1/20RESULTS FROM CLEOJ. Rosner, at Miami 2010, Ft. Lauderdale, December 14–19, 2010

Cornell Electron Storage Ring (CESR): e+e− collisions, 1979-2008.

A wealth of data on charm and bottom quarks; analysis continuing.

Today: Some recent results, emphasis on spectroscopy

The CESR site at Cornell

Data samples and analyses

Charmonium radiative decays: pure E1?

Spin-singlet P-wave charmonium

CP- and flavor-tagged Dalitz plots

Ds decay constant

Spin-singlet S-wave bottomonium

P-wave bottomonium radiative transitions

2/20CLEO III AND CLEO-c DETECTORS

Solenoid Coil Barrel Calorimeter

Drift Chamber

Inner Drift Chamber /Beampipe

EndcapCalorimeter

IronPolepiece

Barrel MuonChambers

MagnetIron

Rare EarthQuadrupole

SC Quadrupoles

SC QuadrupolePylon

2230104-002

CLEO-c

Ring Imaging CherenkovDetector

CLEO III: Silicon vertex detector; replaced with inner chamber (“ZD”)sensitive to longitudinal position for CLEO-c

Photon ∆E/E = (5%, 2.2%) at (0.1,1) GeV; charged trk. ∆p/p = 0.6% at 1 GeV

3/20DATA SAMPLES AND ANALYSES

Will not report today on pioneering CLEO results above bottomthreshold; first observation of B0 = bd, B+ = bu. Lower-energysamples include:

Initial Integrated Decaystate luminosity (pb−1) products

Charmonium ψ(3686) 53.8 27 M totaland charm ψ(3770) 818 5.3 M DD

ψ(4170) 586 0.6 M D+s D

∗−s + c.c.

Bottomonium Υ(1S) 1056 20.81 ± 0.37 M totalΥ(2S) 1305 9.32 ± 0.14 M totalΥ(3S) 1387 5.88 ± 0.10 M total

Additional off-resonance samples for continuum studies

Here D0 = cu, D+ = cd, Ds = cs.

CLEO publications: 514 (+ 1 accepted + 2 under review)

As of December 2010, ∼ 30 analyses still in progress

234 CLEO PhDs (+32 CESR + 14 CUSB)

4/20HIGHER MULTIPOLES IN CHARMONIUMRADIATIVE TRANSITIONS

M. Artuso et al. (CLEO), ⇒ PRD 80, 112003 (2009)Analysis initiated by R. Galik ; thesis of James Ledoux (Cornell)

Transitions ψ′ → γχcJ → γγJ/ψ

dominantly electric dipole (E1)

Higher multipoles allowed:

M2 for Jχ = 1; M2 and E3 for Jχ = 2;

No E3 for S ↔ P single-quark trans.

Angular distributions of photons

are sensitive to higher multipoles

M2 transition measures charmed

quark’s total magnetic moment

Relevant to strengths of M1

transitions ψ(nS) → ηc(nS)

Prediction of M2 admixture: G. Karl, S. Meshkov, JLR, PRL 45, 215 (1980)

5/20HELICITY AMPS. AND MULTIPOLES

Five angles describe ψ′ → γχ→ γγJ/ψ decays

Distributions depend on helicity amplitudes Bν′ (“before” χ) and Aν (“after” χ):

Clebsch-Gordan coeffs. relate helicity amps. A (or B) and multipole amps. aJχ

Jγ

M2 amplitudes related to anomalous moment κc of charm quark (potl. indep.!):

aJ=12 ≡

M2√

E12 + M22= −

Eγ

4mc

(1 + κc)

aJ=22 ≡

M2√

E12 + M22 + E32= −

3√

5

Eγ

4mc

(1 + κc) ;

similarly for b amplitudes with sign change, Eγ → Eγ′. These follow from

HI = −ec

2mc

( ~A∗ · ~p + ~p · ~A

∗) − µ~σ · ~H∗ + (spin − orbit term)

ec ≡ 23|e|; µ ≡ (ec/2mc)(1 + κc); ~A

∗ and ~H∗ ≡ ∇× ~A∗ refer to emitted photon

6/20COMPARISON WITH PREVIOUS RESULTS

CLEO-c: circle (two-parameter

fit for Jχ=2); Xtal Ball: diamonds;

E760: ∇; E835: ∆; BES-II: square;

Th. (mc=1.5 GeV, κc = 0): dashes

First significant evidence for

aJ=12 6= 0;

√prediction

Multipoles bJ=12 and aJ=2

2

also significantly non-zero and

in accord with prediction

Multipole bJ=22 not significant;

error reduced w.r.t. previous

No evidence for E3 transitions

Dudek +, PR D 73, 075407; 79, 094504:

aJ=12 = −0.09(7); aJ=2

2 = −0.39(7);

aJ=23 = −0.01(1)

7/20P-WAVE SINGLET CHARMONIUM: hc

Last charmonium state below flavor threshold: hc(1P ), spin-singlet (J/ψ + 30 yr!)seen by CLEO in 2005 [PRL 95, 102003; PR D 72, 092004] in isospin-violatingdecay ψ(2S) → π0hc(1P ) (B1), hc(1P ) → γηc(1S) (B2)

More recently: S. Dobbs + (CLEO), PRL 101, 182003 (2008) [24.5M ψ(2S)]:

M(hc) =3525.28±0.19±0.12 MeV, 〈M(3PJ)〉 −M(hc) =0.02±0.19±0.13 MeV

M. Ablikim + (BESIII), PRL 104, 132002 (2010) [106 M ψ(2S)]:

M(hc) =3525.40±0.13±0.18 MeV, 〈M(3PJ)〉 −M(hc) = −0.10±0.13±0.18 MeV

Error ≃ same as CLEO: Smaller statistical but larger systematic

Hyperfine splitting found small between P-wave states; wave function zero at origin

CLEO saw ηc(1S) both inclusively [B1B2 =(4.22±0.44±0.22) ×10−4]

and in 15 exclusive modes [B1B2=(4.15±0.48±0.77) ×10−4]

BESIII made separate measurements: B1B2 = (4.58±0.40±0.50)× 10−4;

B1 = (8.4 ± 1.3 ± 1.0) × 10−4 ⇒ B2 = (54.3 ± 6.7 ± 5.2)%

8/20hc(1P ) DECAYSG. S. Adams et al. (CLEO), PR D 81, 052013 (2010)

π+π−π0

π+π−π0,

J/ψ veto

3(π+π−)π0

2(π+π−)π0 data

B1B2=(1.9±0.5+0.5−0.3)×10−5

2(π+π−)π0,

non-hc Monte Carlo

9/20CP- AND FLAVOR-TAGGED DALITZ PLOTSJ. Libbyet al. (CLEO), CLNS 10/2070, arXiv:1010.2817 ⇒ PRD

Strong phase difference between D0 and D0 decays to KS,Lh+h−

(h = π or K) is important to learn Cabibbo-Kobayashi-Maskawa(CKM) angle γ/φ3 in B− → K−D decays; ∆φ ≃ 3–4◦

Exploits quantum coherence in ψ(3770) → D0D0.

D → KSK+K− D → KLK

+K−

CPeventag

CPoddtag

↑φ→

↑φ→

10/20Ds DECAY CONSTANTLatest CLEO: P. Naik et al., PR D 80, 112004 (2009); for averages seeJ. Rosner and S. Stone, in 2010 Review of Particle Physics, pp. 861-865

Decay constants fP govern leptonic decays of pseudoscalar mesons P :

Γ(P → ℓν) =G2

F8πf2

Pm2ℓmP

(

1 − m2ℓ

m2P

)2

|Vq1q2|2

Lattice: HPQCD/UKQCD (PRL 100, 062002): fD = 208 ± 4 MeV

CLEO: fD = (206.7 ± 8.5 ± 2.5) MeV via D+ → µ+ν

CLEO: fDs = (259.0± 6.2± 3.0) MeV via Ds → τ+ν and Ds → µ+ν

World average including new BaBar value: fDs = (257.5 ± 6.1) MeV

HPQCD/UKQCD: 241±3 MeV, upwardly revised to 248.0±1.5 MeV[PR D 82. 114504 (2010)]; Fermilab/MILC: 260 ± 10 MeV

Expt: fDs/fD = 1.25 ± 0.06; upper range of theory

Heavy-quark effective theory (HQET): ratio should be close to fBs/fB

governing interpretation of ratio of Bs–Bs and B0–B0 mixing

11/20BOTTOMONIUM SPECTRUM

ηb mass, production rate [BaBar: PRL 101, 071801 (2008); 103, 161801 (2009);CLEO: G. Bonvicini +, PR D 81, 031104(R) (2010)]; hb(9900) search [CLEO]

Plus

E1 radiative

transitions

S ↔ P ↔ D

12/20CLEO Υ(3S) → γηb(1S) ANALYSISNew (cf. BaBar): (1) initial-state radiation (ISR) in e+e− → γ(859 MeV)Υ(1S);(2) finite Γ(ηb) (nominal 10 MeV); (3) angle between γ(920 MeV) and thrust axis[BaBar: cos θT < 0.7; CLEO: bins 0.0–0.3, 0.3–0.7, 0.7–1.0 fit separately]

68.5±6.6±2.0 MeV below Υ

BaBar: 71.4+2.3−3.1 ± 2.7 MeV

66.1+4.9−4.8 ± 2.0 MeV (2S)

Examples of lattice calculations:

HPQCD: 61(14) MeV

RBC/UKQCD: 52.5(1.5) MeV

FNAL/MILC: 54.0±12.4+1.2−0.0

MeV [PRD 81, 034508 (2010)]

B[Υ(3S) → γηb(1S)] =

(4.8±0.5±1.2)×10−4 (BaBar)

(7.1±1.8±1.1)×10−4 (CLEO)

Subtract large peak (⇓) due to χb(2P ) → γΥ(1S)

χb(2P ) ISR ηb

13/20RADIATIVE χbJ(1P ) TRANSITIONSM. Kornicer et al. (CLEO), CLNS/10/2071, arXiv:1012.0589, ⇒ PRD

In search for Υ(3S) → π0hb → π0γηb, photons in the transitionsΥ(3S) → γχb(1P ) and χb → γΥ(1S) are in the 400–500 MeV rangeand can be a problematic background

Electric dipole matrix elements for 3S → 1P are forbidden fora harmonic oscillator potential and highly suppressed for realisticquarkonium potentials (A. K. Grant et al., PR D 53, 2742 (1996)).

Previously known branching fractions involving χb(1P ) states:

Transition Eγ (MeV) B (%) CommentsΥ(3S) → γχb0(1P ) 483.9 0.30 ± 0.11 CLEO, PR D 78, 091103Υ(3S) → γχb1(1P ) 452.1 < 0.17 First reported hereΥ(3S) → γχb2(1P ) 433.5 < 1.9 First reported hereΥ(2S) → γχb0(1P ) 162.5 3.8 ± 0.4 Dominated by CLEO:Υ(2S) → γχb1(1P ) 129.6 6.9 ± 0.4 M. Artuso et al.,Υ(2S) → γχb2(1P ) 110.4 7.15 ± 0.35 PRL 94, 032001 (2005)χb0(1P ) → γΥ(1S) 391.1 < 6 Main χb0 decay hadronicχb1(1P ) → γΥ(1S) 423.0 35 ± 8 Latest measurementχb2(1P ) → γΥ(1S) 441.6 22 ± 4 in 1986!

14/20UNFOLDING 420–450 MeV PHOTONS

Overlap of photon energies meant it was easiest to quote

Bsum =∑

J=1,2B[Υ(3S) → γχbJ(1P )] × B[χbJ(1P ) → γΥ(1S)]

= (1.2+0.4−0.3 ± 0.09) × 10−3 (CUSB, PR D 46, 1928 (1992))

= (2.14±0.22±0.21)×10−3 (CLEO, T. Skwarnicki, ICHEP 2002, Amsterdam)

To unfold J = 1 and J = 2 use Doppler broadening:

Photon resolution ±5 MeV Photon resolution ±10 MeV

15/20Υ(3S) MONTE CARLO AND DATA

Monte Carlo, Υ(1S) → µ+µ− Data, Υ(1S) → e+e− (∆) or µ+µ− (2)

Two-dimensional fit: best sensitivity to J = 1 and J = 2 components

B1≡B[Υ(3S)→γχbJ(1P )]; B2≡B[χbJ(1P )→γΥ(1S)]; B3≡B[Υ(1S) → ℓ+ℓ−].

Take B2(J=1) = (33.0 ± 0.5)%, B2(J=2) = (18.5 ± 0.5)%from new fit to Υ(2S) data; B3 = (2.48 ± 0.05)%

16/20EXTRACTED BRANCHING FRACTIONS

For the sum of J = 1 and J = 2, find∑

B1 × B2 = (2.00 ± 0.15 ±0.22 ± 0.04) × 10−3, agreeing well with 2002 CLEO value

Determinations for individual values of J :

J = 1 J = 2B1 × B2 (10−4) 5.38 ± 1.20 ± 0.94 ± 0.11 14.35 ± 1.62 ± 1.66 ± 0.29

B1 (10−3) 1.63 ± 0.36 ± 0.28 ± 0.09 7.74 ± 0.88 ± 0.88 ± 0.38

Portions of table presented earlier now look like this:

Transition B (%)Previous Now

Υ(3S) → γχb0(1P ) 0.30 ± 0.11 0.30 ± 0.11Υ(3S) → γχb1(1P ) < 0.17 0.163 ± 0.046Υ(3S) → γχb2(1P ) < 1.9 0.774 ± 0.130χb0(1P ) → γΥ(1S) < 6 1.73 ± 0.35χb1(1P ) → γΥ(1S) 35 ± 8 33.0 ± 2.6χb2(1P ) → γΥ(1S) 22 ± 4 18.5 ± 1.4

17/20Γ[Υ(3S) → γχbJ(1P )]: EXPT VS THEORY

ΓJ=0 (eV) ΓJ=1 (eV) ΓJ=2 (eV)

This analysis – 33 ± 10 157 ± 30

Inclusive CLEO expt. 61 ± 23 – –

Moxhay–Rosner (1983) 25 25 150

Gupta et al. (1984) 1.2 3.1 4.6

Grotch et al. (1984) (a) 114 3.4 194

Grotch et al. (1984) (b) 130 0.3 430

Daghighian–Silverman (1987) 42 – 130

Fulcher (1990) 10 20 30

Lahde (2003) 150 110 40

Ebert et al. (2003) 27 67 97

(a) Scalar confining potential. (b) Vector confining potential.

Υ(3S) → γχbJ(1P ) rates differ from expected ∼ E3γ(2J + 1) pattern.

Note

log

scale

18/20THEORY COMPARISONS, CONTINUEDDeviations from expected ∼ E3

γ(2J+1) pattern test models of relativistic corrections

Worth revisiting some of the old calculations within newer frameworks, e.g., NRQCD

Comparison of results for B[χbJ(1P ) → γΥ(1S)] with theoretical predictions (%):

Reference J = 0 J = 1 J = 2CLEO-III 1.73 ± 0.35 33.0 ± 2.6 18.3 ± 1.4

Moxhay–Rosner (1983) 3.8 50.6 22.3Gupta et al. (1984) 4.1 56.8 26.7

Grotch et al. (1984) (a) 3.1 41.9 19.4Grotch et al. (1984) (b) 3.3 43.9 20.3

Daghighian–Silverman (1987) 2.3 31.6 16.6Kwong–Rosner (1988) 3.2 46.1 22.2

Fulcher (1990) 3.1 39.9 18.6Lahde (2003) 3.3 45.7 21.1

Ebert et al. (2003) 3.7 51.5 23.6

(a) Scalar confining potential. (b) Vector confining potential.

Increase of αS(mb) in Kwong-Rosner calculation from 0.18 to 0.214 ± 0.006 leadsto agreement; consistent with compilation by Bethke, EJPC 64, 689 (2009)

19/20CLEO: SOME UNFINISHED BUSINESS

More hadronic transitions in bb systems, e.g., Υ(3S) → γχ′b0 → γηηb

Limits on hb = 11P1(bb) production via Υ(3S) → π0hb → π0γηb orΥ(3S) → π+π−hb → π+π−γηb

Search for Υ(1S) → γηb summing exclusive ηb modes

Emulate ηb, χb, χ′b decays (PYTHIA, . . .?) to compare with branching

fractions in 14 observed modes [CLEO, PRD 78, 091103(R) (2008)].

CLEO: few (if any) “missing” modes in D+s decays [S. Dobbs +, PR

D 79, 112008 (2009)]; inclusive study pointed the way to a few more[J. Y. Ge + (CLEO), PR D 80, 051102(R) (2009)].

Map out D0, D+ inclusive decays in similar manner; missing modes predicted byisospin statistical model include B(D+ → K0π+2π0) ≃ (few %)

Hope to wrap up many CLEO analyses within a year

20/20CONCLUSIONSCLEO continues to contribute to charm and bottom physics

• hc is now well-established; how well can theory predict its mass? Width?

• See M2 amplitudes for χc1 → γJ/ψ, χc2 → γJ/ψ, and ψ′ → γχc1; exclude pureE1 by more than (11, 6)σ for Jχ = (1, 2).

• Strengths of these amplitudes agree with predictions to O(Eγ(′)/mc) withmc = 1.5GeV and κc = 0; lattice did not anticipate M2 contributions so well

• ηb has been confirmed; lattice did better than potential models in predicting it

• CLEO has improved knowledge of radiative transitions involving lowest P-wave bbstates; some suppressed branching fractions measured for first time

• Many questions in meson spectroscopy may require methods beyond the capabilityof current theoretical approaches.

Still learning about (c,b) mesons after more than thirty years; manypotential tests of our understanding of low-energy strong interactions

21/20Jχ = 1, 2 LIKELIHOODS

Two-parameter fit, Jχ = 1:

Prediction for κc = 0, mc = 1.5

GeV is (a2, b2) = (−0.065, 0.029)

(a2, b2) = (0, 0) (•) is 11.1σ

from maximum-likelihood solution ( )

Two-parameter fit, Jχ = 2:

Prediction for κc = 0, mc = 1.5

(a2, b2) = (0, 0) (•) is 6.2σ

from maximum-likelihood solution ( )

( )

( )

22/20DECAYS [J/ψ, ψ(2S)] → γ(π0, η, η′)

T. K. Pedlar + (CLEO), PR D 79, 111101 (R) (2009)

J/ψ → γπ0 BR gives form factor for γ∗ → γπ0. Below calculation by Chernyak +Zhitnitsky, Phys. Rep. 112, 173 (1984). Can theory predict it?

Initial B (10−4) (p∗η/p∗η′)3

state γη γη′

J/ψ 11.01 ± 0.29 ± 0.22 52.4 ± 1.2 ± 1.1 1.229

ψ(2S) ≡ ψ′ < 0.02 1.19 ± 0.08 ± 0.03 1.153

Assuming these decays proceed via cc→ γgg → γ(η, η′), the η/η′ ratio should givethe relative contribution of SU(3) singlet in η and η′

Correcting for p∗3, J/ψ decays give 0.17 ± 0.01 while ψ′ gives < 0.02. Typicalmodel gives ≃ 1/8 so it is B(ψ′ → γη′) that is anomalously low

Reminiscent of strong suppression of certain ψ′ decays such as ρπ; does theoryexpect anything unusual about ψ′?

23/20LOW-MASS pp STATESBESIII (M. Ablikim +, arXiv:1001.5328) confirms BES-II (PRL 91, 022001) low-mass pp threshold enhancement in J/ψ → γpp (producing J/ψ in ψ′ → π+π−J/ψ)

)2(GeV/cp-2mppM0.00 0.05 0.10 0.15 0.20 0.25

)2E

vent

s/(0

.005

GeV

/c

0

10

20

30

40

50

60

70

)2(GeV/cp-2mppM0.00 0.05 0.10 0.15 0.20 0.25

)2E

vent

s/(0

.005

GeV

/c

0

10

20

30

40

50

60

70Not seen in ψ′ → γpp

X(1835) → η′π+π−

may be related

Glueball, baryonium,

a mixture, or neither?

CLEO: Enhancement

above Mpp − 2mp

= 300 MeV should be

considered when fitting

threshold enhancement

M = 1861+6+7−13−26 MeV, Γ < 38 MeV. Can theory say anything about baryon-

antibaryon resonances? Early prediction (including exotics): PRL 21, 950 (1968)

24/20EXCLUSIVE χb ≡ χb(1P ), χ′b ≡ χb(2P ) DECAYS

D. M. Asner et al. [CLEO Collaboration], Phys. Rev. D 78, 091103 (2008).

Identified 14 modes with > 4σ signals in at least one χbJ or χ′bJ decay

Υ(2S) → γχb Υ(3S) → γχ′b Υ(2S) → γχb Υ(3S) → γχ′

b

What do Monte Carlo fragmentation programs (PYTHIA, . . .) predict?