1. June, 14th, 2006Mo Xiaohu1  Mass Measurement at BESIII X.H.MO Workshop on Future PRC-U.S. Cooperation in High Energy Physics Beijing, China, Jun 11-18

2. June, 14th, 2006Mo Xiaohu2 Content 1.Introduction 2.Statistical optimization of  mass measurement 3.Systematic uncertainty study 4.Summary

3. June, 14th, 2006Mo Xiaohu3 Introduction

4. June, 14th, 2006Mo Xiaohu4 Pseudomass method ARGUS CLEO OPAL Belle KEDR Threshold scan BES Points : 12, Lum. : 5 pb  1

5. June, 14th, 2006Mo Xiaohu5 F(x): E.A.Kuraev,V.S.Fadin, Sov.J.Nucl.Phys. 41(1985)466;  (s): F.A. Berends et al., Nucl. Phys. B57 (1973)381. E cm (GeV) BB  r.c.  obs BES:PRD53(1995)20

6. June, 14th, 2006Mo Xiaohu6 E cm (GeV) BES results: the stat. (0.18  0.21 ) is compatible with the syst. (0.25  0.17) M  = 1776.96  0.18  0.25  M  / M  = 1.7  10 – 4  0.21  0.17

7. June, 14th, 2006Mo Xiaohu7 Statistical optimization of Mass Measurement

8. June, 14th, 2006Mo Xiaohu8 Neglecting all experiment uncertainties Luminosity L ; Efficiency  =14% ; Branching fraction: B f =0.1763 0.1784 ; [ B f = B   B   e, PDG04] Background  BG =0. Using Voloshin’s formula for  obs [M.B.Voloshin, PLB556(2003)153.] Statistical optimization

9. June, 14th, 2006Mo Xiaohu9 Statistical optimization for high accurate M  measurement Assume : M  is known. To find : 1.What’s the optimal distribution of data taking point; 2.How many points are needed in scan experiment; 3.How much luminosity is required for certain precision.

10. June, 14th, 2006Mo Xiaohu10 Evenly divided : 1, for E: E 0 +  E,  E=(E f –E 0 )/n 2, for lum. : L =L tot /n= 3pb –1 To eliminate stat. fluctuation, Sampling many times (say, 500)

11. June, 14th, 2006Mo Xiaohu11 E cm  (3.545,3.595) GeV L tot = 30 pb –1 N pt : 3  20 1.Sm  >>  m , using Sm  as criterion; 2.N pt =5. |  m  |

12. June, 14th, 2006Mo Xiaohu12  (E cm ) d  /dE cm max. Sm  =1.48MeV min. Sm  =0.147MeV Random sampling 100 times: E cm  (3.545,3.595) GeV L tot =45 pb –1 N pt =5; 1.Points near threshold lead to small Sm  ; 2.This corresponds to larger derivative of  The largest derivative point may be the optimal data taking point

13. June, 14th, 2006Mo Xiaohu13  (E cm ) d  /dE cm Scheme I: 2 points at region I + N pt (1—20) at region II Scheme II: Only N pt (1—20) at region II II I Scheme I Scheme II Only the points within region I are useful for optimal data taking point L=5 pb –1 for each point

14. June, 14th, 2006Mo Xiaohu14 With the region I, one point is enough! I E cm  (3.553,3.555) GeV L tot =45 pb –1 N pt = 1—6; Where should this one point locate?

15. June, 14th, 2006Mo Xiaohu15 E cm = 3553.81 MeV Sm  = 0.09559 MeV E cm = 3554.84 MeV max d  /dE cm E cm  (3.551,3.595) GeV L tot =45 pb –1 N pt = 1; scan 3553.8 MeV 3554.8 MeV

16. June, 14th, 2006Mo Xiaohu16 L tot (pb –1 )Sm  (MeV) 90.2853 180.1990 270.1550 360.1380 450.1199 540.1051 630.0976 720.0913 1000.0749 10000.0247 100000.0079 One point With lum. L tot

17. June, 14th, 2006Mo Xiaohu17 Systematic Uncertainty Study

18. June, 14th, 2006Mo Xiaohu18 Study of systematic uncertainty 1.Theoretical accuracy 2.Energy spread  E 3.Energy scale 4.Luminosity 5.Efficiency 6.Background analysis

19. June, 14th, 2006Mo Xiaohu19 BES:PRD53(1995)20 Accuracy Effect of Theoretical Formula Energy spread, variation form s=(E cm ) 2 Energy scale, variation form

20. June, 14th, 2006Mo Xiaohu20 E cm = 3554 MeV L tot =45 pb –1 m  = 1776.99 MeV Uncertainty due to accuracy of cross section at level of 3  10 – 3 MeV  old [BES, PRD53(1995)20] fit results: m  = 1777.028 MeV,  m  = 0.105 MeV  new [M.B.Voloshin, PLB556(2003)153] fit results: m  = 1777.031 MeV,  m  = 0.094 MeV  m  = | m  (new) – m  (old) | < 3  10 – 3 MeV Accuracy Effect of Theoretical Formula

21. June, 14th, 2006Mo Xiaohu21  f(E) ; f(E)=a E+b E 2 +c E 3 a=1; b=0; c=0; a=0; b=1; c=0; a=0; b=0; c=1; a=1; b=1; c=1;  m  < 1.5  10 – 3 MeV E cm (GeV) Cross section (nb)  ' ' J/    (1.51MeV)  J/  (1.06MeV)   3   m  < 6  10 – 3 MeV

22. June, 14th, 2006Mo Xiaohu22   f(E) ; f(E)=a E+b E 2 +c E 3 a=1; b=0; c=0; a=0; b=1; c=0; a=0; b=0; c=1; a=1; b=1; c=1; E cm (GeV) Cross section (nb)  ' ' J/  E E E J/  W=E+  (E=M+  );  ～ 10 – 4  m  < 8  10 – 3 MeV

23. June, 14th, 2006Mo Xiaohu23 BES:PRD53(1995)20 Luminosity L : 2%   m  < 1.4  10 – 2 MeV Efficiency  : 2%   m  < 1.4  10 – 2 MeV Branching fraction: B f : 0.5%   m  < 3.5  10 – 3 MeV [ B f = B   B   e, PDG04] Background  BG : 10%   m  < 1.7  10 – 3 MeV [  BG = 0.024 pb –1 : PLR68(1992)3021 ] Total :  m  < 2.02  10 – 2 MeV

24. June, 14th, 2006Mo Xiaohu24 Term  m  (10 – 3 MeV)  m  / m  (10 – 6 ) Theoretical accuracy31.7 Energy spread63.4 Energy scale84.5 Luminosity147.9 Efficiency147.9 Branching Fraction3.52.0 Background1.71.0 Total22.712.7 Summary:systematic

25. June, 14th, 2006Mo Xiaohu25 KEDR Collab., depolarization method: Single energy scale at level of 0.8 keV, or 10 –4 MeV Total systematic error at level of 9 keV, or 10 – 3 MeV Absolute calibration of energy scale Fix, stable, regular, eliminate and controllable UNSTABLE and IRREGULAR, uncontrollable BESI:  E=0.2MeV Bottleneck

26. June, 14th, 2006Mo Xiaohu26 BKG. study Event selection Optimal point Data taking design >100 pb –1, 50 pb –1, >100 pb –1

27. June, 14th, 2006Mo Xiaohu27  Statistical and systematic uncertainties have been studied based on BESI performance experience.  Monte Carlo simulation and sampling technique are adopted to obtain optimal data taking point for high accurate  mass measurement. We found:  optimal position is located at large derivative of cross section near threshold ;  one point is enough, and 45 pb –1 is sufficient for accuracy up to 0.1 MeV.  Many factors have been taken into account to estimate possible systematic uncertainties, the total relative error is at the level of 1.3  10 – 5. However the absolute calibration of energy scale may be a key issue for further improvement of accuracy of  mass. Summary Thanks!

28. June, 14th, 2006Mo Xiaohu28 Backup

29. June, 14th, 2006Mo Xiaohu29 Evenly divided : 1,for E: E 0 +  E,  E=(E f –E 0 )/n 2, for lum. : L =L tot /n= 3pb –1 To eliminate stat. fluctuation, Sampling many times (say, 500) The point below threshold Have no effect for fit results M  =1777.0367 MeV Sm  =0.4273 MeV

30. June, 14th, 2006Mo Xiaohu30 Optimization study shows that:  optimal position is locate at large derivation of cross section near threshold ;  one point is enough,  and 45 pb –1 is sufficient for accuracy up to 0.1 MeV. Summary:statistical 1.What’s the distribution of data taking point ; 2.How many points are needed in scan experiment ; 3.How much luminosity is required for certain precision.

31. June, 14th, 2006Mo Xiaohu31 Improved the previous calculation, accuracy close to 0.1% M.B.Voloshin, PLB556(2003)153. NRQCD, NNLO, accuracy better that 0.1% P.Ruiz-Femenia and A.Pich, PRD64(2001)053001. v h(v) F c (v)  10 –3  S(v)/   10 –3 h(v)

32. June, 14th, 2006Mo Xiaohu32 E cm = 3554 MeV L tot =45 pb –1 m  = 1776.99 MeV Uncertainty due to accuracy of cross section at level of 3  10 – 3 MeV  old fit results: m  = 1777.028 MeV  m  = 0.105 MeV  new fit results: m  = 1777.031 MeV  m  = 0.094 MeV  m  = | m  (new) – m  (old) | < 3  10 – 3 MeV    ±   10 – 4  m  < 10 – 4 MeV    ± 2   10 – 4  m  < 10 – 4 MeV Accuracy Effect of Theoretical Formula