Measurement of the top quark forward-backward production asymmetry and its dependence on event kinematic properties

We present new measurements of the inclusive forward-backward $t\overline{t}$ production asymmetry, $A_{\mathrm{FB}}$, and its dependence on several properties of the $t\overline{t}$ system. The measurements are performed with the full Tevatron data set recorded with the CDF II detector during $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$, corresponding to an integrated luminosity of $9.4{\mathrm{fb}}^{-1}$. We measure the asymmetry using the rapidity difference $\Delta y=y_t-y_{\overline{t}}$. Parton-level results are derived, yielding an inclusive asymmetry of $0.164\pm 0.047(\mathrm{stat}+\mathrm{syst})$. We establish an approximately linear dependence of $A_{\mathrm{FB}}$ on the top-quark pair mass $M_{t\overline{t}}$ and the rapidity difference $|\Delta y|$ at detector and parton levels. Assuming the standard model, the probabilities to observe the measured values or larger for the detector-level dependencies are $7.4\times {10}^{-3}$ and $2.2\times {10}^{-3}$ for $M_{t\overline{t}}$ and $|\Delta y|$ respectively. Lastly, we study the dependence of the asymmetry on the transverse momentum of the $t\overline{t}$ system at the detector level. These results are consistent with previous lower-precision measurements and provide additional quantification of the functional dependencies of the asymmetry.

Figure 1

The rapidity of the hadronically decaying top or antitop quark.

Figure 2

Reconstructed invariant mass of the $t\overline{t}$ system. The last bin contains overflow events.

Figure 3

Resolution of the $x$ or $y$ component of the reconstructed $p_T^{t\overline{t}}$ of the $t\overline{t}$ system as measured in powheg.

Figure 4

Reconstructed $p_T^{t\overline{t}}$ of the $t\overline{t}$ system. The last bin contains overflow events.

Figure 5

(a) The number of observed jets and (b) the number of jets with $b$ tags in the data compared to the signal plus background model. The last bin contains overflow events.

Figure 6

(a) The $E_T$ of the most energetic jet and (b) the transverse momentum of the lepton in the data compared to the signal plus background model. The last bin contains overflow events.

Figure 7

(a) The missing transverse energy and (b) the scalar sum of the transverse energy of the lepton, jets, and ${\mathrm{E̸}}_T$ in the data compared to the signal plus background model. The last bin contains overflow events.

Figure 8

(top) The reconstructed $\Delta y$ distribution and the inclusive reconstruction-level asymmetry compared to the prediction of the signal and background model. (bottom) The difference between the data and prediction divided by the prediction. Note: the left-most and right-most bins are under- and overflow bins, respectively.

Figure 9

(top) The observed background-subtracted $\Delta y$ distribution compared to the SM prediction. Error bars include both statistical and background-related systematic uncertainties. (bottom) The difference between the data and prediction divided by the prediction.

Figure 10

Detector response in $\Delta y$ as modeled by powheg showing the true value of $\Delta y$ as a function of the measured value for all events passing the selection criteria. The size of each rectangle is proportional to the number of entries in that bin.

Figure 11

Acceptance as a function of $\Delta y$ as modeled by powheg.

Figure 12

Results from simulated parton-level $\Delta y$ measurements based on Octet A. The data points show the central values for the simulated results, with the error bars representing the $1\sigma$ spread of the results.

Figure 13

(top) The differential cross section $d\sigma /d(\Delta y)$ as measured in the data after correction to the parton level compared to the SM prediction. Uncertainties include both statistical and systematic contributions and are correlated between bins. (bottom) The difference between the data and prediction divided by the prediction.

Figure 14

The reconstruction-level forward-backward asymmetry as a function of $|\Delta y|$ with a best-fit line superimposed. The errors on the data are statistical, and the shaded region represents the uncertainty on the slope of the prediction.

Figure 15

The background-subtracted asymmetry as a function of $|\Delta y|$ with a best-fit line superimposed. Error bars include both statistical and background-related systematic uncertainties. The shaded region represents the theoretical uncertainty on the slope of the prediction.

Figure 16

The parton-level forward-backward asymmetry as a function of $|\Delta y|$ with a best-fit line superimposed. Uncertainties are correlated and include both statistical and systematic contributions. The shaded region represents the theoretical uncertainty on the slope of the prediction.

Figure 17

The reconstruction-level forward-backward asymmetry as a function of $M_{t\overline{t}}$ with a best-fit line superimposed. The last bin contains overflow events. The errors on the data are statistical, and the shaded region represents the uncertainty on the slope of the prediction.

Figure 18

(a) $M_{t\overline{t}}$ after background subtraction in events with positive and negative $\Delta y$ and (b) background-subtracted $A_{\mathrm{FB}}$ as a function of $M_{t\overline{t}}$ with a best-fit line superimposed. The last bin contains overflow events. Error bars include both statistical and background-related systematic uncertainties. The shaded region in (b) represents the theoretical uncertainty on the slope of the prediction.

Figure 19

The background-subtracted $\Delta y$ distributions for events with (a) $M_{t\overline{t}}<450\mathrm{GeV}/c^2$ and (b) $M_{t\overline{t}}\ge 450\mathrm{GeV}/c^2$. Error bars include both statistical and background-related systematic uncertainties.

Figure 20

(a) The parton-level $M_{t\overline{t}}$ distributions for events with positive and negative $\Delta y$ and (b) the parton-level forward-backward asymmetry as a function of $M_{t\overline{t}}$ with a best-fit line superimposed. The last bin contains overflow events. Uncertainties are correlated and include both statistical and systematic contributions. The shaded region in (b) represents the theoretical uncertainty on the slope of the prediction.

Figure 21

Interfering $q\overline{q}\to t\overline{t}$ (top) and $q\overline{q}\to t\overline{t}j$ (bottom) diagrams.

Figure 22

Expected $A_{\mathrm{FB}}$ as a function of the $p_T^{t\overline{t}}$ of the $t\overline{t}$ system at the parton level from mcfm, powheg, and pythia, as well as a NLO prediction for events where the top-quark pair is produced in association with an extra energetic jet.

Figure 23

The background-subtracted forward-backward asymmetry in the data as a function of the transverse momentum of the $t\overline{t}$ system, compared to both powheg and pythia. Error bars include both statistical and background-related systematic uncertainties. The last bin contains overflow events.

Figure 24

The forward-backward asymmetry as a function of the transverse momentum of the $t\overline{t}$ system for three models at the background-subtracted level: Octet A, SM pythia, and SM pythia normalized by the addition of $\Delta A_{\mathrm{Oct}}$. The last bin contains overflow events.

Figure 25

The background-subtracted forward-backward asymmetry in the data as a function of the transverse momentum of the $t\overline{t}$ system, compared to both powheg and pythia. The model predictions have been normalized by the addition of $\Delta A_{\mathrm{NLO}}$ to powheg and $\Delta A_{\mathrm{LO}}$ to pythia as described in the text. Error bars include both statistical and background-related systematic uncertainties. The last bin contains overflow events.

Figure 26

The measured asymmetries as a function of (a) $|\Delta y|$ and (b) $M_{t\overline{t}}$ in the data at the three different levels of correction. The error bars include both statistical uncertainties and the appropriate systematic uncertainties for each correction level as described in the text. The last bin contains overflow events.

Figure 27

The lepton $p_T$ distribution in events with a $W$ boson and only one observed jet. The last bin contains overflow events.

Figure 28

The forward-backward asymmetry in $q·{\eta }_{\mathrm{lep}}$ at the detector level as a function of (a) $|{\eta }_{\mathrm{lep}}|$ and (b) lepton $p_T$ in events with a $W$ boson and only one observed jet. The error bars on the data include only a statistical contribution, with the uncertainty on the SM prediction shown as a band around the predicted asymmetry. The last bin contains overflow events.