Download - Charmonium
CharmoniumCharmonium
Ted BarnesPhysics Div. ORNLDept. of Physics, U.Tenn.
1) Basic physics2) Theoretical spectrum versus known states3) NEW: open-flavor strong widths4) E1 transitions5) X(3872)
The numbers quoted in 2-4) will appear in T.Barnes, S.Godfrey and E.S.Swanson (in prep.)
I will mainly quote cc potential model results, which provide a useful intuitive picture of charmonium. LGT (C.Morningstar) is not yet competitive for higher mass cc states but is of course the preferred technique and will eventually solve everything.
CharmoniumCharmonium
e
g
Small qq separation
Large qq separation
The QCD flux tube (LGT, G.Bali et al; hep-ph/010032)
LGT simulation showing
the QCD flux tube
Q Q
R = 1.2 [fm]
“funnel-shaped” VQQ(R)
Coul. (OGE)
linear conft.(str. tens. = 16
T)
Physically allowed hadron states (color Physically allowed hadron states (color singlets)singlets)
q3 Conventional quark modelmesons and baryons.
q2q2, q4q,…
multiquarks
g2, g3,…
glueballs
maybe 1 e.g.
qqg, q3g,…
hybrids
maybe 1-3 e.g.s
100s of e.g.s
”exotica” :ca. 106 e.g.s of (q3)n, maybe 1-3 others
(q3)n, (qq)(qq), (qq)(q3),…
nuclei / molecules
(q2q2),(q4q),…
multiquark clusters
controversiale.g.
_
Basis state mixing may be very important in some sectors.
cc mesons states and spectrum
The nonrelativistic quark model treats conventional charmonia
as cc bound states.
Since each quark has spin-1/2, the total spin is
Sqq = ½ x ½ = 1 + 0
Combining this with orbital angular momentum Lqq gives states
of total Jqq = Lqq spin singlets Jqq = Lqq+1, Lqq, Lqq-1 spin triplets
tot.
xxxxx
Parity Pqq
= (-1) (L+1)
C-parity Cqq
= (-1) (L+S)
cc mesons quantum numbers
1S: 3S1 1 ; 1S
0 0 2S: 23S
1 1 ; 21S
0 0 …
1P: 3P2 2 ; 3P
1 1 ; 3P
0 0 ; 1P
1 1
2P …
1D: 3D3 3 ; 3D
2 2 ; 3D
1 1 ; 1D
2 2
2D …JPC forbidden to qq are called “JPC-exotic quantum numbers”.
0 ; 0 ; 1 ; 2 ; 3 …
Plausible JPC-exotic candidates =
hybrids, glueballs (high mass), maybe multiquarks (fall-apart decays).
The resulting cc NL states N2S+1LJ have JPC =
Charmonium
Theoretical spectrum versus known states
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 statesexcept 1D
2 22
3.73 GeV
Below 3.73 GeV: Annihilation and EM decays.
, KK* , cc, , ll..):narrow states.
Fitting cc potential model parameters.s, b, mc, fixed from 1P c.o.g. and all 1S and 2S masses.
blue = expt, red = theory.
s = 0.5111
b = 0.1577 [GeV2]m
c = 1.4439 [GeV]
= 1.1667 [GeV]
Predicted spin-dependent cc 1P multiplet splittings
(sensitive test of OGE)Parameters s, b, mc, fixed from 13PJ c.o.g. and all 1S, 2S masses, prev slide.
blue = expt, red = theory. s = 0.5111
b = 0.1577 [GeV2]m
c = 1.4439 [GeV]
= 1.1667 [GeV]
OGE + lin. scalar conft.1P
1 (not shown) is 8 MeV
below the 3PJ c.o.g.
Scalar conft. gives neg. L*S
23S1 (3672)
21S0 (3635)
33S1 (4073)
31S0 (4047)
43S1 (4407)
41S0 (4387)
33P2 (4320)
33P1 (4272)
33P0 (4202)
31P1 (4281)
23P2 (3976)
23P1 (3927)
23P0 (3853)
21P1 (3936)3P
2 (3560)
3P1 (3507)
3P0 (3424)
1P1 (3517)
23D3 (4170)
23D2 (4161)
23D1 (4144)
21D2 (4160)
3D3 (3810)
3D2 (3803)
3D1 (3787)
1D2 (3802)
23F4 (4351)
23F3 (4355)
23F2 (4353)
21F3 (4353)
3F4 (4025)
3F3 (4032)
3F2 (4032)
1F3 (4029)
3S1 (3087)
1S1 (2986)
Fitted and predicted cc spectrum
blue = expt, red = theory.
s = 0.5538
b = 0.1422 [GeV2]m
c = 1.4834 [GeV]
= 1.0222 [GeV]
Previous fit (1S,2S,1Pcog
.):
s = 0.5111
b = 0.1577 [GeV2]m
c = 1.4439 [GeV]
= 1.1667 [GeV]
cc from the “standard” potential modelS.Godfrey and N.Isgur, PRD32, 189 (1985).
Godfrey-Isgur model cc spectrum (SG, private comm.)
cc from LGT
exotic cc-H at 4.4 GeV
oops… cc has been withdrawn.
Small L=2 hfs.
What about LGT??? An 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.
Charmonium
Open-flavor strong decays
Experimental R summary (2003 PDG)Very interesting open experimental question:Do strong decays use the 3P
0 model decay mechanism
or the Cornell model decay mechanism or … ?
br
vector confinement??? controversial
ee, hence 1 cc states only.
How do strong decays happen at the QCD (q-g) level?
“Cornell” decay model:
(1980s cc papers)(cc) (cn)(nc) coupling from qq pair production by linear confining interaction.
Absolute norm of is fixed!
The 3P0 decay model: qq pair production with vacuum quantum numbers.
L I = g
A standard for light hadron decays. It works for D/S in b1 .
The relation to QCD is obscure.
R and the 4 higher 1-- states
3770
4040
4160
4415
(plot from Yi-Fang Wang’s online BES talk, 16 Sept 2002)
What are the total widths of cc states above 3.73 GeV?
(These are dominated by open-flavor decays.)
< 2.3 MeV
23.6(2.7) MeV
52(10) MeV
43(15) MeV
78(20) MeV
PDG values
Strong Widths: 3P0 Decay Model
1D
3D3
0.6 [MeV]
3D2
-
3D1
43 [MeV]
1D2
-
DD 23.6(2.7) [MeV]
Parameters are = 0.4 (from light meson decays), meson masses and wfns.
Strong Widths: 3P0 Decay Model
33S1
74 [MeV]
31S0
67 [MeV]
3S
DDDD*D*D*D
sD
s
52(10) MeV
partial widths [MeV](3P
0 decay model):
DD = 0.1 DD* = 32.9 D*D* = 33.4 [multiamp. mode]D
sD
s = 7.8
Theor R from the Cornell model.Eichten et al, PRD21, 203 (1980): 4040
DD
DD*
D*D*
4159
4415
famous nodal suppression of a 33S
1 (4040) cc DD
D*D* amplitudes(3P
0 decay model):
1P1 = 0.056
5P1 = 0.251
5F1
= 0
std. cc and D meson SHO wfn. length scale
Strong Widths: 3P0 Decay Model
2D 23D3
148 [MeV]
23D2
93 [MeV]
23D1
74 [MeV]
21D2
112 [MeV]
DDDD*D*D*D
sD
s
DsD
s*
78(20) [MeV]
partial widths [MeV](3P
0 decay model):
DD = 16.3 DD* = 0.4 D*D* = 35.3 [multiamp. mode]D
sD
s = 8.0
DsD
s* = 14.1
Theor R from the Cornell model.Eichten et al, PRD21, 203 (1980): 4040
DD
DD*
D*D*
4159
4415
std. cc SHO wfn. length scale
D*D* amplitudes:(3P
0 decay model):
1P1 = 0.081
5P1 = 0.036
5F1 = 0.141
Strong Widths: 3P0 Decay Model
2P23P
2 83 [MeV]
23P1
162 [MeV]
23P0
29 [MeV]
21P1
86 [MeV]
DDDD*D
sD
s
Strong Widths: 3P0 Decay Model
1F3F
4 9.0 [MeV]
3F3
87 [MeV]
3F2
165 [MeV]
1F3
64 [MeV]
DDDD*D*D*D
sD
s
Charmonium
Radiative transitions
n.b.
I will discuss only E1 because of time limitations.
Yes, M1 is interesting too! J/
c and ’ ’
c give m
c,
and ’ c tests S*S corrections to
orthog. 1S-2S wfns.
1P -> 1S3P
2 3S
1 472 [keV]
3P1 3S
1 353 [keV]
3P0 3S
1 166 [keV]
1P1 1S
0 581 [keV]
426(51) [keV]288(48) [keV]119(19) [keV] -
E1 Radiative Partial Widths
2S -> 1P
23S1 3P
2 39 [keV]
23S1 3P
1 57 [keV]
23S1 3P
0 67 [keV]
21S0 1P
1 74 [keV]
18(2) [keV]24(2) [keV]24(2) [keV] -
Same model, wfns. and params as the cc spectrum. Standard |<
f | r |
i >|2 E1 decay rate formula.
Expt. rad. decay rates from PDG 2002
E1 Radiative Partial Widths
1D -> 1P
3D3 3P
2 305 [keV]
3D2 3P
2 70 [keV]
3P1
342 [keV]
3D1 3P
2 5 [keV]
3P1
134 [keV]
3P0
443 [keV]
1D2 1P
1 376 [keV]
E1 Radiative Partial Widths
3S -> 2P 33S1 23P
2 12 [keV]
33S1 23P
1 38 [keV]
33S1 23P
0 10 [keV]
31S0 21P
1 114 [keV]
3S -> 1P 33S1 3P
2 0.8 [keV]
33S1 3P
1 0.6 [keV]
33S1 3P
0 0.3 [keV]
31S0 1P
1 11 [keV]
E1 Radiative Partial Widths
2D -> 1P23D
3 3P
2 35 [keV]
23D2 3P
2 8 [keV]
3P1
30 [keV]
23D1 3P
2 1 [keV]
3P1
17 [keV]
3P0
32 [keV]
21D2 1P
1 48 [keV]
2D -> 1F
23D3 3F
4 67 [keV]
3F3
5
[keV] 3F
2 15
[keV]
23D2 3F
3 46 [keV]
3F2
6 [keV]
23D1 3F
2 49 [keV]
21D2 1F
3 54 [keV]
2D -> 2P23D
3 23P
2 246 [keV]
23D2 23P
2 54 [keV]
23P1
319[keV]
23D1 23P
2 6 [keV]
23P1
173 [keV]
23P0
515 [keV]
21D2 21P
1 355 [keV]
E1 Radiative Partial Widths
1F -> 1D
3F4 3D
3 351 [keV]
3F3 3D
3 43 [keV]
3D2
375 [keV]
3F2 3D
3 2 [keV]
3D2
66 [keV]
3D
1 524 [keV]
1F3 1D
2 409 [keV]
X(3872)
Belle Collab. S.-K.Choi et al, hep-ex/0309032; K.Abe et al, hep-ex/0308029.
J
DD*MeV
Accidental agreement?X = cc 2 or 2 or …,or a molecular state?
MeV
= 3D1 cc.
If the X(3872) is 1D cc,an L-multiplet is split much more than expected assuming scalar conft.
n.b.DD*MeV
MeV
X(3872) from CDFG.Bauer, QWG presentation, 20 Sept. 2003.
n.b.most recent CDF II: D.Acosta et al, hep-ex/0312021,5 Dec 2003.M = 3871.3 pm 0.7 pm 0.4 MeV
cc from the “standard” potential modelS.Godfrey and N.Isgur, PRD32, 189 (1985).
(3D2 is a typo)
The obvious guess if cc is 2 or 2 .No open-flavor strong decays – narrow.
Charmonium Options for the X(3872)
T.Barnes and S.Godfrey, hep-ph/0311169.
Our approach:
Assume all conceivable cc assignments for the X(3872):
all 8 states in the 1D and 2P cc multiplets.
Nominal Godfrey-Isgur masses were
3D3(3849) 23P
2(3979)
3D2(3838) 23P
1(3953)
3D1(3.82) [(3770)] 23P
0(3916)
1D2(3837) 21P
1(3956)
We assigned a mass of 3872 MeV to each stateand calculated the resulting strong and EM partial widths.
If X = 1D cc:
Total width eliminates only 3D1.
Large, ca. 300 – 500 keV E1 radiative partial widths to J and h
c
are predicted for 1D assignments ( 3D3, 3D
2 ) and 1D
2.
If tot
= 1 MeV these are 30% - 50% b.f.s!
The pattern of final P-wave cc states you populate identifies the initial cc state.
If X = 1D2
cc, you are “forced” to discover the hc!
If X = 2P cc:
23P1 and
21P
1 are possible based on total width alone.
These assignments predict weaker but perhaps accessible radiative branches to J, ’ and
c
c’ respectively.
NOT to J states. (E1 changes parity.)
We cannot yet exclude 5 of the 8 1D and 2P cc assignments.
DD* molecule options
This possibility is suggested by the similarity in mass,
N.A.Tornqvist, PRL67, 556 (1991); hep-ph/0308277.F.E.Close and P.R.Page, hep-ph/0309253.C.Y.Wong, hep-ph/0311088.E.Braaten and M.Kusunoki, hep-ph/0311147.E.S.Swanson, hep-ph/0311229.
n.b. The suggestion of charm meson molecules dates back to 1976:(4040) as a D*D* molecule;(Voloshin and Okun; deRujula, Georgi and Glashow).
XMeV
DD*MeV
(I prefer this assignment.)
Interesting prediction of molecule decay modes:
E.Swanson, hep-ph/0311299: 1 DoD*o molecule with additional comps. due to rescattering.
JJ
Predicted total width ca. = expt limit (2 MeV).
Very characteristic mix of isospins: J andJdecay modes expected.
Nothing about the X(3872) is input: this all follows from OE and C.I. !!!
X(3872) summary:
The X(3872) is a new state reported by Belle and CDF
in only one mode: J . It is very narrow, < 2.3 MeV.The limit on
is comparable to the observed J.
The mass suggests that X is a deuteronlike DoD*o-molecule.Naïvely, this suggests a narrow total X width of ca. 50 keV
and 3:2 b.f.s to DoDo and DoDo.
However, internal rescatter to (cc)(nn) may be important.
This predicts (X) = 2 MeV and remarkable, comparable b.f.s to Jand J [E.S.Swanson, hep-ph/0311299]. The bleedin’ obvious decay mode Jshould be searched for, to test C(X) and establish whether =
Possible “wrong-mass” cc assignments to 1D and 2P levels can be tested by their (often large) E1 radiative transitions to (cc).
Charmonium: Charmonium: SummarySummary
1) The spectrum fits a OGE + linear scalar conft. potential model reasonably well. More cc states will be useful to test this. (Pt. 4.)
2) Some cc states above 3.73 GeV in addition to 2 and 2
are expected to be relatively narrow, notably33DD
33 ( = 0.6 MeV) and 33FF
44 ( = 9 MeV).
3) The multiamplitude strong decays D*D* can be used to establish the dom. strong decay mechanism. b.f.s to DD, DD*, D
s Ds … will be useful too.
[ 3) is my favorite new-age cc topic.]
4) E1 rad: 2 tests S-wave comp.
, DD search for new C=(+) cc states.
5) The X(3872) is likely a Do D*o molecule.
J andJdecay modes?
X = cc options predict large E1 b.f.s to + P-wave cc.