Higher Charmonium

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Higher Charmonium
Ted Barnes Physics Div. ORNL Dept. of Physics,
U.Tenn. GHP2004 Fermilab, 24-26 Oct. 2004

1. Spectrum
2. Strong decays (main topic)
3. Loops

abstracted from T.Barnes, S.Godfrey and
E.S.Swanson, in prep.
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1. Spectrum
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• Charmonium (cc)
• A nice example of a QQ spectrum.
• Expt. states (blue) are shown with the usual L
  classification.

Above 3.73 GeV Open charm strong decays (DD, DD
) broader states except 1D2 2- , 2- -
3.73 GeV
Below 3.73 GeV Annihilation and EM decays. (rp,
KK , gcc, gg, ll-..) narrow states.
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Fitted and predicted cc spectrum Coulomb (OGE)
linear scalar conft. potential model blue
expt, red theory.
LS OGE LS conft, T OGE
as 0.5538 b 0.1422 GeV2 mc 1.4834
GeV s 1.0222 GeV
SS OGE
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cc from LGT
A LGT e.g. X.Liao and T.Manke, hep-lat/0210030
(quenched no decay loops) Broadly consistent
with the cc potential model spectrum. No
radiative or strong decay predictions yet.
lt- 1- exotic cc-H at 4.4 GeV
Small L2 hfs.
1 - cc has returned.
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2. Strong decays (open flavor)
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Experimental R summary (2003 PDG)
How do open-flavor strong decays happen at the
QCD (q-g) level?
Very interesting open experimental question Do
strong decays use the 3P0 model decay mechanism
or the Cornell model decay mechanism or ?
ee-, hence 1- - cc states only.
Cornell decay model (1980s cc papers) (cc)
lt-gt (cn)(nc) coupling from qq pair production by
linear confining interaction. Absolute norm of G
is fixed!
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The 3P0 decay model qq pair production with
vacuum quantum numbers. L I g y y . A standard
for light hadron decays. It works for D/S in b1
-gt wp. The relation to QCD is obscure.
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What are the total widths of cc states above 3.73
GeV? (These are dominated by open-flavor decays.)
43(15) MeV
78(20) MeV
52(10) MeV
lt 2.3 MeV
X(3872)
23.6(2.7) MeV
PDG values
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Strong Widths 3P0 Decay Model
Parameters are g 0.4 (from light meson decays),
meson masses and wfns.
X(3872)
23.6(2.7) MeV
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E1 Radiative Partial Widths
X(3872)
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Strong Widths 3P0 Decay Model
X(3872)
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Strong Widths 3P0 Decay Model
52(10) MeV
X(3872)
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After restoring this p3 phase space factor, the
BFs are D0D0
D0D0 D0D0 0.12 /- 0.06
0.95 /- 0.19 1 /- 0.31

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Y(4040)
Y(4040) partial widths MeV (3P0 decay
model) DD 0.1 DD 32.9 DD
33.4 multiamp. mode DsDs 7.8
Y(4040) -gt DD amplitudes (3P0 decay
model) 1P1 0.056 5P1 - 0.251
- 2 51/2 1P1 5F1 0
famous nodal suppression of a 33S1 Y(4040) cc -gt
DD
std. cc and D meson SHO wfn. length scale
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Strong Widths 3P0 Decay Model
78(20) MeV
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Y(4159)
4415
4159
Y(4159) partial widths MeV (3P0 decay
model) DD 16.3 DD 0.4 DD
35.3 multiamp. mode DsDs 8.0 DsDs 14.1
Y(4159) -gt DD amplitudes (3P0 decay
model) 1P1 0.081 5P1 - 0.036
- 5 -1/2 1P1 5F1 - 0.141
std. cc SHO wfn. length scale
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Strong Widths 3P0 Decay Model
43(15) MeV
DD DD DD DD0 DD1 DD1 DD2 DD0 DsDs DsDs D
sDs DsDs0
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Y(4415)
4415
4159
Y(4415) partial widths MeV (3P0 decay
model) DD 0.4 DD 2.3 DD
15.8 multiamp. New mode calculations DD1
30.6 m lt- MAIN MODE!!! DD1 1.0
m DD2 23.1 DD0 0.0 DsDs
1.3 DsDs 2.6 DsDs 0.7 m
DD
DD
DD
Y(4415) - gt DD1 amplitudes (3P0 decay
model) 3S1 0 lt- !!! 3D1
0.110
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An industrial application of the y(4415).
Sit slightly upstream, at ca. 4435 MeV, and you
should have a copious source of Ds0(2317).
(Assuming it is largely cs 3P0.)
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3. Loops
Future Unquenching the quark model Virtual
meson decay loop effects, qq lt-gt M1 M2
mixing. DsJ states (mixed cs lt-gt DK , how
large is the mixing?) Are the states close to
csgt or DKgt, or are both basis states important?
A perennial question accuracy of the valence
approximation in QCD. Also LGT-relevant (they
are usually quenched too).
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T.Barnes, F.E.Close and H.J.Lipkin,
hep-ph/0305025, PRD68, 054006 (2003).
DsJ(2317,2457)gt DK molecules?
3. reality
(loop effects now being evaluated)
Reminiscent of Weinstein and Isgurs KK
molecules.
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How large are decay loop mixing effects?
Charmed meson decays (God91)
S.Godfrey and R.Kokoski, PRD43, 1679
(1991). Decays of S- and P-wave D Ds B and Bs
flavor mesons. 3P0 flux tube decay model. The
L1 0 and 1 cs Ds mesons are predicted to
Have rather large total widths, 140 - 990 MeV.
( broad to unobservably broad).
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The 0 and 1 channels are predicted to have very
large DK and DK decay couplings. This supports
the picture of strongly mixed DsJ(2317,2457)gt
csgt (cn)(ns)gt states. Evaluation of
mixing in progress. Initial estimates for cc
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Loops evaluated
J/y - M1M2 - J/y 3P0 decay model, std.
params. and SHO wfns.
M1M2 DM J/y PM1M2 J/y
DD - 30. MeV 0.027
DD - 108. MeV 0.086
DD - 173. MeV 0.123
famous 1 4 7 ratio DD DD DD
DsDs - 17. MeV 0.012
DsDs - 60. MeV 0.041
DsDs - 97. MeV 0.060
1/2 2 7/2 DsDs DsDs DsDs
Sum - 485. MeV Pcc 65.
VERY LARGE mass shift and large non-cc component!
Can the QM really accommodate such large mass
shifts??? Other cc states?
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Loops
Init. Sum DM Pcc
cc - M1M2 - cc 3P0 decay model, std.
params. and SHO wfns.
J/y - 485. MeV 0.65
hc - 447. MeV 0.71
c2 - 537. MeV 0.43
c1 - 511. MeV 0.46
c0 - 471. MeV 0.53
hc - 516. MeV 0.46
Aha? The large mass shifts are all similar the
relative shifts are moderate.
Apparently we CAN expect DsJ-sized (100 MeV)
relative mass shifts due to decay loops in
extreme cases. cs system to be considered. Beware
quenched LGT!
Continuum components are large transitions (e.g.
E1 radiative) will have to be recalculated,
including transitions within the continuum.
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• 1) Spectrum
• The known states agree well with a cc potential
  model, except
• small multiplet splittings for L.ge.2 imply that
  the X(3872) is
• implausible as a naive cc state.
• 2) Strong decays (main topic)
• Some cc states above 3.73 GeV are expected to be
  rather
• narrow (in addition to 2- states), notably 3D3
  and 3F4.
• Of the known states, y(4040), y(4159) and y(4415)
  all have
• interesting decay modes 1st 2, DD relative
  amps, and for
• y(4415) we predict DD1 dominance also a
  Ds0(2317) source.
• 3) Loops
• Virtual meson decay loops cause LARGE mass shifts
  and
• cc lt-gt M1M2 mixing. These effects are under
  investigation.