Measurement of the charge asymmetry in top quark pair production in $pp$ collisions at $\sqrt{s}=8\mathrm{TeV}$ using a template method

The charge asymmetry in the production of top quark and antiquark pairs is measured in proton-proton collisions at a center-of-mass energy of 8 TeV. The data, corresponding to an integrated luminosity of $19.6{\mathrm{fb}}^{-1}$, were collected by the CMS experiment at the LHC. Events with a single isolated electron or muon, and four or more jets, at least one of which is likely to have originated from hadronization of a bottom quark, are selected. A template technique is used to measure the asymmetry in the distribution of differences in the top quark and antiquark absolute rapidities. The measured asymmetry is $A_c^y=[0.33\pm 0.26(\mathrm{stat})\pm 0.33(\mathrm{syst})]\%$, which is the most precise result to date. The results are compared to calculations based on the standard model and on several beyond-the-standard-model scenarios.

Figure 1

The (top) symmetric ${\overrightarrow{x}}^{+}$ and (bottom) antisymmetric ${\overrightarrow{x}}^{-}$ components of the binned probability distributions in the observable ${\mathit{\Upsilon }}_{t\overline{t}}$, constructed using powheg [20] with CT10 PDFs [21], for $t\overline{t}$ production from $gg$, $q\overline{q}$, $qg$, and $\overline{q}g$ initial states.

Figure 2

The median value of the logarithm of the ratio of parton energy to measured energy, as a function of measured $p_{\mathrm{T}}$ in three bins of $|\eta |$, for (left) $b$ jets from top quark decay, (center) jets from $W$ boson decay, and (right) other jets.

Figure 3

The conditional probability densities of the CSV $b$-tagging discriminant from simulation for jets from $b$ quarks, jets from $W$ boson decay, and other jets.

Figure 4

The two-dimensional probability density from simulation of jet invariant masses from $W$ boson ($m_{\widehat{c}\widehat{d}}$) and top quark ($m_{\widehat{b}\widehat{c}\widehat{d}}$) decay is shown (top), along with contours in standard deviations (MSD) of the corresponding Gaussian approximation. Probability densities for correct and incorrect jet assignments (middle) are shown (left) for MSD and (right) for $\sqrt{{\chi }_a^2}$ of the leptonically decaying top quark reconstruction. The corresponding likelihood ratios are shown below.

Figure 5

The angle $\pi \mathrm{\Delta }$ of the resultant sum of three vectors spaced at equal angles, in which the magnitude of each is the likelihood of the respective population. The dashed arrows are translations of the $e^{2i\pi /3}$ and $e^{-2i\pi /3}$ vectors which illustrate the construction of the sum. The circle is shown to indicate the relative scale.

Figure 6

The probability distribution of the discriminant $\mathrm{\Delta }$ for (top left) selected $e+\text{jets}$ events and (top right) selected $\mu +\text{jets}$ events, for the simulated $W\mathrm{j}$ and $t\overline{t}$ populations, and for the Mj population, which is modeled from the sideband data with simulated contributions subtracted. The probability distributions in each observable used to construct the discriminant are shown for (middle) $e+\text{jets}$ and (bottom) $\mu +\text{jets}$ channels. The overflow is included in the rightmost bin of the $M_{\mathrm{T}}$ distributions.

Figure 7

The (top) symmetric and (bottom) antisymmetric components of the ${\mathit{\Upsilon }}_{t\overline{t}}^{\mathrm{rec}}$ probability distribution for selected $t\overline{t}$ simulation events in the $e+\mathrm{jets}$ and $\mu +\mathrm{jets}$ channels. The vertical bars show the statistical uncertainties, while the horizontal bars display the bin widths.

Figure 8

The distribution of the statistical uncertainty in $A_c^y$ from measurements using pseudoexperiments, with an expected value of 0.258%. The statistical uncertainty extracted from the data is marked by the arrow.

Figure 9

The bias in the measured charge asymmetry for SM simulations and alternative $t\overline{t}$ models, based on extended powheg SM templates, versus the charge asymmetry in each sample. The beyond-SM samples are MadGraph simulations of ${\mathrm{Z}}^{\prime }$ bosons and axigluons with masses of 200 GeV and 2 TeV. Uncertainty in the bias of the extended powheg model is dominated by the number of pseudoexperiments used, while the uncertainty in the bias of each alternative model is dominated by the statistical uncertainty in the sample. The hatched area shows the systematic uncertainty in the measurement of $A_c^y$ from sources related to the modeling, including simulation statistical uncertainty, renormalization and factorization scales, choice of $t\overline{t}$ generator, top quark mass, and PDFs.

Figure 10

Sample composition is measured using the discriminant $\mathrm{\Delta }$ distribution (top), in a model with contributions from $t\overline{t}$, $W\mathrm{j}$, Mj, and $\mathrm{St}+\mathrm{DY}$. With the sample composition subsequently fixed, the amplitude of the antisymmetric $t\overline{t}$ contribution is measured in the ${\mathit{\Upsilon }}_{t\overline{t}}^{\mathrm{rec}}$ distribution, shown decomposed into symmetric (middle) and antisymmetric (bottom) components. The thick line shows the antisymmetric component of the fit model. The measurements are performed independently on the (left) $e+\text{jets}$ and (right) $\mu +\text{jets}$ samples.

Figure 11

At top, the negative logarithm of the likelihood is shown as a function of $\alpha$ (upper axis) and $A_c^y$ (lower axis), for $e+\text{jets}$ (closed circles) and $\mu +\text{jets}$ (open circles) measurements. The statistical uncertainty in each is given by the intersections of the parabolas with $-\log L=0.5$, which are marked by arrows. The 68% confidence interval of the combined $A_c^y$ measurement is compared with those of the SM predictions by powheg, Kühn and Rodrigo [8], and Bernreuther and Si [9]. At bottom, the antisymmetric component of the ${\mathit{\Upsilon }}_{t\overline{t}}^{\mathrm{rec}}$ distributions in data and the model are shown for (left) $e+\text{jets}$ and (right) $\mu +\text{jets}$, for the central value (solid), and for the upper (dashed) and lower (dotted) limits of the 68% statistical confidence intervals.

Figure 12

Comparison of results from this analysis (template) with those of the CMS 8 TeV unfolding analysis [19], and SM predictions from theoretical calculations of Kühn and Rodrigo [8], Bernreuther and Si [9], powheg, and mc@nlo. The shaded bands correspond to 68% and 95% confidence intervals of the current measurement. The inner bars on the CMS measurements indicate the statistical uncertainty, the outer bars the statistical and systematic uncertainty added in quadrature.