Model-independent and quasi-model-independent search for new physics at CDF

Data collected in run II of the Fermilab Tevatron are searched for indications of new electroweak scale physics. Rather than focusing on particular new physics scenarios, CDF data are analyzed for discrepancies with respect to the standard model prediction. A model-independent approach (Vista) considers the gross features of the data and is sensitive to new large cross section physics. A quasi-model-independent approach (Sleuth) searches for a significant excess of events with large summed transverse momentum and is particularly sensitive to new electroweak scale physics that appears predominantly in one final state. This global search for new physics in over 300 exclusive final states in $927{\mathrm{pb}}^{-1}$ of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ reveals no such significant indication of physics beyond the standard model.

Figure 1

Distribution of observed discrepancy between data and the standard model prediction, measured in units of standard deviation ($\sigma$), shown as the solid (green) histogram, before accounting for the trials factor. The upper pane shows the distribution of discrepancies between the total number of events observed and predicted in the 344 populated final states considered. Negative values on the horizontal axis correspond to a deficit of data compared to standard model prediction; positive values indicate an excess of data compared to standard model prediction. The lower pane shows the distribution of discrepancies between the observed and predicted shapes in 16 486 kinematic distributions. Distributions in which the shapes of data and standard model prediction are in relative disagreement correspond to large positive $\sigma$. The solid (black) curves indicate expected distributions, if the data were truly drawn from the standard model background. Interest is focused on the entries in the tails of the upper distribution and the high tail of the lower distribution. The final state entering the upper histogram at $-4.03\sigma$ is the Vista $3j\tau$ final state, which heads Table 2. Most of the distributions entering the lower histogram with $>4\sigma$ derive from the $3j$ $\Delta R(j_2,j_3)$ discrepancy, discussed in the text.

Figure 2

The invariant mass of the tau lepton and two leading jets in the final state consisting of three jets and one positively or negatively charged tau. (The Vista final state naming convention gives the tau lepton a positive charge.) Data are shown as filled (black) circles, with the standard model prediction shown as the shaded (red) histogram. This is the most discrepant kinematic distribution in the final state exhibiting the largest population discrepancy.

Figure 3

A shape discrepancy highlighted by Vista in the final state consisting of exactly three reconstructed jets with $|\eta |<2.5$ and $p_T>17\mathrm{GeV}$, and with one of the jets satisfying $|\eta |<1$ and $p_T>40\mathrm{GeV}$. This distribution illustrates the effect underlying most of the Vista shape discrepancies. Filled (black) circles show CDF data, with the shaded (red) histogram showing the prediction of Pythia. The discrepancy is clearly statistically significant, with statistical error bars smaller than the size of the data points. The vertical axis shows the number of events per bin, with the horizontal axis showing the angular separation ($\Delta R=\sqrt{\Delta {\eta }^2+\delta {\varphi }^2}$) between the second and third jets, where the jets are ordered according to decreasing transverse momentum. In the region $\Delta R(j_2,j_3)\gtrsim 2$, populated primarily by initial state radiation, the standard model prediction can to some extent be adjusted. The region $\Delta R(j_2,j_3)\lesssim 2$ is dominated by final state radiation, the description of which is constrained by data from LEP 1.

Figure 4

The jet mass distribution in the $bj$ final state with $\sum _{}^{}{p}_T>400\mathrm{GeV}$. The $3j$ $\Delta R(j_2,j_3)$ discrepancy illustrated in Fig. 3 manifests itself also by producing jets more massive in data than predicted by Pythia’s showering algorithm. The mass of a jet is determined by treating energy deposited in each calorimeter tower as a massless 4-vector, summing the 4-vectors of all towers within the jet, and computing the mass of the resulting (massive) 4-vector.

Figure 5

The distribution of $\Delta R$ between the jet and $b$-tagged jet in the final state $bej$. The primary standard model contribution to this final state is QCD three jet production with one jet misreconstructed as an electron. The similarity to the $3j$ $\Delta R(j_2,j_3)$ discrepancy illustrated in Fig. 3 in the region $\Delta R(j,b)<2$ is clear. Less clear is the underlying explanation for the difference with respect to Fig. 3 in the region $\Delta R(j,b)>2$.

Figure 6

Distribution of ${10}^3$ $\tilde{P}$ values from ${10}^3$ CDF pseudo experiments, in which pseudo data are pulled from the standard model prediction. The distribution of $\tilde{P}$ is shown in the unit interval (left), with one entry for each of the CDF pseudo experiments. The distribution of $\tilde{P}$ translated into units of standard deviations is also shown (right). The distribution of $\tilde{P}$ from pseudo experiments is consistent with flat (left), and consistent with a Gaussian when translated into units of standard deviations (right), as expected.

Figure 7

Top left: the Sleuth final state $b\overline{b}{\ell }^{+}{\ell }^{\prime -}\mathrm{p̸}$, consisting of events with one electron and one muon of opposite sign, missing momentum, and two or three jets, one or two of which are $b$-tagged. Data corresponding to $927{\mathrm{pb}}^{-1}$ are shown as filled (black) circles; the standard model prediction is shown as the (red) shaded histogram. Top right: the same final state with $t\overline{t}$ subtracted from the standard model prediction. Bottom row: the Sleuth final state $Wb\overline{b}jj$, with the standard model $t\overline{t}$ contribution included (lower left) and removed (lower right). Significant discrepancies far surpassing Sleuth’s discovery threshold are observed in these final states with $t\overline{t}$ removed from the standard model background estimate. If the top quark had not been predicted, Sleuth would have discovered it.

Figure 8

Left: the final state ${\ell }^{+}{\ell }^{\prime -}\mathrm{p̸}$, consisting of events with an electron and muon of opposite sign and missing transverse momentum, in $927{\mathrm{pb}}^{-1}$ of CDF data. Right: the same final state with standard model $WW$, $WZ$, and $ZZ$ contributions subtracted, and with the Vista correction factors refit in the absence of these contributions. Sleuth finds the final state ${\ell }^{+}{\ell }^{\prime -}\mathrm{p̸}$ to contain a discrepancy surpassing the discovery threshold of $\tilde{\mathcal{P}}<0.001$ with the processes $WW$, $WZ$, and $ZZ$ removed from the standard model background.

Figure 9

The distribution of $\mathcal{P}$ in the data, with one entry for each final state considered by Sleuth.

Figure 10

The most interesting final states identified by Sleuth. The region chosen by Sleuth, extending up to infinity, is shown by the (blue) arrow just below the horizontal axis. Data are shown as filled (black) circles, and the standard model prediction is shown as the shaded (red) histogram. The Sleuth final state is labeled in the upper left corner of each panel, with $\ell$ denoting $e$ or $\mu$, and ${\ell }^{+}{\ell }^{\prime +}$ denoting an electron and muon with the same electric charge. The number at upper right in each panel shows $\mathcal{P}$, the fraction of hypothetical similar experiments in which something at least as interesting as the region shown would be seen in this final state. The inset in each panel shows an enlargement of the region selected by Sleuth, together with the number of events ($\mathrm{SM}$) predicted by the standard model in this region, and the number of data events ($d$) observed in this region.

Figure 11

Transverse momentum distribution of reconstructed objects (labeling columns) arising from single particles (labeling rows) with $p_T=25\mathrm{GeV}$ shot from a single particle gun into the central CDF detector. The area under each histogram is equal to the number of events in the corresponding misidentification matrix element of Table 4, with the vertical axis of each histogram scaled to the peak of each distribution. A different vertical scale is used for each histogram, and histograms with fewer than ten events are not shown. The horizontal axis ranges from 0 to 50 GeV.

Figure 12

A few of the most discrepant distributions in the final states $ej$ and $j\mu$, which are greatly affected by the fake rates $p(j\to e)$ and $p(j\to \mu )$, respectively. These distributions are among the 13 significantly discrepant distributions identified as resulting from coarseness of the correction model employed. The vertical axis shows the number of events; the horizontal axes show the transverse momentum and pseudorapidity of the lepton. Filled (black) circles show CDF data, and the shaded (red) histogram shows the standard model prediction. Events enter the $ej$ final state either on a central electron trigger with $p_T>25\mathrm{GeV}$, or on a plug electron trigger with $p_T>40\mathrm{GeV}$. The fake rate $p(j\to e)$ is significantly larger in the plug region than in the central region of the CDF detector. Muons are identified with separate detectors covering the regions $|\eta |<0.6$ and $0.6<|\eta |<1.0$.

Figure 13

A few of the most discrepant distributions in the final states $j\tau$ and $j\gamma$, which are greatly affected by the fake rates $p(j\to \tau )$ and $p(j\to \gamma )$, respectively. The vertical axis shows the number of events; the horizontal axes show the transverse momentum and pseudorapidity of the tau lepton and photon. Filled (black) circles show CDF data, and the shaded (red) histogram shows the standard model prediction. The distributions in the $j\gamma$ final state are among the 13 significantly discrepant distributions identified as resulting from coarseness of the correction model employed.

Figure 14

The probability for a generated parton to be misreconstructed as a one-prong $\tau$, as a function of the parton’s generated $p_T$. Filled (red) circles show the probability for a jet arising from a parent quark to be misreconstructed as a one-prong tau. Filled (blue) triangles show the probability for a jet arising from a parent gluon to be misreconstructed as a one-prong tau.

Figure 15

The distribution of transverse momentum and azimuthal angle for photons and jets in the $\gamma \mathrm{p̸}$ and $j\mathrm{p̸}$ final states, dominated by cosmic ray and beam halo muons. The vertical axis shows the number of events in each bin. Data are shown as filled (black) circles; the standard model prediction is shown as the shaded (red) histogram. Here the “standard model” prediction includes contributions from cosmic ray and beam halo muons, estimated using events containing fewer than three reconstructed tracks. The contribution from cosmic ray muons is flat in $\varphi$, while the contribution from beam halo is localized to $\varphi =0$. The only degrees of freedom for the background to these final states are the $\mathtt{c}\mathtt{o}\mathtt{s}\mathtt{m}\mathtt{i}\mathtt{c}$ $\gamma$ and $\mathtt{c}\mathtt{o}\mathtt{s}\mathtt{m}\mathtt{i}\mathtt{c}$ $j$ correction factors, whose values are determined from the global Vista fit and provided in Table 1.

Figure 16

Variation of the $k$-factors for inclusive $W$ and $Z$ production under different choices of parton distribution functions, from the Alekhin parton distribution error set [47]. The correlation of the uncertainty on these two $k$-factors due to uncertainty in the parton distribution functions is 0.955.

Figure 17

Calculation of the $\gamma \gamma j$ $k$-factor, as a function of jet transverse momentum. The effect of changing the factorization scale by a factor of two in either direction is also shown (small black points with error bars).