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 Mass Measurement at BESIII

 Mass Measurement at BESIII. X.H.MO. Workshop on Future PRC-U.S. Cooperation in High Energy Physics Beijing, China, Jun 11-18. Content Introduction Statistical optimization of  mass measurement Systematic uncertainty study Summary. Introduction. Pseudomass method ARGUS CLEO

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 Mass Measurement at BESIII

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

  2. Content • Introduction • Statistical optimization of  mass measurement • Systematic uncertainty study • Summary Mo Xiaohu

  3. Introduction Mo Xiaohu

  4. Pseudomass method • ARGUS • CLEO • OPAL • Belle • KEDR • Threshold scan • BES Points : 12 , Lum. : 5 pb1 Mo Xiaohu

  5. B BES:PRD53(1995)20 r.c. obs Ecm (GeV) 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. Mo Xiaohu

  6. Ecm (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 Mo Xiaohu

  7. Statistical optimization of Mass Measurement Mo Xiaohu

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

  9. Statistical optimization for high accurate M measurement • Assume : M is known . • To find : • What’s the optimal distribution of data taking point; • How many points are needed in scan experiment; • How much luminosity is required for certain precision. Mo Xiaohu

  10. Evenly divided : 1, for E: E0 + E, E=(Ef–E0)/n 2, for lum. : L =Ltot /n= 3pb –1 To eliminate stat. fluctuation, Sampling many times (say, 500) Mo Xiaohu

  11. Ecm (3.545,3.595) GeV Ltot= 30 pb –1 Npt : 3 20 | m| • Sm>> m , using Sm as criterion; • Npt =5. Mo Xiaohu

  12. Random sampling 100 times: Ecm (3.545,3.595) GeV Ltot=45 pb –1 Npt =5; (Ecm) min. Sm =0.147MeV max. Sm=1.48MeV • Points near threshold lead to small Sm ; • This corresponds to larger derivative of  d/dEcm The largest derivative point may be the optimal data taking point Mo Xiaohu

  13. L=5 pb –1 for each point (Ecm) I Scheme I: 2 points at region I+Npt(1—20) at region II Scheme II: Only Npt(1—20) at region II d/dEcm II Only the points within region I are useful for optimal data taking point Scheme II Scheme I Mo Xiaohu

  14. I Ecm (3.553,3.555) GeV Ltot=45 pb –1 Npt = 1—6; With the region I, one point is enough! Where should this one point locate? Mo Xiaohu

  15. Ecm (3.551,3.595) GeV Ltot=45 pb –1 Npt = 1; scan Ecm = 3553.81 MeV Sm = 0.09559 MeV Ecm = 3554.84 MeV max d/dEcm 3553.8 MeV 3554.8 MeV Mo Xiaohu

  16. One point With lum. Ltot Mo Xiaohu

  17. Systematic Uncertainty Study Mo Xiaohu

  18. Study of systematic uncertainty • Theoretical accuracy • Energy spread E • Energy scale • Luminosity • Efficiency • Background analysis Mo Xiaohu

  19. BES:PRD53(1995)20 Accuracy Effect of Theoretical Formula Energy spread, variation form s=(Ecm)2 Energy scale, variation form Mo Xiaohu

  20. Ecm = 3554 MeV Ltot=45 pb –1 m = 1776.99 MeV Accuracy Effect of Theoretical Formula 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 – 3MeV Uncertainty due to accuracy of cross section at level of 3 10 – 3 MeV Mo Xiaohu

  21. J/ Cross section (nb) J/ (1.06MeV)  f(E) ; f(E)=a E+b E2+c E3 a=1; b=0; c=0; a=0; b=1; c=0; a=0; b=0; c=1; a=1; b=1; c=1;  '   (1.51MeV) m < 1.5 10 – 3MeV   3  m < 6 10 – 3MeV Ecm (GeV) Mo Xiaohu

  22. W=E+ (E=M+ );  ～ 10– 4 J/ Cross section (nb) EJ/   f(E) ; f(E)=a E+b E2+c E3 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  m < 8 10 – 3MeV Ecm (GeV) Mo Xiaohu

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

  24. Summary:systematic Mo Xiaohu

  25. Absolute calibration of energy scale BESI: E=0.2MeV Fix, stable, regular, eliminate and controllable UNSTABLE and IRREGULAR, uncontrollable 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 Bottleneck Mo Xiaohu

  26. Event selection Data taking design Optimal point BKG. study >100 pb –1 , 50 pb –1 , >100 pb –1 Mo Xiaohu

  27. Summary • 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. Thanks! Mo Xiaohu

  28. Backup Mo Xiaohu

  29. Evenly divided : 1,for E: E0 + E, E=(Ef–E0)/n 2, for lum. : L =Ltot /n= 3pb –1 M=1777.0367 MeV Sm =0.4273 MeV To eliminate stat. fluctuation, Sampling many times (say, 500) The point below threshold Have no effect for fit results Mo Xiaohu

  30. Summary:statistical • What’s the distribution of data taking point ; • How many points are needed in scan experiment ; • How much luminosity is required for certain precision. 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 . Mo Xiaohu

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

  32. Ecm = 3554 MeV Ltot=45 pb –1 m = 1776.99 MeV Accuracy Effect of Theoretical Formula 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 – 3MeV •  ±  10 – 4 • m < 10 – 4MeV •  ± 2  10 – 4 m < 10 – 4MeV Uncertainty due to accuracy of cross section at level of 3 10 – 3 MeV Mo Xiaohu

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