On models of new physics for the Tevatron top $A_{\mathrm{FB}}$

The Collider Detector at Fermilab (CDF) has observed a top forward-backward asymmetry discrepant with the standard model prediction at $3.4\sigma$. We analyze models that could generate the asymmetry, including flavor-violating $W^{\prime }$s, horizontal $Z_H^{\prime }$s, triplet and sextet diquarks, and axigluons. We consider the detailed predictions of these models for the invariant mass and rapidity distributions of the asymmetry at the parton level, comparing against the unfolded parton-level CDF results. While all models can reproduce the asymmetry with the appropriate choice of mass and couplings, it appears at first examination that the extracted parton-level invariant mass distributions for all models are in conflict with Tevatron observations. We show, however, that, on closer examination, $t\overline{t}$ events in $Z_H^{\prime }$ and $W^{\prime }$ models have considerably lower selection efficiencies in high invariant mass bins as compared to the standard model, so that $W^{\prime }$, $Z_H^{\prime }$, and axigluon models can generate the observed asymmetry while being consistent with the total cross-section and invariant mass spectrum. Triplet and sextet models have greater difficulty producing the observed asymmetry while remaining consistent with the total cross-section and invariant mass distribution. To more directly match the models and the CDF results, we proceed to decay and reconstruct the tops, comparing our results against the raw CDF asymmetry and invariant mass distributions. We find that the models that successfully generate the corrected CDF asymmetry at the parton level reproduce the more finely binned uncorrected asymmetry very well. Finally, we discuss the early LHC reach for discovery of these models, based on our previous analysis [M. I. Gresham, I.-W. Kim, and K. M. Zurek, arXiv:1102.0018.].

Figure 1

Tree level $t\overline{t}$ production diagram with mediator $M$ exchange.

Figure 2

Parton-level forward-backward asymmetry for events with $t\overline{t}$ invariant mass greater than 450 GeV versus leading-order cross-section in picobarns for various models. The mass (in GeV) and coupling of the mediator are indicated by ($\genfrac{}{}{0ex}{}{\mathrm{mass}}{\mathrm{coupling}}$). A comprehensive scan of models was carried out, and only representative points are shown. The coupling shown for axigluons is $g_A^q=-g_A^t$ (supposing $g_V^q=g_V^t=0$), while the coupling shown for $Z_H^{\prime }$ and $W^{\prime }$ models is $g_R$ (assuming $g_L=0$), and the quoted couplings for triplets and sextets are $g=\sqrt{(g_L^2+g_R^2)/2}$. For comparison against observations, the horizontal shaded area lies in the $\pm 1\sigma$ region of the measured (parton-level) value of $A_{\mathrm{FB}}(m_{t\overline{t}}>450\mathrm{GeV})$. The vertical lines lie at the central value of the CDF $t\overline{t}$ production cross-section ($7.5\pm 0.48\mathrm{pb}$), divided by a K-factor of 1.3 or 1. The SM marker lies at the value of the LO standard model cross-section and the NLO value for the SM forward-backward asymmetry. Note that care must be taken when comparing the new physics cross-sections against the standard model cross-section, as the selection efficiencies for the new physics models can be lower. This is discussed in more detail in the main text.

Figure 3

Efficiencies after showering events with PYTHIA and making the cuts detailed in Sec. 4 on final state leptons and jets, with the hatched regions corresponding to $1\sigma$ errors based on the limited statistics of the sample. Fine binning (left panel) and coarse binning (right panel) are shown for comparison to the invariant mass spectrum and two-bin asymmetry, respectively. No detector effects have been taken into account here. Black bars are for LO standard model. All samples are LO matched.

Figure 4

Event distribution densities for benchmark models at the parton level. The vertical axis is top quark pseudorapidity, and the horiztonal axis is $t\overline{t}$ invariant mass. Contours indicate constant event density.

Figure 5

$A_{\mathrm{FB}}$ for $Z_H^{\prime }$, $W^{\prime }$ models with couplings as indicated in the legend (with $g=g_R$, $g_L=0$), with the hatched regions corresponding to $1\sigma$ errors based on the limited statistics of the sample. The contribution to $A_{\mathrm{FB}}$ includes both $t$-channel $Z_H^{\prime }$, $W^{\prime }$ exchange and single $Z_H^{\prime }$, $W^{\prime }$ production. The [red] bars in the upper right and lower left quadrants of each panel are the CDF observation with $1\sigma$ errors, while the [blue] bars in the lower right quadrants indicate the NLO SM contribution from 1, which has not been included in the LO contribution calculated via MadGraph and PYTHIA. The last bin includes all events with $m_{t\overline{t}}>450\mathrm{GeV}$ and $|\Delta y|>1$, respectively.

Figure 6

$A_{\mathrm{FB}}$ for triplet, sextet and axigluon models with couplings as indicated in the legend, with the hatched regions corresponding to $1\sigma$ errors based on the limited statistics of the sample. The [red] bars in the upper right and lower left quadrants of each panel are the CDF observation with $1\sigma$ errors, while the [blue] bars in the lower right quadrants indicate the NLO SM contribution, which has not been included in the LO contribution calculated via MadGraph and PYTHIA. The last bin includes all events with $m_{t\overline{t}}>450\mathrm{GeV}$ and $|\Delta y|>1$, respectively.

Figure 7

$\frac{d\sigma }{d{m}_{t\overline{t}}}$ for the benchmark models appearing in Figs. 5, 6. The Tevatron measured cross-section ([red] crosses, from 58), and LO SM cross-section with the same SM parameters and fixed renormalization scale used to generate benchmark model events are also shown. No K-factors are applied.

Figure 8

$A_{\mathrm{FB}}^{t\overline{t}}(m_{t\overline{t},i})$ for $W^{\prime }$, $Z_H^{\prime }$, triplet, sextet and axigluon models. The higher [red] crosses are the CDF values reconstructed from data. The level [blue] crosses with smaller error bars are the MC@NLO expectation. The last bin includes all events with $m_{t\overline{t}}>700\mathrm{GeV}$.

Figure 9

$A_{\mathrm{FB}}^{t\overline{t}}(q,m_{t\overline{t},i})$ as defined in Eq. (14) for $W^{\prime }$, $Z_H^{\prime }$, triplet, sextet, and axigluon models. Here, the data are divided according to the charge, $q$, of the lepton in the event. The upper black ($q>0$) and lower [red] ($q<0$) crosses are the CDF values reconstructed from data (with background subtracted).

Figure 10

Number of expected $t\overline{t}$ events with $5.3{\mathrm{fb}}^{-1}$ at the Tevatron, distributed over $m_{t\overline{t}}$. Events were passed through PGS and then tops were reconstructed using the algorithm detailed in 52. The crosses indicate CDF’s measurement, with expected background (as estimated by CDF) subtracted. The small [green] histograms at the upper left of the first and last panels are our SM sample, and the paler [purple] histograms represent model samples. For SM and model samples, a fixed number of events were generated, and then event counts were scaled appropriately for $5.3{\mathrm{fb}}^{-1}$ integrated luminosity.

Figure 11

$A_{\mathrm{FB}}^{t\overline{t}}$ and $A_{\mathrm{FB}}^{p\overline{p}}$ in low ($m_{t\overline{t}}<450\mathrm{GeV}$) and high ($m_{t\overline{t}}\ge 450\mathrm{GeV}$) $t\overline{t}$ invariant mass bins for $Z_H^{\prime }$, $W^{\prime }$, triplet, sextet, and axigluon models. Lower [red] and higher [blue] crosses with large error bars are the CDF values reconstructed from data in the lab and CM frames, respectively. Lower [purple] and higher [green] crosses with small error bars indicate the SM NLO predictions for the same frames.

Figure 12

$A_{\mathrm{FB}}^{t\overline{t}}$ in $t\overline{t}$ low ($m_{t\overline{t}}<450\mathrm{GeV}$) and high ($m_{t\overline{t}}\ge 450\mathrm{GeV}$) invariant mass bins for benchmark models. The simulated data samples were partitioned according to whether the event had more than five jets with $p_T>20\mathrm{GeV}$ and $|\eta |<2$. The CDF measured lab frame asymmetry for 4-jet and $5+$-jet samples is shown as pale [red] crosses and black crosses, respectively.

Figure 13

$A_{\mathrm{FB}}^{t\overline{t}}(m_{t\overline{t}})$ for $Z_H^{\prime }$ model with various cuts on the $t\overline{t}$ reconstruction ${\chi }^2$. The last bin includes all events with $m_{t\overline{t}}>700\mathrm{GeV}$. The [red] crosses are the CDF values reconstructed from data. CDF used a likelihood algorithm for top reconstruction but made no ${\chi }^2$ cut.

Figure 14

Parton-level lepton forward-backward asymmetry for $t\overline{t}$ events in which both tops decay leptonically, and in which both leptons pass the rapidity cuts corresponding to those used in the recent CDF analysis 53. The [red] points indicated by the crosses are extracted from the results in 53. (a) $A_{\mathrm{FB}(\Delta y_{{\ell }^{+}{\ell }^{-}})}$ as a function of $|\Delta y|=|y_{{\ell }^{+}}-y_{{\ell }^{-}}|$. (b) $A_{\mathrm{FB}(\Delta y_{{\ell }^{+}{\ell }^{-}})}=\frac{N(y_{{\ell }^{+}}-y_{{\ell }^{-}}>0)-N(y_{{\ell }^{+}}-y_{{\ell }^{-}}<0)}{N(y_{{\ell }^{+}}-y_{{\ell }^{-}}>0)+N(y_{{\ell }^{+}}-y_{{\ell }^{-}}<0)}$ as a function of ${\ell }^{+}{\ell }^{-}$ invariant mass.