Gamma gamma physics at Belle Sadaharu Uehara KEK

Gamma gamma physics at Belle Sadaharu Uehara (KEK) PHIPSI 13 September 9 -12, 2013 Sapienza University of Rome

KEKB Accelerator and Belle Detector • Asymmetric e- e+ collider 8 Ge. V e- (HER) x 3. 5 Ge. V e+ (LER) s=10. 58 Ge. V (4 S) Beam crossing angle: 22 mrad • Continuous injection • Luminosity Lmax=2. 1 x 1034 cm-2 s-1 ∫ Ldt 1040 fb-1　　 High momentum/energy resolutions CDC+Solenoid, Cs. I Vertex measurement – Si strips Particle identification TOF, Si-aerogel, CDC-d. E/dx, RPC for KL/muon S. Uehara, Belle, Phipsi 13, Sept. 2013 2

Two-Photon Collisions and Hadron/QCD Physics Hadron production from collisions of virtual or quasi-real photons Perturbative/Non-perturbative QCD hadrons Resonances Hadron/photon form factors Single resonance formation in gg(*) collisions Zero-tag with pt-balance requirement for the hadron system Q 2<<W 2 (gg c. m. energy), Q 2<<EQCD 2 (Energy scale of QCD) Measurement of Ggg B( final state) Single-tag process (Q 2 dependence in gg* collisions) Measurement of transition form factor S. Uehara, Belle, Phipsi 13, Sept. 2013 3

gg K 0 S The first measurement of the differential cross section in W = 1. 05 – 2. 4 Ge. V with 972 fb-1 Belle data W: c. m. energy of gg collisions ar. Xiv: 1307. 7457[hep-ex], submitted to PTEP 　(Progress of Theoretical and Experimental Physics) Study of resonances including exotic candidates (e. g. glueball state) This process is dominated by resonances in W < ~ 2. 4 Ge. V W > 2. 4 Ge. V -- Update of the previous Belle publication (W. T. Chen et al. , PLB 651, 15 (2007), 397. 6 fb-1) 　　QCD study – Angular and W dependences Charmonia: Partial decay widths for cc 0 and cc 2 Search for cc 0(2 P) etc. , which is to be 3. 80 – 3. 93 Ge. V S. Uehara, Belle, Phipsi 13, Sept. 2013 4

Cross section integrated over the angle Five resonance-like peaks visible below 3 Ge. V W and angular dependence of the efficiency Covering W = 1. 05 – 4. 0 Ge. V |cos q*|<0. 8 Belle (972 fb-1) S. Uehara, Belle, Phipsi 13, Sept. 2013 5

Formula for differential cross section • At low energy (W < 3 Ge. V) • S, D 0, G 0, D 2 , G 2 Partial wave amplitudes J = L = 0, 2, 4 (even only) and total two-photon helicity = 0 or 2 – give W dependence of each partial wave assuming resonance and continuum components • YJm : spherical harmonics – Each determines the angular dependence of the wave – But, not mutually independent S. Uehara, Belle, Phipsi 13, Sept. 2013 6

Fit with S and D waves for W < 2. 0 Ge. V Hat amplitudes to visualize, model independent f 0(1710) f 2’(1525) f 2(1270) - a 2(1320) S. Uehara, Belle, Phipsi 13, Sept. 2013 7

Fit results for W < 2. 0 Ge. V f 2(1270) - a 2(1320) interference and f 2’(1525) Two solutions are found, and they are combined • Destructive interference btw. f 2 (1270)and a 2 (1320) confirmed • First attempt to include interference effect in measuring of f 2’(1525). S. Uehara, Belle, Phipsi 13, Sept. 2013 8

Fit results for W < 2. 0 Ge. V (cont. ) f. J(1710) Scalar rather than tensor! (in contrast to L 3) f 0(1710) : Ggg>O(10 e. V) indicates not likely a pure glueball S. Uehara, Belle, Phipsi 13, Sept. 2013 9

Fit Results for resonances in W>2. 0 Ge. V f 2(2200)-f 0(2500) is the best solution (in all trials of J= 0, 2, 4) • The resonance parameters Fit • Significances – 3. 4σ for f 2(2200) over f 0(2200) – 4. 3σ for f 0(2500) over f 2(2500) evaluated from min. (Δχ2) for every sys. source f 2(2200) f 0(2500) S. Uehara, Belle, Phipsi 13, Sept. 2013 10

Charmonia cc 0 and cc 2 Yield cc 0 Interference between cc 0 and continuum Product of two-photon decay width and B(K 0 S) cc 2 cc. J(2 P) region S. Uehara, Belle, Phipsi 13, Sept. 2013 11

QCD Studies: Angular dependence Assume non-resonant effect in 2. 6 < W < 3. 3 Ge. V ; we know there is a resonance near 2. 5 Ge. V W= 2. 4 – 3. 3 Ge. V ds/d|cosq*| 1/sina q* Handbag: a = const. = 4 p. QCD: a not const, depend on W for neutral-meson pair No tendency is seen to converge to 4 at high energies S. Uehara, Belle, Phipsi 13, Sept. 2013 12

W-dependence s W-n p. QCD predictions for charged-meson pair for neutral-meson pair n = 6 (p+p-, K+K- etc. ) = Dimensional counting rule n=10 (K 0 s etc. ) by Chernyak PLB 640, 246 (2006) ar. Xiv 1212. 1304 [hep-ph] Close to n=10, agree with p. QCD prediction S. Uehara, Belle, Phipsi 13, Sept. 2013 13

“gg meson pair” (six final states) from Belle QCD Test in 2. 4 – 4. 1 Ge. V energy region Differential cross section ds/d|cos q*| for these reaction processes are measured. S. Uehara, Belle, Phipsi 13, Sept. 2013 14

Three kinds of QCD Studies for 2. 4 – 4. 1 Ge. V Region Angular dependence p 0 p 0 Energy dependence Cross-section ratio s(p 0 p 0)/s(p+p-) p 0 p 0 hh s(hp 0)/s(p 0 p 0) 0 0 Difference of the slopes s W -n S. Uehara, Belle, Phipsi 13, Sept. 2013 15

Summary of the six channels ~ sin-4 q* for charged meson pairs is predicted by p. QCD 2. 6 – 3. 3 < 0. 8 Cross-section ratio s(p 0 p 0) : s(hh) Angular dependence Theory (Brodsky and Lepage) h in SU(3) octet Theory Slope parameter VP = -18 deg Belle 1 : 0. 24 Rf : 0. 36 Rf 2 1: 0. 46 Rf : 0. 62 Rf 2 1: (0. 48 0. 06) : (0. 37 0. 04) Rf : Squared form factor ratio of h/p 0 s(K+K-)/s(p+p-) = 0. 89 0. 04(stat. ) 0. 15(syst. ) s(p 0 p 0)/s(p+p-) = 0. 32 0. 03 0. 05, s(K 0 S)/s(K+K-) changes ~ 0. 10 to ∼ 0. 03 S. Uehara, Belle, Phipsi 13, Sept. 2013 16

p 0 Transition Form Factor gg* p 0 Coupling of neutral pion with two photons Good test for QCD at high Q 2 Single-tag p 0 production in two-photon process with a large-Q 2 and a small-Q 2 photon Theoretically calculated from pion distribution amplitude and decay constant Measurement: |F(Q 2)|2 = |F(Q 2, 0)|2 = (ds/d. Q 2 )/(2 A(Q 2)) |F(0, 0)| 2 = 64 p. Ggg/{(4 pa)2 m. R 3} A(Q 2) is calculated by QED Detects　e (tag side) and p 0 Q 2 = 2 EE’(1 – cos q) from energy and polar angle of the tagged electron S. Uehara, Belle, Phipsi 13, Sept. 2013 17

Ba. Bar’s Measurement p 0 transition form factor (TFF) measured by Ba. Bar is larger than the asymptotic p. QCD prediction above Q 2>10 Ge. V 2 Ba. Bar, PRD 80, 052009 (2009) 442 fb-1 Below Q 2<8 Ge. V 2, the Ba. Bar result supports the CLEO result. h and h’ TFFs from Ba. Bar PRD 84, 052001(2011) are consistent with p. QCD predictions. CZ: . Chernyak, Zhitnitsky ASY: Lepage, Brodsky BMS: Bakulev, Mikhailov, Stefanis Explanation of this situation for the (p 0, h, h’)-TFF’s within standard QCD calculations is difficult. S. Uehara, Belle, Phipsi 13, Sept. 2013 18

Belle measurement: Extraction of p 0 Yield Positron-tag Electron-tag Int. Luminosity : 759 fb-1 (Larger than Ba. Bar’s) PRD 86, 092007 (2012) Fit Mgg distribution by Double Gaussian (for signal) + 2 nd-Order Polynomial (for background) in each Q 2 bin S. Uehara, Belle, Phipsi 13, Sept. 2013 19

Belle result The cross sections from p-tag and e-tag are evaluated, separately, and then combined. p 0 Transition Form Factor Ba. Bar Belle Q 2 max = 1. 0 Ge. V 2 for the less-virtual photon Corrected for s = 10. 58 Ge. V No rapid growth above Q 2>9 Ge. V 2 is seen in Belle result. ~ 2. 3 s difference between Belle and Ba. Bar in 9 – 20 Ge. V 2 Fit with an asymptotic parameter Q 2|F(Q 2)|= BQ 2/(Q 2+C) B = 0. 209 0. 016 Ge. V Consistent with the QCD value (0. 185 Ge. V) S. Uehara, Belle, Phipsi 13, Sept. 2013 20

Summary • dσ/d|cos q*| of γγ→K 0 S is measured for the first time for 1. 05<W <2. 4 Ge. V - f 2(1270) and a 2(1320) interfere indeed destructively - f 0(1710) is favored over f 2(1710) , Ggg > O(10 e. V) Not likely a pure glueball - f 2(2200) and f 0(2500) favored • QCD test using measurements of six processes of γγ→meson pair ( p+p-, K+K-, p 0 p 0, K 0 S, hp 0, hh , for W = 2. 4 – 4. 1 Ge. V) - W-dependence of K 0 S , n ~10 predicted by p. QCD, is confirmed p+p-, K+K- ( n=6 predicted, n=7 – 8 measured) - Systematic QCD studies using W and angular dependences and cross section ratio of these exclusive processes are now possible • Measurement of gg* p 0 transition form factor - Steep increase in Q 2 > ~ 9 Ge. V 2 observed by Ba. Bar is not seen by Belle - Belle result is consistent with the QCD asymptotic value S. Uehara, Belle, Phipsi 13, Sept. 2013 21

backup S. Uehara, Belle, Phipsi 13, Sept. 2013 22

Nature of • R = f. J or a. J (J = even) • Destructive interference between f. J and a. J – (D. Faiman, H. J. Lipkin and H. R. Rubinstein, PL 59 B, 269 (1975)) based on OZI (Okubo-Zweig-Iizuka) rule and isospin S. Uehara, Belle, Phipsi 13, Sept. 2013 23

Selection Criteria 4 Pions from 2 Ks’s - L 4 (filtering) brings non-negligible inefficiency (At least 1 track with pt > 0. 3 Ge. V, dr<1 cm and |dz|< 4 cm) - Trigger restricted in bit#3(ff_t 2 oc, Trigger A) #27(loe_fs_o, Trigger B) #24(hadron_a=loe_sss_tc, Trigger C) - Low. Mult – 4 track (previous page) - 4 charged pions (L(K)/(L(K)+L(p))<0. 8) with |Spt|<0. 2 Ge. V/c - No neutral pion candidate with pt>0. 1 Ge. V/c - Just two Ks candidates with z-matching @vertex |Dz| < p. K[cm/Ge. V/c] + 1. 6 cm pp invariant mass@vertex |Mpp – m. K|<20 Me. V/c 2 - Two Mpp mass conditions: |MK 1 – MK 2|<10 Me. V/c 2 - Vertices off IP (only for W>2 Ge. V) : rvi > (W - 2 Ge. V) x 0. 1 cm/Ge. V S. Uehara, Belle, Phipsi 13, Sept. 2013 24

Selection Criteria (continued) The 2 Ks-vertex distances and tr. -momentum relations etc. - Distance between the vertices in the rj , d. Vr > +0. 5 cm (d. Vr has a sign according to the relative momentum of the 2 Ks’s) - 3 D distance d. V > 0. 7 cm OR 2 D distance d. Vr > +0. 3 cm - Projected vertex distance on the relative momentum dv < 0. 7 cm - |Spt(Ks)| < 0. 1 Ge. V/c - Refined cut for the Ks mass | <MK> - m. K| < 5 Me. V/c 2, <MK> = (MK 1 + MK 2)/2 - ECL total energy cut EECL < EK 1 + EK 2 – 0. 3 Ge. V, EKi – Ks’s total energy calculated from its lab. momentum S. Uehara, Belle, Phipsi 13, Sept. 2013 25

Ks Selection Final Ks. Ks mass-cut z-matching @vertex Solid : W<2. 5 Ge. V Dashed: W>2. 5 Ge. V Ks-mass vs Ks-mass Cut lines for [M(Ks 1) + M(Ks 2)]/2 and |M(Ks 1) – M(Ks 2)| S. Uehara, Belle, Phipsi 13, Sept. 2013 26

Ks Ks vertex distances 2 D vertex distance 3 D vertex distance W=1. 1 -1. 2 Ge. V Tr. mometum diff. and vertex position diff. must be in parallel Sharp peaks near 0 cm seen only in Exp. are from Direct 4 p (p+p-) production backgrounds. S. Uehara, Belle, Phipsi 13, Sept. 2013 27

Background Subtractions (1) - Non-exclusive (Ks. X) backgrounds Estimated from a fit of |Spt*| distributions S. Uehara, Belle, Phipsi 13, Sept. 2013 28

Background Subtractions (2) - Non-Ks Ks(4 p-process) backgrounds Estimated from <MK> sideband Non-exclusive and non-Ks --- very small (typically ~1% level) 1. 4 -1. 6 Ge. V S. Uehara, Belle, Phipsi 13, Sept. 2013 29

Cross section integrated over the angle ds d|cosq*| Black --- |cosq*|<0. 8 Blue --- |cosq*|<0. 6 Orange --- |cosq*|<0. 6 (previous, Belle 2007) S. Uehara, Belle, Phipsi 13, Sept. 2013 30

Systematic errors From correlation study of different Exp# settings in data and signal MC A Half of the subtraction + 2% from pt-fit (quad. sum) Loose-cut sample Correlation of the two triggers About 10% of the inefficiency S. Uehara, Belle, Phipsi 13, Sept. 2013 31

Hat amplitudes • We rewrite • are mutually independent → obtain “hat amplitudes”: through fitting dσ/dΩ 　　　　　　　 – They contain interference terms – Yet, they convey useful information on partial waves S. Uehara, Belle, Phipsi 13, Sept. 2013 32

W < 2 Ge. V : f 0(1710) assumption • Parameterization • Fix param. of f 2(1270) and a 2(1320). Free f 2‘(1525) • Then fit dσ/dΩ (20 free param. ) • phases in D 2 are relative to f 2(1270) S. Uehara, Belle, Phipsi 13, Sept. 2013 33

Systematic uncertainties + σ and -σ 34

Resonances in M=1. 7 – 2. 4 Ge. V (from PDG 2012) S. Uehara, Belle, Phipsi 13, Sept. 2013 35

Fitting the region W > 2 Ge. V • Parameterization B. W. = f. J(2200) and/or f. J(2500) with J=0, 2 and 4 • Then fit dσ/dΩ (typically 16 free parameters) S. Uehara, Belle, Phipsi 13, Sept. 2013 36

Fit results for 13 assumptions S. Uehara, Belle, Phipsi 13, Sept. 2013 37

Upper limit for cc 2(2 P) Ks. Ks We use a counting method No knowledge for cc 0(2 P) 2 events in M 2 G N UL = 5. 32 for 90%CL without assuming interference 90% CL UL, 1 s of syst. err. shifted is not known, but conjectured to be around 500 e. V Poisson(m=5. 32; n<=2) = 0. 10 S. Uehara, Belle, Phipsi 13, Sept. 2013 38

Upper limit for X(3915) Ks. Ks PDG 2013 X(3915) = cc 0(2 P) Same counting as that in cc 2(2 P) 2 events in M 2 G N UL = 5. 32 for 90%CL without assuming interference Same method, the same events Almost same M and G Spin and angular distribution are different. 90% CL UL, 1 s of syst. err. shifted S. Uehara, Belle, Phipsi 13, Sept. 2013 39

Upper limit for hc Ks. Ks P and CP violating process (PDG 2012 BF < 4. 2 x 10 -4) Fit function Fluctuation ? of 1 – 2 s N UL = 15 ( = 85 ) for 90%CL without (with) interference k=0 (0<k 1) k cannot be determined by the fit 90% CL: UL D(2 ln. L) = (1. 64)2 floating the other parameters 1 s of syst. err. shifted World severest upper limits S. Uehara, Belle, Phipsi 13, Sept. 2013 40

Cross sections integrated over angle p +p - s(|cosq*|<0. 6) K+ Kp 0 p 0 p +p Ks 0 Those for hp 0 and hh are shown in other slides S. Uehara, Belle, Phipsi 13, Sept. 2013 41

W-dependences at high energies Assume or expect s(W) ~W-n p 0 p 0 hp 0 p +p Fitted and reproduced Slope parameter n different among the reactions Charmonium contributions not included/removed K +K K S 0 p 0 p 0 hh S. Uehara, Belle, Phipsi 13, Sept. 2013 42

Efficiency determined by MC (twice of Ba. Bar’s definition) Efficiency for the Signal Process at Belle Normalized to Q 22 max = 1. 0 Ge. V 2 Black: 4 S energy Red: 5 S energy Up-down structures in the efficiencies are due to Bhabha-veto trigger condition correlated in the (cosqe, cosqgg) plane The trigger efficiency is defined for the acceptance after the selection S. Uehara, Belle, Phipsi 13, Sept. 2013 43

p 0 p 0 background MC c. m. scattering angle wrt g*g axis Experimentally identified gg* p 0 p 0 Noise from Signal Process Reproduced by f 2(1270) Background contamination in signal is estimated by the p 0 p 0 background MC which is normalized to the observation, as 2% S. Uehara, Belle, Phipsi 13, Sept. 2013 44

Calibrations using Radiative-Bhabha (VC) Events Bhabha-veto threshold is measured in real data of Virtual-Compton process of (e)eg and is tuned in Trigger Simulator Lab. angle distributions Q 2 dependence g e dots: Exp. histograms: MC e. DR: cos q Exp. /MC Ratio for Efficiency for “Bhabha-Mask” ×”Bhabha-veto” S. Uehara, Belle, Phipsi 13, Sept. 2013 45

Comparisons with Previous Measurements and Fits Fit A (suggested by Ba. Bar) Q 2|F(Q 2)| = A (Q 2/10 Ge. V 2)b Ba. Bar: A = 0. 182 0. 002 ( 0. 004) Ge. V b = 0. 25 0. 02 Belle: A = 0. 169 0. 006 Ge. V b= 0. 18 0. 05 c 2/ndf = 6. 90/13 ~1. 5 s difference from Ba. Bar Fit B (with an asymptotic parameter) Q 2|F(Q 2)|= BQ 2/(Q 2+C) No rapid growth above Q 2>9 Ge. V 2 is seen in Belle result. ~ 2. 3 s difference between Belle and Ba. Bar in 9 – 20 Ge. V 2 Belle: B = 0. 209 0. 016 Ge. V C = 2. 2 0. 8 Ge. V 2 c 2/ndf = 7. 07/13 B is consistent with the QCD value (0. 185 Ge. V) S. Uehara, Belle, Phipsi 13, Sept. 2013 46