1. Study of e+e- annihilation at low energies Vladimir Druzhinin Budker Institute of Nuclear Physics (Novosibirsk, Russia) SND - BaBar Lepton-Photon, August, 2007

2. 2 e + e - annihilation into hadrons J PC =1 - - states spectroscopy, study of their decays Calculation of hadronic contributions into a  and  QED (m Z ) Dominant uncertainty from lowest order hadronic piece. Cannot be calculated from QCD (“first principles”) – but: we can use experiment (!)    hadhad had  From dispersion relations

3. 3 R(s) is defined as: R(s) is one of the most fundamental quantities in high energy physics: its global structure reflects number of quarks and their colors; used for QCD tests and as a source of QCD parameters plays special role in precision measurements: uncertainty M.Davier talk at tau06 arXiv:hep-ph/0701163 central value a  [exp] - a  [SM] = (27.5  8.4)  10 -10  3.3 standard deviations

4. 4 Current/Future activities in R VEPP-2M VEPP-2000 KLOE, ISR BaBar, ISR BES, VEPP-4 R e + e - c.m. energy

5. 5 ISR method Mass spectrum of hadronic system f in the e + e -  f  reaction is related to cross section of e + e -  f reaction at E=m. Measurement of hadronic cross sections in wide energy range in single experiment Two approaches: with and without detection of the ISR photon The advantage of the approach with detected photon is low dependence of the detection efficiency on mass of hadronic system and its internal substructure.

6. 6 Measurement of R in Novosibirsk VEPP-2M collider: 0.36-1.4 GeV in c.m., L  3  10 30 1/cm 2 s at 1 GeV Detectors CMD-2 and SND: 60 pb -1 collected in 1993-2000 All major hadronic modes are measured: e+e-  KK,  e+e-  Still a lot of data to analyze !

7. 7 Measurement of R in Novosibirsk New result: e + e - → K + K - in range 1.05 – 1.4 GeV (SND) arXiv:0707.2279arXiv:0707.2279 e + e - c.m. energy Cross section (nb)

8. 8 1.2-4.2% 0.6% / 0.8% 0.7% Pion form factor 1.3% 3.2% Systematic error CMD-2 SND

9. 9 Comparison of CMD-2 and SND E < 0.55 GeV0.6 < E < 1 GeV ∆(SND-CMD2)≈1.2%±3.6% ∆(SND-CMD2)≈-0.53%±0.34% Syst.error

10. 10 Pion form factor (KLOE)

11. 11 New KLOE measurement Improvements: trigger, filter, luminosity Future improvements:  /  ratio data taken at E=1 GeV arXiv:0707.4078 preliminary Model dependence due to  →f 0  for LA

12. 12 KLOE: e + e - →  0 arXiv:0707.4130

13. 13 BaBar R measurement program using ISR

14. 14 Objective : Cross section measurements for all significant processes, e + e  → f, from threshold to c.m. energy ~ 4.5 GeV Purpose : Significantly improve understanding of the spectroscopy of J PC = 1  states, and resonant substructure of their decays Combine the cross section measurements to obtain improved precision on the c.m. energy dependence of R in the region 1-2 GeV Reactions for which results have been published : e + e   pp e + e        e + e     , K + K -     , K + K -     , 2K + 2K - e + e               K + K -     New results presented here : e + e   K + K     K S K     K + K                      Work in progress on :      K + K ,              

15. 15 BaBar ISR:          Very important mode for a  and  QED Preliminary precision: 8% in peak 5% Good agreement with SND Huge improvement above 1.4 GeV First measurement above 2.5 GeV BaBar preliminary

16. 16 BaBar ISR:          BaBar preliminary Intermediate states:   a         f  

17. 17 BaBar ISR:          +-+- non  

18. 18 BaBar ISR:           Internal structure:         X =      X =  (1300) or a 1 (1260)     Sys. error: 7% at 1.7 GeV

19. 19 BaBar ISR :      f 0 (980) 1.35  0.03 0.45  0.14 1.66  0.01 0.22  0.04 BaBar,3    BaBar,3 

20. 20 BaBar ISR:          Systematic error: 10% below 3 GeV Internal structure:              f   f        f    m=2.15  0.04  0.05 GeV  =0.35  0.04  0.05 GeV 

21. 21 BaBar ISR: K + K -        K + K -      K+K-K+K- K+K-K+K- K+K-K+K-  10% sys. err.

22. 22 BaBar ISR: K + K -    K S K -   K+K-K+K- KSK-KSK- Dominant decay mode for  Systematic error: 5% for K S K -   6% for K + K -   Agreement with DM1, DM2 Significant improvement in accuracy

23. 23 BaBar ISR : K + K -    K S K -   Dominant intermediate states: K*(980)K and K 2 *(1430)K Dalitz plot population for K S K -  + final state strongly depends on relation between I=0 and I=1 amplitudes: M=M  (  I=0 -  I=1 )+M 0 (  I=0 +  I=1 ) From Dalitz plot fit isovector and isoscalar cross sections can be extracted both for K*(980)K and for K 2 *(1430)K K*(980)K I=1 K*(980)K I=0 K 2 *(1430)K I=1 K 2 *(1430)K I=0

24. 24 BaBar ISR:   e + e - →  is best channel for study of excited  -state. Contribution of  -like states is suppressed by OZI rule. e + e - →   is suitable for search of exotic isovector resonances. For ordinary isovector states,   decay is suppressed by OZI rule. The cross section is described by single resonance with m=1600±30 MeV,  =200±100 MeV

25. 25 Fit to e + e - → , K * K Parameters  (1680): PDG m=1723 ± 20 MeV, 1680 ± 20  = 371 ± 75 MeV, 150 ± 50  ee = 580 ± 60 eV, B  /B K*K  1/3 In  channel the peak with m=2139 ± 35 MeV,  =76 ± 62 MeV is seen with 2 sigma significance e + e - →  f 0 (980) M=2175±18 MeV  =58±25 MeV

26. 26 BaBar measurement summary To calculate R in the energy range 1-2 GeV the processes                  K + K -, K S K L, K S K L  K S K +     must be measured.

27. 27 BaBar ISR: Baryon Form factors The ratio of form factors |G E /G M | can be obtained from the analysis of the baryon angular distribution. The terms corresponding G M and G E have angular dependence close to 1+cos 2  and sin 2 , respectively. Nonzero relative phase between form factors leads to polarization of outgoing baryons. For  final state,  decay can be used to measure polarization. (s=1/2) cross section depends on two form factors, electric G E and magnetic G M. From the measurement of cross section we extract effective form factor

28. 28 Cross section and  form factor

29. 29 Angular distribution M 2 , GeV/c 2 NN bkg |G E /G M | 2.23-2.401203 ± 5 2.40-2.809610 ± 6 2.23-2.40 2.40-2.80 Results on |G E /G M | ratio are consistent both with |G E /G M |=1 valid at threshold and with results for e+e- → pp where this ratio was found to be greater than unity near threshold.

30. 30  polarization MC Data MC (no polarization): flat distribution with zero slope  no dependence of detection efficiency on cos   Slope in data is 0.020 ± 0.097 for M 2  <2.8 GeV Symmetric 90% CL interval for average polarization -0.22 <   < 0.28 Under |G E |=|G M | assumption -0.76 < sin  < 0.98 The  polarization is measured using correlation between the directions of  polarization vector and momentum of decay proton in  rest frame.

31. 31 Octet baryon form factors

32. 32 Test of CVC hypothesis hadrons   W  e+e+ e – CVC: I =1 & V W: I =1 & V,A  : I =0,1 & V Hadronic physics factorizes in Spectral Functions. Isospin symmetry connects I=1 e + e – cross section to vector  spectral functions: branching fractions mass spectrum kinematic factor (PS)

33. 33 Comparison of e+e- and  data  →  

34. 34 Comparison of e + e - →4  cross sections with  →4   spectral functions

35. 35 Conclusion Significant progress is reached in measurement of exclusive e + e - channels in mass range below 3 GeV Most important results expected during next year: final -     (KLOE),       (BABAR,CMD-2), new -     (BaBar) Obtained data allow to determine parameters of excited   -states. Simultaneous fit of all channels? There are significant discrepancies between tau and e+e- data for  final states. New data from Babar and Belle on tau decays are expected

36. 36 m=1.88±0.03 GeV  =130±30 MeV m=1.86±0.02 GeV  =160±20 MeV 3(  +  - ) 2(  +  - )  0  0 +-00+-00

37. 37 Belle analysis of  →   EPS2005 Proceedings – hep-ex/0512071