Prospects of Searches for Neutral, Long-Lived Particles using which Decay to Photons using timing at CDF

We present the prospects of searches for neutral, long-lived particles which decay to photons using their time of arrival measured with a newly installed timing system on the electromagnetic calorimeter (EMTiming) of the Collider Detector at Fermilab (CDF). A Monte Carlo simulation shows that EMTiming can provide separation between decay photons from neutral, long-lived particles and prompt photons from standard model backgrounds. Using gauge mediated supersymmetry breaking (GMSB) $\tilde{\chi}_{1}^{0}\rightarrow\gamma\tilde{G}$ models we estimate a quasi-model-independent sensitivity using only direct neutralino pair production, and also estimate the expected 95\%~confidence level exclusion regions for all superpartner production as a function of the neutralino mass and lifetime. We find that a combination of single photon and diphoton analyses should allow the Tevatron in run~II to easily extend the exclusion regions from ALEPH at LEP~II at high neutralino masses and lifetimes, and cover parts of the theoretically favored $m_{\tilde{G}}< \mathrm{few}$~$\mathrm{keV}/c^2$ GMSB parameter space.

Time-ordered sequence of events:

The plots are:

Figure 1: A schematic diagram of a long-lived neutralino decaying to a photon and a gravitino in the CDF detector. The neutralino emanates from the collision at $(\vec{x}_{i},t_{i})$ and after a time $\tau$ it decays. While the gravitino leaves the detector the photon travels to the detector wall and deposits energy in the EM calorimeter where its final location $\vec{x}_{f}$ and arrival time $t_{f}$ can be measured. A prompt photon would travel directly from $\vec{x}_{i}$ to $\vec{x}_{f}$. The difference between the actual time the neutralino/photon needs, $\Delta t=t_{f}-t_{i}$, and the time a prompt photon would need, $\frac{|\vec{x}_{f}-\vec{x}_{i}|}{c}$, is defined as $\Delta s$. The SM typically produces prompt photons which have $\Delta s$~=~0~ns, whereas photons from delayed decays from SUSY have $\Delta s>0$~ns, assuming a perfect measurement.

Figure 2:

The efficiency for events to pass the various $\Delta s$ cuts as a function of the neutralino lifetime at $m_{\tilde{\chi}}$=~110~\munit. The results are separated into single and diphoton events for which the neutralino decays in the detector, and for $\Delta s \ge 5.0$~ns. For any $\Delta s$ restriction above 0 the efficiency approaches zero at $\tau_{\tilde{\chi}}$~=~0~ns, since all photons ideally have $\Delta s=0$~ns. For high $\tau$ neutralinos have a higher probability to leave the detector. For any $\Delta s$ requirement one can find an efficiency maximum at about 5-10~ns. Single photon events have higher efficiency towards higher $\Delta s$ requirements and/or higher lifetimes, due to increasing probability for a photon to leave the detector. Thus, we expect a $\gamma\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$ \textcolor{black}{to provide the best sensitivity for very low lifetimes, and a $\gamma$~+~}$E_{T}\!\!\!\!\!\!\!/\,\,\,$ \textcolor{black}{analysis to be best for higher lifetimes.

Figure 3:

The efficiency as a function of the neutralino mass at a lifetime $\tau_{\tilde{\chi}}$\textcolor{black}{~=~10~ns for single and diphoton events for which the neutralino decays in the detector and for $\Delta s$ $\ge 5.0$~ns. The ratio of single to diphoton events is roughly independent of the neutralino mass and constant as a function of $\Delta s$. One can see a soft {}``dip'' in the efficiency curve in a mass range of 40~}\munit$-$80~\munit. This effect is production dependent and due to a change in the $p_{T}$ distribution of the neutralinos (for more details see Appendix~\ref{sec:neutralinoboost}).

Figure 4:

The distribution of $\Delta s_{12}$ and $E_{T}\!\!\!\!\!\!\!/\,\,\,$ for signal and background in the $\gamma\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$ analysis (not to scale). The distributions are (a) from direct neutralino pair production, with $m_{\tilde{\chi}}=70$~\munit\ and $\tau_{\tilde{\chi}}=10$~ns, (b) QCD background and (c) direct neutralino pair production, with $m_{\tilde{\chi}}=110$~\munit\ and $\tau_{\tilde{\chi}}=10$~ns. The solid and dashed lines show the cuts with and without EMTiming system usage respectively that give the smallest 95\%~C.L. cross section limit. In (a) there is more additional acceptance from allowing large $\Delta s_{12}$ events due to the lower mass, compared to (c), which is why the sensitivity is significantly improved with timing in this mass region (see Fig.~\ref{cap:xsectionsN1-gammagamma}).

Figure 5:

The distribution of $\Delta s$ vs. $E_{T}\!\!\!\!\!\!\!/\,\,\,$ for signal and background in the $\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$~+~0~jets analysis (not to scale). The distributions are (a) from direct neutralino pair production, with $m_{\tilde{\chi}}=110$~\munit\ and $\tau_{\tilde{\chi}}=10$~ns, and (b) from SM background. The solid and dashed lines show the cuts with and without timing system usage respectively that give the smallest 95\%~C.L. cross section limit.

Figure 6: The expected 95\%~C.L. cross sections limits on direct neutralino pair production in the $\gamma\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$ analysis. The top plot shows the limits as a function of $\tau_{\tilde{\chi}}$ for $m_{\tilde{\chi}}$~=~110~\munit. The bottom plot shows the limits as a function of $m_{\tilde{\chi}}$ for $\tau_{\tilde{\chi}}$~=~20~ns for both with and without a timing system for comparison. The luminosity is $2\ \mathrm{fb}^{-1}$. As expected at $\tau_{\tilde{\chi}}=0$~ns the cross sections merge as the timing system has no effect. For higher $\tau_{\tilde{\chi}}$ the sensitivity goes down as more photons leave the detector, but the difference of the limits increases as $\Delta s$ gets larger for the signal and timing becomes more helpful. The limits get better as the mass goes up since more of the events pass the kinematic requirements, however the timing system only provides real additional sensitivity at the lowest masses where the neutralino momentum distribution is softer.

Figure 7: The expected 95\% C.L. cross section limits on direct neutralino pair production in the $\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$~+~0~jets analysis. The top plot shows the limits as a function of $\tau_{\tilde{\chi}}$ for $m_{\tilde{\chi}}$~=~110~\munit. The bottom plot shows the limits as a function of $m_{\tilde{\chi}}$ for $\tau_{\tilde{\chi}}$~=~20~ns for both with and without a timing system. The luminosity is $2\ \mathrm{fb}^{-1}$. As in Fig.~\ref{cap:xsectionsN1-gammagamma}, for higher $\tau_{\tilde{\chi}}$ the sensitivity goes down as more photons leave the detector, but the difference of the limits increases as $\Delta s$ gets larger for the signal and timing becomes more helpful. The curves do not merge at 0~ns lifetime since cosmic ray backgrounds always contribute at high $\Delta s$ and the timing system always has some effect on the cross section limit. The rise from 10~ns to 0~ns originates in an increasing probability towards zero lifetime for two photons to remain in the detector, yielding lower efficiency for a single photon analysis. The limits get better as the mass goes up since more of the events pass the kinematic requirements.

Figure 8: This plot combines the $\gamma\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$ and $\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$~+~0~jets analysis results for neutralino pair production for \textcolor{black}{$2\ \mathrm{fb}^{-1}$} of data and is \textcolor{black}{a 2-dimensional visualization of Figs.~\ref{cap:xsectionsN1-gammagamma} and \ref{cap:xsectionsN1-gamma}.} The contours of constant cross section limit are shown as the solid lines, and the separation line between the regions where the two different analyses provide the best sensitivity is given by the dotted line; \textcolor{black}{the $\gamma$~+}~$E_{T}\!\!\!\!\!\!\!/\,\,\,$~+~0~jets analysis shows better cross section limits than a $\gamma\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$ analysis \textcolor{black}{in the mass and lifetime range above the dashed line.} The shaded regions delineate the contours of the ratio of \textcolor{black}{the 95\%~C.L. cross section limits between with and without timing information. The ratio is greatest for a low neutralino mass and a lifetime of 10-20~ns, and lowest for a high mass and low lifetime.

Figure 9:

The distribution of $\Delta s$ vs. $E_{T}\!\!\!\!\!\!\!/\,\,\,$ for signal and background in the $\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$~+~jets analysis (not to scale). The distributions are (a) from full GMSB production, with $m_{\tilde{\chi}}=110$~\munit\ and $\tau_{\tilde{\chi}}=10$~ns, (b) from SM background and (c) from both as a function of $\Delta s$ after the baseline $E_{T}\!\!\!\!\!\!\!/\,\,\,$ cut of 25~GeV. The solid and dashed lines show the cuts with and without timing system usage respectively that give the smallest 95\%~C.L. cross section limit.

Figure 10: The expected 95\%~C.L. cross section limits on full GMSB production in a $\gamma\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$ analysis. The top plot shows the limits as a function of $\tau_{\tilde{\chi}}$ for $m_{\tilde{\chi}}$~=~110~\munit. The bottom plot shows the limits as a function of $m_{\tilde{\chi}}$ for $\tau_{\tilde{\chi}}$~=~20~ns for both with and without a timing system. The luminosity is $2\ \mathrm{fb}^{-1}$. The results are similar to those in Fig.~\ref{cap:xsectionsN1-gammagamma}.

Figure 11: The expected 95\%~C.L. cross section limits on full GMSB production in a $\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$~+~jets analysis. The top plot shows the limits as a function of $\tau_{\tilde{\chi}}$ for $m_{\tilde{\chi}}$~=~110~\munit\ and the bottom plot as a function of $m_{\tilde{\chi}}$ for $\tau_{\tilde{\chi}}$~=~20~ns for both with and without timing. The luminosity is $2\ \mathrm{fb}^{-1}$. For all but the lowest lifetimes the timing information significantly improves the cross section limits. Note that here the cross sections merge at zero lifetime since we have neglected cosmics in this analysis following} \cite{key-8, key-34}.

Figure 12: This plot combines the $\gamma\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$ and \textcolor{black}{$\gamma$~+}~$E_{T}\!\!\!\!\!\!\!/\,\,\,$\textcolor{black}{~+~jets analysis results for a full GMSB model simulation} for \textcolor{black}{$2\ \mathrm{fb}^{-1}$} and is \textcolor{black}{a 2-dimensional visualization of Figs. \ref{cap:xsectionsgmsb-gammagamma} and \ref{cap:xsections-gmsb-gammaMET}.} The contours of constant cross section limit are shown as the solid lines. The separation line between the regions where the two different analyses provide the best sensitivity is given by the dotted line. \textcolor{black}{The $\gamma$~+}~$E_{T}\!\!\!\!\!\!\!/\,\,\,$ \textcolor{black}{+~jets analysis shows better cross section limits than} a $\gamma\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$ analysis \textcolor{black}{in the mass and lifetime range above the dashed line.} The shaded regions delineate the contours of constant ratio of \textcolor{black}{the 95\% C.L.- cross-section limits between with and without timing information. The EMTiming system has its most effective region at high lifetime while the kinematics give the best separation at high masses.

Figure 13: The expected 95\%~C.L. exclusion regions as a function of neutralino lifetime and mass for full GMSB production at $2\ \mathrm{fb}^{-1}$ luminosity for the $\gamma\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$ and the $\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$~+~jets analysis separately. The region below the dashed line is the expected exclusion region from kinematics alone, i.e., where no timing information is used.

Figure 14: The expected 95\%~C.L. exclusion regions as a function of neutralino lifetime and mass for full GMSB production from the overlap of both the $\gamma\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$ and the $\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$~+~jets analysis for $1\ \mathrm{fb}^{-1}$ and $2\ \mathrm{fb}^{-1}$ luminosity. The result is compared to the direct and indirect search limits from ALEPH at LEP~II~\cite{key-3, key-15} and the $m_{\tilde{G}}=1$~$\mathrm{keV}/c^2$ line as an indicator for the theoretically favored region from cosmological considerations~\cite{key-27}. The Tevatron in run~II should be able to significantly extend the LEP~II limits and provide sensitivity in the favored region for all masses below about 150~\munit\ for the considered GMSB model line.

Figure 15: The expected 95\%~C.L. cross section limit for full GMSB production at \textcolor{black}{$m_{\tilde{\chi}}$~=~110~}\munit\ \textcolor{black}{ and} $\tau_{\tilde{\chi}}$\textcolor{black}{~=~40~ns} as a function of the fraction of the background from cosmic ray sources for a $\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$~+~jets analysis. The cross section limits rise approximately linearly as a function of the fraction and 10\% provides an outer bound on this fraction. A more reasonable fraction is probably 1-5\% which roughly doubles the cross section limit value.

Figure 16: The 95\%~C.L. cross section limits vs. timing system resolution for} \textcolor{red}{}\textcolor{black}{$m_{\tilde{\chi}}$~=~110~}\munit\ \textcolor{black}{and} $\tau_{\tilde{\chi}}$\textcolor{black}{~=~40~ns at $2\ \mathrm{fb}^{-1}$ luminosity in the $\gamma$~+~}$E_{T}\!\!\!\!\!\!\!/\,\,\,$~+~jets \textcolor{black}{analysis. As expected, for large resolution the cross section with EMTiming approaches the cross section without EMTiming. A system resolution of 1.0~ns improves the cross section limit by a factor of about 20, but this varies as a function of mass, lifetime as well as on the analysis. It is reasonable to assume that the resolution will be within 20\% of the nominal 1.0~ns presented here.

Figure 17: The $\Delta s$ distribution as a function of the event lifetime in the neutralino lab frame for a toy Monte Carlo simulation. In general, $\Delta s$ is proportional to $\tau_{\mathrm{evt,L}}$. At large $\tau_{\mathrm{evt,L}}$ most of the neutralinos leave the detector and are not shown here. The spread perpendicular to $\Delta s\sim\tau_{\mathrm{evt,L}}$ originates in variations of the neutralino momentum as well as in variations in the travel time of the photon due to detector geometry. Essentially, photons with large $\Delta s$ require a neutralino with a long lifetime.

Figure 18: The $\Delta s$ distribution as a function of the boost of the neutralino for a lifetime {}``slice'' of 8.5~ns~$\leq\tau_{\mathrm{evt,L}}\leq$~9.0~ns. In the region 1.0~<~boost~<~1.5 neutralinos remain in the detector and can produce a large $\Delta s$. Neutralinos with high boost, that is high $p_{T}$, are more likely to leave the detector or, if they don't, produce low $\Delta s$. Thus, events with the largest $\Delta s$ are produced by neutralinos with large lifetimes and low boosts.

Figure 19: The efficiency as a function of the event lifetime, $\tau_{\mathrm{evt}}$, of the neutralino. We distinguish between events in which the neutralino remains in the detector, and events with photons of medium and large $\Delta s$. The efficiency is 100\% for prompt} decays (a small difference shows up as a binning effect) for a photon to be identified, but \textcolor{black}{only a very small efficiency for events with low $\tau_{\mathrm{evt}}$ at large $\Delta s$. At large $\tau_{\mathrm{evt}}$ only few events stay in the detector, however if a neutralino is long-lived and stays in the detector, it has large $\Delta s$. We note that the true efficiency shape depends on the production mechanism i.e. the neutralino $p_{T}$ distribution.

Figure 20: The neutralino $\frac{p_{T}}{m}$ distribution for masses 40~$\mathrm{GeV}/c^2$, 80~\munit\ and 140~\munit\ for neutralino pair production. For a mass of 80~\munit\ the maximum moves towards higher $\frac{p_{T}}{m}$ and the distribution broadens compared to 40~\munit, yielding a greater fraction of high $p_{T}$ neutralinos which either leave the detector or produce low $\Delta s$ photons, and thus a loss in efficiency. For higher masses the maximum remains constant and the distribution narrows so the efficiency rises.

Figure 21: The relationship between $\Delta s$ and the impact parameter, $b$, of a photon from \textcolor{black}{\small $\tilde{\chi}_{1}^{0}\rightarrow\gamma\tilde{G}$} decays in a GMSB model with $m_{\tilde{\chi}}=110$~\munit\ and $\tau_{\tilde{\chi}}=10$~ns. The solid lines show the selection requirements that give us the smallest 95\%~C.L. cross section limit in a $\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$~+~jets analysis. The photons without impact parameter measurement are assigned a $b<0$~m. Due to the low cut on the impact parameter there are about as many events in the low-$\Delta s$ high-$b$ as in the high-$\Delta s$ low-$b$ region. This leads to a similar efficiency for a pure $b$-cut compared to a pure $\Delta s$ cut. The combined restriction leads to improved signal sensitivity.

Figure 22: A comparison of the expected exclusion regions as a function of neutralino mass and lifetime for the GMSB model at $2\ \mathrm{fb}^{-1}$ luminosity for a $\gamma$~+~$E_{T}\!\!\!\!\!\!\!/\,\,\,$~+~jets analysis with photon pointing and timing. While timing generally yields a higher sensitivity than pointing, both methods would, if available and combined, extend the exclusion region further than either of them alone.

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Last updated Mar 09, 2005 by Peter Wagner