1. Review of Two-Photon Results from Belle
H. Nakazawa
National Central University (Taiwan)
April 9, 2008

2. γγ→X Cross section Two-photon partial width for a resonance R W=M(γγ)
No γγ collider
Large flux
For hadron production ~1nb for W>0.8GeV
C=even resonances ↔ C=odd in e+e- annihilation
W=M(γγ)

3. Two-Photon Process at Belle
No-tag method: Use of |Σpt *|≈0
Select events from quasi-real two-photon collisions
Estimation of background fraction
W ≲ 4.5 GeV　accessible with available luminosity
W ≲ 2.4 GeV
Meson spectroscopy with Partial wave analysis
Information to solve light scalar puzzle
Glueball search
W ≳ 2.4 GeV
QCD study based on quark model
W^n dependence of cross section
Angular distributions for hadron pair production
Charmonium study : PhiPsi06 (see talk by S. Uehara)

4. QCD calculations for Hadron Pair Production
BL:Brodsky & Lepage PRD24,2848(1981)
BC:Benayoun & Chernyak NPB329,285(1990)
meson
baryon
DKV:Diehl et al. PLB532,99(2002)
Handbag Model
meson
baryon
Diquark Model
Kroll et al. PLB316,546(1993)
Berger et al. EPJ C28,249(2003)

5. KEKB Accelerator and Belle Detector
8 GeV e- x 3.5 GeV e+
√s=10.58 GeV
Beam crossing 22 mrad
∫Ldt = 803.8/fb
Peak e34/cm2/s
Trigger Efficiency
σpt/pt ~ (0.19pt /β)%　with CDC+SVD
PID with ACC + TOF + dE/dx
Muon detection by KLM　for pt>0.8GeV/c
Trigger
More than 80% efficiency for
averaged-pt > 0.55 GeV/c for two track events
Pure neutral events can be triggered as well
γγ➙π+π-

6. γγ→K+K-, π+π- (2.4<W<4.1GeV)
PLB615, 39(2005)
87.7/fb
Bkg subtraction using |Σpt *|
pt>0.8GeV/c
KLM effectively removes μ+μ- bkg

7. γγ→K+K-, π+π- (2.4<W<4.1GeV)
Both modes have the same tendency
Angular dependence
consistent with QCD prediction of
sin-4θ* for W>3GeV
Steeper for W<3GeV
Cross section ~ W^n
Consistent with QCD prediction of n=-6 within error for W>3GeV
PLB615, 39(2005)
W>3GeV ) ( / - + p s K
0.89±0.04±0.15
Mode BL BC
DKV
σ0(K+K-)/σ0(π+π-)
2.3
1.06 1

8. γγ→KSKS (2.4<W<4.0GeV)
PLB651, 15(2007) ) ( - + p M t S
|cosθ*| < 0.6
N evt
Гγγ(keV)
χc0
134±12
2.50±0.23±0.26±0.62
χc2
38±7
0.46±0.08±0.05±0.08

9. γγ→KSKS (2.4<W<4.0GeV)BC
DKV
n= -10.5±0.6±0.6
(1/Wn dependence)
Mode BL BC
DKV
σ0(K+K-)/σ0(π+π-)
2.3
1.06 1
σ0(KSKS)/σ0(K+K-)
0.017
0.005
0.08

10. γγ→f0(980)→π+π- f0(980) 85.9/fb Nature of f0(980)
PRD(R) 75, (2007)
85.9/fb
Nature of f0(980)
Γγγ(f0(980)) measurement
For previous measurements Boglione and Pennington
found two solutions; peak solution v.s. dip solution
Fit to f2(1270) region with nominal values has a good χ2/DOF of 1.1
The mass shift is explained by interference effect
π-μ separation by comparing
energy deposit btw data & MC
γγ→η’→ππγ bg subtracted
f0(980)
f2(1270)

11. γγ→f0(980)→π+π- M [MeV/c2] Г[MeV] Гγγ[eV] “peak” solution
KK contribution
Interference with J=0 continuum
Non-interference J=2 continuum
“peak” solution
M [MeV/c2]
Г[MeV]
Гγγ[eV]
Model
Гγγ[keV]
uubar,ddbar
ssbar
KKbar molecule
Four-quark
0.27

12. γγ→π0π0 |Σpt*| GeV/c 95/fb All neutral calorimeter based trigger
arXiv: v1
BELLE-CONF-0768
95/fb
All neutral
calorimeter based trigger
Track (pt > 0.1GeV) veto
|Σpt*| < 0.05 GeV/c
ε~ 1% - 11%
W=0.9GeV
|cosθ*|=0.05
W=0.66GeV
|cosθ*|=0.05
W=1.18GeV
|cosθ*|=0.65
3.6<W<4GeV
|cosθ*|<0.4
|Σpt*| GeV/c

13. γγ→π0π0 Estimated Bkg Resolution is corrected by unfolding method
Comparison with Crystal Ball (1990)

14. γγ→π0π0
Up to J=2 waves
Including J=4 waves

15. γγ→π0π0 Partial wave parameterization 0.8<W<1.6 GeV, J <= 2
Each wave includes polynomial continuum
Interference terms are decomposed into 3 YJλ terms
f0(Y) (may be f0(1370) and/or f0(1500)) considered
D2 includes f2’(1525) with nominal value
KK contribution to f0(980) is consistent with zero and is therefore omitted
f2(1270) contribution to D0 wave is considered with D2^2 : D0^2 = 1 : r02

16. ˆ γγ→π0π0 f0(980) f0(Y) Preliminary results f2(1270)
B(f2(1270)→γγ)=(1.57± )e-5
f0(980) ˆ S2
χ2/NDF=1.66 ↔ 2.36(f0(Y) absence)
f0(Y)

17. Analysis with 223/fb on going
γγ→π0π0
Analysis with 223/fb on going

18. γγ→ K+K- (1.4<W<2.4GeV)
Euro.Phys.J, C32, 323(2004)
67/fb
|Σpt *|<0.1GeV/c
f2’(1525) and 3 other resonances
No continuum contribution needed with this model above 1.7GeV
No evidence for the narrow fJ(2220) glueball candidates

19. Baryon Pair Production
PLB621, 41(2005)
hep-ex/ v1
2.025<W<4.0GeV
For ppbar
89/fb
QCD prediction of W^-10 cannot be ruled out
for W>3.2 GeV
Transition to asymptotic behavior may be seen
Σ pair and Λ pair
464/fb
Converge to ppbar
No prediction explains this behaviour
<

20. Summary
We have measured various hadron pair production in two-photon process
For W ≲ 2.4 GeV partial wave analyses have been performed for γγ➙π+π-, π0π0, K+K- processes to study light mesons
For W ≳ 2.4 GeV Cross sections have been measured for γγ➙ π+π-, π0π0, K+K-, KSKS, ppbar, ΣΣbar, ΛΛbar processes
Angular dependence, W dependence, and cross section ratios among the different processes are compared to QCD predictions.
The ηc , χc0 ,χc2 charmonia have been observed in these processes

21. bus

22. p g ® Tensor Resonances in - + BELLE-CONF-0662p g - +
Tensor Resonances in
BELLE-CONF-0662
Maximum kinetic energy available for a pion Q=E(3pi)-3mpi

23. p g ® Tensor Resonances in - + (3) Prelim.p g - +
(3)
4 resonances coupling amp , phase 
Prelim.
Ggg　consistent w PDG
Effiはどこで

24. γγ→ K+K- (1.4<W<2.4GeV)
Euro.Phys.J, C32, 323(2004)
67/fb
|Σpt *|<0.1GeV/c
63455 ev

25. γγ→ K+K- (1.4<W<2.4GeV)
Partial Wave Analysis for differential cross section
(J,λ)=(0,0),(2,0),(2,2) assumed
Drastic change at GeV
Sin-4θ* trend may begin to contribute

26. Allowed ( J, λ) for γγ system
Forbidden states
Initial state:γγ system
　　From gauge invariance and Bose symmetry
Spin-Parity JP=1±, 3-, 5-, …
Helicity λ=1
λ=2 for 0+, 2+, 4+,…
λ=0 for 3+, 5+,…
Allowed states when considering J<=2 only
(JP,λ)=(0-, 0), (2±, 0), (2+, 2)

27. Interference between different two-photon (JP,λ)’s
(2+,2) and others
No interference between different helicity states
after azimuthal angle integration -> Ignored
{(0-, 0) and (2+,0)}, {(2-,0) and (2+,0)}
For λ=0, no interference between states with different (-1)JP after photon helicity summation -> Ignored
(0-,0) and (2-,0)
No interference after polar angle integration
-> Taken into account