Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://zebu.uoregon.edu/~uochep/talks/talks01/FCP2001talk.pdf Äàòà èçìåíåíèÿ: Fri Apr 13 01:02:41 2001 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 11:40:06 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï

The Rb and Rc Measurements at SLD
Sean Walston University of Oregon Representing the SLD Collaboration

Frontiers in Contemporary Physics II March 5-10, 2001, Nashville Tennessee


Improved Rb and Rc Results
"

New Winter 2001 Rb Result With Improved Event Selection Bias Correction: R b = 0.21705 ± 0.00094 ± 0.00079

"

Summer 2000 Result as Reported at ICHEP: R b = 0.21669 ± 0.00094 ± 0.00101

"

New Winter 2001 Rc Result With Improved Multitag Analysis (Better Statistics): R c = 0.1757 ± 0.0032 ± 0.0024

"

Summer 2000 Result as Reported at ICHEP: Rc = 0.1732 ± 0.0041 ± 0.0025


What are Rb and R
"

c

Fraction of Hadronic Z0 Decays producing Bottom or Charm Quarks
Rb = Rc = Z Z
0 0

b¯ b

Hadrons Z
0

c¯ c

Z

0

Hadrons

"

Must Identify:
: Hadronic Events : Bottom Events : Charm Events


Why Measure Rb?
/

Window onto the Top Quark (Vtb ~ 1, Rb proportional to mt2) Rb is a Precision Test of the Standard Model The Zbb vertex is sensitive to certain types of new physics which primarily couple to heavy families (Higgs Couplings linear with mass)

/

/


b

The Zbb Coupling
"

Z0 b

SM Radiative Corrections: Rb
b t Z0 t b W Z0 W
-

SM Rad. Cor.

= 0.0035
W b t Z0 b W t b b

W+ t

b Z0 b

"

Corrections from a Second Higgs Doublet
H+ t Z
0

b

H+ Z0 H- t

b Z0 b SUSY(max) b k Z0 b

t H+ t

b

+
H+

t b

b

"

Corrections from Supersymmetric Particles: Rb
~ tj Z
0

= 0.0025
i j ~ tk b b

b
i

~ ti Z0 ~ tj

+
~ tj

i b


History of the Rb Measurement
History of Rb (From Particle Data Books 1992, 1994, 1996, 1998, 2000)

0.235

Experimental
0.23 0.225 0.22 0.215 0.21 0.205 0.2 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Standard Model Tree Level Value


Features of SLC/SLD
/ Small, Stable Beams:
· x : < 1.5 µm · y : ~ 0.5 µm · z : ~ 1.0 mm

/ VXD3 CCD Vertex Detector


VXD3
/ Natural 3-D Space Points
from 307,000,000 Pixels!!!

/ Pixels 20 x 20 x 20 µm / Single hit precision < 4 µm / Radial Lever Arm:
A Inner Radius = 28 mm A Outer Radius = 48 mm

/ Impact Parameter Resolution:

r

= 7.8 = 9.7

33 p sin p sin
3/ 2



µm µm



33
3/ 2

rz


Topological Vertexing
"

Tracks Parameterized as Gaussian Probability Tubes in 3D Vertices are Regions with High Overlap

"


Hadronic Event Selection
: Visible Energy from Charged Tracks > 18 GeV : At least 7 Tracks in the Central Tracking Chamber

Transverse Momentum pT > 0.2 GeV : At least 3 of these Tracks must have links to the Vertex Detector
:

: Within Detector Acceptance
:

cos Th

rust

< 0.71

: 3 Jets or Less (ycut= 0.02)


How to Measure Rb
"

Separate Hadronic Events into 2 Thrust Hemispheres Apply b-Tags to each Hemisphere Count up the Numbers of:
: :
Hemisphere 1

"

"

b-Tagged Hemispheres Double b-Tagged Events
IP Hemisphere 2 Thrust Axis

"

Assume from Monte Carlo mistagging efficiency and Hemisphere Correlation


The Vertex Mass Tag
M =

VTX

tracks
p Missing p
T T



m



p

2 T

p

T

Vertex Axis

p Charged Tracks

VTX

Vertex

IP


SLD c/b Selection Neural Net
No. of Hemispheres
3500 3000 2500 2000 1500 1000 500 0

SLD Preliminary Data MC

/ Vertex Mass / Vertex Momentum · lower for b than for c

b c
uds
0 1 2 3 4 5
2

/ Decay Length · higher for b than for c
6

Mass (GeV/c )

/ Track Multiplicity · higher for b than for c
c-events
50 Pvtx 40 45 40 35 30 30 25 20 20

No. of Hemispheres

10

4

SLD Preliminary Data MC

b-events

10

3

b

c
10
2
10

15 10 5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Mvtx

uds

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Neural Net c-b separation


Choice of c/b Selection Cut
= Pick Cut on c/b
Rb/Rb (%)

SLD Preliminary 97-98
3

Selection Neural Net Output Such that Overall Uncertainty on Rb is Minimized
= Neural Net c/b

2.5

2

Net Uncertainty (exc. Rc & ev-sel) Statistics Rc±0.06 udsc Physics Sys. (exc. Rc) Correlation Systematic Detector Systematics

1.5

Selection Output > 0.75

1

0.5

0

0

0.1

0.2

0.3

0.4

0.5 0.6 0.7 0.8 0.9 Neural Net c-b separation


Tag Efficiencies and Purities
tag efficiency/purity

SLD Preliminary 97-98 data
1
88.2 94.5 96.5 97.7 98.5 99.1

tag efficiency/purity

1
90.9 86.3

SLD Preliminary 97-98 data
81.9

0.8

91.5 b=98.3% 75.6 83.7 72.3 71.7 70.5 69.1 67.4 65.5 63.5 61.1

0.8

72.9

0.6
57

0.6

0.4

b b(measured) b c uds

b=61.7%

0.4

c c(data) c b uds

77.7

c=84.5%

c=17.4%
18.7 21 22.5

0.2

0.2
9.7

15.5

0

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Neural Net c-b separation

0

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 Neural Net c-b separation

b-Tag Efficiency and Purity b=61.7% b=98.3%

c-Tag Efficiency and Purity c=17.4% c=84.5%


Rb vs. c/b Selection Cut
Rb
0.224 0.222 0.22 0.218 0.216 0.214 0.212 0.21 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

SLD Preliminary 97-98 data

Neural Net c-b separation cut


Event Selection Bias
A Hadronic Event Selection Designed to Include All Hadronic Z0 Decays A NJets < 4 removes ~8% of events. According to JETSET, this removes
more udsc-events than b-events
1 Event Selection Bias

A Bias from:
(1) B-Hadron Decays have wider jets 1 4 jets not so easily resolved (2) Reduced gluon radiation in b-events due to large b-quark mass 1 Fewer true 4-jet events

A Effect of (1) is reliably estimated using our simulation which is carefully
tuned to B-dacay data from ARGUS and CLEO and B-production data from LEP and SLC
Rb = 0.00074


Effect of the b-Quark Mass
A Previously, JETSET Used to Evaluate a Correction
1 Full Amount of Correction taken as Systematic Error

A Improved Understanding:
: Running b-mass measured by Delphi/SLD at mb(MZ) ~ 3 GeV : LO Calculation of 4-jet rate as a funtion of quark mass

A Scale the Monte Carlo Track Level 4-jet rate difference from the
running b-mass effect by the theoretical expectation for a running b-mass of 3 +/- 1 GeV

A Previous event selection bias correction:
1 Rb = 1 Rb =

0.00176 ± 0.00067 0.00140 ± 0.00022

A Improved event selection bias correction:


Latest Rb Result
"

Summer 2000 Result as Reported at ICHEP:

Rb = 0.21669 ± 0.00094 ± 0.00101
"

New Winter 2001 Result With Improved Event Selection Bias Correction:

Rb = 0.21705 ± 0.00094 ± 0.00079


Brand New Tags for R
"

c

b-Tags
­ ­

Standard "Hard" b-tag 1 NN c/b Selection Output > 0.75 "Soft" b-tag, "b-ish" 1 0.75 > NN c/b Selection Output > 0.50 Standard "Hard" c-tag 1 NN c/b Selection Output < 0.30 "Soft" c-tag, "c-ish" 1 0.30 < NN c/b Selection Output < 0.50

"

c-Tags
­ ­


Brand New Improved Rc Scheme
/ Analogous to Double Tag method used in Rb, but worse! 4 Tags this time! / A Hard Tag in one hemisphere yields very high purity in the opposite
hemisphere (kind of like MC Truth). In this way, the hard tags can calibrate the soft tags

/ Assume from Monte Carlo:
: uds-Mis-Tagging Efficiencies : c-Mis-Tagging Efficiency for the Hard b-Tag : Correlations / Calculate From Data: : Tagging Efficiency for each Tag : Mis-Tagging Efficiencies for all but the Hard b-Tag : Rb and Rc / Weight each Tag by Statistical and Systematic Errors. Softer Tags have: : Lower Statistical Errors : Higher Systematic errors / Fit the Weights to Minimize the Net Error


Latest Rc Result
"

Summer 2000 Result as Reported at ICHEP:

Rc = 0.1732 ± 0.0041 ± 0.0025
"

New Winter 2001 Result With Multitag Analysis:

Rc = 0.1757 ± 0.0032 ± 0.0024


Rb and Rc Measurements
Rb Measurements (Winter-2001)
0.2159±0.0009±0.0011 0.2163±0.0007±0.0006 0.2174±0.0015±0.0028 0.2176±0.0011±0.0014 0.2171±0.0009±0.0008 0.21664±0.00068
SM
0.212 0.214 0.216 0.218 0.22 0.222

Rc Measurements (Winter-2001)
ALEPH Lepton ALEPH c-counting 0.1675±0.0062±0.0103 0.1738±0.0047±0.0113 0.1692±0.0047±0.0097 0.167 ±0.011 ±0.012 0.166 ±0.012 ±0.009 0.161 ±0.010 ±0.009 0.180 ±0.010 ±0.012 0.173 ±0.014 ±0.009 0.1757±0.0032±0.0024 0.1729±0.0032 SM
0.14 0.15 0.16 0.17 0.18 0.19 0.2

ALEPH Multi-var

DELPHI Multi-var

DELPHI c-counting OPAL c-counting

L3 Impact+Lept

ALEPH D* incl/excl DELPHI D* incl/excl OPAL D* incl/excl

OPAL VtxNN+Lept

SLD VtxMass NN
Update

ALEPH D excl/excl SLD Multi-tag
New

World Average

Inc.+0.0003 for -exchange

World Average


Conclusions
"

Both Rb and Rc are Consistent with the Standard Model for mt = 175 GeV Rb Measured to Level of 0.3%
R
R R
SLD b

"

= 0.2171 ± 0.0009 ± 0.0008
= 0.21664 ± 0.00068 = 0.2158 ± 0.0002

World Average b Standard Model b

"

Rc Measured to Level of 1.9%
SL Rc D = 0.1757 ± 0.0032 ± 0.0024

R R

World Average c Standard Model c

= 0.1729 ± 0.0032 = 0.1723 ± 0.0001