidden-charm in-variant mass spectra.

In summary, the newly observed structure Y (4274) in theJ/ψφ invariant mass spectrum is first interpreted as the S-wave Ds Ds0(2317) + h.c. molecular charmonium well from thedynamical study of the system composed of the pseudoscalarand scalar charmed mesons. Furthermore, we predict the S-waveD D0(2400) + h.c. molecular charmonium appearing as the cousinof Y (4274), which is consistent with the enhancement structurearound 4.2 GeV in the J/ψω invariant mass spectrum from B de-cay [2,3]. Thus, the enhancement structures including the presentY (4274), the previous Y (4140) and Y (3930) observed in the J/ψφ

[1,2] and J/ψω [2,3] invariant mass spectra respectively, can beaccommodated well in the uniform framework of the molecularcharmonium. In addition, we find two possible event clusters inthe J/ψφ invariant mass spectrum might related to the molecu-lar charmonia, which can be tested by high-statistic experimentaldata in future experiment.

Acknowledgements

X.L. thanks Dr. Jun He for his help of fitting data. This project issupported by the National Natural Science Foundation of Chinaunder Grants Nos. 10705001, 11035006, 11047606, 10947204,

344 X. Liu et al. / Physics Letters B 699 (2011) 341–344

10625521, 10721063, the Ministry of Science and Technology ofChina (2009CB825200), and the Ministry of Education of China(FANEDD under Grant No. 200924, DPFIHE under Grant No.20090211120029, NCET under Grant No. NCET-10-0442, the Fun-damental Research Funds for the Central Universities under GrantNo. lzujbky-2010-69).

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