Review of Two-Photon Results from Belle H. Nakazawa National Central University (Taiwan) April 9, 2008 PhiPsi08@INFN

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)

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)

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)

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 1.7118e34/cm2/s Trigger Efficiency σpt/pt ~ (0.19pt + 0.30/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-

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

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

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

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

γγ→f0(980)→π+π- f0(980) 85.9/fb Nature of f0(980) PRD(R) 75, 051101(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)

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 1.3-1.8 ssbar 0.3-0.5 KKbar molecule 0.2-0.6 Four-quark 0.27

γγ→π0π0 |Σpt*| GeV/c 95/fb All neutral calorimeter based trigger arXiv:0711.1926v1 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

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

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

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

ˆ γγ→π0π0 f0(980) f0(Y) Preliminary results f2(1270) B(f2(1270)→γγ)=(1.57±0.01+1.39 - 0.14)e-5 f0(980) ˆ S2 χ2/NDF=1.66 ↔ 2.36(f0(Y) absence) f0(Y)

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

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

Baryon Pair Production PLB621, 41(2005) hep-ex/0609048v1 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 <

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

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

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

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

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 2.1-2.3 GeV Sin-4θ* trend may begin to contribute

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)

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