Transcript Exotic ccbar Resonances

ITEP Winter School, 13-20 Feb 2010
New charmonium resonances
Roman Mizuk, ITEP
Outline
Potential Models
Traditional charmonium states
New charmonium resonances
X(3872)
1- - states from ISR
3940 family
Z±
Bottomonium
Charmonium – meson containing cc quarks
Family of excited states: c , J/ , cJ , hc , (2S) , …
“Hydrogen atom” of QCD
System
Ground triplet state
Name
Mass, MeV
G, MeV
(v/c)2
POSITRONIUM
e+e-
Ortho-
1
5 10-15
~0.0001
QUARKONIUM
uu,dd
r
800
150
~1.0
ss
f
1000
4
~0.8
cc

3100
0.09
~0.25
bb

9500
0.05
~0.08
Basic properties of most states  simple picture of non-relativistic cc pair.
non-relativistic
relativistic
Quantum Mechanics
Quantum Field Theory
two-body problem
Number of particles is not conserved
 multi-body problem
Hydrogen atom
non-relativistic
Srödinger equation
relativistic
Dirac equation
  2 Ze 2 
 n
En n   
 
r 
 2m
bispinor
  i   eA n  0

Ze 

  
r 
A  

 A0 


Z 2 R1
En   2
n
R1  13.6eV


Ze 2 
 n  i   n
 0  En 
r 

Precise description of hydrogen atom. EXCEPT FOR LAMB SHIFT.
Field Theoretical description of bound state
eAmplitude:
p
+
+…
+
Analytic continuation into complex energy plane.
Im E
Re E
poles
bound states
mp+me
Hydrogen atom (2)
Solutions of Dirac equation
correspond to sum
+
+
+…
charge, distorts Coulomb potential
+ … = running
too small effect to reproduce Lamb shift
+…
reproduces Lamb shift
No way to account for in Dirac equation.
not a single particle!
~ = v/c

Non-potential effects are small if electron is slow in the time scale
when additional degrees of freedom are present in the system.
Potential Model of Charmonium
+
+ …=
+
+ …
+…
Not justified:
constituent quark, heavier by 300MeV
V (r )  
 s (r )
r
 r
QCD motivated
potential
Assume that charm quark is heavy enough to neglect
non-potential effects.
(M(2S) – MJ/ ) / QCD = 590 MeV / 200 MeV is not small.
Open question: why Potential Models work reasonably well for charmonium?
Charmonium Potentials
V (r )  
 s (r )
one-gluon exchange,
asymptotic freedom
r
 r
“Cornel model”
confining potential,
“chromoelectric tube”
There are other parameterizations, respecting or
not respecting
QCD asymptotics.
After parameters of
potential are fit to data,
the potentials become
very similar.
0.1<R<1fm
c J/ c2 (2S)
Charmonium levels without spin
2s
1p
2s
1d
1p
Coulomb
1s
1s
2s
QCD
1s
1p
Harmonic
oscillator
Relativistic Corrections
fine structure of states
spin-singlet triplet splitting
not commute with
Assign Lorentz structure to potentials
Lˆ
short distance
u uv vV q 


vector
Breit-Fermi expansion to order v2/c2 
2
v
confining
u u v vVs q 2 
scalar
Charmonium Levels
M, GeV
building blocks
4.50
(4415)
4.25
(4160)
(4040)
c2(2S)
4.00
(3770)
3.75
c(2S)
(2S)
hc
3.50
c2
c1
c0
spectroscopic notation
conserved QN
n(2S+1)LJ
JPC
S=0 L=0
1S
0
0– +
c , c(2S)
S=1 L=0
3S
1
1– –
J/ , (2S) ,
(4040) , (4415)
S=0 L=1
1P
1
1+ –
hc
S=1 L=1
3P
1
3P
2
3P
3
0+ +
1+ +
2+ +
c0
c1
c2 , c2 (2S)
S=1 L=2
3D
1
1– –
(3770), (4160)
3.25
J/
3.00
2.75
c
0– +
1– –
P = (–1)L+1
C = (–1)L+S
S = s1 + s2 = { 0, 1 }
J=S+L
n – radial quantum number
1+ –
(0,1,2)+ +
JPC
(3770) = 13D1 + 0.2 23S1 “S - D mixing”
Predictions of
Potential Models
State
Experim
M, GeV
Predictions of Potential Models
Potential models reproduce also
annihilation widths
J/, (2S)→ℓ+ℓc, cJ →  and
radiative transitions btw. charmonia.
JPC
Hadronic mass in Lattice QCD
Calculate 2-point Green function G(t,0) = 0O (t)O(0)+0,
creating hadron at time 0 and destroying at time t.
For this
Average over all possible configurations of fields
generated on lattice and weighted with exp(iS). → exp(–S)
Operator O has required quantum numbers: JPC, flavor content
and is projected on zero momentum.
Expect: G(t,0) = A1exp(im1t) + A2exp(im2t) + A3exp(im3t) + ...
→ A1exp(–m1t) + A2exp(–m2t) + A3exp(–m3t) + ...
Multi exponential t-dependence of Green function
complicates identification of excited states.
Minkovsky → pseudo-Euclidian space.
from first principles
Charmonium in Lattice QCD
Potential for static charm quarks. Shape is similar to that of phenomenological models.
quenched approximation
Predictions for charmonia up to the 1st radial excitation exist.
Still a lot of room for improvement.
QCD Sum Rules
Green function is calculated analytically.
Restricted to small interval of t,
contributions from ground and higher states more difficult to resolve.
Application restricted to lowest states only.
Summary on Potential Models
– Only model relation to underlying fundamental theory of QCD.
difficult to assign uncertainties to results
+ Using 3-4 parameters can describe a lot of data.
right choice of variables?
good predictive power
o In many cases the only available theoretical approach.
higher resonances
Shape of potential in agreement with Lattice QCD estimations,
and with perturbative QCD calculations (at small distances).
success of phenomenology
Useful framework for refining our understanding of QCD
and guidance towards progress in quarkonium physics.
Observation of J/
BNL AGS
SLAC SPEAR e+e- annihilation
Mark I first 4 detector
extracted 28 GeV p-beam
Be target
p + Be → e+e- + X
, nb
, nb
e  e   hadrons
Richter et al.
e e     
, nb
Ting et al.
M( e+e- )
Width of t
J/ is very narrow, JPC=1– –.
ee  ee
E c.m.s.
“Heavy but very narrow !”  November 1974 revolution.
Every possible explanation was suggested.
 Observation of charm quark.
 Quarks generally recognized as fundamental particles.
Charm quark was predicted by GIM mechanism to cancel divergence in kaon box diagram.
Observation of (2S)
two weeks after observation of J/
SLAC SPEAR
Mark I
Event Display
(2S) → J/ +J/ → e+e-
(2S) is very narrow, JPC=1– –.
Observation of
cJ
c
– DASP, DESY (1976)
– Crystall Ball, SLAC (1980)
c
– DASP (1977)
c(2S) – CBall (1980)
Crystal Ball: sphere
with 900 NaI crystals
 e  e   hadrons
2
R

N
e
c q
 e  e       
 e e   
 



4 2

3s
First results on R above DD threshold
– SPEAR (1975).
4 peaks above 3.7 GeV :
Why J/ is so narrow?
G, MeV
0.093 ± 0.002 0.327 ± 0.011 27 ± 4
2S
J/
c
~s3
‾
c
‾
c
c0
27 ± 1
85 ± 12
(3770) (4040)
C-parity
1/3 2/3
c
c
11 ± 1

c
g
‾
c
g
e,,q
e,,q
¯
For J/ strong decays are suppressed so much
that EM decays are competitive.
DD*
D*D*
DD
at
threshold
Charmonium level scheme after 1980
10 states were observed:
• 6 ’s directly produced in
e+e– annihilation.
• 3 P-levels are well seen in
(2S) radiative transitions.
• The ground state c was
observed in radiative decays
of J/ and (2S).
Charmonium level scheme before 2002
Superconducting Coil (1.5T)
Instrumented Flux Return (IFR)
[Iron interleaved with RPCs].
Silicon Vertex Tracker (SVT)
e+ (3 GeV)
e– (9 GeV)
Drift Chamber
[40 stereo lyrs](DCH)
B-factories
e+e– → Y(4S)
BaBar
Belle
E = 10.6 GeV
L ~ 2*1034/cm2/s
530 + 1000 fb-1
CsI(Tl) Calorimeter (EMC)
[6580 crystals].
Cherenkov Detector (DIRC)
[144 quartz bars, 11000 PMTs]
e+e– → сharmonium
CLEO-c BES-II
E = 3.0 - 4.8 GeV
L ~ 1033/cm2/s
pp¯ collider
CDF
D0
E ~ 1.8 TeV
Aerogel Cherenkov cnt.
n=1.015~1.030
SC solenoid
1.5T
3.5 GeV e+
CsI(Tl) 16X0
TOF counter
8 GeV e–
Tracking + dE/dx
small cell + He/C2H5
Si vtx. det.
3 lyr. DSSD
m / KL detection
14/15 lyr. RPC+Fe
Charmonium production at B factories
in B decays
γγ fusion
Any quantum numbers can be produced,
to be determined from angular analysis.
double charmonium production
initial state radiation
JPC =
JPC = 0± +, 2± +
1– –
Only JPC = 0± + observed so far.
Reconstruction of B decays
• In (4S) decays B are produced almost at rest.
• ∆E = Ei - ECM/2  Signal peaks at 0.
• Mbc = { (ECM/2)2 - (Pi)2}1/2  Signal peaks at B mass (5.28GeV).
B0J/ KS
∆E, GeV
Mbc, GeV
Observation of c(2S)
B  (KSK) K
M = 2654  6  8 MeV/c2
G < 55 MeV
Belle (2002) in B decays and in
double charmonium production.
Confirmed by BaBar and CLEO-c in
two-photon production, and by BaBar
in double charmonium production.
c(2S)
M = 2630  12 MeV/c2
e+e– J/ X
Good agreement with potential models
for mass, width and 2-photon width.
Width: 6±12 (CLEO) and 17± 8 MeV (BaBar)
average Γ = (14 ± 7) MeV
Observation of hc
(2S) → 0 hc → 0  c
hc
M(hc) = (3524.4 ± 0.6 ± 0.4) MeV
G < 1 MeV
Potential model expectations: M(hc) = centre of gravity of χc states =
1/9 * [(2*2+1) * M(χc2) + (2*1+1) * M(χc1) + (2*0+1) * M(χc0) ] = 3525.3 ± 0.3 MeV
5.5
c2(2S) in  interactions
395fb-1
e+
2005, BELLE
M = 3931  4  2 MeV/c2
G = 20  8  3 MeV
e–
γ
γ
e+
χс2’
D
D
e–
Поляризация
consistent with J=2
J=0 disfavored 2/dof=23.4/9
2009, BaBar
Width and 2-photon width are in good agreement
with models, mass is 50 MeV lower.
Charmonium Levels 2010
Mass (MeV)
(2S+1)L
J
Y
(4415)
(4160)
(4040)
’c2
X
’c ′
c J/
New:
X
c2 c1
Y
3 identified charmonia.
(3770) DD
– mass
– decay pattern
– quantum numbers
that do not fit expectations.
h
c0 hcc
(Potential Models)
JPC
~10 states with
??
New charmonium(like) states
states contain cc
About 10 charmonium(like) states do not fit expectations.
Have Potential Models finally failed?
yes, but coupled channel effect was taken into account
Exotics?
u
c
c
tetraquark
c u
compact diquarkdiantiquark state
c
hybrid
g state with excited qluonic
degree of freedom
π c
c
u
u
c c–
π
π
molecule
two loosely bound
D mesons
hadrocharmonium
charmonium embedded
into light hadron
X(3872)
CP
X(3872)
B→Xsγ
487
336
Belle citation count
480
Phys.Rev.Lett.91 262001, (2003)
7th anniversary!
Swanson, CharmEx09
PRL91,262001 (2003)
X(3872) was observed by Belle in
B+ → K+ X(3872)
→ J/ψ π+ π-
2S
X(3872)
Confirmed by CDF, D0 and BaBar.
Recent signals of X(3872) → J/ψ π+ πpp collisions
PRL103,152001(2009)
arXiv:0809.1224
PRD 77,111101 (2008)
direct production
only 16% from B
PRL93,162002(2004)
Mass & Width
 M  = 3871.52  0.20 MeV,
 Γ  = 1.3  0.6 MeV
Close to D*0D0 threshold:
m = – 0.42  0.39 MeV
 [ – 0.92, 0.08 ] MeV at 90% C.L.
Branching Fractions
Br(B+
X
K+)
 Br(X  J/
+
-)
(8.10  0.92  0.66)  10-6
=
(8.4  1.5  0.7)  10-6
Absolute Br?  missing mass technique
PRL96,052002(2006)
K
reconstruct
only
B
Xcc
mX2=(pB+ – pK+)2
(4S)
B-
(4S) 4-momentum
from beam energy
Br(B+  X K+) < 3.210–4
at 90%C.L.
Br(X  J/ + -) > 2.5%
K+ momentum
in B+ c.m.s.
Radiative Decays & J/ 
hep-ex/0505037
PRL102,132001(2009)
J/ 
J/ 
X(3872) → J/ + - 0
subthreshold production of 
+-0
2S 
Decay modes
Br relative to J/+-
J/ 
0.15  0.05
J/ 
0.33  0.12
2S 
1.1  0.4
J/ 
1.0  0.5
 CX(3872) = +
X(3872) → J/+CX(3872) = +  C+- = –

(|+1,-1 – |-1,+1)  ( r )
1. Isospin (+-) = 1
2. L(+-) = 1
 IJPC of r0
isospin
M (+-)
PRL96,102002(2006)
hep-ex/0505038
L=0
L=1
 M (+-) is well described by r0→+- (CDF: + small interfering →+- ).
 X(3872) → J/ +-  X(3872) → J/ r0
Spin & Parity
PRL98,132002(2007)
Angular analyses by Belle and CDF
excluded JP = 0++, 0+-, 0-+,
1-+ ,1+-, 1--,
2++, 2-- , 2+-,
3--, 3+-
2-+
1++
1-0++
 JPC = 1++ or 2–+
2–+ is disfavored by
1. Br(X → (2S) γ) / Br(X → J/ γ) ~ 3
2. Observation of D*0D0 decay
 multipole suppression
 centrifugal barrier at the threshold
JP = 1++ are favorite quantum numbers for X(3872).
2–+ not excluded.
X(3872) → D*0D0
B K
arXiv:0810.0358
D0D*0
D*→Dγ
PRD77,011102(2008)
4.9σ
B+& B0 D0D*0K
D*→D0π0
605 fb-1
347fb-1
Flatte vs BW similar result: 8.8σ
~2
Shifted X(3872) mass
in D*D final state
 influence of nearby
D*D threshold.
X(3872) Experimental Summary
JPC = 1++
(2–+ not excluded)
M = 3871.52  0.20 MeV ,
Γ = 1.3  0.6 MeV
Close to D*0D0 threshold: m = – 0.42  0.39 MeV.
Decay modes
Br relative to J/ r0
J/ r0
1
J/ 
1.0  0.5
J/ 
0.17  0.05
(2S) 
1.1  0.4
D*0D0
~10
Br(X(3872)  J/ r0) > 2.5%
(90% C.L.)
Is there cc assignment for X(3872)?
JPC = 1++   c1′
~100 MeV lighter than expected
1++
2-+
3872
Br( c1′ → J/ )
Br( c1′ → J/ +-)
expect
30
measure
0.170.05
JPC = 2–+  η c2
Expected to decay into light hadrons
rather than into isospin violating mode.
 X(3872) is not conventional charmonium.
Tetraquark?
PRD71,014028(2005)
Maiani, Polosa, Riquer, Piccini;
Ebert, Faustov, Galkin; …
[cq][cq]
[cu][cu]
[cd][cd]
[cu][cd]
Predictions:
1. Charged partners of X(3872).
2. Two neutral states ∆M = 8  3 MeV,
one populate B+ decay, the other B0.
Charged partner of X(3872)?
PRD71,031501,2005
B0
B-
 No evidence for
X–(3872)  J/ –0
X(3872)–
M(J/π–π0)
X(3872)–
M(J/π–π0)
excludes isovector hypothesis
X(3872) Production in B0 vs. B+
B0→XK0s
arXiv:0809.1224 605 fb-1
5.9
M(J/)
 No evidence for neutral partner of X(3872) in B0 decays.
Two overlapping peaks in J/ +- mode?
PRL103,152001(2009)
No evidence for two peaks m < 3.2 MeV at 90% C.L.
Tetraquarks are not supported by any experimental evidence
for existence of X(3872) charged or neutral partners.
D*0D0 molecule?
Swanson, Close, Page; Voloshin; Kalashnikova, Nefediev; Braaten; Simonov, Danilkin ...
MX
= 3871.52  0.20 MeV
(MD*0 + MD0) = 3871.94  0.33 MeV
m = – 0.42  0.39 MeV
Weakly bound S-wave D*0D0 system
a few fm
Predict different line shapes for J/+- and D*0D0 modes:
Bound state
J/+-
Virtual state
D0D00
D*0D0
J/+-
D0D00
D0D*0 molecule
Br(X(3872)  J/ )
~1
Br(X(3872)  J/ r)
Br(X(3872)   )
~3
Br(X(3872)  J/ )
Large isospin violation due to 8 MeV difference
between D*+D- and D*0D0 thresholds.
Similar ratio is expected for c1 decays
 c1 admixture?
Large production rate in B decays and in pp  c1 ?
Bound or virtual?
c1 admixture?
 Analysis of data
Kalashnikova, Nefediev arXiv:0907.4901
State
c1 admixture
Belle data
bound
~ 30%
BaBar data
virtual
~0
~2 experimental difference reverses conclusion
 Present statistics are insufficient to constrain theory?
There are other similar analyses which differ in the fit functions:
Braaten, Stapleton
Zhang, Meng, Zheng
arXiv: 0907.3167
0901.1553
theorists here should agree on the proper form & then
experimenters should use it in a proper unbinned fit
Coupled Channels Effect
 Corrections to energy levels.
 If cc-DD coupling is strong enough – DD molecule.
B → X(3872) K 
arXiv:0809.1224 605 fb-1
X(3872)
sideband
non-resonant Kπ
Mass(Kπ)
Br(B0 →X(K+π–)non_res) Br(X→J/ψπ+π–) = (8.1±2.0+1.1–1.4)  10–6
Br(B0 →XK*0) Br(X→J/ψπ+π–) < 3.4  10–6 at 90% C.L.
Br(BJ/ K*0)
Br(BJ/ KNR)
~4
DD* molecular models for the X(3872) attribute its production
& decays  charmonium to an admixture of c1′ in the wave fcn.
But BKX(3872) is very different from BK charmonium.
KX3872
K′
Kc1
Belle arXiv 0809.0124
Belle arXiv 0809.0124
Belle PRD 74 072004
M(K)
M(K)
KJ/
Kc
M(K)
Belle F.Fang Thesis
BaBar PRD 71 032005
M(K)
M(K)
Conclusions
Potential models have model relation to QCD by describe a lot of data.
Finally potential models failed to describe charmonium?
X(3872) – heavy, very narrow! at D*D threshold.
Isospin violating decay is not suppressed.
Favorite interpretation is D*0D0 molecule.
Open question: (1) bound or virtual, (2) admixture of conventional charmonium.
probably only next generation experiments will answer this
Theoretical analysis of coupled channel effects.
description of X(3872) within potential models?
More interesting charmonium-like states to come next lecture.