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\begin{flushright}
{\large \DZ note 3621\\
 15 January 1999}
\end{flushright}

\begin{center}
\Huge
A Silicon Track Trigger for the \DZ Experiment in Run~II -- \\
Further Physics Benefit Studies\\
\vspace{3cm}
\Large
Addendum to the proposal (P908)\\
submitted to the PAC in September 1998\\
\vspace{5cm}
The \DZ Collaboration\\
15 January 1999\\
\end{center}
\vspace{0.15cm}
\clearpage

\normalsize
\tableofcontents
\clearpage

\section {Introduction}

Having a good trigger system is extremely important for a hadron collider experiment because
the event rate from collisions is many orders of magnitude higher than the rate at which events 
can be recorded.
After the upgrade of the Fermilab Tevatron collider, the collision rate in run II seen by the \DZ detector 
will be effectively equal to the beam crossing rate, i.e. several MHz. 
This is about a factor of $10^5$  higher than the tape writing speed which will be less than 50 Hz. 
The role of the trigger is to reject as much of the  overwhelming
``minimum bias'' background of the ``typical'' events as possible while maintaining high efficiency
for the ``interesting events'' that one wants to record for off-line analysis.   
Even after the reduction of unwanted events by the trigger, the recorded event sample is still 
dominated by background.
For example, the total cross section for \tt\ production is about 6 pb, to be compared with the total 
\pp\ interaction cross section of about 80 mb, so even after a reduction of the 
background by a factor of $10^5$ 
the fraction of \tt\ events in the recorded event sample is at best 1 in $10^5$.

In the upgraded \DZ detector, the rejection of background events is done by a 
three-stage trigger system, denoted
level 1 (L1), level 2 (L2) and level 3 (L3). The L1 trigger has the task of reducing the 
event rate to 10 kHz, which is the maximum
rate at which the information from  the  SMT (the silicon microstrip detector) can be digitized. 
The subsequent trigger 
levels then
need to reduce the rate so that it fits into the bandwidth of the next stage: L2 is designed to 
be able to  receive 10 kHz and has
to reduce this input rate to an output (accept) rate of at most 1 kHz, which is the maximum rate 
that L3 can handle. The final
triggering stage, L3, then has to match its output (accept) rate to the rate 
at which events can be recorded (20Hz).
If the input rate offered to one of the triggering stages is close to the maximum admissible one, 
deadtime losses become
important. Such deadtime losses effectively reduce the data taking efficiency 
indiscriminately for background and signal events.
In  practice we try to avoid running under such conditions because the deadtime 
losses can depend on luminosity, beam conditions
(``cleanliness'' of the beam), and are difficult to  measure and model. 
If the trigger rates become too high one chooses to prescale some of the 
triggers which has the  same effect on the efficiency (i.
e. loss of both background and signal events), but is better under control. 
For signals whose cross section is very small, it is
clear that prescaling should be avoided at all costs. This can only be done if 
the trigger system has access to sufficiently many
powerful tools which allow selective rejection of the unwanted background.

In our proposal to the PAC \cite{pac1}  we showed that the Silicon Track Trigger 
(STT) provides powerful tools for rate control by
background rejection: due to its ability for $b$ - tagging at L2,
it allows trigger rate reductions by substantial factors (two
and higher) with negligible,  or  very small, loss in efficiency for  a wide range  
of  channels with $b$ quarks in the final
state,  e.g. top production (both 
\tt\ and single top), Higgs production with decay into $b \bar b$, 
as well as for $b$ - physics studies.
Furthermore we argued that due to the better momentum resolution, 
trigger thresholds in $p_t$ would be sharpened, thus leading to a
reduction in trigger rate.
In the  present document we elaborate on some of these issues and 
 respond to the request of the PAC for a more
quantitative assessment of the ultimate physics benefit of the STT in
terms of measurements and discoveries.

\section {Search for the Higgs Boson}

\subsection{Higgs discovery prospects at the Tevatron}
The most promising process in which to observe Higgs boson production at the Tevatron is 
associated production with vector bosons. In the recently held Higgs -- SUSY workshop 
at Fermilab \cite{hswkshop},
the following conclusions were reached about the prospects of finding the SM Higgs 
at the upgraded Tevatron:\cite{conway}
\begin{itemize}
\item there is no single golden discovery channel; combining all channels, 
and both experiments (CDF and \DZ), is crucial;
\item both experiments need to {\bf optimize  trigger efficiency, $m_{b \bar b}$ resolution, 
$b$ tagging efficiency.}
\item implicitly, all studies assume that both experiments have $b$ - tagging at the trigger level.
\end{itemize}
Under these conditions:
\begin{itemize}
\item if there is no SM Higgs Boson, CDF and \DZ can exclude it 
at 95\% CL up to 120 GeV mass in Run II, and with 10 fb$^{-1}$
can extend exclusion up to 190 GeV
\item if there is a SM Higgs Boson, with 30 fb$^{-1}$ it can be 
discovered at the 3 to 5 $\sigma $ level, 
 up to 190 GeV mass.

\end{itemize}
Sensitivities for some of the final states are given in 
Table \ref{tab:Hsensit}\cite{conway, jesik}.

\begin{table}[h]
\begin{center}                                                          
\caption{Higgs Boson production at the Tevatron: expected number of signal ($S$) 
and background ($B$) events and 
sensitivity for 1 fb$^{-1}$ of data;
assumptions are: 
%  CDF and \DZ combined data (Gaussian approximation in combination),  
improved (by 30\%) $m_{\bbbar}$ resolution and run II acceptance.
Most of the numbers are from John Conway's summary talk\cite{conway}; the row
``alternate'' is from a \DZ study\cite{jesik}.}
\label{tab:Hsensit}
\vspace{2mm}
\begin{tabular}{|c|c||c|c|c|c|c|} \hline
 & & \multicolumn{5}{c|}{Higgs Mass (GeV)}\\
    Channel       & quantity&  90 & 100 & 110 & 120 & 130 \\ \hline
                  &  $S$ & 2.5 & 2.2 & 1.9 & 1.2 & 0.6 \\
$\nu \bar \nu$\bb &  $B$ & 10  & 9.3 & 8.0 & 6.5 & 4.8 \\
                  & \ssb & 0.8 & 0.7 & 0.7 & 0.5 & 0.3 \\ \hline
                  &  $S$ & 8.9 & 6.7 & 4.6 & 3.2 & 2.1 \\
$\nu \bar \nu$\bb &  $B$ & 51  &  47 &  43 & 41  & 37  \\
(alternate)       & \ssb & 1.2 & 1.0 & 0.7 & 0.5 & 0.3 \\ \hline
            	  &  $S$ & 8.4 & 6.6 & 5.0 & 3.7 & 2.2 \\
$\ell    \nu$\bb  &  $B$ & 48  &  52 & 48  & 49  & 42  \\
            	  & \ssb & 1.2 & 0.9 & 0.7 & 0.5 & 0.3 \\ \hline
            	  &  $S$ & 1.0 & 0.9 & 0.8 & 0.5 & 0.3 \\
$\ell^+\ell^-$\bb &  $B$ & 3.6 & 3.1 & 2.5 & 1.8 & 1.1 \\
            	  & \ssb & 0.5 & 0.5 & 0.5 & 0.4 & 0.3 \\ \hline
            	  &  $S$ & 8.1 & 5.6 & 3.5 & 2.5 & 1.3 \\
$q \bar q    $\bb &  $B$ & 6800& 3600& 2800& 2300& 2000\\
            	  & \ssb & 0.10& 0.09& 0.07& 0.05& 0.03\\ \hline
\end{tabular}
%\begin{tabular}{|c|c|c|c|c|c|c|} \hline                                 
%                  &            & \multicolumn{5}{c|}{Higgs mass (GeV)} \\
%channel           & quantity   &   90   &  100   &  110   &  120   &  130    \\ \hline
%                  &   S        &   3.2  &   2.9  &  2.5   &  1.6   &   0.8  \\
%$\nu \bar \nu$\bb &   B        &   10.0 &   9.3  &  8.0   &  6.5   &   4.8  \\                                                        
%                  &$S/\sqrt{B}$&   1.0  &   1.0  &  0.9   &  0.6   &   0.4  \\ \hline
%                  &   S        &  10.9  &   8.6  &  6.5   &  4.8   &   2.9  \\
%$\ell     \nu$\bb &   B        &  48    &   52   &  48    &  49    &   42   \\                                                  
%                  &$S/\sqrt{B}$&   1.2  &   0.9  &  0.7   &  0.5   &   0.3  \\ \hline     
%                  &   S        &   1.4  &   1.2  &  1.0   &  0.7   &   0.4  \\
%$\ell^+\ell^-$\bb &   B        &   3.6  &   3.1  &  2.5   &  1.8   &   1.1  \\                                            
%                  &$S/\sqrt{B}$&   0.7  &   0.7  &  0.6   &  0.5   &   0.4  \\ \hline     
%                  &   S        &   8.1  &   5.6  &  3.5   &  2.5   &   1.3  \\
%$q \bar q    $\bb &   B        & 6800   & 3600   & 2800   & 2300   &  2000  \\                                            
%                  &$S/\sqrt{B}$&   0.10 &  0.09  & 0.07   & 0.05   &  0.03  \\ \hline
%\end{tabular}
\end{center}
\end{table}


\subsection{Higgs search in the channel $Z H \to \nu \bar \nu b \bar b$} 
This is a channel that we had not considered seriously in our previous studies.
From the studies done for the recent Higgs -- SUSY workshop at Fermilab 
\cite{hswkshop} it became
clear, however, that 
        for standard-model Higgs masses below about 130 GeV, 
this channel contributes substantially to  the significance in Higgs
        searches\cite{conway, jesik}, {\bf provided one has an efficient trigger for it.}
This is illustrated in Table \ref{tab:Hsensit} which shows two sets of
numbers for $S, B,$ and \ssb\ for this final state  obtained by two different
analyses\cite{jesik, weiming} using different cuts for rejection of the top
quark background.

Since the last PAC meeting we have generated 
2000 such events and processed them through the full \DZ upgrade detector
simulation (GEANT). Applying our run II trigger simulation to these events, we
find that due to bandwidth constraints the best achievable trigger 
efficiency without the STT is 35\%.  With the STT, the trigger efficiency is 80\%.   
The best standard trigger has the requirements \Etmiss$>40$~GeV (L1 and L2)
and at least one level two jet with $E_T>10$~GeV.   The best trigger when STT
information is included requires at level one two jets, one satisfying
$E_T>10$~GeV and another satisfying $E_T>7$~GeV and requires at level two 
at least two jets $E_T>20$~GeV and at least two tracks 
with impact parameter significance $S_b>2$. 
Thanks to the improvement in trigger efficiency, the luminosity required to
        obtain a given significance for the final states with neutrinos
decreases by a factor of 0.68 with the STT.  
This implies that in this final state, a 110 GeV Higgs would give a 
3$\sigma$ effect in 
10 fb$^{-1}$ of data instead of 14 fb$^{-1}$ (for \DZ alone).   
%(Crudely calculated from the SHW log-scale plot.)
In other words: the STT offers the only way to trigger on these events with good efficiency. 
Not having this trigger would
seriously jeopardize our capability of observing the Higgs boson in one of the more promising final states.
In this context it should also be mentioned that in run I, bandwidth limitations did not allow us to 
have  an unprescaled dijet + missing $E_t$ trigger, which is the kind of trigger needed to 
collect events of this type. Extrapolating from this run I experience, 
it can be surmised that this would {\it a fortiori} also 
be the case in run II. Due to its superior \MET resolution the \DZ detector is 
expected to be better suited 
than CDF to trigger on such events. Not having the STT would mean giving up this advantage.

\subsection {Higgs and technicolor searches in $j j b \bar b$ and 
$b \bar b b \bar b$ final states}

        These arise from $W H, Z H \to j j b \bar b$ \cite{anna, roco, valls}, 
$ \rho_T \to W + \pi_T \to j j b \bar b $ \cite{technic}, and
$  h A \to b \bar b b \bar b$ \cite{carena, baertata}.    
The cross sections times branching 
ratios for these 
        processes are given in Table~\ref{tab:sigmaH}.
\begin{table}[h]
\caption{Cross section times branching ratio and assumed masses for hadronic
final states of SM Higgs, technicolor and MSSM Higgs production.}
\label{tab:sigmaH}
\begin{center}
\begin{tabular}{|c|r|c|}\hline
channel & $\sigma \times  BR$ (fb) &  masses (GeV)\\ \hline
$W H \to j j b \bar b$      & 320  &  $M_H = 100 $\\
$\rho_T \to j j b \bar b$   & 3400 &  $M_{\rho_T} = 250,~ M_{\pi_T} = 110$\\
$h A \to b \bar b b \bar b$ & $10\cdot tan^2(\beta)$ &$ M_h = M_A = 100$\\ 
\hline
\end{tabular}
\end{center}
\end{table}

        Although the QCD background is huge (typically $10^6$ fb), we will
        want to look for confirming signals in these channels if evidence for a Higgs signal has been 
observed in other channels.  Also, for
        large enough $\tan \beta $, all of   $h A$ production could
	 lead to the final 
        state with four $b$'s,  so we {\sl must} have these events.    

The initial significance \ssb\ is discouraging for all of these.
It should be kept in mind, however, that having these data will allow detailed
studies to be done which may well lead to the development of new analysis
techniques or improvement of old ones which can be used to improve the
signal-to-background ratio. Our experience from the top analysis in run I has 
shown that this is
indeed possible.
Initially,  the $ t \bar t \to all~jets$  seemed hopeless, but we managed to 
muster enough ingenuity in the development of new
        techniques that we had  a $3\sigma$ effect in the end.
At the recent Higgs-Susy workshop it was shown \cite{pushpa} that
for $ W H \to \ell \nu b \bar b $, a multivariate analysis using neural nets
gives  a large increase in sensitivity (about a factor of 2 in significance).
In the \DZ top analysis, the relative gain in sensitivity for the all-jets channel was
nearly 4 times larger than in the lepton + jets channel. If we assume that the
NN improvement ratio (alljets/lepton+jets) is the same
        for $W H$ as for top, then, given
the result shown at the Higgs-SUSY workshop, we could see an order of magnitude
improvement in sensitivity over what we now have.

It is clear from the above  that we do not want to throw away these events, even
if at present we do not yet have an exact understanding of how we will extract
the signal from the overwhelming background.  Having these hadronic final state events 
may be crucial in confirming a Higgs discovery and will be  indispensable in 
finding technicolor. Use of the STT to trigger on
these events is crucial in maximizing efficiency for these signals
(see Table~\ref{tab:efficH}).

\begin{table}[h]
\begin{center}
\caption {Number of events per fb$^{-1}$ recorded for each of the three 
hadronic  channels with and without the STT (based on analysis of 
ref.\cite{anna}, assuming a factor 4 improvement from multivariate analysis
with neural networks for fixed background of 3800 events).}
\label{tab:efficH}
\vspace{2mm}
\begin{tabular}{|c|c|c|}\hline
& \multicolumn{2}{c|}{number of events per fb$^{-1}$} \\
channel & without STT & with STT \\ \hline
$ W H +Z H $&  6       &   20 \\
$ \rho_T$  & 63       &  200 \\
$h A $     &$0.2\cdot \tan^2 \beta$ & $> 0.7 \cdot \tan^2\beta$ \\ \hline
\end{tabular}
\end{center}
\end{table}
\vspace{-5mm}
\section{$Z \to b \bar b$}


In our proposal P908 to Fermilab \cite{pac1} we showed that the STT would allow us to trigger on
\Zbb\ events with a low trigger rate while maintaining an acceptable efficiency, while without the STT, 
the efficiency would be reduced by substantial factors (the precise value depending on the 
bandwidth that can be allocated to such a trigger). 
 Without the STT, the only way to control the trigger rate 
would be to prescale (thus reducing efficiency) or to raise the trigger threshold -- 
which would cut into the signal and in
addition distort the dijet spectrum, thus making it difficult to extract the \Zbb\  signal above the \bb\
dijet background.

The ability to accumulate a sample of \Zbb\ events is extremely important:
The \Zbb\ is {\sl the only state } where we have a known mass which
is reconstructed from jets.  Even though it applies directly  only for $b$ jets, 
we will use this
% (and it will be the only method) 
to put errors
on our understanding of the jet energy scale for all jets (light quarks and
gluons as well).  If we want to do jet spectroscopy for top and/or Higgs, we 
{\sl need} 
to be able to see a \Zbb\ signal. Such a signal would have implications for both top-quark 
and Higgs-boson physics. 
It would serve to calibrate the jet energy scale, which currently gives rise to one of the largest 
systematic uncertainties in the top mass measurement \cite{mtop}, 
and to measure the $b$-tagging efficiency.
It would also provide proof that we can see a \bb\ resonance and allow to measure the observed line shape. 
Furthermore, these events could also be used as a control sample with which  to develop new jet 
energy algorithms with the aim of optimizing the energy resolution 
(by  using both tracking and calorimeter information).
This would be vital for the proposed searches for the decay $H\to\bbbar$ of the Higgs boson during Run II 
\cite{conway,tev2000}. 
It is encouraging that the CDF collaboration has recently observed a \Zbb\ signal in a 
data sample triggered on single muons from Run I \cite{CDF_Zbb}.


In response to questions asked by the PAC, we have done further studies\cite{zbb2} to verify that a 
signal for \Zbb\ can be seen with the \DZ detector above the expected background from strong 
\bb\ production. 
We have used PYTHIA-generated \Zbb\ events and dijet background, smeared with \DZ detector 
resolution, and with the background normalized to
measured cross sections
%measured by the \DZ collaboration during Run I ($\approx240$ nb)
\cite{b_xsec}.
We then apply a number of kinematic selection cuts whose purpose is to improve the 
signal-to-background ratio. 
These cuts are similar to the ones used by CDF in their recent observation of a \Zbb\ signal\cite{CDF_Zbb} 
and are described in \cite{zbb2}. 
The STT allows us to control the background trigger rate by tuning the stringency of the 
displaced vertex requirement (see \cite{pac1, zbb1}). If we want to limit the trigger rate 
for the \Zbb\ trigger to 20 Hz, this corresponds to a signal trigger efficency of 20\%.
 
%Assuming a trigger efficiency of 20\% (corresponding to a trigger rate of %20 Hz) 
With this trigger efficency, and assuming 50\% off-line $b$ tagging efficiency, 
we expect to reconstruct about 43{,}000 events from \Zbb\
decays and 570{,}000 from strong \bb\ production. (Note that the tagging efficiency expected in run II is
actually higher than this, so this is a conservative estimate). 
Note that using a muon triggered sample as CDF has done in run I \cite{CDF_Zbb}
would limit the number of reconstructed \Zbb\ events in Run II to about 900,
over a background of about 10,000. 

The double-tagged and 
untagged spectra shown in figure~\ref{fig:RunII_exp} are populated with
the number of events expected when using the STT. We find that the shape of 
the non-resonant \bb\ background is consistent 
with that of the (light quark, i.e. untagged) dijet background, so we can use 
the untagged diject spectrum as 
representative of the background (including the non-resonant \bb\ contribution).
Subtraction of the normalized untagged spectrum yields
the \Zbb\ signal shown in Fig.~\ref{fig:RunII_Zbb}.
Performing a fit with a Gaussian curve to the background subtracted spectrum, we find a width 
($\sigma $) of about 11.5 GeV,  consistent with the resolution used in the generation of the signal.
The statistical uncertainty of the mean of the Gaussian is found to be 0.28\%.
From this we  conclude that
we can expect to be able to measure the \Zbb\ peak position to about ${1\over 3}$\% precision.
   This includes statistical uncertainties in the background subtraction
   and assumes that, in addition to a \Zbb\ signal trigger using the STT,
   we have a control trigger without the STT requirement prescaled to
   about the same rate as the signal trigger. 

\begin{figure}[p]
\vspace{-1.5cm}
\begin{center}
\mbox{\psfig{figure=zbb_fig06a.ps,height=3.5in}}
\caption{ Invariant \bb\ mass spectra for background ($\bullet$) 
and signal + background ($\circ$) expected from Run II;
the number of events corresponds to the expected numbers of reconstructed events.}
\label{fig:RunII_exp}
\mbox{\psfig{figure=zbb_fig07a.ps,height=3.5in}}
\caption{Background subtracted \bb\ invariant mass spectrum expected from Run II with superimposed fit.}
\label{fig:RunII_Zbb}
\end{center}
\end{figure}
 

\section{Studies of the top quark}

In our proposal\cite{pac1} we have shown that the proposed trigger processor can 
be very useful in controlling the (background dominated) trigger rates both for 
\tt\ and single top production. It is difficult to translate this directly into a
quantitative measure of an  ultimate physics benefit, e.g. in terms of improvements
in measurement precision. The reason for this difficulty lies in the fact that the final net gain
due to the additional trigger processor will depend on other parameters, e.g.
the instantaneous luminosity, the beam quality, the final trigger menu adopted 
by the collaboration (i.e. the bandwidth allocated to the various triggers);
the latter may depend on  requests for bandwidth for new 
physics topics of which  we are presently not aware.

Here we address one issue which can be quantified now: the improvement 
in the top mass measurement due to the better jet energy scale calibration mentioned 
in the previous section.
We start out from our run I top mass measurement using \tt\ events with a 
lepton + jets final state \cite{mtop}. In our top mass determination, we found that the sources of 
systematic uncertainties are jet energy calibration, event generation (gluon radiation
from initial and final state), detector simulation (detector noise, pileup,
Monte Carlo sample sizes), and fit procedure. 
The jet energy scale in run I is known to $\pm $(2.5\%+0.5~GeV). 
The presently used method of $p_T$ balancing in dijet or $\gamma$+jet events is systematically
limited at a precision of about 1\%. We hope that we might achieve 1.5\% uncertainty if we 
push the present method as far as we can.

To extrapolate to run II, we make the following assumptions:
\begin{itemize}
\item integrated luminosity in Run II is 2 fb$^{-1}$
\item trigger, selection and reconstruction efficiency for top events in Run II is the same as in Run I
\item all systematic errors except the jet energy calibration
   scale as $1/\sqrt{\int{\cal L}\mbox{d}t}$
\item with STT, the jet energy scale is determined from the \Zbb\ signal, as described in 
the previous section,
i.e. to a precision of $\pm {1\over 3}$\%;\\
without STT, we use the best value we think we might be able to obtain with the present method, 
i.e.  $\pm 1.5$\%.
 
\item the jet scale uncertainty contribution to the  top mass
      measurement error is obtained  by scaling from the corresponding 
Run I uncertainties. 
\end{itemize}

Table~\ref{tab:mtopmass} summarizes the top mass measurement uncertainties  for Run I, 
as well as the values expected for Run II.
We see that without the use of the \Zbb\  signal, the contribution from the 
jet energy scale calibration would dominate the
systematic uncertainty. The \Zbb\ signal allows us to reduce this
uncertainty dramatically.

\begin{table}[h]
\begin{center}
\caption{Uncertainties on top mass measurement from lepton + jets channel, as obtained in run I, 
and as expected for run II, with and without improved jet energy scale using the \Zbb\ signal.}
\label{tab:mtopmass}
\vspace{1mm}
\begin{tabular}{|l|c|c|c|} \hline

                             &  Run I       &     Run II    &      Run II  \\ 
                             &              &  w/o \Zbb\    & w/ \Zbb\     \\ \hline
 integrated luminosity       & 100 pb$^{-1}$&   2 fb$^{-1}$ &      2 fb$^{-1} $\\ \hline
 jet energy calibration      &              &               &                  \\
uncertainty                  & 2.5\% + 0.5 GeV&  1.5\%      &  0.3\%  \\  \hline   

systematic errors on top     &              &               &                  \\
mass from                    &              &               &                  \\
\quad jet energy calibration & 4.0 GeV      & 2.2 GeV       & 0.5 GeV \\
\quad event generation       & 3.1 GeV      & 0.7 GeV       & 0.7 GeV \\
\quad detector simulation    & 1.6 GeV      & 0.4 GeV       & 0.4 GeV \\
\quad fit procedure          & 1.3 GeV      & 0.3 GeV       & 0.3 GeV \\
total systematic             &  5.5 GeV     &     2.3 GeV   &      1.0 GeV\\
 statistical                 &  5.6 GeV     &     1.3 GeV   &      1.3 GeV\\
 total                       &  7.8 GeV     &     2.7 GeV   &      1.6 GeV\\  \hline
\end{tabular}
\end{center}
\end{table}

A preliminary study\cite{brian} of the top mass determination in the all-jets 
channel from Run I data 
finds that the statistical error is about
20 GeV, and the systematic uncertainty (dominated by the jet energy scale uncertainty) is about 6.5 GeV.
For the extrapolation  to run II, we use similar assumptions as in the lepton + jet case, 
with the additional assumption that (thanks to the SMT)
the $b$-tagging efficiency for jets from top decay will be three times higher in run II
than in run I.
This then leads to an expected statistical error on the top mass from the all-jets channel 
of about 1.7 GeV and a total systematic error 
 of 2.6 GeV without the \Zbb\ signal, and about 1 GeV with.
Here again, the use of the \Zbb\ signal has a dramatic impact on the precision of the mass measurement.
\section{B - Physics}

In our original PAC proposal, as an example of a $B$ - physics measurement,
 we showed that the STT
in conjunction with single muon and dimuon triggers would allow us to achieve
32\% efficiency for \bkspsi , \psimumu \ events, while without 
the STT the efficiency is at most 24\%. We also showed that  
the STT can be
used to control the L2 trigger rate while preserving good signal efficiency.

In response to the request from the PAC, we provide here information on 
the precision with which we expect to  measure 
$\sin 2\beta$ in run II (see \cite{fs-bphysics, fs-bnsf} for details).

Given the trigger efficiencies mentioned above,
we estimate the number of fully reconstructed events in 2 fb$^{-1}$:\\
\begin{tabular}{lll}
 \tab  \bkspsi , \psimumu   & with STT:  & 8500 events\\
 \tab  \bkspsi , \psimumu  & without STT: & 6400 events\\
 
\end{tabular}

%(For comparison, CDF quotes 10,000 \psimumu\ and  5,000 \psiee\ events for 2~fb$^{-1}$).
\bigskip

Then, assuming a net flavor tagging efficiency of 5\% (including mis-tagging)
(see \cite{fs-bnsf}), we obtain the following $\sin 2 \beta$ errors:\\
\begin{tabular}{lll}
\tab \bkspsi , \psimumu  & without STT: & error = 0.168\\
\tab \bkspsi , \psimumu  & with    STT: & error = 0.146\\
\end{tabular}

\bigskip

Given that $\sin 2\beta$ is constrained between 0.56 and 0.94
at 95\% C.L. based on indirect measurements, that uncertainty would 
correspond to a direct measurement of CP violation with a significance of about 4$\sigma$.

   With the new preshower detectors installed on the inner face of the calorimeter,
    \DZ will also have the capability in Run II to identify and trigger on 
    low pt electrons. Preliminary studies\cite{etrig} suggest
    that we could achieve similar trigger efficiency for the 
\psiee\
    decay mode as for the muons. In that case, the $\sin 2\beta$ uncertainty 
    would be further reduced to $\Delta (\sin 2 \beta) \approx 0.1 $.
%and the \DZ measurement would become quite comparable to CDF expectations. 
These two determinations should be 
    relatively uncorrelated and thus provide a strong test of CP violation.




\section{Trigger rates}

At the presentation to the PAC in October, we were asked to quantify the trigger rate 
reduction due to the better resolution of the SMT.
As an example we show in Fig.~\ref{fig:elec} and Fig.~\ref{fig:dielec}
 the trigger rates vs luminosity for central electron triggers, with and without 
 using the STT\cite{bornali}. 
It can be seen that use of the STT leads to a reduction of the trigger rate by about a factor of 2.
Note that a 
reduction by a factor of two gives us the possibility to either lower the $p_t$
threshold or allow other triggers to be activated.


\begin{figure}[p]
\vspace{-1.5cm}
\begin{center}
\mbox{\epsfig{figure=el_c_3.eps,height=3.5in}}
\caption{Rate vs luminosity for L2 central electron trigger, $p_t > 3$GeV, with
 and without use of STT.} 
\label{fig:elec}
\vspace{4mm}
\mbox{\epsfig{figure=diel_c_3.eps,height=3.5in}}
\caption{Rate vs luminosity for L2 central dielectron trigger, $p_t > 3$GeV, 
with and without use of STT.}
\label{fig:dielec}
\end{center}
\end{figure}
 
\section{Conclusion}

In this document we have provided further arguments to strengthen the physics case for the 
implementation of 
the Silicon Track Trigger, a trigger processor for the \DZ silicon detector.
We have shown that the proposed STT will be an indispensable asset in the search for
the Higgs boson and  technicolor in Run II. 
Furthermore we have demonstrated that it will improve the top mass measurement precision, as well as
the precision of the measurement of the CP violation parameter $\sin 2 \beta$.
We have also shown that it is a powerful tool to control trigger rates at L2. 
These rate reductions at L2 are  important in maintaining high efficiency for many 
interesting physics channels with $b$ - quarks in the final state, but can indirectly also benefit 
other physics signals (without $b$ quarks)  by freeing up bandwidth at L2.

The STT is essential to allow the full exploitation  of the \DZ detector's physics potential in run II.

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\end{document}
