Measurement of the Ë b
Lifetime in the Decay Mode
Ë b ! J= Ë
LEPP Journal Club
January 22, 2004
Robyn Madrak
Harvard University
Decay Modes
• First seen unambiguously
at CDF in Л b ! J= Л
– Only measured mass
• Lifetimes measured at
– CDF/LEP in Л b ! Л clч
ц
– LEP in baryon decays
tagged by Лl
2
Why measure the Ë b Lifetime ?
• Test theoretical models used in predictions of
heavy quark quantities
 Not only interesting in themselves - need to extract weak
interaction quantities from measureables
• Currently, experiment and theory disagree
• Besides this measurement, lifetime measured only
in semileptonic decay modes
• Initially expected to have huge amount of data by
now  very competitive measurement
3
Discrepancy:
• Theory predictions work well for B à ; B s
• But not Л b (though others claim 0.85 could be
accommodated)
4
Measurements up to Now
average b-baryon
lifetimeЛ
all semileptonic
measurements
b
5
Sources of Lifetime Differences
 In the simple spectator model, same lifetime for all
hadrons with same heavy quark
• The heavier the quark, the more valid the
approximation
È( b) =
9V2cbG 2FM 5b
192ù 3
• With more sophisticated theory, lifetimes are
different, due to
 Pauli Interference
 Weak Annihilation (for mesons)
 Weak Exchange, or scattering (for baryons)
6
Sources of Lifetime Differences:
1.) Pauli Interference
Same final state
=>interference
Different final
states
7
Sources of Lifetime Differences:
2.) Weak Annihilation
• Only in mesons
• In B-but not B 0
8
Sources of Lifetime Differences:
3.) Weak Exchange: Main source of lifetime
difference for B 0=( Ë b )
•
Helicity suppressed in mesons, but not
9
baryons (no antiquarks)
The Fermilab p pbar Accelerators
• Upgraded for Run
II
• cm energy of 1.96
TeV (was 1.8)
• 36p on 36pbar
bunches (was 6X6)
• 396 ns bunch
crossing time:
required many
detector upgrades
(was 3.5 us)
10
The CDFII Detector
Central Calorimeter
Time of Flight
Muon Chambers
CMU
CMP
CMX
Plug Upgrade Calorimeter
Beamline
Silicon Vertex Detector
(SVXII)
Solenoid
Drift Chamber
(COT)
11
The CDFII Detector
12
The COT
•End view: Fraction of the endplate
•8 “superlayers”
• alternating planes of sense
wires (readout) and field
sheets(ground)
• alternating axial and stereo (2
°) superlayers
Closeup of cell layout
in 1 superlayer
13
The COT
sense wires
field sheet
Segments
(in 8 layers)
Tracking in a Nutshell:
•Form line segments in 4 axial layers
•Do axial fit, connecting segments
•Form segments in stereo layers
•Add stereo segments to fit
14
•Final fit
This measurement: Full Reconstruction
Ë B ! J= Ë : baryon equiv. of golden mode J= K 0s
• Ë ! pù
J= ! ö + ö à
• Reconstruct p + ; ù à ; ö + ö à
Cons:
• Fewer events - larger statistical error
Pros:
• Potentially smaller systematic error
• Less background due to full reco
• Have a signal invariant mass peak  signal and
background regions well defined
• Good vertex for decay length (use multiple tracks)
• Do not rely on MC as in semileptonic case (can’t
15
measure momentum of n  boost(bg) is unknown)
Data Sample
• 65 pb^-1 with SVX
fully functional
• J/y sample: from
dedicated J/y trigger
Muon stubs
(J/y->mm)
MC event
 Level 1: Two online, opp. Q
tracks, pT>1.5 GeV, good trackstub match (CMU or CMX)
 Level 2: Auto
 Level 3: Full tracking, cut on
m(mm), track-stub matching
• Reconstructing L->pp:
 compute invariant mass of all
opp. Q tracks
 use p/p mass hypothesis for
higher/lower momentum
Proton track
particle (Need maximal
efficiency: No dE/dx or TOF)
Pion track
16
Scheme for Measuring the Lifetime
• Use control
sample:
B 0 ! J= K 0s
• kinematically
similar
• well-known
lifetime:
ct = 2.7 cm
462 æ5öm
ct = 7.9 cm
same cuts except for a few cases (m(L) not m(Ks))
 4 track kinematic fit: vertex constrain J/y and L or Ks (V0’s)
 Mass constrain M(mm) to world average m(J/y) (better mass resolution)
 Constrain Ks to “point” back to J/y
• Measure control sample lifetime
 agrees with world average? If so, measure Lb lifetime
17
Analysis Cuts
•No dE/dx cut
•No TOF
 use in future
with more statistics
Lb: Need max
efficiency now
•pt cut only for p’s
from Ks, not
efficient for L
0
•get rid of B
•remove pairs of
real J/y and L or Ks
0
that are not B, Lb
Quantity
Value
Purpose
Tracks
N(COT axial) > 20
well -measured momenta
N(COT stereo) > 16
Muons
J/y
> 2 rf SVX hits
well -measured Lxy
pT(m)>1.5 GeV
reinforce trigger
prob(c2) > 0.1%
quality vertex
3.01 < m(mm) < 3.17 GeV
V0
Ks
prob(c2) > 0.1%
quality vertex
Lxy > 0.25 cm
bg rejection
0.477 < m(pp) < 0.517
pT(p) > 0.4 GeV
L
B/Lb
1.104 < m(pp) < 1.128
! 0.48 < m(pp) < 0.513
Ks veto
prob(c2) > 0.1%
good 4-track vertex
cos(q) > 0.9999
18
pointing
J/y Candidates
• ~600k candidates
with 3 or more r-f
SVX hits
• S/B = 5.1
• width = 17.6 MeV
19
Ks and L Candidates After Cuts
•Very clean  Most B/Lb background comes from pairs of
0
real J/y and real Ks, L
20
0
0
Event Yields: B control sample
21
Event Yields: Lb
22
•J/y Ks background: expect 1 event at <= 5.5 GeV
A Lb candidate event in data
muon tracks
proton
pion
23
Proper Decay Time
 500 mm
• Need proper decay
time ct for each event
 10 cm
 primary vertex
 secondary vertex
• Need pT(Lb)
ct = L
1
бì í
= L
mB
б pB
=
mB
L xy б pB
T
24
Unbinned Maximimum Likelihood Fit
• Fit mass histogram to
determine
signal/background
regions, and background
fraction fb
• Functional for for ct in
signal region:
F isi g( cьB ) =
Exp( ct i ; cьB ) к G( ct i ; ыict ; sct )
G:detector resolution smearing
• And in background region:
F ibgr
= (1 а f à а f + ) бG( ct
i
; ыict ; sct )
Exp: real long lived distribution
+
{
f+
( à ct) i =õ +
б
e
;
õ+
fà
(ct) i =õ à
б
e
;
õà
• Fit signal and background simultaneously
( ct ) i > 0
( ct ) i < 0
25
Control Sample Mystery
• The control sample
lifetime came out low!
ct=363  27 mm
PDG = 462 mm
significance = 3.7s
Why???
• Measured the correct
0
lifetime with 5k B events
with full simulation
• Checked for fitter
bias/bugs using Toy MC
(next)
26
Fitter Checks with Toy MC
• Want to check fit for any possible bias, bugs
 Generate 5k “fake” experiments (Toy MC)
° same number of events as in data, same S/B
these have:
º distributions functional forms same as in data
º errors on ct drawn from a histogram (of data errors)
B toy MC
generated ct = 414 mm
ave fit ct = 4130.45
B toy MC - ct PULL
fit mean = 4  2 mm
width = 1.05  0.02
27
Answer: COT Tracking Algorithms
•
1
Two algorithms:
SL (from Run I) links full line
segments (in each of 8 layers)
2 HL (new) for high pT efficiency
- looks for hits along a line to the
beamline after finding an outer
0
layer segment
- easy to believe it would be biased
- IS biased for Ks
Segments
(in 8 layers)
Use ONLY HL:
Use ONLY SL:
ct = 33836mm
ct = 41431mm
•ALSO:
•by dropping
“supplementary”
algorithm, we lose
NO events
For this
analysis we
28
use SL only
0
Fit for B Control Sample
F = (1 à f b)F s + f bF b
F s = G ê Exp(cü)
F b = (1 à f + à f а ) â G
+{
(f + =õ + ) áe( ct=х + )
(f + =õ + ) áe(а ct=х + )
ct < 0
ct > 0
Fit Results
G (prompt bg)
l-
(tails)
within 1.5 s of
PDG world ave of
462 mm
l+
(tails + real long-lived
bg)
fit quantity
value
error
ct
414um
31
sct
1.26
0.05
f-
0.029
0.009
l-
499um
139
f+
0.13
0.02
l+
fb
307um
43
0.571
0.028
29
Fit for Lb Lifetime
cь( Л B = 374 ж 78 цm) = 1:25 ж 0:26 ps
30
Cross Checks and Systematics
•Cross Checks:
•Fitting Method
•Splitting of data into separate samples
•Treatment of long-lived particles (V0’s)
•Systematics
•SVX Alignment
•Fitting Model
•Gaussian resolution function
•“Careful Systematics” (from cross checks)
31
Alternative Fitting Method:2d Simultaneous
Mass and Lifetime Fit
• Fit mass and ct distributions simultaneously:
F ilik = ( 1 а f B ) бF isig бM isig + f bgr бF ibgr бM ibgr
• gaussian: M isig
• linear: M ibgr
• Fit parameters:
f cь; sct ; f B ; f + ; f à ; х + х à ;
m B ; ыm B ; C 0g
32
Cross Check #1: Results with 2d Simult. Fit
B0
Lb
• With this fit:
420 ж 42цm
• With this fit:
351 ж 69цm
• With separate fit:
414 ж 31цm
• With separate fit:
374 ж 78цm
33
Cross Check #2: Luminosity Effect in Control
Sample
•Observed B mass width larger in later data than in earlier
•Could not find specific change in detector configuration as cause
Divide data into bins of instantaneous luminosity
L < 1:17 cm а 2sа 1
1:17 < L < 1:7 cm а 2sа 1
Low lumi
L > 1:7 cm а 2sа 1
mid lumi
hi lumi
34
Cross Check #2: Luminosity Effect in B 0
Control Sample
Standard (separate) fit:
•low lum:
43839mm
Standard (separate) fit:
•hi lum:
38355mm
 OK (only 0.8 s difference) 
35
Cross Check #3:Treatment of V0 ‘s
•Ks and L are long-lived (ct=2.7 cm and 7.9 cm)
•Many decay outside of SVX
•We use only SVX hits consistent with being on tracks
(based on COT-only info)
•A reasonable analysis may have rejected all SVX hits for36V0’s
V0 Tracking: Cross Check Results for B
0
•With COT-only tracks
for Ks, lifetime is
smaller:
Compare to 414  31 mm
• But in that case, the
sample changes, and the
difference is still < 1 s
OK
37
d vs. f :
3
barrels:
Systematic #1: SVX Alignment
Getting the systematic:
Barrel 1
Barrel 2
Barrel 3
Projection:
RMS = 7
mm
-Use higher statistics
80 mm
B+ J/y K+
-Try a series of “inferior”
alignment tables
-Also try alignment where
SVX wafers are “bowed” out
systematically by 100mm
-Quantify variation in lifetime:
5 mm
38
Systematic #2: Fitting Model
•Current model is well motivated, but can imagine others:
> Convolute background exponentials with gaussian resolution
(instead of adding)
 B lifetime is 11 mm lower
> Add an additional positive going tail in background function
 no change
> Use mass errors and fit for scale factor on mass errors
instead of B width
B lifetime is 22 mm higher
> Separately fit sidebands and signal region
B lifetime is 2 mm higher
•Take largest variation as sytematic: 22 mm
39
Systematic #3: Resolution Function
1 ) Fit for sct: scale
factor for resolution 1.26  0.05
2) Other studies with
inclusive J/y’s (not
specifically B’s):
3) Fit those results to a function
f
0:950 + 0:0308 г (pT(J= ) а 2:86)
1:075
1:036
pT( J= ) < 9
9 ф pT( J= ) ф 10
pT(J= ) > 10
4) Scale our errors by function and
fix sct to 1.0 in lifetime fit
5) Remeasure B lifetime: 1mm smaller
40
Luminosity Effect in B Control Sample
Revisited: Cross Check of a Cross Check
0
•Separate fit:
•low lum:
43839mm
•high lum:
38355mm
•All OK
(only 0.8 s difference)
•BUT with 2-d simultaneous fit:
•low lumi: 45540 mm, hi lumi: 32450 mm: 2s difference
•STILL USE SEPARATE FIT FOR CENTRAL VALUE, THOUGH
Assign systematic for Lb as N ss(t ot al) в ( cьpdg а cь(hi
where ct(hi L) is from the separate fit
N (hi L)
L) )
= 25mm
41
V0 Tracking: Results for B
0
• Looked into treatment of Ks before… now
we look a little deeper…
•Divide into bins of Lxy(Ks):
Cross check
from before:
this was OK
•The worry here: Very small lifetime for COT-only in
smallest bin of Lxy(Ks)
42
V0 Tracking: Another Effect
• Given this and the previous effect, Assign systematic as:
cь( B o)(our method) а cь( B 0)(COT а only K 0s) = 26цm
Allows SVX hits when appropriate
43
Summary
•Systematics:
Source
Value(mm)
ct Resolution function
SVX Alignment *
1
5
Occupancy
25
Fitting Model
22
V0 Tracking
26
Total
43
*From Bs lifetime control sample
cü(Ë b) = 374 æ 78(stat:) æ 43(syst:)öm
ü(Ë b) = 1:25 æ0:26( stat:) æ0:14( syst:)ps
(world average = 1.229  0.080 ps )
44
Implications
with
•ct(Lb) = 374  89 mm (this measurement)
•ct(B) = 462  5 mm
ü(Ë b)
ü(B 0)
= 0:81 æ0:19
45
More Data: Predictions
 < 10% error
with 3X more data
Already on tape!
46
Conclusions
We’ve measured the Lb lifetime in LbJ/y L
ü(Ë b) = 1:25 æ0:26( stat:) æ0:14( syst:)ps
From this we extract a lifetime ratio which is
consistent both with theory and the current world
average
(Though the two of those disagree)
This result will be much more interesting with 3 times
the data
(The data are available now! Work in progress...)
47
Operator Product Expansion
• Coefficients ci calculable
within perturbation theory
•Matrix elements contain
long-distance physics
•Terms 1 and 2 calculable both
for mesons and baryons
•Term 3 is for PI, WA, and
WS, harder for baryons
•lifetime differences between
mesons begin in term 3,
between baryons and mesons
in term 2
48