\(\newcommand{\ttbar}{\rm{t\bar{t}}}\) \(\newcommand{\DYtt }{\rm{DY\rightarrow\tau\tau}}\) \(\newcommand{\DYeemm }{\rm{DY\rightarrow ee/\mu\mu}}\) \(\newcommand{\gev}{\rm{GeV}}\) \(\newcommand{\pt}{p_{T}}\) \(\newcommand{\mt}{m_{T}}\) \(\newcommand{\Ht}{H_T}\) \(\newcommand{\MET}{\mbox{$E\kern-0.50em\raise0.10ex\hbox{/}_{T}$}}\) \(\newcommand{\met}{\mbox{$E\kern-0.50em\raise0.10ex\hbox{/}_{T}$}}\) \(\newcommand{\sys}{\text{sys.}}\) \(\newcommand{\stat}{\text{stat.}}\) \(\newcommand{\et}{E_{\text{T}}}\) \(\newcommand{\Et}{E_{\text{T}}}\) \(\newcommand{\mll}{\rm{m_{ll}}}\) \(\newcommand{\mtt}{m_{\ttbar}}\) \(\newcommand{\afb}{A_{\text{FB}}}\) \(\newcommand{\AFB}{A_{\text{FB}}}\) \(\newcommand{\qeta}{q_{\ell}\eta_{\ell}}\) \(\newcommand{\deta}{\Delta\eta_{\ell}}\) \(\newcommand{\afblep}{A_{\text{FB}}^{\ell}}\) \(\newcommand{\afbdeta}{A_{\text{FB}}^{\ell\ell}}\) \(\newcommand{\afbtt}{A_{\text{FB}}^{\ttbar}}\) \(\newcommand{\fbm}{\rm{fb}^{-1}}\) \(\newcommand{\atanh}{a\cdot\tanh(\frac{1}{2}\qeta)}\) \(\newcommand{\atanhdeta}{a\cdot\tanh(\frac{1}{2}\deta)}\)

\(\ttbar\) \(\afb\) Tevatron Combination

Abstract

Inclusive \(\afbtt\)


People: Ziqing, Andy
Method: BLUE

Experiment\(\afbtt\)Stat. uncertaintySyst. uncertaintyTotal uncertaintyWeight
Combination 0.1290.024-
CDF l+jets0.1640.0390.0260.0470.24
CDF DIL 0.12 0.11 0.07 0.13 0.02
D0 l+jets 0.1060.0270.0130.0300.62
D0 DIL 0.1800.0610.0320.0690.12
Table I: \(\afbtt\) results summary


Need to confirm the numbers and the correlations.
Waiting on CDF DIL result.
CDF l+jets CDF DIL D0 l+jets D0 DILCorrelation
Background shape/normalization (0.022)Background (0.04) Background model/sample composition (0.01) Background (0.007) 0
Parton shower/IFSR (0.011) Parton shower/IFSR (0.04) Signal model (0.005) Signal (0.014) 1
JES (0.007) JES (0.02) Detector model (0.003) Detector (0.003) *
Correction procedure (0.004) Correction procedure (0.02) Unfolding (0.005) Unfolding (0.027) 0
Color reconnection (0.001) Color reconnection (0.03) - - 1
PDF (0.001) PDF (0.01) PDF and pileup (0.004) PDF (0.006) 1
Table II: \(\afbtt\) systematic correlations

Differential \(\afbtt\)


People: Andy, Ziqing
Method: Simultaneous linear fit w/ correlation matrices

Figures quoted from NNLO calculation paper (arxiv:1411.3007). Need make our own figures, as well as fit.
Ziqing will ask Mitov for the NNLO predictions shown in these figures.
Tev-MTT-asym.png Tev-Y-asym.png
Fig 1. Differential \(\afbtt\) vs. \(\Delta y\) and \(\mtt\).

(From Mitov) NLO/NNLO calculation of differential \(\afbtt\) (click to expand)

NLO \(\afbtt\) vs. \(\mtt\)
\(\mtt\)CentralScale upScale down
400 0.040965 0.031918 0.057560
500 0.077134 0.058666 0.114006
600 0.108416 0.080109 0.169806
700 0.156047 0.109581 0.274931
NNLO \(\afbtt\) vs. \(\mtt\)
\(\mtt\)CentralScale upScale down
400 0.054114 0.048035 0.059366
500 0.097872 0.085032 0.104552
600 0.134845 0.122229 0.139443
700 0.177355 0.158747 0.182646
NLO \(\afbtt\) vs. \(\Delta y\)
\(\Delta y\)CentralScale upScale down
0.25 0.021418 0.016402 0.031058
0.75 0.064087 0.049352 0.092494
1.25 0.107546 0.082647 0.155339
1.75 0.169140 0.129381 0.247943
NNLO \(\afbtt\) vs. \(\Delta y\)
\(\Delta y\)CentralScale upScale down
0.25 0.027164 0.024092 0.029377
0.75 0.081462 0.072261 0.087042
1.25 0.135765 0.121353 0.144122
1.75 0.207849 0.187123 0.215060

CDF l+jets \(\afbtt\) vs. \(\Delta y\) covariance matrices (click to expand)

binedges: [0.0, 0.5, 1.0, 1.5, 2.0]
Stat
[[  1.13977e-03   1.46093e-03   3.93225e-05  -1.10372e-03]
 [  1.46093e-03   3.19528e-03   2.11568e-03   7.56456e-04]
 [  3.93225e-05   2.11568e-03   6.42883e-03   9.49611e-03]
 [ -1.10372e-03   7.56456e-04   9.49611e-03   1.75047e-02]]
Correction procedure
[[  1.25924e-05   2.84727e-05  -1.61021e-06  -6.53740e-05]
 [  2.84727e-05   6.43795e-05  -3.64083e-06  -1.47817e-04]
 [ -1.61021e-06  -3.64083e-06   2.05898e-07   8.35942e-06]
 [ -6.53740e-05  -1.47817e-04   8.35942e-06   3.39390e-04]]
Parton shower
[[  3.49955e-05   1.19599e-04  -6.40000e-05  -1.66401e-04]
 [  1.19599e-04   4.08739e-04  -2.18724e-04  -5.68688e-04]
 [ -6.40000e-05  -2.18724e-04   1.17044e-04   3.04316e-04]
 [ -1.66401e-04  -5.68688e-04   3.04316e-04   7.91230e-04]]
Color Reconnection
[[  2.01509e-04  -1.32928e-04  -2.68942e-05  -2.25692e-04]
 [ -1.32928e-04   8.76881e-05   1.77411e-05   1.48881e-04]
 [ -2.68942e-05   1.77411e-05   3.58940e-06   3.01217e-05]
 [ -2.25692e-04   1.48881e-04   3.01217e-05   2.52777e-04]]
Parton-distribution functions
[[  7.91484e-08   2.87094e-07  -2.57429e-07  -1.03701e-06]
 [  2.87094e-07   1.04138e-06  -9.33769e-07  -3.76152e-06]
 [ -2.57429e-07  -9.33769e-07   8.37281e-07   3.37284e-06]
 [ -1.03701e-06  -3.76152e-06   3.37284e-06   1.35869e-05]]
Initial- and final-state radiation
[[  4.16204e-05  -2.08028e-05   7.34803e-06   6.08806e-05]
 [ -2.08028e-05   2.26953e-04   1.01953e-04  -9.51519e-05]
 [  7.34803e-06   1.01953e-04   5.28164e-05  -2.08202e-05]
 [  6.08806e-05  -9.51519e-05  -2.08202e-05   1.08397e-04]]
Jet energy scale
[[  2.34816e-05   4.68342e-06  -2.10997e-05  -2.84021e-06]
 [  4.68342e-06   2.27047e-04   1.17004e-05   1.79439e-04]
 [ -2.10997e-05   1.17004e-05   2.00788e-05   1.52168e-05]
 [ -2.84021e-06   1.79439e-04   1.52168e-05   1.43644e-04]]
Background shape
[[  2.81258e-04   4.84214e-04  -8.07515e-05  -7.36295e-04]
 [  4.84214e-04   8.46120e-04  -1.34430e-04  -1.28991e-03]
 [ -8.07515e-05  -1.34430e-04   2.48726e-05   2.03200e-04]
 [ -7.36295e-04  -1.28991e-03   2.03200e-04   1.96732e-03]]
Background normalization
[[  2.71302e-05   8.93855e-05   1.68667e-04   2.25808e-04]
 [  8.93855e-05   2.94498e-04   5.55704e-04   7.43968e-04]
 [  1.68667e-04   5.55704e-04   1.04859e-03   1.40384e-03]
 [  2.25808e-04   7.43968e-04   1.40384e-03   1.87943e-03]]

CDF l+jets \(\afbtt\) vs. \(m_{\ttbar}\) covariance matrices (click to expand)

binedges: [350, 450, 550, 650, 750]
Stat
[[ 0.00207  0.00147 -0.00028 -0.00154]
 [ 0.00147  0.00384  0.00228 -0.00043]
 [-0.00028  0.00228  0.00711  0.01037]
 [-0.00154 -0.00043  0.01037  0.02483]]
Correction procedure
[[  1.39550e-04  -2.47869e-05   1.13814e-07   2.68672e-04]
 [ -2.47869e-05   4.40267e-06  -2.02157e-08  -4.77217e-05]
 [  1.13814e-07  -2.02157e-08   9.28245e-11   2.19124e-07]
 [  2.68672e-04  -4.77217e-05   2.19124e-07   5.17268e-04]]
Parton shower
[[  6.20060e-06  -2.39476e-05   1.82790e-04   8.04667e-05]
 [ -2.39476e-05   9.24894e-05  -7.05963e-04  -3.10775e-04]
 [  1.82790e-04  -7.05963e-04   5.38856e-03   2.37212e-03]
 [  8.04667e-05  -3.10775e-04   2.37212e-03   1.04424e-03]]
Color Reconnection
[[  2.03428e-05  -2.51836e-05   3.09914e-05   3.75096e-05]
 [ -2.51836e-05   3.11764e-05  -3.83662e-05  -4.64355e-05]
 [  3.09914e-05  -3.83662e-05   4.72142e-05   5.71444e-05]
 [  3.75096e-05  -4.64355e-05   5.71444e-05   6.91631e-05]]
Parton-distribution functions
[[  2.84806e-08   5.38819e-08  -4.67260e-08  -1.21511e-07]
 [  5.38819e-08   1.01938e-07  -8.84000e-08  -2.29884e-07]
 [ -4.67260e-08  -8.84000e-08   7.66599e-08   1.99354e-07]
 [ -1.21511e-07  -2.29884e-07   1.99354e-07   5.18420e-07]]
Initial- and final-state radiation
[[  6.25008e-05   7.22701e-06   3.22104e-05   2.20334e-04]
 [  7.22701e-06   3.26410e-04   3.86906e-04  -1.40672e-03]
 [  3.22104e-05   3.86906e-04   4.67582e-04  -1.57205e-03]
 [  2.20334e-04  -1.40672e-03  -1.57205e-03   7.07692e-03]]
Jet energy scale
[[  1.56312e-04  -4.46902e-05  -3.91673e-04  -5.09709e-04]
 [ -4.46902e-05   1.58908e-04   2.15588e-04  -8.96057e-05]
 [ -3.91673e-04   2.15588e-04   1.05488e-03   1.11034e-03]
 [ -5.09709e-04  -8.96057e-05   1.11034e-03   2.04108e-03]]
Background shape
[[ 0.00044  0.00031  0.00019  0.00043]
 [ 0.00031  0.00028  0.00019  0.00026]
 [ 0.00019  0.00019  0.00013  0.00016]
 [ 0.00043  0.00026  0.00016  0.00045]]
Background normalization
[[  6.12575e-05   1.26875e-04   1.64606e-04   2.40938e-04]
 [  1.26875e-04   2.62781e-04   3.40927e-04   4.99022e-04]
 [  1.64606e-04   3.40927e-04   4.42336e-04   6.47478e-04]
 [  2.40938e-04   4.99022e-04   6.47478e-04   9.47780e-04]]

\(\afblep\)


People: Ziqing, Andy
Method: Simultaneous fit with \(\atanh\) function

Fit based on statistical uncertainties only. Ziqing will redo the fit once he has all the systematics collected and correlations agreed on.
CDF_D0_LepAFB.png
Fig 2. Differential \(\afblep\) vs. \(\qeta\).
Experiment \(\afblep\)stat.syst.weight
BLUE combination 0.0700.018-
CDF l+jets 0.1050.024+0.022
-0.017		0.356
CDF DIL 0.0720.0520.0300.086
D0 l+jets 0.0500.027+0.020-0.0240.336
D0 DIL 0.0440.0370.0110.221
Table III: \(\afblep\) summary
CDF l+jets CDF DIL D0 l+jetsD0 DIL Correlation
Backgrounds (0.015) Backgrounds (0.029) Background modeling/normalization (0.0085) Background modeling/normalization (0.0072) 0
Recoil modeling (+0.013-0.000) Asymmetric modeling (0.006) - - 1
- Symmetric modeling(0.001) - - -
Color reconnection (0.0067) - - - -
Parton showering (0.0027) - - - -
PDF (0.0025) PDF (0.004) PDF/PDF choice(0.0022) - 1
JES (0.0022) - Jet Energy Measurement (0.003) Jet Reco/Jet Energy Measurement (0.0034) *
IFSR (0.0018) - - - -
- - B-tagging/Taggability(0.005/0.009) B-tagging/Taggability(0.0008/0.0018)1
- - - Lepton ID/Trigger (0.0014/0.0026)-
--Top Mass/ Reco. \(P_{T}^{(\ttbar)}\) (0.004/0.002)--
Table IV: \(\afblep\) systematic correlations
Table of stat/syst uncertainties PER BIN goes here. Will put in CDF numbers first.

Differential \(\afblep\) systematic correlations (click to expand)

Source of uncertainty CDF l+jets CDF DIL D0 l+jets D0 DIL
Bin edges [0,0.12][0.12,0.24][0.24,0.34][0.34,0.46][0.46,0.59][0.59,0.73][0.73,0.89][0.89,1.5] [0,0.10][0.10,0.26][0.26,0.42][0.42,0.61][0.61,0.81][0.81,2.0] [0,0.125][0.125,0.375][0.375,0.625][0.625,1.0][1.0,1.5] [0,0.4][0.4,1.2][1.2,2.0]
Bin Centroid 0.0650.1800.2890.4000.5240.6640.8071.03 0.0530.1820.3450.5090.7131.066 0.0640.2470.4990.7951.202 0.1970.7771.520
Asymmetry -0.071-0.0260.0560.1160.1750.0870.0630.116 0.0230.1280.0640.1230.0020.117 0.0050.0050.0260.0190.132 -0.0610.1030.057
Stat. uncertainty 0.0470.0450.0460.0450.0440.0460.0460.044 0.140.0970.0940.0920.1060.100 0.0610.0440.0470.0460.065 0.0520.0450.101
Total syst. uncertainty 0.0770.0500.0490.0460.0560.055 +0.008
-0.007		+0.013
-0.018		+0.017
-0.015		+0.020
-0.023		+0.026
-0.030
Backgrounds
Recoil modelling
(Asymmetric modelling)
Symmetric modelling
Color reconnection
Parton showering
PDF
JES
IFSR
Table XXX(a): \(\afblep\) systematic correlations

\(\afbdeta\)


People: Ziqing, Andy
Method: Simultaneous fit with \(\atanhdeta\) function

Will put the two sets of points on the same plot and do a simultaneous fit.
CDF_D0_DilAFB.png
Fig 3. Differential \(\afbdeta\) vs. \(\deta\).
Experiment \(\afbdeta\)stat.syst.weight
BLUE combination 0.1010.042-
CDF DIL 0.0760.0720.0370.26
D0 DIL 0.1230.0540.0150.74
Table V: \(\afbdeta\) summary
CDF DIL D0 DIL Correlation
Backgrounds (0.037)0.00880
Asymmetric modeling (0.012)-0
JES (0.003)-0
Symmetric modeling (0.004)-0
-Object ID (0.006)0
-Hadronization (0.0092)0
-MC statistics (0.0037)0
Table VI: \(\afbdeta\) systematic correlations
Table of stat/syst uncertainties PER BIN goes here. Will put in CDF numbers first.

Differential \(\afbdeta\) systematic correlations (click to expand)

Source of uncertainty CDF DIL D0 DIL
Bin edges
Table XXX(b): \(\afbdeta\) systematic correlations

Summary


Ziqing will update this once CDF DIL result and combination results are ready.
Tevatron_Top_Asymm.png
Fig 4. Summary of Tevatron inclusive AFB results.


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