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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 - PowerPoint PPT Presentation
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June, 14th, 2006 Mo Xiaohu 1
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, 2006 Mo Xiaohu 2
Content
1.Introduction2.Statistical optimization
of mass measurement 3.Systematic uncertainty
study4.Summary
June, 14th, 2006 Mo Xiaohu 3
Introduction
June, 14th, 2006 Mo Xiaohu 4
Pseudomass method• ARGUS• CLEO• OPAL• Belle• KEDRThreshold scan• BES
Points : 12 , Lum. : 5 pb1
June, 14th, 2006 Mo Xiaohu 5
!,
1 i
Ni
i
n
ii N
ePPLFii
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.
Ecm (GeV)
B r.c.
obs
BES:PRD53(1995)20
June, 14th, 2006 Mo Xiaohu 6
Ecm (GeV)
BES results:the stat. (0.18 0.21 )is compatible withthe syst. (0.25 0.17)M =1776.96 0.18
0.25 M / M = 1.7 10 – 4
0.21 0.17
June, 14th, 2006 Mo Xiaohu 7
Statistical optimization of
Mass Measurement
June, 14th, 2006 Mo Xiaohu 8
Neglecting all experiment uncertaintiesLuminosity 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.]
Statistical optimization
June, 14th, 2006 Mo Xiaohu 9
Statistical optimization for high accurate M measurementAssume : 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, 2006 Mo Xiaohu 10
Evenly divided :1, for E: E0 + E, E=(Ef–E0)/n2, for lum. : L =Ltot /n= 3pb –1
To eliminate stat. fluctuation, Sampling many times (say, 500)
June, 14th, 2006 Mo Xiaohu 11
Ecm (3.545,3.595) GeVLtot = 30 pb –1 Npt : 3 20
1. Sm >> m , using Sm as criterion;
2. Npt =5.
| m
|
June, 14th, 2006 Mo Xiaohu 12
(Ecm)
d/dEcm
max. Sm=1.48MeVmin. Sm =0.147MeV
Random sampling 100 times:Ecm (3.545,3.595) GeVLtot =45 pb –1 Npt =5;
1. Points near threshold lead to small Sm ;
2. This corresponds to larger derivative of
The largest derivativepoint may be the optimaldata taking point
June, 14th, 2006 Mo Xiaohu 13
(Ecm)
d/dEcm
Scheme I:2 points at region I + Npt(1—20) at region II Scheme II:Only Npt(1—20) at region II
II
I
Scheme I
Scheme II
Only the pointswithin region I are useful for optimal data taking point
L=5 pb –1 for each point
June, 14th, 2006 Mo Xiaohu 14
With the region I, one point is enough!
I
Ecm (3.553,3.555) GeVLtot =45 pb –1 Npt = 1—6;
Where should this one point locate?
June, 14th, 2006 Mo Xiaohu 15
Ecm = 3553.81 MeV Sm = 0.09559 MeV Ecm = 3554.84 MeV max d/dEcm
Ecm (3.551,3.595) GeVLtot =45 pb –1 Npt = 1; scan
3553.8 MeV
3554.8 MeV
June, 14th, 2006 Mo Xiaohu 16
Ltot (pb–1) Sm (MeV)
9 0.285318 0.199027 0.155036 0.138045 0.119954 0.105163 0.097672 0.0913
100 0.07491000 0.0247
10000 0.0079
One pointWith lum.
Ltot
June, 14th, 2006 Mo Xiaohu 17
Systematic Uncertainty Study
June, 14th, 2006 Mo Xiaohu 18
Study of systematic uncertainty
1.Theoretical accuracy 2.Energy spread E 3.Energy scale 4.Luminosity 5.Efficiency 6.Background analysis
June, 14th, 2006 Mo Xiaohu 19
BES:PRD53(1995)20
Accuracy Effect of Theoretical Formula
Energy spread, variation form
s=(Ecm)2
Energy scale, variation form
June, 14th, 2006 Mo Xiaohu 20
Ecm = 3554 MeV
Ltot =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 MeVnew [M.B.Voloshin, PLB556(2003)153] fit results: m = 1777.031 MeV , m = 0.094 MeVm = | m (new) – m (old) | < 3 10 – 3 MeV
Accuracy Effect of Theoretical Formula
June, 14th, 2006 Mo Xiaohu 21
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;m < 1.5 10 – 3 MeV
Ecm (GeV)
Cross section (n
b)
'
J/
/
/
/
/
J
J
J
J
EfEfEfEf
(1.51MeV)
J/
(1.06MeV)
3 m < 6 10 – 3 MeV
2
20
32
GJ
GC
Eq
June, 14th, 2006 Mo Xiaohu 22
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;
Ecm (GeV)
Cross section (n
b)
'
J/
E
EJ/
/
/
/
/
J
J
J
J
MMME
EEEW
W=E+ (E=M+ ); ~ 10– 4
m < 8 10 – 3 MeV
June, 14th, 2006 Mo Xiaohu 23
BES:PRD53(1995)20
Luminosity L : 2% m < 1.4 10 – 2 MeVEfficiency : 2% m < 1.4 10 – 2 MeV Branching fraction: Bf : 0.5% m < 3.5 10 – 3 MeV[ Bf = 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
June, 14th, 2006 Mo Xiaohu 24
Term m
(10 – 3 MeV) m / m
(10 – 6)Theoretical accuracy 3 1.7
Energy spread 6 3.4
Energy scale 8 4.5
Luminosity 14 7.9
Efficiency 14 7.9
Branching Fraction 3.5 2.0
Background 1.7 1.0
Total 22.7 12.7
Summary:systematic
June, 14th, 2006 Mo Xiaohu 25
KEDR Collab. , depolarization method:Single energy scale at level of 0.8 keV, or 10 –4 MeVTotal 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, 2006 Mo Xiaohu 26
BKG.study
Eventselection
Optimalpoint
Data taking design
>100 pb –1 , 50 pb –1 , >100 pb –1
June, 14th, 2006 Mo Xiaohu 27
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, 2006 Mo Xiaohu 28
Backup
June, 14th, 2006 Mo Xiaohu 29
Evenly divided :1,for E: E0 + E, E=(Ef–E0)/n2, for lum. : L =Ltot /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
June, 14th, 2006 Mo Xiaohu 30
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, 2006 Mo Xiaohu 31
smB ,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)
Fc(v)10–3
S(v)/ 10–3
h(v)
new
June, 14th, 2006 Mo Xiaohu 32
Ecm = 3554 MeV
Ltot =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 MeVnew 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