Baryonium、
Baryonium
、Hybrid and Glueball
in Charmonium Energy Region
---hadronic
--h d
hadronic
i spectroscopy
Cong
Congg-Feng
gQ
Qiao
Graduate University
Chinese Academy of Sciences
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Contents
z Introduction
I t d ti
z Charmonium
Charmonium--like states-states--the
the experimental
realities
z Charmed
Ch
d Baryonium
B
Baryonium、
i 、Hybrid
H b id and
d Glueball
Gl b ll
z Summary
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I Introduction
I.
z After
Aft the
th discovery
di
off J/ψ
J/ in
i 1974,
1974 the
th
potential model was proposed, which can
d
describe
ib charmonium
h
i
very well,
ll like
lik the
th
Cornell potential
z The success of potential model makes people
believe its legitimacy in describing meson mass
spectrum, especially in heavy sector
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Ch
Charmonium
i
spectroscopy:
t
experimental
i
t l
measurements vs theoretical p
predictions.
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z Many resonant states predicted by
potential model were confirmed by
experiments in the past decades
z Nevertheless, the QCD does not rule out
the existence of soso-called “exotic
exotic”” states,
that is hadronic states other than regular
meson and baryon, like glueball, hybrid,
multiquark
lti
k state,
t t etc.
t
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z B- and Charm
Charm--factories p
provide large
g
dataset for studying the charm and beauty
hadrons, which enables even the study of
exotic states feasible
z Exotic
o states
s a s sstudy
udy may
ay sshed
d light
g on
o the
nature of nonnon-perturbative interaction and
enrich our knowledge of hadron physics
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II. Experiment Realities
Puzzles: we bump into the exotic state era
z The discovery of X(3872) in 2003 exhibit unusual
properties which can’
can’t be explained as conventional
charmonium
h
i
state
t t
z There were many models being proposed for the
interpretation of X, the most popular ones include
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Soon after
S
ft X(3872)
X(3872), a series
i off new hadronic
h d i structures,
t t
like Ys, were observed by different experiment groups
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According to the production mechanism,
the newly found charmoniumcharmonium-like states X
X,
Y, Z can be categorized in four groups:
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These are unexpected states
z These states’
states’ quantum number, mass, and
decay patterns make them unlike the
conventional charmonium states
z Via ISR method, many 1 − − states were
discovered, by this method the final state has
the same quantum number with photon
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z Y(4260), Y(4360), Y(4660), their mass are much
higher than open charm threshold, while decay
patterns are not as same as usual states
z Z(4433) has electric charge, which is obviously
exotic states with hidden charm
z How to understand these unusual structures
b
becomes
a hot
h t topic
t i currently
tl
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III.Charmed Baryonium、
Baryonium、Hybrid
and Glueball
Baryonium
Λ c − Σc
z In
I b
baryonium
i
scheme
h
can be
b taken
k as
basis vector, one can make up four baryonbaryonantibaryon
tib
configuration
fi
ti
z Due to the spin structure of Fermions, many
fine structures exist naturally,
y, then it mayy
explain why there exist so many 1 − − states
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zY(4260)
(
) is treated as loosely
y bound
state of Lamda_c and anti Lamda_c
zImitate the isospin for proton and
neutron,, introducing
g CC-spin
p
QCF，
QCF
，PLB2006
PLB2006，
，JPG2008
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Heavy hadrons properties:
¾ Heavy flavor hadron contains both
heavy
y and light
g q
quark,, so it has
heavy quark symmetry and chiral
y
y
symmetry
¾ In order to deal with baryon anti
anti--
baryon bound state, we employ the
Heavy flavor chiral perturbation
theory
Yan Cheng,
Yan,
Cheng Cheung
Cheung, Lin
Lin, Lin and Yu
Yu, PRD
PRD, 1992
1992, 1993
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¾ Heavy flavor chiral perturbative theory
collecting both heavy and light
properties of quarks in the hadrons,
which extend chiral perturbation
theory to heavy sector
¾ In terms of Heavy flavor chiral
perturbation theory
theory, we make use of
the method of treating NN potential to
extract potential
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L
Lagrangian
i
z In dealing with the light meson system
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z Lagrangian
g
g
containing
g heavy
yq
quarks
hc
Yan,, Cheng,
g, Cheung,
g, Lin,, Lin and Yu,, PRD,, 1992,, 1993
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z Expand the above Lagrangian we obtain what
is relevant to our problem:
− g 4 − ++
L4 =
Σ ∂ μ π + Λ + + H .c
2 fπ
z We may get the two body scattering amplitude,
and then doing the nonnon-relativistic expansion
and spinor reduction
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In terms of heavy quark chrial perturbative
theory, following steps are necessary
1) Compute the scattering amplitude, defined in terms of
the S matrix element
2) Perform the non-relativistic limit and including
form factor
3) Obtain the potential V(r) via the Fourier transform
4) Solving Schrodinger Equation
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C t ib ti to
Contribution
t potential
t ti l
z Due to isospin conservation in strong
interaction,, the potential
p
is generated
g
at
loop level
z In principle all terms at the fourth order
should be included
z The basic diagrams are:
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After a lengthy calculation, one finally obtain the
potential
Chen and QCF, Arxiv: 1102.3487
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The
potential beheaves like
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With the obtained potential, by solving Schrodinger equation
one can readily
dil gett
baryonium
b
i
eigenvalue
i
l off
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The binding energies for
and
systems go like
In all: the heavy baryonium may really exist!
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Charmonium Hybrid
zIn the framework of Q
QCD Sum Rules,,
the twotwo-point correlation function reads
Here, the interpolating current J goes like
QCF, Tang, Hao and Li, arXiv:1012.2614
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The typical diagrams concerned about are
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z After taking the standard QCD Sum
Rule p
procedures,, we obtain:
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In
I the
th end
d we obtain
bt i the
th masses off 1-1-charmonium hybrid and bottomium hybrid, as:
zThe
Th above
b
theoretical
h
i l predictions
di i
may
confront to the experimental data now
or later
l
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Glueball
zIn recent years,
years BESII and III observe
hadronic structures around proton
proton-proton threshold
threshold, like X(1835),
X(1835) X(1859),
X(1859)
X(2120) and X(2370)
zPossibly, the X(1859) is a proton
proton--proton
bound state
state, or a glueball,
glueball or a mixture
of exotic state with other regular states
Hao QCF and Zhang,
Hao,
Zhang Phys.Lett.B642:53,2006
Phys Lett B642:53 2006
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zWe calculate the mass of 0^0^-+ tripletriple-
gluon state in the framework of Sum
g
Rules
zThe mass lying between 1.9 to 2.7 GeV,
which is in the energy
gy region
g
of BES
newly found structures
zOur calculation favors the baryoniumbaryonium-
glueball mixing
g
gp
picture for BES
observation
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zIn the framework of QCD Sum Rules,
the twotwo-point correlation function reads
Here, the interpolating current J goes like
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The typical diagrams concerned about are
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zAfter taking the standard QCD Sum Rule
procedures, we obtain the mass of triple
gluon glueball is about 2 GeV
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IV Summary
IV.
S
z Our calculation in heavy baryon chiral theory favors
the existence of heavy baryonium
z The potential sensitivity on coupling constants and
energy cutoff in our calculation looks unnatural and
asks for further investigations
z One should also investigate the potential while two
b
baryonbaryon
-like
lik triquark
ti
k clusters
l t
carrry colors
l
z The tough and confusing annihilation channel effect
on the heavy baryonium potential should be clarified
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z We recalculate the 1^-1^-- charmonium hybrid in the
framework of QCD Sum Rules
z The trigluon condensate contribution is taken into
account, and we find it is necessary to attain a stable
h b id mass
hybrid
z The correct interpolate current is employed in our
calculation
z The predicted hybrid mass lying in 4.52GeV, hence
neither of the Y(4260), Y(4360) and Y(4660) states
could be a p
pure hybrid
y
sate
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z We calculated the triple gluon glueball
mass, and found it lies in the region of
BES recently observed structures
z The relation between glueball, hybrid
and
d baryonium
b
i
with
ith the
th exotic
ti
structures observed in experiment
d
deserves
more investigations
i
i i
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Thank for your attention!
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