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?