Transcript Higher Charmonium Spectrum Strong decays (main topic) L’oops

Ted Barnes
Physics Div. ORNL
Dept. of Physics, U.Tenn.
GHP2004
Fermilab, 24-26 Oct. 2004
Higher Charmonium
1)
2)
3)
Spectrum
Strong decays (main topic)
L’oops
abstracted from T.Barnes, S.Godfrey and E.S.Swanson, in prep.
1. Spectrum
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, l l ..):
narrow states.
Fitted and predicted cc spectrum
Coulomb (OGE) + linear scalar conft. potential model
blue = expt, red = theory.
L*S OGE – L*S conft,
T OGE
S*S OGE
as = 0.5538
2
b = 0.1422 [GeV ]
mc = 1.4834 [GeV]
s = 1.0222 [GeV]
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.
<- 1
+-
1 cc has
returned.
Small
L=2 hfs.
-+
exotic cc-H at 4.4 GeV
2. Strong decays (open flavor)
How do open-flavor strong decays happen at the QCD (q-g) level?
Very interesting R
open
experimental
question:
Experimental
summary
(2003
PDG)
3
Do strong decays use the P0 model decay mechanism
or the Cornell model decay mechanism or … ?
+ -
e e , hence 1
--
cc states only.
“Cornell” decay model:
(1980s cc papers)
(cc) <-> (cn)(nc) coupling from qq pair
production by linear confining interaction.
Absolute norm of G is fixed!
g0
br
g0
vector confinement???
controversial
3
The P0 decay model: qq pair production with vacuum quantum numbers.
LI= g y y .
A standard for light hadron decays. It works for D/S in b1 -> wp.
The relation to QCD is obscure.
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
X(3872)
< 2.3 MeV
23.6(2.7) MeV
PDG values
Strong Widths: 3P0 Decay Model
Parameters are g = 0.4 (from light meson decays), meson masses and wfns.
1D
X(3872)
3
D3
D2
3
D1
1
D2
3
DD
0.5 [MeV]
43 [MeV] 23.6(2.7) [MeV]
-
E1 Radiative Partial Widths
X(3872)
1D -> 1P
3
3
3
3
D3 ->
D2 ->
3
D1 ->
1
P2
305 [keV]
P2
P1
70 [keV]
342 [keV]
P2
P1
3
P0
5 [keV]
134 [keV]
443 [keV]
3
3
3
D2 -> 1P1
376 [keV]
Strong Widths: 3P0 Decay Model
3
1F
X(3872)
DD
DD*
D*D*
DsDs
F4
8.3
F3
84
3
F2 161
1
F3
61
3
[MeV]
[MeV]
[MeV]
[MeV]
Strong Widths: 3P0 Decay Model
3S
33S1 74 [MeV]
31S0 80 [MeV]
DD
DD*
D*D*
DsDs
52(10) MeV
X(3872)
3
After restoring this “p phase space factor”, the BFs are:
0 0
DD
0.12 +/- 0.06
:
0
D D*
0
0.95 +/- 0.19
:
0
D* D*
0
[1] +/- 0.31
Y(4040)
Theor R from the Cornell model.
Eichten et al, PRD21, 203 (1980):
4415
4040
4159
D*D*
DD*
DD
Y(4040) -> D*D* amplitudes
3
( P0 decay model):
1
P1
5
P1
5
F1
= + 0.056
1/2
= - 0.251 = - 2 * 5 * 1P1
= 0
Y(4040) partial widths [MeV]
3
( P0 decay model):
DD
DD*
D*D*
DsDs
= 0.1
= 32.9
= 33.4 [multiamp. mode]
= 7.8
famous nodal suppression
3
of a 3 S1 Y(4040) cc -> DD
std. cc and D meson SHO wfn. length scale
Strong Widths: 3P0 Decay Model
2D
DD
DD*
D*D*
DsDs
DsDs*
23D3 148 [MeV]
23D2
92 [MeV]
3
2 D1
74 [MeV] 78(20) [MeV]
1
2 D2 111 [MeV]
Y(4159)
Theor R from the Cornell model.
Eichten et al, PRD21, 203 (1980):
4415
4040
4159
D*D*
DD*
DD
Y(4159) -> D*D* amplitudes:
3
( P0 decay model):
Y(4159) partial widths [MeV]
3
( P0 decay model):
1
DD = 16.3
DD* = 0.4
D*D* = 35.3 [multiamp. mode]
DsDs = 8.0
DsDs* = 14.1
P1
5
P1
5
F1
= + 0.081
-1/2
= - 0.036 = - 5 *1P1
= - 0.141
std. cc SHO wfn. length scale
Strong Widths: 3P0 Decay Model
4S
DD
DD*
D*D*
DD0*
DD1
DD1’
DD2*
D*D0*
DsDs
DsDs*
Ds*Ds*
DsDs0*
43S1
41S0
78 [MeV]
61 [MeV]
43(15) [MeV]
Y(4415)
Theor R from the Cornell model.
Eichten et al, PRD21, 203 (1980):
4040
4415
4159
Y(4415) partial widths [MeV]
3
( P0 decay model):
D*D*
DD = 0.4
DD* = 2.3
D*D* = 15.8 [multiamp.]
DD*
DD
New mode calculations:
DD1 = 30.6 [m] <- MAIN MODE!!!
DD1’ = 1.0 [m]
DD2* = 23.1
D*D0* = 0.0
DsDs = 1.3
DsDs* = 2.6
Ds*Ds* = 0.7 [m]
Y(4415) - > DD1 amplitudes:
3
( P0 decay model):
3
S1
D1
3
=
0 <- !!!
= + 0.110
An “industrial application” of the y(4415).
Sit “slightly upstream”, at ca. 4435 MeV, and you should have
3
a copious source of D*s0(2317). (Assuming it is largely cs P0.)
3. L’oops
Future: “Unquenching the quark model”
Virtual meson decay loop effects,
qq <-> M1 M2 mixing.
DsJ* states (mixed cs <-> DK …, how large is the mixing?)
Are the states close to |cs> or |DK>, or are both basis states important?
A perennial question: accuracy of the valence approximation in QCD.
Also LGT-relevant (they are usually quenched too).
|D
sJ
*+(2317,2457)>
= DK molecules?
T.Barnes, F.E.Close and H.J.Lipkin,
hep-ph/0305025, PRD68, 054006 (2003).
3. reality
(loop effects now being evaluated)
Reminiscent of Weinstein and Isgur’s “KK molecules”.
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.
3
P0 “flux tube” decay model.
+
+
The L=1 0 and 1 cs “Ds”
mesons are predicted to
Have rather large total widths,
140 - 990 MeV. (= broad to
unobservably broad).
P
+
J = 1 (2457 channel)
+
P
+
J = 0 (2317 channel)
+
The 0 and 1 channels are predicted to have very large
DK and D*K decay couplings.
This supports the picture of strongly mixed
*+
|DsJ (2317,2457)> = |cs> + |(cn)(ns)> states.
Evaluation of mixing in progress. Initial estimates for cc …
L’oops evaluated
[ J/y - M1M2 - J/y ]
M 1 M2
DM [J/y]
M [J/y]
1 2
DD
- 30. MeV
0.027
DD*
- 108. MeV
0.086
D*D*
- 173. MeV
0.123
DsDs
- 17. MeV
0.012
DsDs*
- 60. MeV
0.041
Ds*Ds*
- 97. MeV
0.060
Sum =
- 485. MeV
Pcc = 65.%
PM
3
P0 decay model,
std. params. and SHO wfns.
famous 1 : 4 : 7 ratio DD : DD* : D*D*
1/2 : 2 : 7/2
DsDs : DsDs* : Ds*Ds*
VERY LARGE mass shift
and large non-cc component!
Can the QM really accommodate such large mass shifts??? Other “cc” states?
L’oops
Init.
Sum DM
Pcc
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
[ cc - M1M2 - cc ]
3
P0 decay model,
std. params. and SHO wfns.
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.
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, D*D* relative amps, and for
y(4415) we predict DD1 dominance; also a D*s0(2317) source.
3) L’oops
Virtual meson decay loops cause LARGE mass shifts and
cc <-> M1M2 mixing. These effects are under investigation.