Notre Dame Afb Seminar 2009

Glenn Strycker – University of Michigan Notre Dame HEP Seminar – 2009-11-24
Measurement of the Forward-Backward
Asymmetry in Top Quark Pair Production
in pp Collisions at 1.96 TeV
Glenn Strycker
University of Michigan
On behalf of the CDF Collaboration

Measurement of the Forward-Backward
in pp Collisions at 1.96 TeV
Glenn Strycker
1999-2003 2003-2010

Outline
 People Involved
 What is Afb – why study it?
 Theoretical Predictions
 Previous Measurements
 FNAL and CDF Overview
 Measurement Techniques
 Correction Procedure
 Conclusion

People Involved
University of Michigan:
University of California, Davis:
Also much work done by the Karlsruhe group:
J. Wagner, T. Chwalek, W. Wagner
Glenn Strycker Dan Amidei Monica Tecchio
Tom Schwarz Robin Erbacher

The Top Forward-Backward Production Asymmetry
has already generated a lot of interest…
Asymmetries in tt Production

Simple Asymmetries in the tt System
t
p p
t
(cos 0) (cos 0)
(cos 0) (cos 0)
t t
t t
N N
fb N NA
 
 
  
  
Forward-Backward Asymmetry:
(cos 0) (cos 0)
(cos 0) (cos 0)
t t
t t
N N
C N NA
 
 
  
  
Charge Asymmetry:
(cos 0) (cos 0)tt
N N    C fbA A
Assuming CP parity holds,
 

t
θ
 Use θ, Cos(θ), rapidity (y), Delta y, etc. to measure Afb
 Which variable do we use?
 Which reference frame should we use?
 Possible to do the more complicated measurement
cos
fbdA
d θ
p
t

t
 Use θ, Cos(θ), rapidity (y), Delta y, etc. to measure Afb
 Which variable do we use?
 Which reference frame should we use?
 Possible to do the more complicated measurement
cos
fbdA
d θ
p
t
1
ln
2
L
L
E p
E p
 
  
 y

 In lowest order QCD, top quark production is symmetric
 NLO QCD predicts a small asymmetry
 Asymmetries are important tools for understanding weak
interactions, as well as for searching for additional (chiral) couplings
t
p p
t

Theoretical Predictions
+
+
tt
ttj
Ctt = -1 Ctt = +1
Ctt = -1 Ctt = +1
Halzen, Hoyer, Kim; Kuhn, Rodrigo
Dittmaier, Uwer, Weinzier; Almeida, Sterman, Vogelsang
Afb ~ +10-12%
Afb (NLO)
Afb (NNLO)
Consensus working value Afb ~ 5 ± 1.5%
~ -7%
~ -1%

+
+
tt
ttj
Ctt = -1 Ctt = +1
Ctt = -1 Ctt = +1
Halzen, Hoyer, Kim; Kuhn, Rodrigo
Dittmaier, Uwer, Weinzier; Almeida, Sterman, Vogelsang
Afb ~ +10-12%
Afb (NLO)
Afb (NNLO)
~ -7%
~ -1%
Note that ggtt results in no asymmetry, so our
measurement will be diluted by 15% before any other effects
Consensus working value Afb ~ 5 ± 1.5%

Lagrangian for Axigluon+Gluon
Ferrario and Rodrigo – Physical Review D 80, 051701(R) (2009)

c = βcos(θ)

Vector coupling
mG = mass of axigluon
ΓG = width of axigluon
Axial coupling

gluon exchange
gluon propagator

Interference Term

Note that there is a
symmetric part and
an asymmetric part

Pole term for axigluon

Again, note that there
is a symmetric part and
an asymmetric part

Since we observe no pole in
Mtt, this constrains the possible
values for gA and gV that give a
positive asymmetry

Allows us to restrict regions
for coupling parameters that
won’t change tt cross section

Recent Measurement History
Previously Blessed Results (1.9 fb-1):
Afb cos(θ) method: Afb = 0.17 ± 0.08 (Davis/Michigan)
Afb ∆y method: Afb = 0.24 ± 0.14 (Karlsruhe)
Phys. Rev. Lett. 101, 202001 (2008)
D-zero Results (0.9 fb-1):
Afb = 0.12 ± 0.08 ± 0.01

Fermilab and CDF
Fermilab and CDF...

Fermilab
 Tevatron
~4 miles around
 1.96 TeV Collisions
 Over 6 fb-1 data
integrated luminosity
 We're still the most
energetic and highest
luminosity hadron
collider on Earth!

Fermilab

Event Reconstruction

Event Reconstruction
Reconstruction
 Match jets to b, b, up, down
 Constrain fit W mass to 80.4 GeV/c2
 Constrain fit for a 175.0 GeV/c2 Top
 Float momenta of jets within known
resolution
 Use combination with lowest χ2
?
?
2
2
2
2
2
2
2
2
2
2,,
2
2,,
)()()()(
,
)(
,
)(2
top
topbl
top
topbjj
w
wl
w
wjj
j
fitUE
j
measUE
j
i
fiti
t
measi
t
MMMMMMMM
yxj
pp
jetslep
pp











 




Top Pair Production and Decay
Top signals
isolated using
secondary vertex
= “b-tag”
Lepton + Jets mode:
qq → g → tt → (W+b)(W-b) → (l+νb)(qqb) → l+ + Et + 4j + ≥ 1 “tagged” jet
Vertex for b-quarks
is roughly ½ mm
Charm jets are only
tagged ~1/10 the time

Selection
 Measurement is performed using
semi-leptonic top pair decays
 3.2 fb-1
of CDF data
 ≥ 4 jets (Et > 20 GeV and |η| < 2)
 ≥ 1 b-tagged jet
 1 electron (Et > 20 GeV and |η| < 1) –or–
1 muon (Pt > 20 GeV/c and |η| <1)
 Missing Transverse Energy > 20 GeV
776 Candidate Events
Data Sample

Selection
 3.2 fb-1
of CDF data
 ≥ 4 jets (Et > 20 GeV and |η| < 2)
Data Sample

 Hadronic top decay is more accurately
reconstructed, so we will measure yhad
 Get hadronic top charge from lepton
 Invoke CP invariance and multiply
hadronic-only distribution by -1 * lepton
charge to find equivalent top rapidity in
each event
 Measure Afb using -Qlep• yhad in the lab
frame, count forward and backward
events
 Correct Afb back to parton level
backward forward
→ W–
b → l ν b
→ W+
b → j j b
t t
Measurement Techniques

Selection
 3.2 fb-1
of CDF data
 ≥ 4 jets (Et > 20 GeV and |η| < 2)
Backgrounds
 Use W+Jets tagged backgrounds to model
the ttbar tagged backgrounds present in the
semi-leptonic sample
Data Sample
167 ± 34 Background Events

Data Sample
Say number of events
and number of events in
backgrounds.
Process
W+HF Jets 86.56 ± 27.40
Mistags (W+LF) 27.43 ± 7.70
Non-W (QCD) 33.44 ± 28.06
Single Top 7.82 ± 0.50
WW/WZ/ZZ 7.57 ± 0.74
Z+Jets 4.78 ± 0.59
Top 569.08 ± 78.81
Total Prediction 736.64 ± 89.22
167 ± 34 Predicted Background
Selection
 3.2 fb-1
of CDF data
 ≥ 4 jets (Et > 20 GeV and |η| < 2)
Backgrounds
 Use W+Jets tagged backgrounds to model
the ttbar tagged backgrounds present in the
semi-leptonic sample

Raw Asymmetry
Signal MC is MC@NLO, normalized so signal+background = number of data events

Raw Asymmetry
Signal MC is MC@NLO, normalized so signal+background = number of data events
We wish to correct
for this shape

Background Subtraction
 Background has a known asymmetry that modifies the top Afb measurement
 Check anti-tagged data and MC for consistency and cross-section
 Subtract backgrounds from our data
Backgrounds in W+Jets

• We subtract off this total background from the data shape, 167
events out of 776 data events, which has Afb = -0.059 ± 0.0079
• Negative values mostly due to electroweak processes (W+HF)

Background Afbs

Asymmetry Correction Technique
 We optimize for number of bins and
bin spacing
 Reconstruction of the event causes
smearing between bins. We use a
matrix unfolding technique to correct
for this effect.
 Acceptance efficiencies also bias our
sample, so an analogous correction is
made using an acceptance matrix
Sij = Nij
recon/Ni
truth
Aii = Ni
sel/Ni
gen
Ncorrected = A-1•S-1•Nbkg-sub
Bin smearing

Sij = Nij
recon/Ni
truth
Aii = Ni
sel/Ni
gen
Ncorrected = A-1•S-1•Nbkg-sub
Corrected Asymmetry Measurement

Test of Method
 We make control samples with known
asymmetry by reweighting Pythia Cos(θ)
signal in the ttbar frame by
1+A•Cos(θtt)
 Propagate these changes to obtain
appropriate factors for reweighting Ypp
 Check corrected measurement vs
known Afb for Cos(θtt) signal

Raw Afb = 9.8 ± 3.6%
Bkg-sub Afb = 14.1 ± 4.6%
Final Corrected Afb = 19.3 ± 6.5%

Raw Afb = 9.8 ± 3.6%
Bkg-sub Afb = 14.1 ± 4.6%
~3σ significance
from LO QCD (A=0%)

Raw Afb = 9.8 ± 3.6%
Bkg-sub Afb = 14.1 ± 4.6%
>2σ significance
from NLO (A~5%)

nominal bkg QCD difference Wbb difference new uncertainty
0.187 0.200 0.013 0.178 -0.009 0.013
Sigma is the max abs value of these two differences
Background subtraction is our largest component
of the systematic error. We have two main
sources: background shape and size.
For the shape uncertainty:
 Take the QCD (or WHF) contribution of the
background and rescale it to have the method II
number of events.
 Make a distribution using “Reweighted Signal +
Modified Bkg”
 Subtract off the original Method II background,
unfold, and measure an Afb.
 Compare with nominal value
Background Shape Systematic Uncertainty

Calc. Uncert.
Background Shape 0.011
Background Size 0.018
ISR/FSR 0.008
JES 0.002
PDF 0.001
MC Generator 0.003
Shape / Unfolding 0.006
Total Uncertainty 0.024
Vary simulated data by ±σ and calculate Afb difference with known sample
Systematic Uncertainties and Final Result

Systematic Errors and Result
Calc. Uncert.
ISR/FSR 0.008
JES 0.002
PDF 0.001
MC Generator 0.003
Final Corrected Afb = 19.3 ± 6.5 ± 2.4%

Calc. Uncert.
ISR/FSR 0.008
JES 0.002
PDF 0.001
MC Generator 0.003
Statistical error dominates total error
Systematic Uncertainties and Final Result

Raw Afb = 9.8 ± 3.6%
Bkg-sub Afb = 14.1 ± 4.6%
Final Corrected Afb = 19.3 ± 6.5% ± 2.4%

q q t t
F F
C
2
G
2 2 2 2
G G G
2
2 2 2 2
G G G
T C πβ2 2 2dσ
S Ndcos θ 2s
2s (s-m ) q t 2 2
V V(s-m ) +m Γ
q t s
A A (s-m ) +m Γ
q 2 q 2 t 2 2 2
V A V
t 2 2 2 q q t t
A V A V A
= α 1+c + 4m
+ [g g (1+c + 4m )
+2g g c]+
×[((g ) +(g ) )((g ) (1+c + 4m )
+(g ) (1+c + 4m ))+8g g g g c]
{
}
Back to theory…

2
2 2 2 2
2
2 2 2 2
2 2 2
cos 2
2 ( ) 2 2
( )
( )
2 2 2 2 2
2 2 2
1 4
[ (1 4 )
2 ]
[(( ) ( ) )(( ) (1 4 )
( ) (1 4 )) 8 ]
{
}
q q t t
F F
C
G
G G G
G G G
T Cd
S Nd s
s s m q t
V Vs m m
q t s
A A s m m
q q t
V A V
t q q t t
A V A V A
c m
g g c m
g g c
g g g c m
g c m g g g g c





  
  
  
  
 
   
   

2
2 2 2 2
2
2 2 2 2
2 2 2
cos 2
2 ( ) 2 2
( )
( )
2 2 2 2 2
2 2 2
1 4
[ (1 4 )
2 ]
[(( ) ( ) )(( ) (1 4 )
( ) (1 4 )) 8 ]
{
}
q q t t
F F
C
G
G G G
G G G
T Cd
S Nd s
s s m q t
V Vs m m
q t s
A A s m m
q q t
V A V
t q q t t
A V A V A
c m
g g c m
g g c
g g g c m
g c m g g g g c





  
  
  
  
 
   
   
Frampton, Shu, and Wang – [hep-ph] arxiv:0911.2955 IPMU-09-0135

Future Plans
• dA/dM (Afb vs Mtt)
• dA/dy (Afb as a function of y)
• increase data set
• understand the systematic
uncertainties better
• submit thesis!

Conclusions
 Previous results (1.9 fb-1):
Afb cos(θ) method: Afb = 17 ± 8%
 Current results (3.2 fb-1):
Afb -Q*yhadtop method: Afb = 19.3 ± 6.5 ± 2.4%
 Are measured values are higher than the 5% SM
prediction, but consistent within ~2 sigma
lab
lab

and while our current asymmetry
measurement is quite exciting…

Stay tuned for more
exciting asymmetries!

The End

Backup Slides
Backup
Slides

Measurement of Forward-Backward
in ppbar Collisions at 1.96 TeV
Glenn Strycker
1999-2003
2003-2010

Previous Methods
 Earlier Michigan/Davis measurements counted forward and
background events from a Cos(θ) distribution in the lab frame.
 Karlsruhe group investigated ∆y, the difference in rapidity
between the top and antitop. This quantity is Lorentz-invariant,
so the corresponding Afb is a measurement in the ttbar frame.

CDF
The CDF Detector

CDF
Here are several important components of CDF

CDF
Construction of CDF

CDF Geometry
y=0 y=2
Rapidity Geometry of CDF
y=1
1
ln
2
L
L
E p
y
E p
 
  
 

Various Plots of Observables

Jet Energies

Jet Rapidities

Validation Plots for Fitter Variables
Overflow bin

Validation Plots for Fitter Variables

Reconstructed W Quantities

Reconstructed B Quantities

Background Systematics – Size
nominal afb less less difference more more difference new uncertainty
0.187 0.176 -0.011 0.200 0.013 0.012
What if our Method II numbers are off?
Then we will be subtracting off the wrong
amount of background.
Use our reweighted dataset for three cases:
1) subtract off background + find Afb
2) subtract off 0.75x background
3) subtract off 1.25x background
 Use |more-less|/2 if the
more/less values are on either
side of the nominal value
 Use |max difference/2| if
values are on the same side

“Reweight Function” Systematic
nominal Cos+Cos^6 diff Cos+Sin^2 diff Cos^5 diff Cos^3 diff new uncertainty
0.187 0.185 -0.002 0.188 0.001 0.195 0.007 0.193 0.006 0.004
What if our reweighted shape
does not match the data? 1+A*Cos()
Cos^6
Sin^2
Cos^5
Cos^3
Cos() Rapidity Y
Uncertainty (for now) is the max abs value of these differences divided by 2
A = 0.20A = 0.20
If we are reweighting central or outer bins more heavily
than we should, our unfolding technique will have error.
To find the uncertainty...
 Use several functions, each with an “A” parameter
 Adjust A to get a given true asymmetry in the lab frame
 Compare the unfolded Afb for each function with our
nominal 1+A*cos(θtt) reweighted MC.

Signal Systematics
What if our MC parameters are incorrect, introducing error into our unfolding
matrices? To measure this uncertainty we use the following method:
 generate MC with more/less of various components
 reweight by same A parameter as used earlier
 use our original unfolding matrices to find a corrected Afb
 compare to our original nominal value.
nominal afb less more less difference more difference new uncertainty
ISR 0.187 0.191 0.186 0.004 -0.001 0.003
FSR 0.187 0.172 0.178 -0.015 -0.009 0.007
JES 0.187 0.181 0.189 -0.006 0.002 0.004
PDF 0.187 0.183 0.189 -0.004 0.002 0.002
TopMC 0.187 0.175 -0.012 0.012

Verify Correction Procedure
Now that we've subtracted background we
can calculate our smear and acceptance
matrices from truth info in MC.
How do we know that this unfold
method is returning reasonable
values? We test our method on MC
reweighted to have an asymmetry.
We will calculate the corrected
measurement and compare with the
truth asymmetry of the signal MC

Reweighted Shapes
To test unfolding method, we use “fake”
data samples with different forms of
known asymmetry AFB.
Simplest case:
add linear (1+AFBcos(θtt)) term to Pythia
MC true cos(θ) distribution in ttbar
frame.
 Define weights:
 Ni is the content of bin i-th
 ni is the content of ith
bin assuming a
AFBcos(θi) distribution
 Reweight events in reconstructed
cos(θ) using wi
i
ii
N
nN
iw 


Test of method
Propagation of Afb from ttbar frame to lab frame rapidity
 We make control samples with known
asymmetry by reweighting Pythia Cos(θ)
signal in the ttbar frame by
1+A•Cos(θtt)
 Propagate these changes to obtain
appropriate factors for reweighting Ypp
 Check corrected measurement vs
known Afb for Cos(θtt) signal

Correction Bias Check
 First plot (truth info precut) shows the dilution of true Afb caused
by changing reference frames (center of momentum → lab frame)
 Second plot shows the statistical fluctuations across subsets of
the MC sample – MC is consistent with itself

Nominal Comparison – Reweighted MC
We use the standard technique of simulating
the entire analysis and varying the model
assumptions to understand their effect and
calculate the systematic uncertainty.
In this analysis, in order to find the correct
uncertainties we must first generate a
sample having a known asymmetry.
black = ttbar MC
blue = 0.20 reweight
Rapidity Y
 reweight cos(θtt) distribution → rapidity distribution as
explained on previous slides
 choose our “A” parameter such that our final corrected rapidity
Afb in the reweighted sample is closest to that observed in the
corrected data measurement.

Test of 1+A•Cos(θ) Hypothesis
The simplest form of an asymmetry is 1+A•cos(θtt)
 Use Pythia MC (initial Afb=0) and reweight by 1+A•cos(θtt) in the rest frame
 Propagate reweights to lab frame and rapidity variable to make a template
 Set up binned likelihood fit to data rapidity distribution using signal (templates)
plus background contribution (Gaussian-constrained to background parameters)
 The good fit to the data supports the linear hypothesis

Rapidity Template Fit
We can test our 1+Acos(θtt) linear hypothesis by
comparing template models with the data
 Set up binned likelihood fit to data rapidity
distribution using signal (templates) plus
background contribution (Gaussian-constrained
to M24U parameters)
 Find minimum of -log(likelihood) vs Afb
tt
 From template generation, we found the dilution
factor to be Afb
pp/Afb
tt = 0.5593 ± 0.0023,
which we use to convert results to ppbar frame

Rapidity Template Fit
-log(likelihood) fit is tested with PE's
and is found to have good coverage
Here is the best fit – 30% asymmetry
in the ttbar frame

Asymmetry Analogy
 Who has the better football team?
 Which metric should we use? (overall record, scores, Heisman winners?)
 Are the differences (asymmetries) statistically significant?
-VS-
Afb = Asymmetry“Forward-Backward” →
A“Football”

Asymmetry Analogy
-VS-
21 Wins
1887 1888(2)
1898 1899
1900 1902
1908 1942
1978 1981
1985 1986
1991 1994
1997 1999
2003 2006
2007 2009
15 Wins
1909 1943
1979 1980
1982 1987
1988 1989
1990 1993
1998 2002
2004 2005
2008
1 Tie
1992
Asymmetry is
A = 16.2% ± 15.8%
LARGE Asymmetry, but
*NOT Statistically Significant!
*In fact, A>1910 = 3.6% ± 18%
Afootball
=
WinsMichigan
− WinsND
Total GamesPlayed
Information from Wikipedia and http://grfx.cstv.com/photos/schools/nd/sports/m-footbl/auto_pdf/07fbguidehistory.pdf

Asymmetry Analogy
Information from Wikipedia and http://grfx.cstv.com/photos/schools/nd/sports/m-footbl/auto_pdf/07fbguidehistory.pdf
“Score Asymmetry” is
Ascore = 11.6% ± 2.7%
only a medium-sized asymmetry,
but a 4.4 sigma significance
A=
Points Michigan
− PointsND
Total Points Scored
– To be unbiased, we should look at
MC and choose our “best” variable
before using it to measure data. Notre Dame won by... Michigan won by...

Asymmetry Analogy
 Choosing the “correct” variable isn't trivial
 There are additional convolutions, smearing, acceptance
effects, and systematic errors to take into account
 Maybe physics is easier than football! (At least we have MC...)
Afb = Asymmetry“Forward-Backward” →
A“Football”

Calc. Uncert.
ISR/FSR 0.008
JES 0.002
PDF 0.001
MC Generator 0.003
Systematic Errors and Result
Hmm... statistical error
dominates total error

Simple Asymmetries in the tt System
t
p p
t
( 0) ( 0)
( 0) ( 0)
t t
t t
N y N y
fb N y N yA
  
  
Forward-Backward Asymmetry:
( 0) ( 0)
( 0) ( 0)
t t
t t
N y N y
C N y N yA
  
  
Charge Asymmetry:
( 0) ( 0)tt
N y N y   C fbA A
Assuming CP parity holds,
 

Fermilab
This slide should have last weeks
data, total data, estimates of
future integrated luminosity, etc.

Publications Referencing Our Results
ArXiv:0906.5541 – Ferrario and Rodrigo

 Forward-backward Afb – does the top preferentially go one way or the other?
 Count events from rapidity distribution in lab frame and calculate:
Afb = (forward-backward)/total
 QCD at lowest order predicts 0 asymmetry
 NLO processes predicted an asymmetry Afb = 5±1.5% lab
 Unexpected new top production processes with chiral or axial couplings may
cause an additional asymmetry
+
+
t
p p
t

2
2 2 2 2
2
2 2 2 2
2 2 2
cos 2
2 ( ) 2 2
( )
( )
2 2 2 2 2
2 2 2
1 4
[ (1 4 )
2 ]
[(( ) ( ) )(( ) (1 4 )
( ) (1 4 )) 8 ]
{
}
q q t t
F F
C
G
G G G
G G G
T Cd
S Nd s
s s m q t
V Vs m m
q t s
A A s m m
q q t
V A V
t q q t t
A V A V A
c m
g g c m
g g c
g g g c m
g c m g g g g c





  
  
  
  
 
   
   

 Are more top quarks produced in the direction of the proton?
 First order measurement – simply count numbers produced forward and backward
 To increase sensitivity, account for acceptance and reconstruction effects
t
p p
t

Notre Dame Afb Seminar 2009

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