LHC and Tevatron constraints on a $W^{\prime }$ model interpretation of the top quark forward-backward asymmetry

Aspects of a flavor-changing $W^{\prime }$ model with right-handed couplings are addressed in this paper in light of Tevatron and LHC data. Our fit to the Tevatron top-quark forward-backward asymmetry and the $t\overline{t}$ inclusive cross section includes higher-order loop effects in the effective interaction. The higher-order corrections change the best-fit value of the $W^{\prime }$ effective coupling strength as a function of the $W^{\prime }$ mass. The consistency of the model is checked against the shape of the $t\overline{t}$ invariant mass distribution. We use these updated $W^{\prime }$ parameters to compute the expected contributions from $W^{\prime }t$ associated production and, for the first time, $W^{\prime }{W}^{\prime }$ pair production at the LHC. We do a full Monte Carlo simulation of the $t\overline{t}X$ final state, including interference between the $t{W}^{\prime }$-induced $t\overline{t}j$ process and the standard model $t\overline{t}j$ process. Interference effects are shown to be quantitatively important, particularly when the $W^{\prime }$ mass is large. The jet-multiplicity distribution in $t\overline{t}$ jet production at 8 TeV constrains the $W^{\prime }$ model severely.

Figure 1

(a) and (b) illustrate the $W^{\prime }$ loop correction to the $d\overline{d}g$ vertex. (c) shows the $t\overline{d}$ contribution to the $W^{\prime }$ width.

Figure 2

The ratio of the width and the mass of the $W^{\prime }$ boson determined from the parameters of our best fits at the Tevatron. The values of ${\chi }^2$ in the light-shaded (yellow) region are not greater than 1. In the dark shaded (green) region they are not greater than the standard model (SM) value of ${\chi }^2$. For comparison, we show LO results when the $\mathcal{O}({\alpha }_R)$ contributions are not included: Between the (red) dashed lines, ${\chi }^2$ is not greater than 1, and between the (red) dotted line ${\chi }^2$ is not greater than its SM value.

Figure 3

Results of our fit to (a) the inclusive total cross section ${\sigma }_{t\overline{t}}$ and (b) the forward-backward asymmetry $A_{FB}^{t\overline{t}}$. In (c) we show the values of $\chi$ from our fit for a 1000 GeV $W^{\prime }$ boson. The light-shading (yellow) shows the $1\sigma$ region from our combined fits. The dark-shading (green) shows the $2\sigma$ region. The (black) solid line is the result with NLO vertex corrections included, while the (red) dashed line is the result without the NLO vertex corrections. The horizontal (blue) dashed lines in (a) and (b) denote the central values of the Tevatron data. The (blue) dotted line in (c) shows the value of $\chi$ for the SM.

Figure 4

(a) The parameter $V_{td}^{\prime }$ obtained from our fits to ${\sigma }_{t\overline{t}}$ and $A_{FB}^t$ is shown as a function of the $W^{\prime }$ mass. (b) The coefficient $2{\alpha }_R{m}_t^2/({\alpha }_S{m}_{W^{\prime }}^2)$ obtained from our fits is shown as a function of the $W^{\prime }$ mass. Values of ${\chi }^2$ in the light-shaded (yellow) region remain less than 1. Values of ${\chi }^2$ in the dark-shaded (green) region are not greater than the SM ${\chi }^2$. For comparison, we show the results without NLO $\mathcal{O}({\alpha }_R)$ contributions: In the region between the (red) dashed lines ${\chi }^2$ is not greater than 1, and in the region between the (red) dotted lines ${\chi }^2$ is not greater than the SM ${\chi }^2$.

Figure 5

The $m_{t\overline{t}}$ distribution (upper two panels) and the normalized $m_{t\overline{t}}$ distribution (lower two panels) from the SM and the $W^{\prime }$ model. Left: ($m_{W^{\prime }}=500\mathrm{GeV}$, $g_R=3.8$); Right: ($m_{W^{\prime }}=1000\mathrm{GeV}$, $g_R=7.0$). The (blue) solid line is the SM NLO QCD prediction obtained from the MCFM [41] code. The lighter dashed (red) line shows the $W^{\prime }$ model prediction without the NLO vertex correction, and the darker dashed (black) line shows the $W^{\prime }$ model prediction with the NLO vertex correction included. The pure SM part of the $W^{\prime }$ model prediction is corrected to the NLO QCD level. The circles denote the Tevatron data along with their uncertainties.

Figure 6

The cut acceptance for $t\overline{t}$ events as a function of $m_{t\overline{t}}$. The solid (black) line is the SM value. Acceptances in the $W^{\prime }$ model are shown for a 500 GeV $W^{\prime }$ dotted (red) line and a 1 TeV $W^{\prime }$ dashed (blue) line.

Figure 7

Normalized cross section as a function of jet multiplicity for jets with (a) $p_T>30$, (b) $p_T>60$ and (c) $p_T>100\mathrm{GeV}$. The data are from the CMS Collaboration [44]. The dashed (red) lines are the results of the simulation shown in the CMS paper, whereas the solid (black) line is our simulation.

Figure 8

(a) Example of standard model production of $t\overline{t}d$ production in a $dg$ interaction, (b) $W^{\prime }$ model production of $t\overline{t}d$, (c) $W^{\prime }$ exchange contribution to production of $t\overline{t}d$. Interference occurs between the processes (a) and (b), and between (a) and (c).

Figure 9

Normalized cross sections as a function of jet multiplicity for jets with $p_T>30$ (left panels), $p_T>60$ (middle panels), and $p_T>100\mathrm{GeV}$ (right panels). The figures in the upper row are the results for $m_{W^{\prime }}=500\mathrm{GeV}$ and $V_{td}^{\prime }=4.195$. The figures in the lower row are the results for $m_{W^{\prime }}=1\mathrm{TeV}$ and $V_{td}^{\prime }=6.634$. The (black) solid line is our SM simulation. The (blue) dotted lines represent our $W^{\prime }$ model results.

Figure 10

(a) The 95% exclusion bound in the parameter space of $V_{td}^{\prime }$ vs $m_{W^{\prime }}$ from ${\chi }^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.$ fits to the LHC jet-multiplicity distribution in the inclusive $t\overline{t}X$ process at 8 TeV. The (blue) dashed line is the 95% exclusion bound. The dotted and dashed (red) lines and the light (yellow) and dark (green) shaded regions have the same meanings as those in Fig. 4. (b) The 95% exclusion bound shown for $2{\alpha }_R{m}_t^2/({\alpha }_S{m}_{W^{\prime }}^2)$ vs $m_{W^{\prime }}$.

Figure 11

The normalized distribution as a function of jet multiplicity for jets with $p_T>30$ (left panels), $p_T>60$ (middle panels), $p_T>100\mathrm{GeV}$ (right panels). The figures in the upper row are the results for $m_{W^{\prime }}=500\mathrm{GeV}$ and $V_{td}^{\prime }=4.195$. The figures in the lower row are the results for $m_{W^{\prime }}=1\mathrm{TeV}$ and $V_{td}^{\prime }=6.634$. The (red) dashed lines represent the results without the interference between $t{W}^{\prime }+X$ and SM $t\overline{t}+X$ production. The (blue) dotted lines are the results with interference included.

Figure 12

The cross sections as a function of jet multiplicity for jets with $p_T>30$ (left panels), $p_T>60$ (middle panels), $p_T>100\mathrm{GeV}$ (right panels). The figures in the upper row are the results for $m_{W^{\prime }}=500\mathrm{GeV}$ and $V_{td}^{\prime }=4.195$. The figures in the lower row are the results for $m_{W^{\prime }}=1\mathrm{TeV}$ and $V_{td}^{\prime }=6.634$. The (red) dashed lines represent the results without the interference between the $t{W}^{\prime }+X$ and the SM $t\overline{t}+X$ production. The (blue) dotted lines are the results with interference included.

Figure 13

Cross sections as a function of jet multiplicity for jets with $p_T>30$ (left panels), $p_T>60$ (middle panels), $p_T>100\mathrm{GeV}$ (right panels). Results in the upper row are for $m_{W^{\prime }}=500\mathrm{GeV}$ and $V_{td}^{\prime }=4.195$, whereas those in the lower row are for $m_{W^{\prime }}=1\mathrm{TeV}$ and $V_{td}^{\prime }=6.634$. The (blue) dotted lines represent the complete calculation. The (sky blue) shadowed region is the contribution from the $W^{\prime }{W}^{\prime }$ pair production process.