Search for heavy, long-lived neutralinos that decay to photons at CDF II using photon timing

We present the results of the first hadron collider search for heavy, long-lived neutralinos that decay via ${\tilde{\chi }}_1^0\to \gamma \tilde{G}$ in gauge-mediated supersymmetry breaking models. Using an integrated luminosity of $570\pm 34{\mathrm{pb}}^{-1}$ of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$, we select $\gamma +\mathrm{\text{jet}}+\mathrm{\text{missing transverse energy}}$ candidate events based on the arrival time of a high-energy photon at the electromagnetic calorimeter as measured with a timing system that was recently installed on the CDF II detector. We find 2 events, consistent with the background estimate of $1.3\pm 0.7$ events. While our search strategy does not rely on model-specific dynamics, we set cross section limits and place the world-best 95% C.L. lower limit on the ${\tilde{\chi }}_1^0$ mass of $101\mathrm{GeV}/c^2$ at ${\tau }_{{\tilde{\chi }}_1^0}=5\mathrm{ns}$.

Figure 1

Feynman diagrams of the dominant tree-production processes at the Fermilab Tevatron for the SPS 8 GMSB model line. The taus and second photons, if available, can be identified as jets in the detector. Note that only one choice for the charge is shown.

Figure 2

(a) The schematic of a long-lived ${\tilde{\chi }}_1^0$ decaying into a $\tilde{G}$ and a photon inside the detector. While the $\tilde{G}$ leaves undetected the photon travels to the detector wall and deposits energy in the detector. A prompt photon would travel directly from the collision point to the detector walls. Relative to the expected arrival time, the photon from the ${\tilde{\chi }}_1^0$ would appear “delayed.” (b) The $t_{\mathrm{corr}}$ distribution for a simulated GMSB signal at an example point of $m_{{\tilde{\chi }}_1^0}=100\mathrm{GeV}/c^2$ and ${\tau }_{{\tilde{\chi }}_1^0}=5\mathrm{ns}$ as well as for standard model and noncollision backgrounds.

Figure 3

The definitions of the $\alpha$ and $\beta$ incident angles using schematic diagrams of a long-lived ${\tilde{\chi }}_1^0$ decaying to a photon and a $\tilde{G}$ in the CDF detector. The angles $\alpha$ and $\beta$ are the projections of the incident angle $\psi$ at the front face of the calorimeter in the $(r,z)$- and the $(r,\varphi )$-plane, respectively.

Figure 4

The distribution of the total incident angle $\psi$ at the front face of the calorimeter for simulated photons from ${\tilde{\chi }}_1^0$’s with $m_{{\tilde{\chi }}_1^0}=110\mathrm{GeV}/c^2$. “Prompt” photons from ${\tilde{\chi }}_1^0$’s with a lifetime of 0 ns (solid) are compared to photons from ${\tilde{\chi }}_1^0$’s with a lifetime 10 ns (dashed). The dotted histogram shows the distribution for a lifetime of 10 ns for photons with $2.0\le t_{\mathrm{corr}}\le 10\mathrm{ns}$ and shows that, as expected, delayed photons can have a significant incident angle.

Figure 5

A simulation of the ID variable distributions (minus their requirement value) for photons in a GMSB model with $m_{{\tilde{\chi }}_1^0}=110\mathrm{GeV}/c^2$. The solid line is for prompt photons, simulated as decay photons from ${\tilde{\chi }}_1^0$’s with a lifetime of 0 ns and the dashed line is for photons from long-lived ${\tilde{\chi }}_1^0$’s with a lifetime of 10 ns. Entries to the left of the dashed vertical line pass the corresponding requirement. The bin at $-2.8$ in (d) collects the photons that have no track within the isolation cone. In (f) the bin at $-6$ shows the photons that have no 2nd CES cluster nearby. The distributions for all ID variables do not change significantly between the prompt and the long-lived case except for slight deviations in the energy isolation in (b) as discussed in the text.

Figure 6

The efficiencies for photons and electrons to pass the ID requirements in Table 1 vs incident angles $\alpha$ and $\beta$. The solid squares represent MC photons from ${\tilde{\chi }}_1^0\to \gamma \tilde{G}$ decays ($m_{{\tilde{\chi }}_1^0}=110\mathrm{GeV}/c^2$, ${\tau }_{{\tilde{\chi }}_1^0}=10\mathrm{ns}$) while the empty circles represent electrons from a $W\to e\nu$ data sample that pass the requirements in Table 2. The efficiency falls by $\sim 15\%$ from 0° to 60° in $\beta$. This effect is mostly due to the energy isolation requirement, as discussed in the text.

Figure 7

A comparison of the PMT asymmetry, ${\mathrm{A}}_{\mathrm{P}}$, for a $\mathrm{\text{photon}}+{\mathrm{E̸}}_T$ sample that contains both PMT spikes and real photons, and a sample of electrons from $W\to e\nu$ events. PMT spikes can be effectively removed by requiring the asymmetry to be less than 0.6.

Figure 8

Plots (a), (b), and (c) show the $t_0$, $z_0$, and their correlation, respectively, for the reconstructed highest $\Sigma p_T$ vertex in $W\to e\nu$ events. The fits in (a) and (b) are both a single Gaussian. The falloff in the (b) at $|z|\simeq 60\mathrm{cm}$ is due to the requirement that all tracks have $|z|<70\mathrm{cm}$. In the search the vertex is required to have $|z|<60\mathrm{cm}$.

Figure 9

The difference in $t$ and $z$ between two arbitrarily selected sets of tracks from the same reconstructed vertex in a $W\to e\nu$ data set with the electron track removed from the vertexing. This is a measure of the vertex resolution. (a) is fit with one Gaussian while (b) is fit with two. Note that the factor of $\sqrt{2}$ is already taken out.

Figure 10

The difference in $t$ (a) and in $z$ (b) between the electron track and the highest $\Sigma p_T$ reconstructed vertex (without the electron track participating in the vertexing) in $W\to e\nu$ events. The distributions are centered at zero and fit with double Gaussians, indicating that there is no bias in the clustering procedure. The secondary Gaussian contains events where the electron does not originate from the highest $\Sigma p_T$ vertex in the event.

Figure 11

The clustering efficiency as a function of the number of tracks using (a) the subset method and (b) the window method, and (c) as a function of the $\Sigma p_T$ of the tracks using the window method. Note that a cluster is required to have at least 4 tracks and the efficiency is 100% for $\Sigma p_T>15\mathrm{GeV}/c$ in this search.

Figure 12

A comparison between MC (solid) and collision data (points) for $t_{\mathrm{corr}}$ for electrons from a $W\to e\nu$ sample. The distributions are well centered around 0 and the resolutions of collision data and MC fit well with a fully corrected RMS of 0.64 ns.

Figure 13

The $t_{\mathrm{corr}}$ distribution for electrons in a sample of $W\to e\nu$ events. In plot (a) the two Gaussians correspond to the cases when the highest-$\Sigma p_T$ vertex is associated to the electron track and when it is not. These cases can be separated by requiring a match between the vertex and the electron track in both space and time (b) and excluding matched events (c).

Figure 14

The mean and RMS of the $t_{\mathrm{corr}}$ distribution for electrons from various subsamples of $W\to e\nu +\mathrm{\text{jets}}$ events where each entry reflects a different combination of the electron $E_T$, jet $E_T$, and ${\mathrm{E̸}}_T$ event requirements. There are slight shifts as the requirements vary. While the mean of the distribution is close to zero, the systematic variation on the mean of the primary Gaussian of the prompt time distribution is conservatively taken to be 0.2 ns in the background estimates.

Figure 15

The mean and RMS of the $t_{\mathrm{corr}}$ distribution for electrons from $W\to e\nu$ events, where the wrong vertex is picked, as a function of $\eta$.

Figure 16

Illustrations of a beam halo event interacting with the detector. In both figures the muon path is indicated with an arrow. (a) A comparison of the time distributions of prompt collision events with beam halo photon candidates for three example towers in the calorimeter shows that the mean time changes as a function of tower $\eta$ and is always less than zero. The $y$-axes are in arbitrary units. (b) An illustration of how the beam halo interacts with the calorimeter. The muon travels through multiple towers in the hadronic calorimeter at high $\eta$ before hitting the electromagnetic calorimeter.

Figure 17

The variables used to separate cosmic and beam halo backgrounds in the $\gamma +{\mathrm{E̸}}_T$ sample without a vertex. Beam halo muons deposit energy in many HAD towers as they interact with the detector at high $|\eta |$ and many EM towers as they traverse the central portion of the calorimeter along the beam halo direction.

Figure 18

The $t_{\mathrm{corr}}$ distributions for the cosmic ray (a) and beam halo (b) backgrounds in the $\gamma +{\mathrm{E̸}}_T$ sample without a collision.

Figure 19

The number of beam halo photon candidates as a function of $\varphi$. Most photons arrive at $\varphi \approx 0$.

Figure 20

The expected 95% C.L. cross section limit as a function of the lower value of the $t_{\mathrm{corr}}$ requirement for a GMSB example point with $m_{{\tilde{\chi }}_1^0}=100\mathrm{GeV}/c^2$ and ${\tau }_{{\tilde{\chi }}_1^0}=5\mathrm{ns}$. The values of the kinematic sample requirements are held at their optimized values.

Figure 21

The $t_{\mathrm{corr}}$ distribution including the control and signal regions, after all but the timing cut for all backgrounds, for the expected signal and the observed data. A total of 508 events is observed in the full time window. The two observed events in the signal region, $2.0\le t_{\mathrm{corr}}\le 10\mathrm{ns}$, are in the first signal time bin (marked with a star). This is consistent with the background expectation of $1.3\pm 0.7$ events.

Figure 22

The predicted and observed photon $E_T$, jet $E_T$, ${\mathrm{E̸}}_T$, and $\Delta \varphi ({\mathrm{E̸}}_T,\mathrm{\text{jet}})$ distributions for the signal region after the final event selection requirements. The GMSB distributions are for $m_{{\tilde{\chi }}_1^0}=100\mathrm{GeV}/c^2$ and ${\tau }_{{\tilde{\chi }}_1^0}=5\mathrm{ns}$. There is no evidence for new physics.

Figure 23

The expected and observed cross section limits as a function of the ${\tilde{\chi }}_1^0$ lifetime at a mass of $100\mathrm{GeV}/c^2$ (a) and as a function of the ${\tilde{\chi }}_1^0$ mass at a lifetime of 5 ns (b). Shaded green (darker shading) is the 6.4% uncertainty-band for the production cross section. The yellow shaded region (lighter shading) is the variation in the expected limit due to the statistical variation on the number of background events in the signal region ($\sim 30\%$).

Figure 24

The contours of constant 95% C.L. cross section upper limit for the observed number of events in the detector.

Figure 25

The expected and observed 95% C.L. exclusion region along with the most stringent published LEP limits from ALEPH [10]. The highest mass reach of $108\mathrm{GeV}/c^2$ (expected) and $101\mathrm{GeV}/c^2$ (observed) is achieved at a lifetime of 5 ns.

Figure 26

The expected 95% C.L. exclusion region after a scaling of the background prediction and the uncertainties for a luminosity of $2{\mathrm{fb}}^{-1}$ and $10{\mathrm{fb}}^{-1}$, respectively. The shaded band shows the parameter space where $1\le m_{\tilde{G}}\le 1.5\mathrm{keV}/c^2$.