Non-strange partner of strangeonium-like state Y(2175)

Abstract

Inspired by the observed Y(2175) state, we predict its non-strange partner
Y(1915), which has a resonance structure with mass around 1915 MeV and width
about $317\sim 354$ MeV. Experimental search for Y(1915) is proposed by
analyzing the $\omega f_0(980)$ or $\omega \pi\pi$ invariant mass spectrum of
the $e^+e^-\to \omega f_0(980), \omega \pi\pi$ and $J/\psi\to \eta \omega
f_0(980)$ processes, which are accessible at Belle, BaBar, BESIII and
forthcoming BelleII. Considering similarity between two families, the
comparison of the mass spectra of $\omega$ and $\phi$ families can provide
important information on the 1D state of $\phi$ family, $\phi(1910)$, which has
a very broad resonance structure with mass around 1910 MeV regarded as the
strangeonium partner of $\omega(1650)$. This also answers the question why the
1D state $\phi(1910)$ is still missing in experiment. This is supported by our
former study on the properties of Y(2175), which explains Y(2175) as the 2D
strangeonium because our theoretical total width is comparable with the Belle
data.

Full text

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arXiv:1202.4139v1 [hep-ph] 19 Feb 2012
Non-strange partner of strangeonium-like state Y(2175)
Xiao Wang1,2, Zhi-Feng Sun1,2, Dian-Yong Chen1,3, Xiang Liu1,2∗,†and Takayuki Matsuki4
1Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS, Lanzhou 730000, China
2School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
3Nuclear Theory Group, Institute of Modern Physics of CAS, Lanzhou 730000, China
4Tokyo Kasei University, 1-18-1 Kaga, Itabashi, Tokyo 173-8602, Japan
(Dated: February 21, 2012)
Inspired by the observed Y(2175) state, we predict its non-strange partner Y(1915), which has a resonance
structure with mass around 1915 MeV and width about 317 ∼ 354 MeV. Experimental search for Y(1915)
is prpopsed by analyzing the ωf0(980) or ωππ invariant mass spectrum of the e+e−→ ωf0(980),ωππ and
J/ψ → ηωf0(980) processes, whichareaccessible at Belle, BaBar, BESIIIand forthcoming BelleII.Considering
similarity between two families, the comparison of the mass spectra of ω and φ families can provide important
information on the 1D state of φ family, φ(1910), which has a very broad resonance structure with mass around
1910 MeV regarded as the strangeonium partner of ω(1650). This also answers the question why the 1D state
φ(1910) is still missing in experiment. This is supported by our former study on the properties of Y(2175),
which explains Y(2175) as the 2D strangeonium because our thoretical total width is comparable with the Belle
data.
PACS numbers: 13.25.Jx, 12.38.Lg
The BaBar Collaboration first reported the observa-
tion of strangeonium-like state Y(2175) in e+e−
φ(1020)f0(980) [1], which was later confirmed by BESII in
J/ψ → ηφ(1020)f0(980) [2] and by Belle in the e+e−→
φ(1020)f0(980),φ(1020)π+π−processes [3]. As the only one
XYZ state with light flavor, Y(2175) has stimulated theorists
to consider various theoretical explanations (see Refs. [4–11]
in more details).
What is more important on the observation of Y(2175) is
that Y(2175), combined with the observed Y(4260) [12] and
Υ(10860) [13], forms a complete series of flavors [14], which
is mainlydueto the similarity amongdecay processesof these
particles,
→
e+e−→

Y(2175) →
Y(4260) →
Υ(10860) → Υ(1S,2S)π+π−bottom
A natural deduction from Eq. (1) is that there must exist
a non-strange counterpart of Y(2175), which can decay into
ω(782)π+π−. However, until now such a non-strange partner
of Y(2175) is still missing in experiment. Thus, the study of
the non-strange partner of Y(2175) can not only provide valu-
able information on further experimental search, but will also
be helpfulto reveal the underlyingphysics ofY(2175). It is no
doubt that this is an intriguing and important research topic.
Spectroscopy: If comparing the mass spectra of ω and φ
meson families just shown in Fig. 1, one notices that the mass
gap of ω(782) and ω(1420) is similar to that of φ(1020) and
φ(1680),where ω(782)/φ(1020)and ω(1420)/φ(1680)are 1S
and 2S states, respectively. In addition, the mass difference
between ω(782) and φ(1020) (∼ 240 MeV) is only 20 MeV
smaller than that betweenω(1420)and φ(1680)(∼ 260MeV).
φ(1020)π+π−
J/ψπ+π−
strange
charm
.
(1)
∗Corresponding author
These phenomena reflect the similar dynamics describing ω
and φ meson families. Thus, the study of ω and φ meson
families canbe borrowedfromeach other,whichenablesus to
estimate masses of the missing states in these meson families.
Among these observed states in ω meson family, ω(1650)
is a good candidate for 1D state [15], while the correspond-
ing partner of ω(1650) is missing in φ family. The mass gap
between ω(1650) and ω(1420) (∼ 230 MeV) can be applied
to estimate the mass of 1D state in φ family, which is around
1910 MeV corresponding to our predicted φ(1910) in Fig. 1.
FIG. 1: (Color online.) Comparison of isoscalar light vector mesons.
Besides these well established ω(782), ω(1420), ω(1650), φ(1020),
and φ(1680), the newly observed strangeonium-like state Y(2175)
with two predicted states Y(1915) and φ(1910) are also listed here.
Adopting the same discussion as above, we can naturally
estimate themass ofthe non-strangepartnerof Y(2175). If the
mass difference between the non-strange partner of Y(2175)

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and ω(1420) is the same as that between Y(2175)and φ(1680)
(∼ 495 MeV), the mass of the non-strange partner of Y(2175)
should be close to 1915 MeV, which corresponds to Y(1915)
listed in Fig. 1. The above estimate is based on the conven-
tional quarkonium explanation for Y(2175).
In addition, the quantitative analysis of the Regge trajec-
tories seems to support these mass assignments, which is de-
rived from the IG(JPC) = 0−(1−−) trajectory on the (n, M2)
plane with the relation M2= M2
M0, n, and µ2are the ground state mass, the radial quan-
tum number,and the slope parameter of the trajectory, respec-
tively. The analysis of the Regge trajectories further indicates
that Y(2175) should be a 2D strangeonium while 3S assign-
ment can be excluded. Thus, its non-strange partner Y(1915)
is a 2D state in the ω meson family. The above analysis re-
quires µ2= 1.29 GeV2consistent with the range given in Ref.
[17]. Exclusion of 3S assignment to Y(2175) is supported by
Ref. [18] since the predicted width, around 380 MeV, for 3S
vector strangeonium is far away from the measured width of
Y(2175) [1–3].
Decay: As the non-strange partner of Y(2175), Y(1915)
mainly decays into meson pairs. Thus, studyingthe strongde-
cay of Y(1915) can provide valuable information on its total
width and partial decay widths, which will be helpful in fur-
ther experimental search for Y(1915). Of course, we can eas-
ily extend the same framework to calculate the strong decay
of its strange partnerY(2175),which can test the 2D strangeo-
nium assignment to Y(2175). Besides estimating the mass of
φ(1910), in this letter we also calculate the strong decay of
φ(1910). This study will answer the question why φ(1910) is
still missing in present experiment and how to search for it
in future experiment. In addition, we also present the results
of φ(1680), ω(1420) and ω(1650) decays, which can test the
reliability of the phenomenologicalmodel of strong decay.
We adopt the quark pair creation (QPC) model [19–21]
to calculate the Okubo-Zweig-Iizuka allowed strong decays
of the states discussed above. For process A(q(1)¯ q(2)) →
B(q(1)¯ q(3))+C(q(4)¯ q(2)), the transition matrix element reads
as ?BC|TQPC|A? = δ3(KB+ KC)MMJAMJBMJC(K). By the
transition operator depicting the quark pair created from the
vacuum
0+ (n − 1)µ2[16, 17], where
TQPC = −3γ
?
m
?1 m;1 − m|0 0?
?
dk3dk4δ3(k3+ k4)
×Y1m
?k3− k4
2
?
χ34
1,−mϕ34
0ω34
0d†
3i(k3) b†
4j(k4),
we can deduce the concrete expressions of MMJAMJBMJC(K).
In the definition of TQPC, subscripts i and j are the SU(3)
color indices of the created quark and anti-quark from the
vacuum. χ34
|k|ℓYℓm(θk,φk) is the ℓth solid harmonic polynomial. ϕ34
(u¯ u + d¯d + s¯ s)/√3 and ω34
flavorandcolorsinglets, respectively. Dimensionlessconstant
γ = 8.68 is the strength of the quark pair creation from the
vacuum, which is determined by fitting the experimentaldata.
1,−mdenotes a triplet state of spin. Yℓm(k) ≡
0= δα3α4/√3(α = 1,2,3) means
0
=
The strength of s¯ s creation satisfies γs= γ/√3 [20]. By the
relation [23]
√2L + 1
2JA+ 1
MJB,MJC
×?JBMJBJCMJC|JMJA?MMJAMJBMJC(K),
we obtain the partial wave amplitude MJL(A → BC), where
J = JB+JCandJA+JP= JB+JC+L. Thus,thedecaywidth
is expressed as Γ = π2|K|?
three momentum of meson B or C in the center of mass frame
of meson A. MAdenotes the mass of meson A. In calculat-
ing the spatial integral of the decay amplitude, the harmonic
oscillator (HO) wave function Ψnrℓm(k) = Rnrℓ(R,k)Ynrℓm(k)
is adopted to describe the meson wave function involved in
the decays, where parameter R in the HO wave function is ob-
tained by reproducingthe realistic root mean square radius by
solving the Schr¨ odinger equation with the effective potential
[26].
In Fig. 2, we show the total and partial decay widths of
the predicted Y(1915) dependent on R. Its total decay width
can reach up to 317 ∼ 354 MeV corresponding to the range
R = 3.5 ∼ 4.5 GeV−1, which make the experimental search
for Y(1915)become possible, where its main decay modes in-
clude ρa0(980), b1(1235)π, ρ(1450)π, ρπ, f0(980)ω and KK
(see the left diagram of Fig. 2 in more details). Just because
Y(1915) is predicted as the non-strange partner of Y(2175),
thus a realistic experimental study of Y(1915) can be via the
e+e−→ f0(980)ω or e+e−→ f0(980)ππ process, which
is supported by our calculation, where the decay width of
Y(1915) → f0(980)ω is around 5.86 ∼ 16.22 MeV. Besides
directly producing Y(1915) by the e+e−collision, the BESIII
experiment can be as an ideal platform to search for Y(1915),
i.e., the study of the f0(980)ω invariant mass spectrum of the
J/ψ → ηf0(980)ω decay. Additionally, we also find several
partial decay width ratios
MJL(A → BC) =
?
?L0JMJA|JAMJA?
J,L|MJL|2/M2
A, where |K| is the
Γ(b1(1235)π)
Γ(ρ(1450)π)≈ 1.3 ∼ 3.5,Γ(b1(1235)π)
Γ(a0(980)ρ)
Γ(f0(980)ω)≈ 9 ∼ 19,
which are not too dependent on the variation of R value. To
some extent, these ratios can be served as the further experi-
mental test to the predicted Y(1915).
For ω(1650), the calculated total decay width when tak-
ing R = 3.5 ∼ 4.5 GeV−1is overlap with the result given
by Achasov et al. in Ref. [25] if considering the experimen-
tal error. Checking the data of ω(1650) listed in Particle Data
Group(PDG) indicates that different experimentsgave the ex-
perimental widths different from with each other. Our calcu-
lation partly supports the measurement result of ω(1650) in
Ref. [25], where ω(1650) is a state with broad width. The
ω(1650) results presented in Fig. 2 also show that b1(1235)π
is its dominantdecay channel, which almost contributes to the
total width of ω(1650). In addition, its main decay modes in-
clude ρπ, ωη, KK and K∗K, where ω(1650) decays into ρπ
Γ(a0(980)ρ)
≈ 0.6 ∼ 1.7,

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3
and ωη were seen in experiments [24]. Thus, the results in
Fig. 2 also support ω(1650) as a 1D ω state. Furthermore,
our study of ω(1650) raises one issue: further experimental
measurement of the resonance parameter for ω(1650) will be
helpful to clarify the present mess of total width of ω(1650),
where we are inclined to ω(1650) as a broad state according
to our investigation, which can be tested by future experi-
ment. Here, we also listed some partial decay width ratios,
which do not strongly depend on the model parameters, i.e.,
Γ(b1(1235)π)/Γ(ρπ) ≈ 5.9 ∼ 8.8, Γ(ρπ)/Γ(ωη) ≈ 2.9 ∼ 3.9,
Γ(ρπ)/Γ(KK∗) ≈ 7.1 ∼ 9.3, Γ(b1(1235)π)/Γ(KK∗) ≈ 55.0 ∼
62.3, Γ(ωη)/Γ(KK∗) ≈ 2.3 ∼ 2.4, Γ(KK∗)/Γ(KK) ≈ 0.7 ∼
1.2 and Γ(ρπ)/Γ(KK) ≈ 6.4 ∼ 8.5.
3.5 3.75
R (GeV−1)
4 4.25 4.5
10
−4
10
−2
10
0


K*K
K*(1410)K
K1(1400)K
η′(958)ω
K K
ω η
0
5
10
15
20
25


K1(1270)K
h1(1170)η
f0(980)ω
ρπ
0
100
200
300
400
Y(1915)


Total Width
b1(1235)π
ρ(1450)π
ρ a0(980)
3.53.75
R (GeV−1)
4 4.25 4.5
0
0.2
0.4
0.6
0.8
5
10
15
20
25
30
100
200
300
400
500
600
700
800
RVUE Data
ω(1650)
3.5 3.75
R (GeV−1)
44.25 4.5
0
0.5
1
0
5
10
15


0
50
100
150
200
BaBar Data
ω(1420)
FIG. 2: (Color online.) The total (black solid line) and partial decay
widths of Y(1915), ω(1650) and ω(1420) and the comparison with
the experimental data (red dashed line with yellow band).
There exist five decay channels open for ω(1420) listed in
Fig. 2. Among these decay channels, ρπ, b1(1235)π, ωη and
KK are its maindecaychannelsthoughthese decaywidths are
dependentonparameterR. AsindicatedinPDG,ρπchannelis
the dominant decay channel for ω(1420), which is confirmed
by our calculation. Besides, b1(1235)π was seen in experi-
ment, which is also supported by our result. When compar-
ing the total width with the experimental data (see Fig. 2),
we find that our result is comparable with the BaBar recent
data, where the measured width of ω(1420) is 130± 50± 100
MeV by analyzing the e+e−→ ωπ−π−γ process [27]. Thus,
ω(1420) as 2S state is further confirmed by our phenomeno-
logical study.
In the following, we illustrate the decay behavior of
φ(1910). At present, vector strangeonium with 1D is still ab-
sent in experiment. If the predicted φ(1910) is the candidate
for such a 1D state, our calculation indicates that φ(1910)
is a very broad state with total width around 822 ∼ 1047
MeV just shown in Fig. 3.
finding very broad structure in experiment, it naturally ex-
plains why the present experiment has not observed any ev-
idence of vector strangeonium with 1D quantum number. If
one experimentally searches φ(1910), the result presented in
Fig. 3 shows that φ(1910) mainly decays into K1(1270)K,
K∗K, K∗K∗, KK and ηφ(1020), where K1(1270)K channel is
the dominant decay of φ(1910) since the branching ratio of
φ(1910) → K1(1270)K can reach up to (79 ∼ 84)%. Apart
fromthetotalwidthinformationofφ(1910),wealsofindsome
φ(1910)partial decay widthratios, i.e., Γ(K1(1270)K)/Γtotal≈
0.66 ∼ 0.85, Γ(KK∗)/Γ(KK) ≈ 0.8 ∼ 2.6, Γ(K∗K∗)/Γ(ηφ) ≈
2.54 ∼ 5.71 and Γ(K1(1270)K)/Γ(KK∗) ≈ 5.32 ∼ 16.27,
which are stable in the rangeof R discussed here. These infor-
mation is also valuable for further experimental investigation
of φ(1910).
Because of the difficulty of
700
100
800
900
1000
1100
φ(1910)
10
20
30
40
50
60
70
80
90
3.53.75
R (GeV−1)
44.254.5
10
−6
10
−4
10
−2
10
0
150
70
200
250
300
350
Belle Data
Y(2175)


Total Width
K* K
K*(1410) K
K* K*
K K
K1(1270) K
K1(1270) K*
f0(980)φ(1020)
η φ(1020)
10
20
30
40
50
60


3.53.75
R (GeV−1)
44.25 4.5
10
−4
10
−2
10
0


K1(1400) K
h1(1170) η
h1(1170) η′
h1(1170) f0(980)
K*
2(1430) K
η′(958) φ(1020)
33.25
R (GeV−1)
3.53.754
0
50
100
150
200
PDG Data
φ(1680)
FIG.3: (Color online.) Thetotal and partial decay widthsof φ(1910),
Y(2175) and φ(1680) as strangeonia with 1D, 2D and 2S quantum
numbers, respectively.
As a test of the QPC model, one can see that the result

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4
of φ(1680) is consistent with the existing experimental mea-
surement. Calculation of φ(1680) → K∗K confirms K∗K as
the dominant decay channel of φ(1680) given by experiment
[24]. In addition, when taking R = 3.4 GeV−1, the calcu-
lated Γ(KK)/Γ(K∗K) = 0.07 is in agreement with experimen-
tal valuelisted in PDG while the correspondingtotal widthare
93 MeV, which is close to the lower limit of the PDG data (see
Fig. 3 in more details).
For clarifying whether the observed Y(2175) can be ex-
plained as the conventional strangeonium, we also calculate
the total and partial widths of Y(2175) with the assignment of
2D vector strangeonium. We can find the overlap of theoreti-
cal and Belle results in the range of R = 3.94 ∼ 4.84 GeV−1,
which is consistent with the estimate of R value for 2D s¯ s
states [26]. However, the calculated total width is far larger
than the width measured by BaBar [1] and BES [2]. If adopt-
ing the Belle measurement, we can conclude that it is reason-
able to explain Y(2175) as a 2D state in φ family. Of course,
the measurement of its resonance parameter will be helpful to
furthertest this assignment to Y(2175). In Fig. 3, we also give
the main decay modes of Y(2175), which can provide impor-
tant information to experimental search for Y(2175) through
its other decays, where ratios Γ(K1(1270)K)/Γ(KK) ≈ 1.5 ∼
2.3 and Γ(K∗K∗)/Γtotal ≈ 0.1 ∼ 0.6 weakly depend on the
model parameter.
Insummary,thesimilarity betweenthe φ andω families en-
ables the study of these meson families to be borrowed from
each other. Stimulated by the observation of strangeonium-
like state Y(2175), we first predict its non-strange partner
Y(1915) by the mass spectrum analysis, where Y(1915) with
other states listed in Eq. (1) seems to form a complete series
of flavors. The study of Y(1915) decay behavior indicates that
Y(1915) is a broad state with width around 317 ∼ 354 MeV.
Considering its main decay modes, we further propose that
e+e−→ f0(980)ω, f0(980)ππ or J/ψ → ηf0(980)ω can be as
the realistic process of searching for the predicted Y(1915).
Besides the prediction of Y(1915), we also obtain the infor-
mation on 1D state in the φ family by the comparison of mass
spectraof φandω families. Ourstudyshows thatthis 1D state
is a very broad resonance structure with mass of about 1910
MeV, which naturally explains why the present experiment
have not foundany evidence of this state since it is not easy to
identify broad structure in experiment. As the strange partner
of the predicted Y(1915), Y(2175) could be explained as a 1D
strangeonium. The phenomenological study presented in this
letter is not only helpful to reveal the underlying properties of
these light hadrons, but also will serve further experimental
investigation.
Acknowledgement X.L. would like to thank Dr.
Ping Shen for useful discussion of the Belle measure-
ment. This project is supported by the National Natural
Science Foundation of China under Grant Nos. 11175073,
11005129, 11035006, the Ministry of Education of China
(FANEDD under Grant No. 200924, DPFIHE under Grant
No.20090211120029, NCET, the Fundamental Research
Cheng-
Funds for the Central Universities), and the West Doctoral
Project of Chinese Academy of Sciences.
†Electronic address: xiangliu@lzu.edu.cn
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