1.  decay BRs and Spectral Functions ( and requirement on detector design ) 苑 长 征 中国科学院高能物理研究所 Z-factory Workshop 2012 年 11 月 16-18 日 1

2. Outline Why improve  BR and SF measurement How to improve Requirement on detector design Summary 2

3. Why  BR and SF Lepton Universality Asymptotic behavior of QCD Strange quark mass & Vus Test CVC a  and running  3 Refer to Shaomin’s talk yesterday

4. Magnetic Anomaly Schwinger 1948 QED Prediction: Computed up to 5 th order [Kinoshita et al.]    QEDQED QEDHadronicWeakSUSY...... or other new physics ? 4

5. 5 Magnetic Anomaly Contributions to the Standard Model (SM) Prediction: Source (a)(a) Reference QED ~ 0.3  10 –10 [Schwinger ’48 & others] Hadrons ~ (15  4)  10 –10 [Eidelman-Jegerlehner ’95 & others] Z, W exchange ~ 0.4  10 –10 [Czarnecki et al. ‘95 & others] The Situation 1995    hadhad had  Dominant uncertainty from lowest order hadronic piece. Cannot be calculated from QCD (“first principles”) – but: we can use experiment (!)

6. e + e - data Fit with  +  +  ’+  ’’ describes data pretty well (Gounaris and Sakurai’s parametrization). Pi form factors from all the available experiments data: DM1, TOF, OLYA, CMD, DM2, CMD2, SND (KLOE excluded due to systematic bias) Latest BaBar results not in this plot.

7. The Role of  Data through CVC – SU(2) hadrons   W  e+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) fundamental ingredient relating long distance (resonances) to short distance description (QCD) 7

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10. 10 Three energies for  physics Threshold: 3.555 GeV –  almost static; cross section <0.3 nb; 非共线与非共面性 –Eff ~ 10-20% –high precision m  measurement, maybe BR? B factory: 10.58 GeV –Cross section: 0.8nb –Background: large; eff~10% –However, statistics is huge –Low BR channels; modes with K; searches Z-pole: 91 GeV –Cross section: 1.5 nb; Lorentz boost large –Low multiplicity, Z background low –Back-to-back; eff~80%, mainly acceptance –Global analysis of all channels, limited by statistics

11. Global analysis 11 1.Very clean  events can be selected with very simple selection criteria. Low track multiplicity Back-to-back Low invariant mass Total energy not very small 2.Subtract background 3.Classify all the events

12. 12  decays Pure leptonic Semi-leptonic –Cabibbo favoured –Cabibbo suppressed Rare and forbidden –Lepton Flavor Violation –Lepton Number V –Baryon Number V

13. Classification 13 Divide into 14 classes according to PTID [ cannot separate  /K! ] n(TRK) n(  0 )

14. Statistical error from global analysis n i follows multinomial distr. –  2 n i =Np i (1-p i ) –N=  n i –p i =n i /N –No error from N Non-global case, Poisson distr. –  2 n i =n i –+ additional error from N 14 300k  ’s

15. Non-  background at 1.2% level Non-  background measured from data directly –Bhabha –Dimu –Two-photon processes –Low multiplicity  qq events 15

16. The EM calorimeter ExperimentsALEPHDELPHIL3OPAL TypeLead sheet + wire chamber [radius~200 cm] Lead-gas High- Density Proj. Chamber BGO crystal [radius=52 cm] Lead glass Read out45 layers grouped in 3 stacks readout in longitudinal 40 layers grouped in 9 readout in longitudinal 11000 crystals No longitudinal readout 11704 lead glass blocks No longitudinal readout Radiative length22X 0 18X 0 21X 0 25X 0 Granularity12x12 mrad 2 17x2 mrad 2 27x27 mrad 2 40x40 mrad 2 Angular resolution 0.32+2.7/  E mrad 1 mrad in  2 mrad in  ~ 3 mrad~ 11 mrad Energy resolution.01+.18/  E0.31/E 0.44  0.027 5% at 100 MeV, 1% > 2 GeV.002+.063/  E E  threshold >350 MeV> 500 MeV Analysis technique cuts NNcuts  Paper Phys. Rep.EPJCUnpublishedEPJC 16

17. Real/fake photons Lots of low energy photons Lots of fake photons ALEPH Data MC truth 17

18. Real/fake photons Use 6 variables to discriminate photons Real photons Fake photons 18

19. Resolved & merged  0 Minimum opening angles between two photons from a  0 decay  =(2m/p)  =14 mrad for E=20 GeV Depends strongly on the granularity Transverse & longitudinal information of the cluster helps resolve merged  0 19

20. Efficiency matrix Global efficiency is large (~80%) Inefficiency mainly due to geometric coverage Cross contamination due to missing  /  0 20

21. Systematic errors Dominant error is  /  0 reconstruction Could be improved with better EM calorimeter Better fake photon simulation will also help 21

22. Results on BRs Statistical error > systematic error Statistical precision can improve with more data Systematic errors are measured with data, also limited by statistics, can be improved with more data 22

23. Tau Branching Fractions (combined and corrected) ALEPH, Phys. Rep. 421, 191 (2005) 23 Spectral functions can be obtained by unfolding the mass spectra!

24. Lessons Need to do global analysis For charged tracks –Good momentum measurement –Good  /K separation (PID for tracks up to 40 GeV?) –Good vertex if wants to measure lifetime For  /  0 –Good geometric coverage –Very fine granularity with longitudinal readout –Good energy resolution and angular resolution –Very low photon energy threshold, better < 200 MeV 24

25. A Z-factory detector ILD  AZD (arXiv:1006.3396) Meet all the requirement for  physics (even at Ecm=500 GeV) May be further optimized for Z- factory 25

26. ILD 26 98%x4  coverage Where to put the coil?

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28. Tracking of ILD 28

29. Tracking of ALEPH 29

30. ECAL of ILD 30 Affect  0 reconstruction!

31. ECALs 31 PropertiesALEPHDELPHIILD TypeLead sheet + wire chamber [radius=185 cm] Lead-gas HPC [radius=208 cm] Si-W [radius=185 cm] Read out45 layers 3 stacks readout in longitudinal 40 layers 9 readout in longitudinal 10 8 channels 20+9 longitudinal readout Radiative length22X 0 18X 0 23.6X 0 Granularity12x12 mrad 2 17x2 mrad 2 3x3 mrad 2 Angular resolution 0.32+2.7/  E mrad1 mrad in  2 mrad in  0.5/  E mrad Energy res.0.01+0.18/  E0.31/E 0.44  0.0270.166/  E  0.011 E  threshold for  physics >350 MeV> 500 MeV> 150 MeV 50x50  m 2 digital readout, 10 12 channels?!

32. Summary  BR and SF need to be measured at Z- factory [200 pb -1 @ LEP  25 fb -1 @ GigaZ] A fine granularity ECAL is necessary for better  /  0 reconstruction ILD is a good model for AZD, more study needed to optimize the design. [is ILD too luxurious for Z-factory?] Need joint effort of other physics groups 32 Thanks a lot!

33. Additional slides 33

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36. 36 LEPTON UNIVERSALITY

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38. 38 Inclusive V+A and V  A Spectral Functions ALEPH, Phys. Rep. 421 (2005) OPAL, EPJ, C7, 571 (1999) Results from ALEPH and OPAL  and their comparison Of purely nonperturbative origin

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41. 41 Running within the Tau Spectrum The spectral functions allow to measure R  (s 0 < m  2 ); and compare the measurement with the theoretical expectation assuming RGE running assuming quark-hadron duality, this is a direct evidence for running strong coupling test of stability of OPE prediction, and hence of trustworthiness of  s (m  2 ) fit result running strong coupling: evidence for quark confinement

42. 42 (k,l)ALEPHOPAL (0,0) 0.39  0.140.26  0.12 (1,0) 0.38  0.080.28  0.09 (2,0) 0.37  0.050.30  0.07 (3,0) 0.40  0.040.33  0.05 (4,0) 0.40  0.040.34  0.04 Strange Spectral Function: SU(3) Breaking determination V us and QCD uncertainties

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44. Why ALEPH  analysis has high precision High energy Low multiplicity High efficiency Low background level Global analysis Good charged track reconstruction Good photon reconstruction (E>350 MeV) 44

45. 45 PRD4, 2821 (1971) Weak decays; well understood Not many decay modes! All the properties are predicted for mass 0.6, 0.8, 0.938, 1.2, 1.8, 3.0 and 6.0 GeV. (m  =1.777 GeV) PDG: Total rate=1/290.6E-15=344E10s

46. 46  branching fraction at threshold Static , mono-chromo , K,  system – is it easy to tag? MC simulation underway

47. 47  -pair at rest (1)  ± →  ± +  (2)  ± →K ± +  m τ = 1.7769 GeV m π = 0.13497 GeV m K = 0.49367 GeV p π = 0.883 GeV p K = 0.820 GeV p π /m τ = 0.497 p K /m τ = 0.461 E cm =3.554 GeV (  pair threshold) Achim Stahl,Inter. J. of Modern Phys. A Vol.21,No.27(2006)5667  p/p=0.32%  p  0.37% MC simulation

48. 48 E cm = 3.554 GeV Energy Spread=1.3 MeV W/o energy spread W/ energy spread To be addressed (via MC study): Backgrounds Tau Non-tau No part ID? Fit momentum spectrum? Precision versus luminosity Other decay modes? SF?