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Resonances and thresholds in charmonium spectra. Yu.S.Kalashnikova, ITEP. Charmonium. Theory: Godfrey-Isgur. M, MeV. ?. 4250. 4000. ?. 3750. DD. 3500. 3250. 3000. 0 -+. 1 --. 0 ++. 1 ++. 2 ++. 1 +-. 2 --. 3 --. 2 -+. 1++(3872). 1--(4260). JPC?(4430). I=1 !?. - PowerPoint PPT Presentation
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Resonances and Resonances and thresholds in thresholds in
charmonium spectracharmonium spectraYu.S.Kalashnikova, ITEP
CharmoniumCharmonium
2
2
4
3
cc
sSS SO T
pH m V
m
V r V V Vr
2Yu.S.Kalashnikova, ITEP
3
3000
3250
3500
3750
4000
4250
0-+ 1-- 0++ 1++ 2++ 1+- 2-- 3-- 2-+
M, MeV
Theory: Godfrey-Isgur
DD
?
??
Yu.S.Kalashnikova, ITEP
1++(3872) 1--(4260)
JPC?(4430)
I=1 !?
4
Weird charmoniaWeird charmoniaand relevant thresholdsand relevant thresholds
Yu.S.Kalashnikova, ITEP 5
X(3872) D0D0* 3872 MeVD+D-* 3879 MeV
Y(4260) DD1 4285 MeV
Y(4325) D*D0 4360 MeV
(4430) D*D1 4430 MeV
Threshold affinity means that the admixture of D-meson pairs in the wavefunction is large
Molecular charmonium
D
D*
uu* vector
D
D*
D*
D
Q exch not enough
exchange drives attraction
1++(3872)
6Yu.S.Kalashnikova, ITEP
S-wave 1- - (1-+ !)
D1
D*
psi
pi
D
D1
D*
D0
pi
Q exch gives cc* + … final statesVerify JPC seek other final states
Other places should occur…
exchange drives attraction
S-wave 0- (I=0 and I=1)also 1- 2-
D*
D1
D1
D*
pi
1--(4260)
JPC?(4460)
I=1 !?
8
DD DD ccc (cc (cccg, cg, cccqqqq))
D
D
D
D
cc
=
+cc
D
D
D
D
DD
D
DD
D
Yu.S.Kalashnikova, ITEP
Coupling to bare state drives attraction
9Yu.S.Kalashnikova, ITEP
Doubling of states in DD Doubling of states in DD c ccc system system
Spectral density w(M) of the cc state
w(M)
M
Difference between bound Difference between bound states of states of quarksquarks and and
hadronshadrons
Yu.S.Kalashnikova, ITEP 10
Hadrons can go on-shell -> non-analyticities
Quark loop
Hadron loop
Polynomial in E
i(E)1/2 + polynomial, E>0
-(-E)1/2 + polynomial, E<0
Should lead to observable Should lead to observable differencedifference
11Yu.S.Kalashnikova, ITEP
The case of XThe case of X
Focus on resonances very close Focus on resonances very close to thresholdto threshold
12
X(3872) X(3872) J/ J/
M(X) = 3871.2 M(X) = 3871.2 0.5 MeV 0.5 MeV
13Yu.S.Kalashnikova, ITEP
X(3875) X(3875) D0D0 D0D000
14Yu.S.Kalashnikova, ITEP
X(3872) X(3872) X(3875) ? X(3875) ?
15
FlattFlattèè analysis analysis
Assumptions:
1++ quantum numbers for the X
X -> D0D*0 -> D0D00 decay chain
J/ and J/ are the main non – DD*
decay modes of the X
Yu.S.Kalashnikova, ITEP
DD* S-waveDD* S-wave
16Yu.S.Kalashnikova, ITEP
Differential Rates:Differential Rates:
0 0 012
2
1 2
( ) 10.62
2
( / ) 1
2
( )2
below j-th threshold
f
j j
gkdBr B KD D
dE D
dBr B K J
dE D
iD E E gk gk
ik
B
B
D0*->D00
B->KX
17Yu.S.Kalashnikova, ITEP
Results (generalities)Results (generalities)
++--J/J/ peak exactly @ D0D0 peak exactly @ D0D0**
peak width 2.3 MeVpeak width 2.3 MeV
D0D0D0D0** coupling is large coupling is large
scaling of Flattè parametersscaling of Flattè parameters
g->g, Ef->Ef, ->, B->B
18
ABelle
a(D0D0*) =(-3.98 –i0.46)
fm
J/
J/
DD
DD
19
X(3872) as a X(3872) as a virtualvirtual state:state:
+-J/ cusp
Large and negative real part of the scattering length (and small imaginary part)
Scaling behaviour of Flattè parameters
Dynamical nature of the X
Yu.S.Kalashnikova, ITEP
20Yu.S.Kalashnikova, ITEP
Why virtual state?Why virtual state?
Br(X -> D0D00)
Br(X -> J/) 9.7 9.7 3.4 3.4
21
Scattering length Scattering length approximation:approximation:
2 21
2 21
0 *01
2 21
2
01 1
1
( / ), 0
( )
( / ), 0
( )
( )
( )
( / )( )
2im
re im
im
re im
im
re im
re im
re re
ai
dBr JE
dE k
dBr JE
dE
kdBr D D
dE k
dBr JE
dE
re>0
22
Bound state is below threshold, and decays only because D*0
has finite width. In the limit of infinitely narrow widththe bound state is stable. As (D*0->D00) 42 keV,
(Xbound -> D0D*00)
In the B-meson decay, together with the bound statecontribution to the rate, there is also continuum contribution. The latter is nonzero even in the narrow-
widthapproximation.
2*42 keV naively
(2-4)*42 keV with FSI interference
Yu.S.Kalashnikova, ITEP
23
In the B-meson decay, the D0D*0 continuum provides the main contribution to D0D00 rate. In the case of the virtual state it is much larger, than for the bound state. So the large ratio
tells that X is a virtual state. It is similar to the virtualstate in the 1S0 nucleon-nucleon scattering rather thanto the deuteron: the system is almost bound.
Yu.S.Kalashnikova, ITEP
Br(B -> KX) Br(X -> DD)
Br(B -> KX) Br(X -> J/)
24
ConclusionsConclusions
The X(3875) can only be related to the The X(3875) can only be related to the X(3872) if we assume the X to be of dynamical X(3872) if we assume the X to be of dynamical originorigin
(molecular charmonium)(molecular charmonium)
However, it is not a bound state, but a virtual However, it is not a bound state, but a virtual oneone
Only much better resolution on Only much better resolution on J/J/ lineshape could confirm or rule out this lineshape could confirm or rule out this
solutionsolution
If the cusp-like lineshape is ruled out, the If the cusp-like lineshape is ruled out, the X(3875) and X(3872) are two different particles X(3875) and X(3872) are two different particles
Yu.S.Kalashnikova, ITEP
25Yu.S.Kalashnikova, ITEP
The EndThe End