Notre Dame Afb Seminar 2009

Page 1Glenn 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 StryckerUniversity of Michigan

On behalf of the CDF Collaboration


Measurement of the Forward-Backward


in pp Collisions at 1.96 TeV



1999-2003 2003-2010


Outline

People Involved What is A

fb – 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 pt

(cos 0) (cos 0)(cos 0) (cos 0)

t t

t t

N Nfb 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)ttN N C fbA A

Assuming CP parity holds,


tθ

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 cosfbdA

d θ

pt



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 cosfbdA

d θ

pt


1ln2

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 pt



Theoretical Predictions

+

+tt

ttj

Ctt = -1 C

tt = +1

Ctt = -1 C

tt = +1

Halzen, Hoyer, Kim; Kuhn, RodrigoDittmaier, 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 C

tt = +1

Ctt = -1 C

tt = +1

Halzen, Hoyer, Kim; Kuhn, RodrigoDittmaier, Uwer, Weinzier; Almeida, Sterman, Vogelsang

Afb ~ +10-12%

Afb (NLO)

Afb (NNLO)

~ -7%~ -1%

Note that ggtt 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 exchangegluon 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: A

fb = 0.17 ± 0.08 (Davis/Michigan)

Afb ∆y method: A

fb = 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

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









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

fitUEj

measUEj

i

fitit

measit

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-quarksis 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




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 -Q

lep• y

had 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




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




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 A

fb measurement

Check anti-tagged data and MC for consistency and cross-section Subtract backgrounds from our data

Backgrounds in W+Jets



fb measurement




fb measurement



Background Subtraction

• 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 has a known asymmetry that modifies the top Afb measurement



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(θ

tt) 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 uncertainty0.187 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 0.011Background Size 0.018

ISR/FSR 0.008JES 0.002PDF 0.001

MC Generator 0.003Shape / Unfolding 0.006Total Uncertainty 0.024

Vary simulated data by ±σ and calculate Afb difference with known sample

Systematic Uncertainties and Final Result


Systematic Errors and Result


ISR/FSR 0.008JES 0.002PDF 0.001


Final Corrected Afb = 19.3 ± 6.5 ± 2.4%




ISR/FSR 0.008JES 0.002PDF 0.001




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

2G

2 2 2 2G G G

2

2 2 2 2G G G

T C π β2 2 2dσS Ndcos θ 2 s

2 s (s- m ) q t 2 2V V(s- m ) +m Γ

q t sA A (s- m ) +m Γ

q 2 q 2 t 2 2 2V A V

t 2 2 2 q q t tA 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 tF F

C

G

G G G

G G G

T CdS Nd s

s s m q tV Vs m m

q t sA A s m m

q q tV A V

t q q t tA 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 tF F

C

G

G G G

G G G

T CdS Nd s

s s m q tV Vs m m

q t sA A s m m

q q tV A V

t q q t tA 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 tF F

C

G

G G G

G G G

T CdS Nd s

s s m q tV Vs m m

q t sA A s m m

q q tV A V

t q q t tA 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 tF F

C

G

G G G

G G G

T CdS Nd s

s s m q tV Vs m m

q t sA A s m m

q q tV A V

t q q t tA 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 tF F

C

G

G G G

G G G

T CdS Nd s

s s m q tV Vs m m

q t sA A s m m

q q tV A V

t q q t tA 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: A

fb = 17 ± 8%

Current results (3.2 fb-1):

Afb -Q*y

hadtop method: A

fb = 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



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.


Fermilab


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

1ln2

L

L

E py

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 uncertainty0.187 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 0.003FSR 0.187 0.172 0.178 -0.015 -0.009 0.007

JES 0.187 0.181 0.189 -0.006 0.002 0.004PDF 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+AFB

cos(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

AFB

cos(θi) distribution

Reweight events in reconstructed

cos(θ) using wi

i

ii

NnN

iw


Test of methodPropagation 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(θ

tt) 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(θ

tt) 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 Wins1887 1888(2)

1898 1899

1900 1902

1908 1942

1978 1981

1985 1986

1991 1994

1997 1999

2003 2006

2007 2009

15 Wins1909 1943

1979 1980

1982 1987

1988 1989

1990 1993

1998 2002

2004 2005

2008

1 Tie1992

Asymmetry is

A = 16.2% ± 15.8%LARGE Asymmetry, but

*NOT Statistically Significant!

*In fact, A>1910

= 3.6% ± 18%

Afootball

=Wins

Michigan−Wins

ND

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−Points

ND

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”




ISR/FSR 0.008JES 0.002PDF 0.001


Systematic Errors and Result


Hmm... statistical error

dominates total error


Simple Asymmetries in the tt System

t

p pt

( 0) ( 0)( 0) ( 0)

t t

t t

N y N yfb 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)ttN 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 A

fb = 5±1.5% lab

Unexpected new top production processes with chiral or axial couplings

may cause an additional asymmetry

+

+

t

p pt




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 tF F

C

G

G G G

G G G

T CdS Nd s

s s m q tV Vs m m

q t sA A s m m

q q tV A V

t q q t tA 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 pt


Education

Notre Dame Afb Seminar 2009