<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">%written by R. Raja Modified 11-Mar-99 to accomodate referee
%edited by I. Stumer (9/98)
%replace intersection point (region) ----&gt; 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}
</pre></body></html>