Measurement of the Inclusive Forward-Backward
Asymmetry and its Rapidity Dependence Afb(|Δy|)
of tt Production in 5.3/fb of Tevatron Data

Glenn L Strycker, Dan Amidei, Andrew Eppig,
Dave Mietlicki, Alexei Varganov, Monica Tecchio
University of Michigan

Thomas A Schwarz, Robin Erbacher
University of California-Davis

Joey Huston
Michigan State University

Documentation
Public Note

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Abstract

We measure the parton level forward-backward asymmetry of pair produced top quarks using 1260 semi-leptonic b-tagged tt events reconstructed with the chi^2 based kinematic fitter. This is an update to the measurements found in CDF-9705, PRL 101, 202001 (CDF-9295), CDF-9122, and CDF-9078. We have increased the dataset from 3.2/fb (data through period 19) up to 5.3/fb (data through period 27). We study the rapidity, y_top, of the top production angle with respect to the incoming parton momentum. In order to measure the production asymmetry in the tt frame, we also study the Lorentz-invariant quantity qΔy. We find the parton-level forward-backward asymmetry to be

Afb (ppbar) = 0.150 ± 0.050stat ± 0.024syst
Afb (ttbar) = 0.158 ± 0.072stat ± 0.017syst

consistent with the result of CDF-9705 and PRL 101 (202001).

These results should be compared with the small ppbar frame charge asymmetry expected in QCD at NLO, Afb = 0.050 ± 0.015. Additionally, we introduce a measurement of the Afb rapidity dependence Afb(|Δy|). We find this to be

Afbttbar(|Δy|<1.0) = 0.026 ± 0.104stat ± 0.055syst
Afbttbar(|Δy|>1.0) = 0.611 ± 0.210stat ± 0.141syst

which we compare with MCFM model predictions 0.039 ± 0.006 and 0.123 ± 0.018 for the inner and outer rapidities, respectively.

Please see our public note for a complete description of our method.
Below are the blessed plots, tables, and numbers for this analysis.

In QCD at LO, the top production angle is symmetric. In NLO a small charge asymmetry develops and appears, in the Tevatron system, as a forward-backward asymmetry of order A = 0.038 in the lab frame and A = 0.058 in the tt rest frame. More generally, unexpected new tt production channels could be revealed in a forward-backward asymmetry.

We study lepton+jets events in which the tt four-vectors are completely reconstructable using only mass constraints on the two top quarks and two W bosons in each event. The asymmetry is measured:

In the lab frame: the well measured rapidity of the hadronic top decay system, y_had, when multiplied by -q of the lepton, is equivalent to y of the top quark, or -y of the antitop quark. We assume CP invariance, and combine events of both lepton charges to measure the inclusive asymmetry in -qy_had
In the tt rest frame: the frame invariant difference of top rapidities is proportional to the y of the top quark in the tt rest frame. We derive this from the lab rapidities of the leptonic and hadronic systems Delta y_t = q(y_lep - y_had)

For each distribution, backgrounds are subtracted, and acceptance and smearing effects as parameterized by Pythia after radiation are deconvolved to yield distributions of these variables at the parton level.

We present calculations of the asymmetry at data, background subtracted, and parton level, as well as a derive the Delta y dependence of the asymmetry.

Table 1 -- Raw Asymmetry Numbers

	-q•yhad			qΔy
	Forward Events	Backward Events	Afb	Forward Events	Backward Events	Afb
Raw	676	584	0.073 ± 0.028	666	594	0.057 ± 0.028
BkgSub	542.0	434.7	0.110 ± 0.036	525.1	451.6	0.075 ± 0.036
Corrected	561.0	414.8	0.150 ± 0.05	570.3	414.5	0.158 ± 0.072
MCFM			0.038 ± 0.006			0.058 ± 0.009

CDF II Preliminary -- L = 5.3 fb^-1

Asymmetries in the lab frame (-qy_had) and tt rest frame (Delta y_t)

Table 2 -- Numbers for Afb(|Δy|)

	Afb(\|Δy\|<1)			Afb(\|Δy\|>1)
	Forward Events	Backward Events	Afb	Forward Events	Backward Events	Afb
Raw	518	497	0.021 ± 0.031	148	97	0.208 ± 0.062
BkgSub	414.3	390.8	0.029 ± 0.040	110.7	60.9	0.291 ± 0.090
Corrected	390.7	371.1	0.026 ± 0.104	179.7	43.4	0.611 ± 0.210
MCFM			0.039 ± 0.006			0.123 ± 0.018

CDF II Preliminary -- L = 5.3 fb^-1

Asymmetry in tt rest frame at large and small |Delta y_t|

Table 3 -- Numbers for Many-binned Afb(|Δy|)

	\|Δy\| < 0.75	0.75 < \|Δy\| < 1.5	1.5 < \|Δy\| < 2.25	2.25 < \|Δy\|
Raw	0.020 ± 0.035	0.117 ± 0.052	0.184 ± 0.140	0.600 ± 0.358
BkgSub	0.030 ± 0.043	0.151 ± 0.007	0.330 ± 0.270	0.858 ± 0.621

CDF II Preliminary -- L = 5.3 fb^-1

Asymmetry in tt rest frame as a function of |Delta y_t| (no parton level values)

Reconstructed -qy_had, equivalent to y_top = -y_tbar in lab frame.

Reconstructed -qy_had separated by lepton charge.

Reconstructed –qy_had in four bins, with background subtraction and corrections to the parton level.

Reconstructed qdeltay, equivilent to y_top - y_tbar.

Reconstructed deltay separated by lepton charge.

Reconstructed qdeltay in four bins, with background subtraction and corrections to the parton level.

The next set of plots explore the Delta y dependence
of the asymmetry in the tt rest frame.

Reconstructed qdeltay in eight bins, for raw data and data-background.

The asymmetry as a function of Delta y, Afb(|deltay|), for raw and background subtracted data.

The asymmetry in the tt rest frame at small and large |Delta y|, including correction to the parton level and comparison with the MCFM prediction.

The next two plots show the distribution of production angles in the lab
and tt rest frame. These contain the same information as the respective rapidities.

The Afb value for cos(theta) in the lab frame matches the raw Afb measured for qy_had.

The Afb value for cos(theta*) in the tt rest frame matches the raw Afb measured for qdeltay.

These last plots show our background shapes and
validation for our background estimation method.

Here are the predicted background shapes (and corresponding Afb values) for the background components of qy_had.

Here are the predicted background shapes (and corresponding Afb values) for the background components of qdeltay.

This plot of antitagged events shows that the background+signal shape for qy_had is good.

This plot of antitagged events shows that the background+signal shape for qdeltay is good.

Table 4 -- Systematic Uncertainties for Data-Background

Systematic Uncertainty	q•yhad	qΔy	Afb(\|Δy\|<1)	Afb(\|Δy\|>1)
Background size	0.012	0.006	0.003	0.030
Background shape	0.011	0.004	0.003	0.015
Total Uncertainty	0.016	0.007	0.004	0.033

CDF II Preliminary -- L = 5.3 fb^-1

Table 5 -- Systematic Uncertainties for Corrected Distributions

Systematic Uncertainty	q•yhad	qΔy	Afb(\|Δy\|<1)	Afb(\|Δy\|>1)
Background size	0.015	0.011	0.002	0.086
Background shape	0.014	0.007	0.005	0.107
ISR/FSR	0.010	0.001	0.004	0.004
JES	0.003	0.007	0.002	0.003
PDF	0.005	0.005	0.054	0.013
Color Reconnection	0.001	0.004	0.007	0.007
MC Generator	0.005	0.005	0.004	0.033
Total Uncertainty	0.024	0.017	0.055	0.141

CDF II Preliminary -- L = 5.3 fb^-1

Table 6 -- Table of Inclusive Results

	q•yhad	qΔy
Data (Raw)	0.073 ± 0.028	0.057 ± 0.028
Data-Background	0.110 ± 0.036 ± 0.016	0.075 ± 0.036 ± 0.007
Corrected	0.150 ± 0.050 ± 0.024	0.158 ± 0.072 ± 0.017
MCFM Prediction	0.038 ± 0.006	0.058 ± 0.009

CDF II Preliminary -- L = 5.3 fb^-1

Table 7 -- Table of Rapidity Dependence Results

	all qΔy	Afb(\|Δy\|<1)	Afb(\|Δy\|>1)
Data (Raw)	0.057 ± 0.028	0.021 ± 0.031	0.208 ± 0.062
Data-Background	0.075 ± 0.036 ± 0.007	0.029 ± 0.040 ± 0.004	0.291 ± 0.090 ± 0.033
Corrected	0.158 ± 0.072 ± 0.017	0.026 ± 0.104 ± 0.055	0.611 ± 0.210 ± 0.141
MCFM Prediction	0.058 ± 0.009	0.039 ± 0.006	0.123 ± 0.018

CDF II Preliminary -- L = 5.3 fb^-1

by Glenn Strycker

Measurement of the Inclusive Forward-BackwardAsymmetry and its Rapidity Dependence Afb(|Δy|)of tt Production in 5.3/fb of Tevatron Data

List of Important Links

Abstract

The next set of plots explore the Delta y dependenceof the asymmetry in the tt rest frame.

The next two plots show the distribution of production angles in the laband tt rest frame. These contain the same information as the respective rapidities.

These last plots show our background shapes andvalidation for our background estimation method.

Measurement of the Inclusive Forward-Backward
Asymmetry and its Rapidity Dependence Afb(|Δy|)
of tt Production in 5.3/fb of Tevatron Data

The next set of plots explore the Delta y dependence
of the asymmetry in the tt rest frame.

The next two plots show the distribution of production angles in the lab
and tt rest frame. These contain the same information as the respective rapidities.

These last plots show our background shapes and
validation for our background estimation method.