New charmonium resonances
description
Transcript of New charmonium resonances
New charmonium resonances
Roman Mizuk, ITEP
ITEP Winter School, 13-20 Feb 2010
Outline
X(3872)
1- - states from ISR
3940 family
Z±
Bottomonium
Potential Models
Traditional charmonium states
New charmonium resonances
Charmonium – meson containing cc quarks
Family of excited states: c , J/ , cJ , hc , (2S) , …
SystemGround triplet state
(v/c)2
Name Mass, MeV G, MeV
POSITRONIUM
e+e- Ortho- 1 5 10-15 ~0.0001
QUARKONIUM
uu,dd 800 150 ~1.0
ss 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.
“Hydrogen atom” of QCD
Quantum Mechanics
two-body problem
Quantum Field Theory
Number of particles is not conserved multi-body problem
non-relativistic relativistic
Hydrogen atom
Precise description of hydrogen atom. EXCEPT FOR LAMB SHIFT.
nnn rZe
mE
22
2
Srödinger equation 21
2
nRZ
En eVR 6.131
Dirac equation 0 neAi
0A
rZe
A
nnn irZe
E
2
0
non-relativistic
relativistic bispinor
Field Theoretical description of bound state
Amplitude: + + …+
Analytic continuation into complex energy plane.
Re E
Im E
e-
p
mp+mepoles
bound states
Hydrogen atom (2)
Solutions of Dirac equationcorrespond to sum + + + …
= running charge, distorts Coulomb potentialtoo small effect to reproduce Lamb shift
+ …
+ …not a single particle!
reproduces Lamb shift
~ = v/c
No way to account for in Dirac equation.
Non-potential effects are small if electron is slow in the time scalewhen additional degrees of freedom are present in the system.
Potential Model of Charmonium
+ + … = constituent quark, heavier by 300MeV
+ + … rr
rrV s )()(
QCD motivated potential
Assume that charm quark is heavy enough to neglect non-potential effects.+ …
(M(2S) – MJ/ ) / QCD = 590 MeV / 200 MeVNot justified: is not small.
Open question: why Potential Models work reasonably well for charmonium?
Charmonium Potentials
rr
rrV s )()(
one-gluon exchange,asymptotic freedom
confining potential, “chromoelectric tube”
c J/ c2 (2S)
“Cornel model”
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
Charmonium levels without spin
Coulomb Harmonic oscillator
QCD
1s 1s
1s
2s 2s1p
1p
1p2s
1d
Relativistic Corrections
fine structure of states spin-singlet triplet splitting
not commute with
2qVvvuu v 2qVvvuu s
Assign Lorentz structure to potentials
L̂
scalar
short distance confining
Breit-Fermi expansion to order v2/c2
vector
Charmonium Levels
P = (–1)L+1
C = (–1)L+S
S = s1 + s2 = { 0, 1 }
J = S + Ln – radial quantum number
JPC
building blocks
S=0 L=0 1S0 c , c(2S)0– +
3S1
J/ , (2S) , (4040) , (4415)
1– –
S=0 L=1 1P1 hc1+ –
S=1 L=1
3P1
3P2
3P3
0+ +
1+ +
2+ +
2.75
3.00
3.25
3.50
3.75
4.00
4.25
4.50
c
J/
hc
c(2S)(2S)
S=1 L=2 3D1 (3770), (4160)1– –
(3770)
(4160)
(4415)
(4040)
0– + 1– – 1+ – (0,1,2)+ +
c2c1c0
c2(2S)
JPC
M, GeV
S=1 L=0
c0
c1
c2 , c2 (2S)
n(2S+1)LJ
(3770) = 13D1 + 0.2 23S1 “S - D mixing”
spectroscopic notation conserved QN
State ExperimPredictions of Potential Models
Predictions of Potential Models
JPC
M,
GeV
Potential models reproduce also
annihilation widths J/, (2S)→ℓ+ℓ-
ccJ→ and
radiative transitions btw. charmonia.
Hadronic mass in Lattice QCD
Average over all possible configurations of fields generated on lattice and weighted with exp(iS).
Min
kovs
ky →
pse
udo-
Euc
lidia
n sp
ace.
Expect: G(t,0) = A1exp(im1t) + A2exp(im2t) + A3exp(im3t) + ...
Multi exponential t-dependence of Green function complicates identification of excited states.
Calculate 2-point Green function G(t,0) = 0O (t)O(0)+0, creating hadron at time 0 and destroying at time t.
Operator O has required quantum numbers: JPC, flavor contentand is projected on zero momentum.
ground state
1st radial excitation
For this
2nd radial excitation
→ exp(–S)
→ A1exp(–m1t) + A2exp(–m2t) + A3exp(–m3t) + ...
from first principles
Charmonium in Lattice QCD
Predictions for charmonia up to the 1st radial excitation exist.Still a lot of room for improvement.
Potential for static charm quarks. Shape is similar to that of phenomenological models.
quenched approximation
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
+ Using 3-4 parameters can describe a lot of data.right choice of variables?
Shape of potential in agreement with Lattice QCD estimations,and with perturbative QCD calculations (at small distances).
Useful framework for refining our understanding of QCDand guidance towards progress in quarkonium physics.
– Only model relation to underlying fundamental theory of QCD.difficult to assign uncertainties to results
o In many cases the only available theoretical approach.
good predictive power
higher resonances
success of phenomenology
Observation of J/
p + Be → e+e- + X
BNL AGS SLAC SPEARextracted 28 GeV p-beam
M( e+e- )
hadronsee
ee
eeee
e+e- annihilation
Be target
Ting et al.
Richter et al.
Width of tJ/ is very narrow, JPC=1– –.
E c.m.s.
, n
b,
nb
, n
b
Mark I first 4 detector
“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)
(2S) → J/ +- J/ → e+e-
Mark I Event Display
SLAC SPEAR
two weeks after observation of J/
(2S) is very narrow, JPC=1– –.
– DASP, DESY (1976)
– Crystall Ball, SLAC (1980)
Observation of
Crystal Ball: sphere with 900 NaI crystals
cJ
c
c – DASP (1977)
c(2S) – CBall (1980)
2qc eN
eehadronsee
R
s
ee3
4 2
First results on R above DD threshold – SPEAR (1975).
4 peaks above 3.7 GeV :
c
c‾ c‾
c
g
g
c
c‾
e,,q
e,,q̄
MeV 0.093 ± 0.002 0.327 ± 0.011
27 ± 4 11 ± 1 27 ± 1 85 ± 12
J 2S c c0 (3770) (4040)
Why J/ is so narrow?
C-parity
~s3
2/31/3
DDat
threshold
DD*D*D*
For J/ strong decays are suppressed so much that EM decays are competitive.
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
Cherenkov Detector (DIRC)[144 quartz bars, 11000 PMTs]
Silicon Vertex Tracker (SVT)
Instrumented Flux Return (IFR) [Iron interleaved with RPCs].
CsI(Tl) Calorimeter (EMC)[6580 crystals].
Superconducting Coil (1.5T)
Drift Chamber [40 stereo lyrs](DCH)
e– (9 GeV)
e+ (3 GeV) e+e– → Y(4S)
e+e– → сharmonium CLEO-c BES-IIE = 3.0 - 4.8 GeVL ~ 1033/cm2/s
BaBar Belle
E = 10.6 GeV
L ~ 2*1034/cm2/s
530 + 1000 fb-1
pp collider CDF D0E ~ 1.8 TeV
¯m / KL detection 14/15 lyr. RPC+Fe
Tracking + dE/dx small cell + He/C2H5
CsI(Tl) 16X0
Aerogel Cherenkov cnt. n=1.015~1.030
Si vtx. det. 3 lyr. DSSD
TOF counter
SC solenoid1.5T
8 GeV e–
3.5 GeV e+
B-factories
in B decays
initial state radiation
JPC = 1– –
double charmonium production
γγ fusion
JPC = 0± +, 2± +
Only JPC = 0± + observed so far.
Any quantum numbers can be produced,to be determined from angular analysis.
Charmonium production at B factories
• 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).
∆E, GeV
Mbc, GeV
Reconstruction of B decays
B0J/ KS
c(2S)
B (KSK) K
e+e– J/ X
M = 2654 6 8 MeV/c2
< 55 MeV
M = 2630 12 MeV/c2
Good agreement with potential modelsfor mass, width and 2-photon width.
Observation of c(2S)
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.
Width: 6±12 (CLEO) and 17± 8 MeV (BaBar)average Γ = (14 ± 7) MeV
(2S) → 0 hc → 0 c
hc
< 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
M(hc) = (3524.4 ± 0.6 ± 0.4) MeV
Observation of hc
M = 3931 4 2 MeV/c2
= 20 8 3 MeV
consistent with J=2 J=0 disfavored 2/dof=23.4/9
Поляризация
395fb-15.5
2005, BELLE
2009, BaBar
γe–
e+
De+
e–
γDχс2’
c2(2S) in interactions
Width and 2-photon width are in good agreement with models, mass is 50 MeV lower.
Charmonium Levels 2010M
ass
(M
eV
)
JPC
(2S+1)LJ
(3770)
(4040)
(4160)
c
’c
J/
(4415)
(Potential Models)
c2 c1 c0hchc
′DD
X Y
Y
??
’c2 X~10 states with – mass – decay pattern – quantum numbersthat do not fit expectations.
3 identified charmonia.
New:
New charmonium(like) states
states contain cc
XYZ
resonances
About 10 charmonium(like) states do not fit expectations.
Have Potential Models finally failed?
Exotics?
c
u
cu
πc
u
c
uu
cu
ccu
πcuc u
cuucc u
cc
gc
cc
g
hybrid
tetraquark molecule
yes, but coupled channel effect was taken into account
c c–π
πhadrocharmoniumcharmonium embedded
into light hadron
compact diquark-diantiquark state
state with excited qluonicdegree of freedom
two loosely boundD mesons
X(3872)
7th anniversary!
Phys.Rev.Lett.91 262001, (2003)
CP
Belle citation count
B→Xsγ
480
487
336
X(3872)
Swanson, CharmEx09
PRL91,262001 (2003)
X(3872) was observed by Belle in
B+ → K+ X(3872) 2S→ J/ψ π+ π-
Recent signals of X(3872) → J/ψ π+ π-
X(3872)
Confirmed by CDF, D0 and BaBar.
pp collisions
PRL93,162002(2004)
arXiv:0809.1224 PRD 77,111101 (2008)
PRL103,152001(2009)
direct productiononly 16% from B
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(X J/ + -) > 2.5%
at 90%C.L.
Absolute Br? missing mass technique
B-
K
XccB
(4S)
PRL96,052002(2006)
reconstructonly
K+ momentum in B+ c.m.s.
Br(B+ X K+) < 3.210–4
Br(B+ X K+) Br(X J/ + -) =(8.10 0.92 0.66) 10-6
(8.4 1.5 0.7) 10-6
(4S) 4-momentumfrom beam energy
mX2=(pB+ – pK+)2
Radiative Decays & J/
CX(3872) = +
J/
X(3872) → J/ + - 0
subthreshold production of
+-0
hep-ex/0505037 PRL102,132001(2009)
Decay modes Br relative to J/+-
J/ 0.15 0.05
J/ 0.33 0.12
S 1.1 0.4
J/ 1.0 0.5
2S J/
CX(3872) = + C+- = – 1. Isospin (+-) = 12. L(+-) = 1
IJPC of 0
PRL96,102002(2006)
hep-ex/0505038
L=1
L=0
M (+-)
X(3872) → J/+- X(3872) → J/0
X(3872) → J/+-
M (+-) is well described by 0→+- (CDF: + small interfering →+- ).
(|+1,-1 – |-1,+1) ( r )
isospin
Angular analyses by Belle and CDF excluded JP =
JPC = 1++ or 2–+
2–+ is disfavored by
JP = 1++ are favorite quantum numbers for X(3872).
0++, 0+-, 0-+,1-+ ,1+-, 1--, 2++, 2-- , 2+-,3--, 3+-
Spin & Parity
2–+ not excluded.
PRL98,132002(2007)
0++
1--
1++
2-+
1. Br(X → (2S) γ) / Br(X → J/γ) ~ 3 multipole suppression2. Observation of D*0D0 decay centrifugal barrier at the threshold
B+& B0 D0D*0K4.9σ
347fb-1
PRD77,011102(2008)
B K D0D*0
605 fb-1
D*→Dγ
D*→D0π0
Flatte vs BW similar result: 8.8σ
arXiv:0810.0358X(3872) → D*0D0
~2
Shifted X(3872) massin D*D final state influence of nearby D*D threshold.
X(3872) Experimental Summary
JPC = 1++ (2–+ not excluded)
Close to D*0D0 threshold: m = – 0.42 0.39 MeV.
Br(X(3872) J/ 0) > 2.5% (90% C.L.)
M = 3871.52 0.20 MeV , Γ = 1.3 0.6 MeV
Decay modes Br relative to J/ 0
J/ 0 1
J/ 1.0 0.5
J/ 0.17 0.05
(2S) 1.1 0.4
D*0D0 ~10
3872
JPC = 1++ c1′
X(3872) is not conventional charmonium.
Is there cc assignment for X(3872)?
JPC = 2–+ η c2
Expected to decay into light hadronsrather than into isospin violating mode.
1++
2-+
Br( c1′ → J/ )Br( c1′ → J/ +-)
measure 0.170.05
expect 30
~100 MeV lighter than expected
[cq][cq]
Tetraquark?Maiani, Polosa, Riquer, Piccini; Ebert, Faustov, Galkin; …
No evidence for X–(3872) J/ –0 excludes isovector hypothesis
X(3872)–
M(J/π–π0) M(J/π–π0)
X(3872)–
PRD71,031501,2005
B0 B-
PRD71,014028(2005)
1. Charged partners of X(3872).2. Two neutral states ∆M = 8 3 MeV,
one populate B+ decay, the other B0.
Predictions:
Charged partner of X(3872)?
[cu][cu]
[cd][cd]
[cu][cd]
X(3872) Production in B0 vs. B+
No evidence for neutral partner of X(3872) in B0 decays.
B0→XK0s
5.9
M(J/)
arXiv:0809.1224 605 fb-1
Two overlapping peaks in J/ +- mode?
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.
PRL103,152001(2009)
D*0D0 molecule?
MX = 3871.52 0.20 MeV(MD*0 + MD0) = 3871.94 0.33 MeV
Weakly bound S-wave D*0D0 system
Swanson, Close, Page; Voloshin; Kalashnikova, Nefediev; Braaten; Simonov, Danilkin ...
Bound state
J/+-D0D00
D*0D0
Virtual state
J/+-
D0D00
m = – 0.42 0.39 MeV
a few fm
Predict different line shapes for J/+- and D*0D0 modes:
D0D*0 molecule
Kalashnikova, Nefediev arXiv:0907.4901
Analysis of dataBound or virtual?c1 admixture?
~2 experimental difference reverses conclusion
Present statistics are insufficient to constrain theory?
Br(X(3872) J/ )Br(X(3872) J/ ) ~1
Large isospin violation due to 8 MeV differencebetween D*+D- and D*0D0 thresholds.
Br(X(3872) )Br(X(3872) J/ ) ~3
Similar ratio is expected for c1 decays c1 admixture?
State c1 admixture
Belle data bound ~ 30%
BaBar data virtual ~ 0
Large production rate in B decays and in pp c1 ?
theorists here should agree on the proper form & thenexperimenters should use it in a proper unbinned fit
There are other similar analyses which differ in the fit functions:
Braaten, StapletonZhang, Meng, Zheng
arXiv: 0907.31670901.1553
Coupled Channels Effect
Corrections to energy levels. If cc-DD coupling is strong enough – DD molecule.
Br(B0 →XK*0) Br(X→J/ψπ+π–) < 3.4 10–6 at 90% C.L.
~90 events
Very weak K
*(892)
Br(BJ/ K*0)
Br(BJ/ KNR)~4
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
DD* molecular models for the X(3872) attribute its production& decays charmonium to an admixture of c1′ in the wave fcn.
But BKX(3872) is very different from BK charmonium.
BaBar PRD 71 032005
Belle arXiv 0809.0124
Belle arXiv 0809.0124
Belle PRD 74 072004
K′
KJ/
Kc1
Kc
Belle F.Fang Thesis
KX3872
M(K)
M(K)
M(K)
M(K)
M(K)
Conclusions
More interesting charmonium-like states to come next lecture.
Open question: (1) bound or virtual, (2) admixture of conventional charmonium.
Potential models have model relation to QCD by describe a lot of data.
X(3872) – heavy, very narrow! at D*D threshold. Isospin violating decay is not suppressed.
Favorite interpretation is D*0D0 molecule.
probably only next generation experiments will answer this
Theoretical analysis of coupled channel effects.description of X(3872) within potential models?
Finally potential models failed to describe charmonium?