INFN Sezione di Roma on behalf of the BABAR Collaboration

Rencontres de Moriond QCD and High Energy Interactions 13 – 20 March, 2010 La Thuile

e+e- → hadrons in ISR and Two-photon reactions with BELLE and BABAR

Fabio Anulli

Outline •  selected ISR results

–  exclusive light hadron final states •  e+e− → π+π−

–  e+e− → open charm

•  selected γγ results –  no-tag mode

•  γγ → π0π0, ηπ0

•  γγ → DDbar

–  single-tag mode •  γγ* → π0,ηc ==> Transition Form Factors

3/16/10  F. Anulli  2 

hadronic contribution to (g-2)µ

•  more results shown yesterday by Pasha Pakhlov on discovery of “exotic charmonium-like” state

3/16/10  F. Anulli  3 

selected ISR results

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mf

2 = ′ s = s(1− x)

ISR @ 10.6 GeV ==> access the same observables as low energy e+e- experiments! •  Quantum numbers at production vertex JPC=1--

•  Continuous ISR spectrum:   whole energy range covered with same detector condition and analysis

  good efficiency down to threshold and up to √s ~5 GeV •  αem suppression compensated by the huge luminosity

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dσe +e − → fγ

(s,mf )dmdcosθγ

∗ =2msW (s,x,θγ

∗) ⋅σe +e − → f

m f( )Radiator function

3/16/10  F. Anulli  4 

The Anomalous Magnetic Moment of the muon

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a µSM =

g − 22

µ

= a µQED + aµ

had + aweak

aµ precisely measured at BNL E821 Phys.Rev.D73,072003(2006) aµ

exp - aµSM = ( 30.1± 8.6 ) × 10-10 (arXiv:0908.4300)

•  Dominant uncertainty from hadronic vacuum polarization. •  Cannot be calculated by QCD “first principles”

R(s) = σ(ee→hadrons)/σ(ee→µµ)

determine it via dispersion relations, by measuring the total hadronic cross section

73% from ππ

Value before BABAR result aµ

had = (690.9 ± 5.3)10-10

62% of uncertainty from ππ

Need to measure R(s) with better than 1% precision!

]2 [GeV/cµµm

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3/16/10  F. Anulli  5 

BABAR measurement of Rππ

ISR γ detected ==> powerful background rejection

Kinematic fit including 1 additional γ : NLO! All efficiencies (trigger, filter, tracking, PID, fit)

from the same data Measure ratio of ππ to µµ to cancel : ee Luminosity, additional ISR, vacuum polarization, ISR γ efficiency

Phys. Rev. Lett. 103, 231801(2009)

]2 [GeV/cµµm

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3/16/10  F. Anulli  6 

BABAR measurement of Rππ

ISR γ detected ==> powerful background rejection

Kinematic fit including 1 additional γ : NLO! All efficiencies (trigger, filter, tracking, PID, fit)

from the same data Measure ratio of ππ to µµ to cancel : ee Luminosity, additional ISR, vacuum polarization, ISR γ efficiency

Phys. Rev. Lett. 103, 231801(2009)

BABAR aµ

ππ[2mπ,1.8GeV] = (514 ± 2.2 ± 3.1) × 10-10

aµhad (10-10) 695.5 ± 4.0exp ± 0.7QCD

aµexp - aµ

SM (10-10) 25.5 ± 8.0

Deviation 3.2 σ

Note: averages taken from M.Davier et al. arXiv:0908.4300

the discrepancy with the esxperimental value is still above 3σ!

previous e+e- average 503.5 ± 3.5tot

new e+e- average 508.4 ± 1.3 ± 2.6

new average from tau 515.2 ± 2.0exp±2.2BF±1.9IB

Including all other contributions from e+e- cross sections

3/16/10  F. Anulli  7 

The ISR program in BABAR e+e– → π+ π–π+π–

unprecedented accuracy!  a factor 2‐3 improvement on determinaHon of contribuHons to aµ

had (×10-10)  

Vigourous campaign that is still in progress: -  ΚS

0Κ-π+, Κ+Κ-π0, Κ+Κ-η PRD 77, 092002, 2008 -  2(π+π-)π0, 2(π+π-)η, Κ+Κ-π+π-π0, Κ+Κ-π+π-η PRD 76, 092005, 2007 -  Κ+Κ-π+π-, Κ+Κ-π0π0, Κ+Κ-Κ+Κ- PRD 76, 012008, 2007 -  3(π+π-), 2(π+π-π0), Κ+Κ-π+π-π+π- PRD 73, 052003, 2006 -  π+π-π+π-, Κ+Κ-π+π-, Κ+Κ-Κ+Κ- PRD 71, 052001, 2005 -  π+π-π0 PRD 70, 072004, 2004 -  pp PRD 73, 012005, 2006 -  ΛΛ, Σ0Σ0, ΛΣ0 PRD 76, 092006, 2007 •  First observations 232 fb-1, 89 fb-1 @ 10.6 GeV •  all analysis with tagged ISR γ ==> efficient background rejection •  only charmless mesons and baryons in this slide

without BABAR with BABAR π+π-π0 2.45 ± 0.26 3.25 ± 0.09

2 (π+π-) 14.20 ± 0.90 13.09 ± 0.44

3 (π+π-) 0.10 ± 0.10 0.11 ± 0.02

2 (π+π-π0) 1.42 ± 0.30 0.89 ± 0.09

UL @ 90% CL 1  34  40 

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BF(Y (4260)→ X )BF(Y (4260)→ J /ψπ +π− )

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X =DD

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X =D*D *

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X =DD *

e+e- annihilation to open charm via ISR: e+e-→ D(*)D(*)

DD

DD*

D*D*

384 %‐1 

Phys.Rev. D79, 092001(2009)

No evidence found:   

3/16/10  8 F. Anulli 

•  Measure properties of heavy charmonium states •  Search for Y(4260) D(*)D(*) decays

•  should be the dominant decay for a ccbar meson

for comparison (from PDG):   

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BF(ψ(3770)→ DD )BF(ψ(3770)→ J /ψπ +π− )

≈400

ψ(3770)

ψ(4040) ψ(4415)

•  Full reconstruction of the hadronic part •  Both charged and neutral final states •  Fit by sum of ψ states with fixed masses&widths from PDG (due to limited statistics)

UL @ 90% CL 1  34  40 

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BF(Y (4260)→ X )BF(Y (4260)→ J /ψπ +π− )

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X =DD

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X =D*D *

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X =DD *

e+e- annihilation to open charm via ISR: e+e-→ D(*)D(*)

DD

DD*

D*D*

384 %‐1 

Phys.Rev. D79, 092001(2009)

Sum of two body  open charm final 

states 

No evidence found:   

BELLE: Phys. Rev. Lett. 98, 092001 (2007)

3/16/10  9 F. Anulli 

•  Measure properties of heavy charmonium states •  Search for Y(4260) D(*)D(*) decays

•  should be the dominant decay for a ccbar meson

for comparison (from PDG):   

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BF(ψ(3770)→ DD )BF(ψ(3770)→ J /ψπ +π− )

≈400

ψ(3770)

ψ(4040) ψ(4415)

•  Full reconstruction of the hadronic part •  Both charged and neutral final states •  Fit by sum of ψ states with fixed masses&widths from PDG (due to limited statistics)

e+e- → γISR D0D* − π+

Phys.Rev.D80,091101(2009) (R) 695 %‐1 

3/16/10  10 F. Anulli 

•  No evident structures: only UL’s ! •  Baseline fit:

•  RBW for ψ(4415) & not-interfering threshold function for non-resonant contribution

σ(e+e–→ψ(4415))×Br(ψ(4415)→D0D*–π+)< 0.76 nb at 90% CL Br(ψ(4415)→ D0D*–π+) < 10.6 % at 90% CL

ψ(4415) Upper Limit  

e+e- → γISR D0D(*) - π+

Phys.Rev.D80,091101(2009) (R) 695 %‐1 

3/16/10  11 F. Anulli 

•  No evident structures: only UL’s ! •  Baseline fit:

•  RBW for y(4415) & not-interfering threshold function for non-resonant contribution

•  Search for exotic states X→D0D*–π+, X=Y(4260), Y(4360), Y(4660), X(4630) •  Perform different fits, each with one exotic X state , the ψ(4415) and non-resonant contribution (not-interfering amplitudes) •  Fix masses and total widths

σ(e+e–→ψ(4415))×Br(ψ(4415)→D0D*–π+)< 0.76 nb at 90% CL Br(ψ(4415)→ D0D*–π+) < 10.6 % at 90% CL

Y(4260) 

ψ(4415) 

UL at 90% CL

3/16/10  F. Anulli  12 

Selected two-photon results in no-tag mode

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σ e+e− → e+e−γ *γ * → e+e−X( ) = σγγ→X (W )dLγγdW

dW∫

•  C-even final states •  JPC = 0±+, 2±+, …. (J=1 forbidden for two real photons)

complementary to e+e- annihilation!

–  Measure exclusive final states with invariant mass up to ~4.5 GeV/c2 –  Beam particles escape with small scattering angle –  q2≈0 : “quasi-real” photons can measure Γγγ –  two-photon events selected with tight pT cut

•  Clear f0(980), f2(1270) peaks •  Structures visible around 1.6 and 2.0

GeV ( f4(2050) ) •  Smooth behaviour above ~2.4 GeV

γγ → π0π0, ηπ0   

γγ → π0π0  γγ → ηπ0 

•  a0(980), a2(1320), a2(1700) seen •  Smooth behaviour above ~2.4 GeV

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σ e+e− → e+e−X( ) = σγγ→X (W )dLγγdW

dW∫

€

dσγγ→X

d cosθ*=

ΔN −ΔB

ΔW Δ cosθ* εdLγγdW

Lee

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σγγ→X (W ) =dσ

d cosθ*∑ Δ cosθ*

ExtracHon of  γγ → X cross section:

Resonance study 

Fit the “asymptoHc” behavior 

PRD79,052009(2009)

PRD78,052004(2008)

PRD80,032001(2009) 

3/16/10  13 F. Anulli 

γγ → ηπ0 : resonance region

Phys.Rev.D80,032001(2009)

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dσdΩ

γγ →π 0π 0( ) = SY00 + D0Y2

0 2+ D2Y2

2 2= S 2Y0

0 2 + D 0

2Y20 2

+ D 2

2Y22 2

fit with a0(980), a2(1320) and a0(Y) in the region W < 1.5 GeV

•  inclusion of a0(Y) gives a better χ2

•  mass and width of a0(Y) significantly smaller than PDG values of a0(1450)

3/16/10  14 . Anulli 

Partial Wave Analysis for 0.9 < W < 1.5 GeV

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S=Aa0 (980)eiφS 0 + Aa0 (Y )

eiφS1 +BS

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D0 =BD0 D2 = Aa2 (1320)eiφD 2 +BD2

Mass (MeV/c2)

Γtot (MeV)

Γγγ B(π0π0) (eV)

a0(980)

a0(980) PDG

a0(Y)

a0(1450) PDG unknown

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982.3−0.7−4.7+0.6+3.1

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75.6 ±1.6−10.0+17.4

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128−2−43+3+502

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1316.8−1.0−4.6+0.7+24.7

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65.0−5.4−32.6+2.1+99.1

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432 + 6−256+1073

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984.7 ±1.2

€

50 −100

€

240−70+80

€

1474 ±19

€

265 ±13

Nominal fit M(a0(Y) = M(a0(1450))

No a0(Y)

χ2/ndf 597.6/429 704.5/430 753.6/433

 γγ → π0π0 : study of the higher mass region

3/16/10  15 F. Anulli 

γγ → π0π0 

fitted slopes σ ∼ W-n ( pQCD: n = 6 )

n 

π0π0 6.9 ± 0.6 ± 0.7 PRD79,052009 (2009)

π+π- 7.9 ± 0.4 ± 1.5 PLB615 ,39 (2005)

Κ+Κ- 7.3 ± 0.3 ± 1.5 PLB615, 39 (2005)

ηπ0 10.5 ± 1.2 ± 0.5 PLB651, 15 (2007)

KSKS 10.5 ± 0.6 ± 0.5 PRD80,032001 (2009)

Isospin symmetry 

leading-order pQCD 

•  fitted region: 3.1 < W < 4.1 GeV; |cosθ*| < 0.6 •  slope compatible with π+π- and pQCD predictions •  cross-section ratio incompatible with LO pQCD

Phys.Rev.D 79, 052009 (2009)

Slope: n = 6.9±0.6±0.7 

σ(π0π0)/σ(π+π-) =  0.32±0.03±0.05 

cross secMon (nb) 

 γγ → π0π0 : study of the higher mass region

Slope: n = 6.9±0.6±0.7 

σ(π0π0)/σ(π+π-) =  0.32±0.03±0.05 

cross secMon (nb) 

3/16/10  16 F. Anulli 

γγ → π0π0 

fitted slopes σ ∼ W-n ( pQCD: n = 6 )

n 

π0π0 6.9 ± 0.6 ± 0.7 PRD79,052009 (2009)

π+π- 7.9 ± 0.4 ± 1.5 PLB615 ,39 (2005)

Κ+Κ- 7.3 ± 0.3 ± 1.5 PLB615, 39 (2005)

ηπ0 10.5 ± 1.2 ± 0.5 PLB651, 15 (2007)

KSKS 10.5 ± 0.6 ± 0.5 PRD80,032001 (2009)

Isospin symmetry 

leading-order pQCD 

|cosθ*| < 0.4 

•  χc0 observed with 7σ •  (1.3σ for χc2 )

•  fitted region: 3.1 < W < 4.1 GeV; |cosθ*| < 0.6 •  slope compatible with π+π- and pQCD predictions •  cross-section ratio incompatible with LO pQCD

Phys.Rev.D 79, 052009 (2009)

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Efficiency‐corrected mass spectrum 

 Discovery (and confirmation) of the χc2(2P) in γγ → DD •  Radial excitaHon states established for 2S+1LJ = 3S1 (ψ) and  1S0 (ηc) •  Lowest 3PJ (χcJ) well established, but nothing known about radial excitaHons •  In 2006, Belle reported the discovery of the Z(3930) idenHfied as the χc2(2P) •  This state and its interpretaHon is now confirmed by BABAR, with consistent parameters 

|!|cos

0 0.2 0.4 0.6 0.8 1

Entr

ies /

0.1

-5

0

5

10

15

20

Angular distribuHon in the Z(3930) region 

J=2 helicity=2 

J = 0  

BELLE BABAR Events (stat. signif.)  64 ± 18  (5.3)  76 ± 18  (5.8) 

Mass (MeV/c2)  3929 ± 5 ± 2   3927 ± 3 ± 1 

Width (MeV)  29 ± 10 ± 2  21 ± 7 ± 4 

Γγγ × BF(ZDD) (keV)  0.18±0.05±0.03  0.24±0.05±0.04 

PRL 96, 082003 (2006) 

arXiv:1002.0281 (2009) submieed to PRD 

3/16/10  17 F. Anulli 

395 fb-1

384 fb-1

BABAR plot: Efficiency-corrected & bckgd-subtracted

results for the Z(3930) <==> χc2(2P)

in the spin=2 hypothesis 

BABAR preliminary

3/16/10  F. Anulli  18 

Two-photon interactions in single-tag mode:

γγ* → π 0, ηc Transition Form Factors

tagged electron inside the detector ==> Off-shell photon Q2 = -q1

2 = -(p-p′)2 > 3 GeV2

electron along beam axis ==> “quasi-real photon” q2 = -q2

2 ~0 GeV2

γγ*→π0 Transition Form Factor

  F(Q2,q2~0) ≡ F(Q2), describing the effect of strong interacHons in γγ*→ π0

  for  Q2 >> Mγγ the process can be factorized:  

3/16/10  19 F. Anulli 

single-tag mode:

  T(x,Q2) calculable  γγ*→ qqbar    φπ(x,Q2)  non‐perturbaHve,  pion distribu5on amplitude (DA)  x is the frac5on of pion momentum carried by one of the quarks 

T(x,Q2)  φπ(x,Q2) 

γγ*→π0 Transition Form Factor

  F(Q2,q2~0) ≡ F(Q2), describing the effect of strong interacHons in γγ*→ π0

  for  Q2 >> Mγγ the process can be factorized:  

3/16/10  20 F. Anulli 

single-tag mode:

  T(x,Q2) calculable  γγ*→ qqbar    φπ(x,Q2)  non‐perturbaHve,  pion distribu5on amplitude (DA)  x is the frac5on of pion momentum carried by one of the quarks 

  ≈14000 events Syst. errors 2.3% (Q2-independent)

  precise measurement in the 4 < Q2 < 9 GeV2 region

  Q2 >10GeV2 : data exceed the asymptotic limit ( Q2F → √2fπ = 0.185 GeV2)

  most models for the pion distribution approach the asymptotic limit from below

  new calculations based on flat pion DA give a better agreement

T(x,Q2)  φπ(x,Q2) 

PRD 80, 052002 (2009)

442 fb-1

Q2 (GeV

2)

|F(Q

2)/

F(0

)|

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50

γγ*→ηc Transition Form Factor

3/16/10  F. Anulli  21 

•  reconstruct ηc → ΚSΚ+-π-+ •  no-tag mode:

•  measure ηc parameters •  determine F(0)

systematic uncertainties independent of Q2 sum up to ~4.3%

LO pQCD 

monopole fit 

469 fb-1

•  fit to the FF distribution with

€

F(Q2) =F(0)

1+Q2 /Λconsistent with both - VMD: Λ = mJ/ψ

2 = 9.6 GeV2

-  Lattice QCD: Λ = 8.4 ± 0.4 GeV2

•  BABAR data lie systematically below a leading-order pQCD calculation (but within the large errors)

Dudek, Edwards PRL97, 172001 (2006) Feldmann, Kroll PLB413, 410 (1997)

Λ = 8.5 ± 0.6 ± 0.7 GeV2 

mass 2982.2 ± 0.4 ± 1.6 MeV/c2

Width 31.7 ± 1.2 ± 0.8 MeV

Γγγ × BF(ηc→KSKπ) 0.374 ± 0.009 ± 0.031 keV

BABAR preliminary

arXiv:1002.3000 (2010) accepted by Phys.Rev.D

•  single-tag mode: •  dσ/dQ2 F(Q2) normalized to F(0)

Conclusions •  Thanks to the very high luminosity of the B-factories BELLE and BABAR

have exploited the full potential of the ISR and two-photon processes for studying low energy hadron physics

☞ A totally new era in charmonium sector opened after the discovery of the X(3872) (in B decays) and Y(4260) via ISR ☞ searches for new “exotic” states routinely performed via ISR, two-photon

fusion and B-decays at B-factories ☞  Two-photon fusion has proven to be a very clean way to study the structure

of low energy scalars ☞ Measurements of exclusive e+e- annihilation processes via ISR, performed

by BABAR, provide the most precise and most complete determination of the hadronic contribution to (g-2)µ and αQED

☹  Unfortunately, only a tiny fraction of the results obtained from the two experiments could been shown here

3/16/10  F. Anulli  22 

Thank you!

BACKUP

3/16/10  23 F. Anulli 

3/16/10  F. Anulli 

24 

aµhad

aµππ in the range 0.630-0.958 GeV

BABAR consistency test: comparison of σµµ with EW prediction: agreement within 0.4±1.1%, dominated by absolute luminosity (±1%)

Fπ fit to BABAR data

KLOE (ISR untagged, 2008)

SND (energy scan)

CMD-2 (energy scan)

γγ*→π0 cross section and TFF    extract number of signal events from fit to the

γγ mass spectrum in each Q2 bin, corrected for data/MC differences and resolution effects

3/16/10  25 F. Anulli 

  ≈14000 events Syst. errors   ~3% 

F. Anulli  26  Bari, April 2, 2009 

γγ → π0π0 : resonance region Phys.Rev.D79,052009(2009) Phys.Rev.D78,052004(2008) 

Wγγ < 1.7 GeV  Wγγ > 1.7 GeV 

f4(2050)

M (MeV/c2) Γγγ (eV)

π0π0 982.2 ± 1.0 +8.1-8.0 286 ± 17 +211

-70

π+π- 985.6 +1.2-1.5

+1.1-1.6 205 +95

-83 +147

-117

PDG 980 ± 10 310 +80-110

(uu+dd)/√2 1300 - 1800

ssbar 300 - 500

k molecule 200 - 600

tetra-quark 270

€

dσdΩ

γγ →π 0π 0( ) = SY00 +D0Y2

0 +G0Y40 2

+ D2Y22 +G2Y4

2 2

f4(2050) f2(1950)

M (MeV/c2) 1885 +14-13 2038 +13

-11

Γ (MeV) 453 ± 20 441 +27-25

Γγγ B(π0π0) (eV) 7.7 +1.2-1.1 54 +23

-14

parameters of f0(980) consistent between π0π0 and π+π- (PRD 75,051101) channel 

inclusion of  both f2(1950) and f4(2050)  looks necessary  

3/16/10  27 F. Anulli