%written by R. Raja Modified 11-Mar-99 to accomodate referee %edited by I. Stumer (9/98) %replace intersection point (region) ----> interaction point (region) %edits and some rewritting by RFG 10/22/98 \section{DETECTOR SCENARIOS } \label{det} The background consists of neutral and charged particles. For neutrons, the longitudinal and radial fluences were found to be comparable. The photons (average energy about 1~MeV) show a clear radial source. The charged particles and the photons do not all point back to the interaction point, but to the general vicinity of the IP, namely to the region where the 20~degree tungsten shield becomes thinner. The flux of secondary muons (Bethe-Heitler pairs) is mainly longitudinal. We would expect this background to pepper the tracking volume with random hits and produce significant energy pedestals in the calorimeter cells. These effects are considered in more detail in the following sections. In general, in designing a strawman detector that must operate in a large background flux we will want to employ as many detector channels as is practical. A strawman muon collider detector design with a few times $10^6$ non-pixel channels would seem reasonable \cite{stevebackdet}. Over the last few years, development of pixel detectors has resulted in a quantum jump in the number of electronic channels. For example, the SLD vertex detector \cite{sld} contains $300\times 10^6$~pixels, and similar numbers of pixels are planned for the LHC vertex detectors. Hence, a strawman muon collider vertex detector employing $10^8-10^9$ pixels would seem reasonable. \subsection{Silicon vertex detector schemes} From table~\ref{neutron}, it can be seen that the radiation damage to silicon detectors is acceptable in terms of the number of hits per year and the resultant lifetime of the detector. This prompts \cite{stevebackdet} us to consider the following options for silicon vertex detector design for the muon collider: \begin{figure*}[htb!] \leavevmode \centering \epsfysize=5cm \epsfbox{rehak1.eps} \caption{Silicon drift vertex detector.} \label{fig:silicon_drift} \end{figure*} \begin{figure*}[htb!] \leavevmode \centering \epsfysize=8cm \epsfbox{columnar_pixel.eps} \caption[Columnar pixel geometry]{Columnar pixel geometry. Courtesy of A.~Sill.} \label{fig:columnar_pixels} \end{figure*} \begin{figure*}[bth!] \leavevmode \centering \epsfxsize=7.5cm \epsfbox{micro_telescope.ps} \caption[Pixel micro-telescope geometry, showing trajectories of 0.2~GeV/$c,$ 0.5~GeV/$c,$ and 1~GeV/$c$ tracks]{Pixel micro-telescope geometry~\cite{micro_telescope}, showing trajectories of 0.2~GeV/$c,$ 0.5~GeV/$c,$ and 1~GeV/$c$ tracks coming from the IP and bending in a 4~T field.} \label{fig:micro_telescope} \end{figure*} \begin{itemize} \item Silicon drift detector. The idea, which is described in the muon collider feasibility study \cite{ref6a,Snowmass96}, is to exploit the time gap between bunch crossings by using the silicon drift detector technology \cite{silicon_drift} (see Fig.~\ref{fig:silicon_drift}). Using $50 \times 300$~$\mu$m$^2$ detectors it should be possible to obtain a resolution of a few microns in the drift direction. This would facilitate a very precise vertex detector, although questions of radiation hardness remain to be resolved for this option. \item Columnar pixels \cite{parker}. The idea is to exploit the very well localized primary vertex position by using long thin tracking pixels that point at the IP and therefore record large ionization signals only for tracks coming from the IP (Fig.~\ref{fig:columnar_pixels}). For example, one can construct $50 \times 50$~$\mu$m$^2$ pixels that are 300~$\mu$m deep. The pixels are produced using controlled feed-through-drilling technology to create a lattice of anodes and cathodes that extend through the 300~$\mu$m thick wafer. \item Pixel micro-telescopes \cite{micro_telescope}. The idea is to replace a single pixel layer with two layers separated by a small distance, and read them out by taking the AND between appropriate pairs. The distance between the layers is optimized so that soft MeV tracks (which are associated with almost 80\% of the predicted background hits) produced in one layer curl up in the magnetic field before reaching the second layer. Thus, the pixel micro-telescope is blind to the soft background hits and also blind to tracks that do not come from the IP. In the example shown in Fig.~\ref{fig:micro_telescope} the top measurement layer has a finer granularity than the bottom confirmation layer. The corresponding rows in the two pixel layers can be read out with different clock speeds to maintain the correct correspondence at the input into the AND gate that registers valid hits in the telescope. If the readout rows are the ones parallel to the beam direction, then variable clock speeds can be used to maintain the correct accepted direction with respect to the IP. \end{itemize} \noindent The challenge of a high background environment is clearly fruitful ground for new ideas. The above considerations suggest that, provided silicon detectors can be used in the inner tracking volume, it should be possible to construct a vertex detector able to tag secondary vertices from short lived particles at a muon collider. Detailed simulations are currently underway to establish this more concretely. \begin{figure*}[hbt!] \leavevmode \centering \epsfysize=10cm \epsfbox{tpc.eps} \caption{Outer tracker TPC.} \label{fig:tpc} \end{figure*} % \subsection{Outer tracking schemes} The predicted background fluxes for a Higgs factory detector at a radius of 50~cm are 200~photons/cm$^2,$ 350~neutrons/cm$^2,$ and 0.08~charged tracks per cm$^2$ per crossing. The neutron flux is therefore about the same as the flux in the inner tracking volume, whereas the photon and charged particle fluxes are significantly less than those predicted at smaller radii. There are two alternative tracking strategies under consideration: \begin{itemize} \item Low field, large tracking volume drift chamber option. This option, which is described in the muon collider book \cite{snowmass9.4.2}, uses a TPC to exploit the 20~$\mu$s time between bunch crossings. This option is viable for the very high energy muon collider ($1.5\times 1.5$~TeV). The large neutron flux necessitates choosing a gas that does not contain hydrogen. A mixture of 90\%~neon plus 10\%~CF$_4$ gives a drift velocity of 9.4~cm/$\mu$s, which is close to that required to match the bunch crossing time. High-$p_T$ tracks from the IP embedded in the predicted background flux have been simulated for the TPC shown in Fig.~\ref{fig:tpc}. The simulation includes ionization, drift and diffusion of the electrons in the gas, multiplication, and other details of the detection process. The majority of the background hits arises from low energy Compton recoils yielding very low energy electrons that have a radius of curvature of less than 1~mm in the 2~T field. Their projection on the readout plane covers not more than one readout pitch (0.3 $\times$ 0.4~cm$^2$). These background electrons, together with the nuclear recoils from neutron scatters, yield large pulses that can be removed by cutting on the maximum acceptable pulse height. The simulation predicts that with an average background flux of 100~photons/cm$^2$, reasonable pulse height cuts remove only 1\% of the effective TPC volume, and yield tracks of high quality. However, it was realized that positive ion build-up may be a problem with the design shown in Fig.~\ref{fig:tpc}. If this problem can be overcome, the design shown in the figure yields a simulated momentum resolution of about 1.2\% for tracks with p$_T = 50$~GeV/$c.$ \item High field, compact silicon tracker option. An alternative strategy is to make a compact tracker by using silicon in a high field (for example, 4~T). \begin{figure*}[htb!] \leavevmode \centering \epsfysize=3cm \epsfbox{alansill_tracker.eps} \caption{Compact tracker geometry in a 4~T field.} \label{fig:alans_tracker} \end{figure*} As an example, consider the geometry shown in Fig.~\ref{fig:alans_tracker} in which a 4-layer pixel vertex detector is surrounded by a 4-layer cylindrical stereo silicon microstrip detector. We take the inner layer of the vertex detector to consist of a cylinder of $50 \times 300$~$\mu$m$^2$ pixels, and the outer 3 vertex layers to consist of spherical shells of $50 \times 50$~$\mu$m$^2$ columnar pixels or pixel micro-telescopes. The resolution of the microstrip detector is chosen to match that of the pixel detector. The system is assumed to correspond to 15\% of a radiation length at $90^\circ$. Using a parametric calculation of the momentum resolution, including multiple scattering, we obtain $\sigma_p/p^2 = 10^{-4}~(10^{-2})~$(GeV/$c)^{-1}$ for p = 100~GeV/$c$~(1~GeV/$c).$ \end{itemize} \noindent Both the low field and high field tracking solutions look interesting and should be pursued with more complete simulations. \subsection{Electromagnetic calorimeter schemes} Background particles entering the electromagnetic calorimeter are expected to give rise to significant energy pedestals in the calorimeter cells. Consider a 4~m long calorimeter that is 25~radiation lengths deep, has an inner radius of 120~cm, and is constructed from $2 \times 2$~cm$^2$ cells. This gives a total of $10^5$ electromagnetic calorimeter towers. The GEANT background calculation predicts that each cell sees on average $n_{\gamma} = 4$ background photons per crossing with a mean energy $E_{\gamma} = 1-2$~MeV. If an electromagnetic shower occupies 9 cells, then the mean background pedestal will be about 70~MeV. This pedestal can be subtracted from the measured energies. The precision of the resulting electron and photon energy measurements will depend on the fluctuations in the mean background energy per cell. For an electromagnetic shower occupying 9 cells, the fluctuations in the pedestals are predicted to be about 10~MeV. This takes into account the fluctuations in the number and the energies of the background photons. \subsection{Hadronic calorimeter schemes} None of the energy generated by background photons in the electromagnetic calorimeter is expected to penetrate into the hadronic calorimeter. GEANT calculations show that the total kinetic energy deposited by neutrons in the calorimeter is of the order of 140~TeV with an average energy of 30~MeV per neutron per crossing for the 4~TeV CoM energy case. In order to estimate what fraction of the kinetic energy of the neutrons will be visible, we should consider the materials involved. For this simulation we have presumed an equal mix by volume of liquid argon (as active medium) and copper (as absorber). At 30~MeV we expect only a small fraction of the neutrons to knock off protons and only about 10\% of the proton ionization to be visible in the liquid. Presuming a hadronic calorimeter with $10^4$ towers, with the material composition described above, the average energy read in the liquid argon will be of the order of 10~MeV per tower with a fluctuation of 5~MeV. In summary, a $50 \times 50$~GeV collider with $4\times 10^{12}$ muons per bunch, the photons and neutrons are expected to generate pedestals of 800 and 100~GeV respectively. The estimates for pedestal fluctuations are at or below the level of the expected electronic noise. Therefore we believe that the subtraction of these pedestals would present little problem both for the electromagnetic and the hadronic calorimeters. The presence of the high neutron background should be taken into account in choosing materials for calorimetry. Liquid argon seems a natural choice for the electromagnetic calorimeter. The energy deposited by the Bethe-Heitler muons in the calorimeter is given in table~\ref{tab-bheitler} as a function of the center of mass energy of the collider. For low center of mass energies, such as the Higgs factory, the Bethe-Heitler muons are not a problem, since there are fewer of them and they leave less energy by catastrophic bremsstrahlung in the calorimeter. For the higher energy option (4~TeV in the CoM or higher), one should explore ways to correct for the energy deposition in the calorimeter, such as pattern recognition of the muon tracks or by using timing information. \subsection{Muon detector schemes} The predicted background flux is expected to be relatively modest beyond a radius of 3~m in the vicinity of the muon detector. Several possible technologies for muon detectors at a muon collider were discussed during Snowmass\cite{Snowmass96}: \begin{itemize} \item Cathode strip chambers. The idea, which is described in the muon collider book \cite{snowmass9.4.2}, is to use MWPCs with segmented cathodes and a short (35~ns) drift time to provide prompt signals for triggering. The precision of the coordinate measurements would be expected to be of order 50~$\mu$m $\times$ a few mm. \item Threshold Cherenkov counter. The idea is to use a gas Cherenkov radiator to exploit the directionality of Cherenkov radiation in order to select high-$p_T$ muons coming from the IP. The device would also give excellent timing resolution (of order 2~ns). \item Long drift jet chamber with pad readout \cite{newatac} (Fig.~\ref{fig:muzaffer}). Drift time provides the z~coordinate, and pad readout provides the r-$\phi$~coordinates. Directionality at the trigger level is provided by the pattern of pad hits within a limited time window. The drift field is provided by cathode strips on grooved G-10 plates. Using 90\% argon plus 10\% CF$_4$ and a maximum drift distance of 50~cm, the maximum drift time is 5~$\mu$s. \end{itemize} \noindent \begin{figure*}[htb!] \leavevmode \centering \epsfxsize=9.5cm \epsfysize=8.0cm \epsfbox{muzaffer.ps} \caption{Long drift jet chamber with pad readout for muon detection at a muon collider. } \label{fig:muzaffer} \end{figure*} At high energy in the CoM, the channel $\mu^+\mu^- \rightarrow \mu^+\mu^- + \textrm{Higgs boson}$ becomes particularly attractive to study using the muon collider, if the forward going muons from the interaction can be detected \cite{newraja}. The method provides a capability to search for any missing neutral state such as the Higgs boson via the missing mass technique. We are investigating methods to improve our forward muon detection capability. %%%%% References % %\begin{thebibliography}{2} %\bibitem{sld} %The SLD CCD vertex detector and its upgrade, The SLD collaboration, %Nuovo Cim. 109A 1027(1996). % %{\sl $\mu^+\mu^-$ Collider: A Feasibility Study}, %The $\mu^+\mu^-$ Collider Collaboration, %BNL-52503; Fermilab-Conf.-96/092; LBNL-38946 (1996). % %\bibitem{silicon_drift} %E. Gatti and P. Rehak, Nucl. Instr. and Meth. 225, 608(1984). % %\bibitem{parker} %Sherwood I. Parker, Christopher J. Kenney, Julie Segal, %{\sl 3D: A New Architecture for Solid State Radiation Detectors.} %UH-511-839-96, 24pp. Submitted to Nucl.Instrum. Methods. % %\bibitem{micro_telescope} %S. Geer and J. Chapman, %{\sl The Pixel Micro-Telescope}, %Contribution to these proceedings. %\end{thebibliography} %\end{document}