We demonstrate that the experimental information currently available for the
Y(4660) is consistent with its being a f_0(980)psi' molecule. Possible
experimental tests of our hypothesis are presented.Comment: 4 pages, 3 figure

Achasov

Ambrosino

Aubert

Barnes

Baru

Braaten

Brodsky

Browder

Bugg

Christoph Hanhart

Close

Ding

Dong

Faessler

Feng-Kun Guo

Gamermann

Godfrey

Hanhart

Hofmann

Kalashnikova

Klempt

Maiani

Mori

Olsen

Pakhlova

Qiao

Rosner

Swanson

Törnqvist

Ulf-G. Meißner

van Beveren

Voloshin

Wang

Weinberg

Yuan

Physics Letters B

English

arXiv

We demonstrate that the experimental information currently available for the Y(4660) is consistent with its being an f(0)(980)psi' molecule. Possible experimental tests of our hypothesis are presented. (C) 2008 Elsevier B.V. All rights reserved

Guo, F.-K.

Hanhart, Chr.

Meissner, U.G.

Juelich Shared Electronic Resources

Evidence that the Y(4660) is a f(0)(980)psi-prime bound state

Crossref

Evidence that the <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>Y</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>4660</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> is an <mml:math altimg="si2.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mi>f</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>980</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:msup><mml:mi>ψ</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:math> bound state

AbstractWe demonstrate that the experimental information currently available for the Y(4660) is consistent with its being an f0(980)ψ′ molecule. Possible experimental tests of our hypothesis are presented

Guo, Feng-Kun

Hanhart, Christoph

Meißner, Ulf-G.

Elsevier - Publisher Connector 

Physics Letters B 665 (2008) 26–29Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Evidence that the Y (4660) is an f0(980)ψ ′ bound state
Feng-Kun Guo a,∗, Christoph Hanhart a, Ulf-G. Meißner a,b
a Institut für Kernphysik, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
b Helmholtz-Institut für Strahlen- und Kernphysik, Universität Bonn, 53115 Bonn, Germany
a r t i c l e i n f o a b s t r a c t
Article history:
Received 14 May 2008
Accepted 21 May 2008
Available online 29 May 2008
Editor: G.F. Giudice
PACS:
14.40.Gx
13.25.Gv
We demonstrate that the experimental information currently available for the Y (4660) is consistent with
its being an f0(980)ψ ′ molecule. Possible experimental tests of our hypothesis are presented.
© 2008 Elsevier B.V. Open access under CC BY license.1. In recent years a large number of new hidden and open
charm states were discovered experimentally above the ﬁrst in-
elastic thresholds. For most of them the masses have in common
that they deviate signiﬁcantly from the predictions of the quark
model [1]—which on the other hand works very well below the
thresholds—and are positioned very close to an s-channel thresh-
old [2]. For recent reviews see, e.g., Ref. [3].
The proximity of the thresholds initiated a lot of theoreti-
cal studies, in order to reveal a possible molecular structure of
those states. E.g., in Ref. [4] the Ds(2317), located just below the
K D-threshold, was studied within the molecular model and the
X(3872), located right at the D¯D∗ threshold, was investigated in
Ref. [5]. However, so far no consensus exists on the true nature of
those states and, e.g., four-quark interpretations [6] and even con-
ventional q¯q states are still under discussion [7].
In Ref. [8] it was argued that there is a way to model indepen-
dently identify hadronic molecules in the spectrum. The method is
based on a time-honored analysis by Weinberg [9] and applies, if
the pole is very close to the threshold of the constituent particles
that form the bound state in an s-wave. The method relates the
effective coupling constant of the bound state to its constituents,
g , directly to the molecular admixture of the state. Especially, one
may write for a pure molecule
g2
4π
= (m1 +m2)
5/2
(m1m2)1/2
√
32, (1)
where m1 and m2 denote the masses of the constituents and  the
binding energy.
* Corresponding author.
E-mail addresses: f.k.guo@fz-juelich.de (F.-K. Guo), c.hanhart@fz-juelich.de
(C. Hanhart), meissner@itkp.uni-bonn.de (Ulf-G. Meißner).0370-2693 © 2008 Elsevier B.V.
doi:10.1016/j.physletb.2008.05.057
Open access under CC BY license.In this Letter we discuss the nature of the Y (4660) as a
candidate for an f0(980)ψ ′ bound state. So far the Y (4660)
was seen only in the π+π−ψ ′ invariant mass distribution in
e+e− → γI S Rπ+π−ψ ′ with a mass of 4664 ± 11 ± 5 MeV and
a width of 48 ± 15 ± 3 MeV [10]. Such a structure was neither
observed in e+e− → γI S Rπ+π− J/ψ [11], nor in the exclusive
e+e− → DD¯, DD¯∗, D∗ D¯∗, DD¯π cross sections [12], nor in the
process e+e− → J/ψD(∗) D¯(∗) [13]. These facts would severely
challenge any attempt explaining the state as a canonical cc¯ char-
monium, e.g. 53S1 as in Ref. [14]. The Y (4660) is suggested to
be a baryonium state in Ref. [15]. The diﬃculties in the canon-
ical charmonium interpretation could be explained naturally, if
the Y (4660) were an f0(980)ψ ′ bound state, because it would
decay dominantly via the decay of the f0(980), i.e. Y (4660) →
ψ ′ f0(980) → ψ ′[ππ ] and Y (4660) → ψ ′ f0(980) → ψ ′[K K¯ ]. The
nominal threshold of the f0(980)–ψ ′ system is at 4666 ± 10 MeV
if we take the PDG value of the f0(980) mass [16]. Note that the
interaction between a heavy quarkonium and a light hadron is ex-
pected to be dominated by the QCD van der Waals interaction
which is attractive [17].
In the ππ invariant mass a clear f0(980) peak is visible.
Clearly, if the Y (4660) were a conventional f0ψ ′ bound state, it
could not decay to this channel. This is possible only because of
the ﬁnite width of the f0(980), mainly due to its decay to the
ππ channel. We will perform our analysis based on the following
reasoning: if the f0 were a stable particle, also the Y (4660) were
stable. Then we could calculate the effective coupling constant of Y
to ψ ′ f0 using Eq. (1). The central assumption is that this coupling
constant does not change as the two pion channel is switched
on—a similar ansatz leads to a successful phenomenology for the
f0(980) treated as a K¯ K molecule [18]. Under this assumption we
can predict not only the prominent component of the width of the
Y (4660) but also its spectral shape using the mass and the over
all normalization as the only input. As additional non-trivial result
F.-K. Guo et al. / Physics Letters B 665 (2008) 26–29 27Fig. 1. Diagram illustrating the most prominent decay channels of the Y (4660) in
the molecular model. The solid black dot denotes the Y f0ψ ′ vertex, whose strength
parameter g is ﬁxed within the molecular model through Eq. (1). The decay vertices
for f0, shown as open circle, are ﬁxed from other data.
we can also predict the strength and the shape of the decay to K¯ K
and γ γ . The possible decay chains are illustrated in Fig. 1. As we
will see, the resulting spectra are in excellent agreement with the
existing data. We interpret this as a strong support in favor of a
molecular interpretation for the Y (4660).
2. The Y (4660) was observed as a structure in the ψ ′ππ in-
variant mass distribution. In addition, in Ref. [10], also the ππ
invariant mass distribution is presented, which was found after
applying an appropriate cut to the ψ ′ππ invariant mass. Both dis-
tributions can be derived from the same differential rate, under
the assumption that the pion pair stems from the decay of an f0.
One gets
d2W(e+e−→ψ ′π+π−)
dM2 dm2ππ
= N∣∣GY (M)∣∣2 dΓ
[π+π−]
Y
dm2ππ
, (2)
where GY (M) denotes the physical Y -propagator, to be speciﬁed
below and N is a normalization constant, which contains, besides
the electron–photon vertex and the photon propagator, both in-
deed constant to very high accuracy in the range of M of relevance
here, also the detector acceptance. The decay Y → ψ ′π+π− is de-
scribed by
dΓ [π
+π−]
Y
dm2ππ
= g
2
8π
θ(M − Mψ ′ππ ) pM2 ρ
[π+π−]
f0
. (3)
Here p denotes the c.m.s. momentum of the ψ ′ for given values
of the ππ invariant mass, mππ , and the ψ ′ππ invariant mass, M ,
and Mψ ′ππ =mππ + Mψ ′ . The effective coupling constant g is not
a free parameter, but can be determined for any given value of the
mass of the Y from Eq. (1). The quantity ρ[π
+π−]
f0
(mππ ) denotes
the π+π− fraction of the f0 spectral function. It is normalized
according to
∫
dm2ππ ρ
[π+π−]
f0
(mππ ) = Γ [π+π−]f0 /Γ totf0 .
With this normalization Eq. (3) goes to the standard expression for
a two particle decay in the stable particle limit for the f0.
A high quality data set for the f0 was collected recently by
KLOE [19] based on the reaction φ → γππ . The data was analyzed
using the so-called kaon loop model [20] and provided parameters
for the f0 with very little uncertainty. To be concrete, we use
ρ[π
+π−]
f0
(m) = 1
π
Im(Ππ
+π−
f0
(m))
|m2 −m2f0 +
∑
ab Πˆ
ab
f0
(m)|2 , (4)
where the Πˆabf0 (m) = Πabf0 (m) − Re(Πabf0 (m f0)) denote the renor-
malized self-energies of the f0 with respect to the channel ab.Analytic expressions are given in Ref. [20].1 The input parame-
ters are taken from the ﬁts provided in Ref. [19]. To be concrete,
for all the curves shown below we used the central values of
the various parameters of ﬁt K2 shown in Table 4 of that refer-
ence, thus we used m f0 = 0.9862 GeV, g f0K+K− = 3.87 GeV, and
g f0π+π− = −2.03 GeV, while the couplings for the neutral chan-
nels were ﬁxed using the isospin relations. We checked that the
other parameter sets give very similar results to the ones discussed
in detail below.
The only missing piece is the physical Y propagator. In Eq. (3)
an explicit expression is given for the partial width to ψ ′π+π− .
However, in order to derive the physical propagator, all relevant
decay channels need to be included. Within our model we assume
that the Y decays predominantly through the f0, thus a consistent
treatment requires that all decay channels of the f0 also contribute
to the width of the Y and thus to the propagator. It is straight-
forward to extend Eq. (3) also to the π0π0 channel as well as to
the kaon channels without any additional free parameters—also for
these channels we use the results of the ﬁt to the KLOE data pre-
sented in Ref. [19]. Thus we get for the total width of the Y at a
given value of M , under the assumption that it is saturated by the
ψ ′ f0 decay
Γ totY
(
M2
)=∑
ab
θ
(
M − Mψ ′ −
√
sabthr
)
×
(M−Mψ ′ )2∫
sabthr
dm2ab
dΓ [ab]Y (M,mab)
dm2ab
, (5)
where sabthr = (ma +mb)2. In order to get a Y propagator with the
correct analytical properties we need to continue the contribution
from the K¯ Kψ ′ channel also to below its threshold. For this we
use a dispersion integral, which gives us an expression for the Y
self-energy, ΠY (M), for arbitrary values of M
ΠY (M) = 1
π
∞∫
M2thr
ds
MYΓ totY (s)
s − M2 − i , (6)
where Mthr = Mψ ′ + 2mπ denotes the lowest physical threshold
of relevance here. Note, this treatment is completely consistent to
what was done for the f0—one way to derive the self-energies
Πabf0
(m) given above is through a dispersion integral with the two-
body phase space as input. With the self-energies at hand we may
now give the expression for the physical propagator of the Y (4660)
GY (M) = 1
M2 − M2Y + ΠˆY (M)
, (7)
where, as above, we deﬁned ΠˆY (M) = ΠY (M) − Re(ΠY (MY )).
3. Our model has only 2 free parameters, namely, the mass
of the Y , MY , and the normalization constant, N , introduced in
Eq. (2). We now proceed as follows: the count rate, R , in the
ψ ′π+π− invariant mass spectrum is given by
R(M)=
M−Mψ ′∫
4m2π
dm2ππ
d2W(e+e− → ψ ′π+π−)
dM2 dm2ππ
, (8)
using the expression for the differential rate W of Eq. (2). The
range of parameters allowed by the data is then determined from
1 We only include the ππ and the K¯ K channels, for the others give a negligible
contribution.
28 F.-K. Guo et al. / Physics Letters B 665 (2008) 26–29Fig. 2. Comparison of the line shape in the ψ ′π+π− invariant mass distribution
derived from the molecular model with the data. The solid line shows the result of
our best ﬁt, while the shaded area shows the uncertainty that emerges from the ﬁt.
The dashed line shows the best ﬁt result, if also the effective coupling is part of the
ﬁt, as discussed in the ﬁnal section.
a ﬁt to the experimental data for the ψ ′π+π− spectrum—we re-
mind the reader that the coupling constant g is ﬁxed from Eq. (1)
for any given value of MY . We ﬁnd
N = 10± 2 GeV3, MY = 4665+3−5 MeV. (9)
This range of mass values corresponds to a range of g = 11, . . . ,
14 GeV for the effective coupling constant. The best ﬁt is shown
as the solid line in Fig. 2—the uncertainty that emerges from the
ﬁt is reﬂected by the grey band. For the best ﬁt χ2/d.o.f. = 0.5.
The ﬁrst observation is that the resulting invariant mass distribu-
tion visibly deviates from a standard Breit–Wigner shape. This is
a direct consequence of our starting assumption, namely that the
Y (4660) is predominantly composed of an f0 and a ψ ′ , not only
since the mass of the Y is very close to the nominal f0ψ ′ thresh-
old, but also because of the proximity of the kaon channels, which
are very important for the structure of the f0.
Since now all parameters of our model are ﬁxed we can pre-
dict other channels. Recently high quality data was measured for
f0 → γ γ [21]. Within our approach we thus predict that the
shape in the ψ ′γ γ invariant mass is identical to that measured for
ψ ′π+π− , however, down scaled by the relevant ratio of branching
ratios. In addition we can also predict the signals for the spectra
of ππ and K K¯ as they emerge from the decay of the Y . The pre-
dicted rate, Rab(mab), again follows directly from Eq. (2)
Rab(mab) =
(4.9 GeV)2∫
(4.5 GeV)2
dM2
d2W(e+e− → ψ ′ab)
dM2 dm2ab
, (10)
where the limits of integration are chosen identical to the cuts
used to get the experimental rate [10]. The corresponding results
are shown in Fig. 3. If a signal of the given shape and strength
were found in the ψ ′ K¯ K invariant mass distribution, it would pro-
vide a strong support for the assumed prominent role of f0ψ ′ for
the structure of the Y .
4. To summarize, we calculated the invariant mass spectrum
for ψ ′π+π− as well as the corresponding ππ and K¯ K spectra
in the mass range of the Y (4660) under the assumption that the
Y (4660) is an f0(980)ψ ′ bound state and f0(980)ψ ′ is its only de-
cay channel of relevance. A very good description of both spectra,
where data exist, was achieved. Especially, we ﬁnd a visible devia-
tion from a Breit–Wigner shape for the ψ ′ππ spectrum, consistentFig. 3. Predictions for the ππ and K¯ K invariant mass distributions.
with the data, although data with better statistics would be very
welcome to strengthen this point.
In principle our method also allows one to estimate the possi-
ble contribution of channels other than f0ψ ′ to the width of the
Y (4660). One just needs to add the term iMYΓadd to the denomi-
nator of GY (M), deﬁned in Eq. (7) and repeat the ﬁtting procedure.
With this we get Γadd = (30± 30) MeV—thus, before better data is
available no reliable bound for the possible additional width can
be deduced. However, it is important to observe that the value ex-
tracted from the current data is consistent with zero within the
uncertainty.
We also checked what happens, if we do not ﬁx the effec-
tive coupling g according to Eq. (1), but allow it to ﬂoat as well.
Then we ﬁnd MY = (4672 ± 9) MeV and g = (13 ± 2) GeV with
χ2/d.o.f. = 0.4. The result of the best ﬁt is shown as the dashed
line in Figs. 2 and 3. Thus the effective coupling constant extracted
from this three parameter agrees to that found before, only that
the three parameter ﬁt prefers a larger value of the mass, partially
inconsistent with a molecular picture—for masses at the higher
end the mass of the Y is even larger than Mψ ′ +m f0 . Also here we
need to conclude that more data are needed to draw a more ﬁrm
conclusion—especially we showed that the K¯ K invariant mass dis-
tribution is quite sensitive to the mass of the Y (4660)—cf. lower
panel of Fig. 3. It is in any case important to stress that the ﬁt
calls for a large coupling constant for Y → f0ψ ′ , which is natu-
F.-K. Guo et al. / Physics Letters B 665 (2008) 26–29 29rally explained by the assumption that the Y (4660) is generated
dynamically in the f0ψ ′ channel.
We take our results as a strong evidence for a molecular in-
terpretation of the Y (4660). We stress that a measurement of the
ψ ′ K¯ K channels as well as an improvement of the resolution of the
existing data would allow for non-trivial tests of our hypothesis.
Acknowledgements
We thank N.N. Nikolaev and A. Nogga for useful discussions.
We are very grateful to C.-Z. Yuan for providing us with the ex-
perimental data. This work is partially supported by the Helmholtz
Association through funds provided to the virtual institute “Spin
and strong QCD” (VH-VI-231) and by the EU Integrated Infras-
tructure Initiative Hadron Physics Project under contract number
RII3-CT-2004-506078.
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Evidence that the Y(4660) is an f0(980)ψ′ bound state 