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
June, 14th, 2006Mo Xiaohu2 Content 1.Introduction 2.Statistical optimization of mass measurement 3.Systematic uncertainty study 4.Summary
June, 14th, 2006Mo Xiaohu3 Introduction
June, 14th, 2006Mo Xiaohu4 Pseudomass method ARGUS CLEO OPAL Belle KEDR Threshold scan BES Points : 12, Lum. : 5 pb 1
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) BB r.c. obs BES:PRD53(1995)20
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 = 0.18 0.25 M / M = 1.7 10 – 4 0.21 0.17
June, 14th, 2006Mo Xiaohu7 Statistical optimization of Mass Measurement
June, 14th, 2006Mo Xiaohu8 Neglecting all experiment uncertainties Luminosity L ; Efficiency =14% ; Branching fraction: B f = ; [ B f = B B e, PDG04] Background BG =0. Using Voloshin’s formula for obs [M.B.Voloshin, PLB556(2003)153.] Statistical optimization
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.
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)
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 |
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
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
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?
June, 14th, 2006Mo Xiaohu15 E cm = MeV Sm = MeV E cm = MeV max d /dE cm E cm (3.551,3.595) GeV L tot =45 pb –1 N pt = 1; scan MeV MeV
June, 14th, 2006Mo Xiaohu16 L tot (pb –1 )Sm (MeV) One point With lum. L tot
June, 14th, 2006Mo Xiaohu17 Systematic Uncertainty Study
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
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
June, 14th, 2006Mo Xiaohu20 E cm = 3554 MeV L tot =45 pb –1 m = MeV Uncertainty due to accuracy of cross section at level of 3 10 – 3 MeV old [BES, PRD53(1995)20] fit results: m = MeV, m = MeV new [M.B.Voloshin, PLB556(2003)153] fit results: m = MeV, m = MeV m = | m (new) – m (old) | < 3 10 – 3 MeV Accuracy Effect of Theoretical Formula
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
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
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 = pb –1 : PLR68(1992)3021 ] Total : m < 2.02 10 – 2 MeV
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 Fraction Background Total Summary:systematic
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
June, 14th, 2006Mo Xiaohu26 BKG. study Event selection Optimal point Data taking design >100 pb –1, 50 pb –1, >100 pb –1
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!
June, 14th, 2006Mo Xiaohu28 Backup
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 = MeV Sm = MeV
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.
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) v h(v) F c (v) 10 –3 S(v)/ 10 –3 h(v)
June, 14th, 2006Mo Xiaohu32 E cm = 3554 MeV L tot =45 pb –1 m = MeV Uncertainty due to accuracy of cross section at level of 3 10 – 3 MeV old fit results: m = MeV m = MeV new fit results: m = MeV m = 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