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{\Large \bf TRIUMF Experiment E614 \\}
{\Large \bf Technical Note 35 \\}

\vspace{0.4cm}

{\Large \bf Backgrounds due to pions in beam  \\}

\vspace{0.4cm}

\rm{\bf M. Shotter, TRIUMF summer student \\}
\rm{\bf D. Gill, TRIUMF\\}

\vspace{0.4cm}

\rm{\bf 20 August 1999 \\}

\end{center}

\begin{abstract}

   In the beam entering the M13 beamline, there will be pions present
as well as the muons that we are interested in. These pions will travel
down the beamline with the muons, and decay to positrons and muons in
various parts of the beamline and detector. This report determines the
positions of the pion and daughter muon decays, and provides an estimation
of background from the positrons produced by these processes.   
\\
\end{abstract}

{\large \bf Pion decays in beamline\\}

   The beamline selects particles according to momentum ( 29.7 MeV/c).
Pions around the production target having this momentum will travel or be pulled 
down the beamline. There will only be such pions around the production
target for a short time every cycle, corresponding to the time when the
beam from the cyclotron is incident upon the production target. These
pions provide a background that we must consider.

   For background, we only really need to consider the part of the beamline
beyond the last bend. Pion decays upstream of the last bend will primarily produce
muons of a different momentum to the rest of the beam and so will not
make it around this last bend. Positrons from decay of these pions or
decay of the daughter muons will be absorbed by all the metal and concrete 
surrounding the beamline and few will make it as far as our detector.
  
   An upper bound on the pion flux at the beam focus 150cm upstream of
the centre of the detector is about 0.5 percent of the surface muon flux. 
(This is an estimate based on the TRIUMF Users Handbook, pg. IV-18a). In the
rest of this report it is assumed that this ratio was measured at the beamline final focus.

   A simulation was carried out with a beam of pions from 300cm upstream of the E614 stopping target; the last bend is about 350cm upstream.\\

{\large \bf GEANT simulation\\}

   Using the RAYS card, a beam of 500000 pions were sent through the 
simulated detector. The decay branch was set to produce 100 percent muons
with spin, and the positions where the pions and muons decayed in the detector
were histogrammed in detail. I have not simulated the pion to positron
direct decay in this simulation as the branching ratio is about 1 percent
so the upper limits of the flux relative to the surface muon is a few parts
in 10$^5$.  

   In addition, the number of pions, muons and positrons entering the detector 
were counted, if the pion and daughter muon did not pass through the 
scintillator: i.e. if a pion did pass through the scintillator, it and 
its daughters are discarded from this background calculation; same
if a muon passed through this scintillator (the positron is discarded).
The pions and muons which originate from these pions decaying in flight
will arrive at a predictable time in the cycle, but the positrons will
arrive at any time in the cycle as they mostly originate from stopped 
muons upstream (more on this later).\\  

\begin{table}
\begin{center}
\begin{tabular}{|c|c|}
\hline
Region of apparatus & Percentage of pions from -300cm \\
            &   decaying in this region \\ \hline
 Decays in flight in beampipe    & 79.5  \\
 Stopping in iron/PVC beampipes  & 0.07 \\
 Stopping in proportional chamber mylar foils  & 0.6 \\
 Stopping in dense stack mylar foils (upstream) & 19.6 \\ \hline
\end{tabular}
\caption{Pion decay statistics}
\end{center}
\end{table}


\begin{table}
\begin{center}
\begin{tabular}{|c|c|}
\hline
Region of apparatus & Percentage of daughter muons  \\
            &   decaying in this region \\ \hline
 Muons do not decay within apparatus & 2.8 \\
 Stopped in beamline pipe material & 78.3 \\
 Near target (mostly upstream side of target holder) & 6.2 \\
 Yoke (old design) & 1.3 \\
 Beamline mylar foils & 1.6 \\
 Upstream DCs & 4.1 \\
 Upstream PCs & 0.8 \\
 Upstream SC & 0.6 \\
 Downstream DCs & 1.6\\
 Downstream PCs & 0.6\\
 Downstream SC & 0.4\\   \hline
\end{tabular}
\caption{Muon decay statistics}
\end{center}
\end{table}


{\large \bf Decay distribution of Pions and Muons \\}

   The position where the pions and muons decayed were histogrammed, in
z and in x-y (Figures 1 and 2 for the pions). The muon decay distribution is complex
so many histograms were needed to see the details. Figure 3 shows that these muons can traverse the entire detector, some eventually stopping downstream, in the chambers and scintillator. Figures 4-7 give the details of the decay positions of these muons. The distribution gives
an indication of how and where the decays occur. I have 
compiled some estimates of the statistics, using the histograms (see tables 1 and 2). I have also listed points relating to the interpretation of some of the data later on in this report.

   The figures quoted in Table 1 are percentages of the pions making
it around the last bend. This is a greater number than the pions
that reach the focus by a factor of 2.5 because many pions decay
between the last bend and the focus. This means that, coming round the
bend, pions make up about 1.25 percent of the particles in the beam.
Remember that this is a worst case scenario.\\


 
\begin{figure}
\begin {center}
\epsfysize=19cm
\epsffile{tn35fig1.eps}
\end{center}
\caption{Pion decay positions}
\end{figure}
 
\begin{figure}
\begin {center}
\epsfysize=19cm
\epsffile{tn35fig2.eps}
\end{center}
\caption{Details of pion decay positions}
\end{figure}
 
 
\begin{figure}
\begin {center}
\epsfysize=19cm
\epsffile{tn35fig3.eps}
\end{center}
\caption{Muon decay positions}
\end{figure}
 
 
\begin{figure}
\begin {center}
\epsfysize=19cm
\epsffile{tn35fig4.eps}
\end{center}
\caption{Details of muon decay positions}
\end{figure}
 
 
\begin{figure}
\begin {center}
\epsfysize=19cm
\epsffile{tn35fig5.eps}
\end{center}
\caption{Details of muon decay positions}
\end{figure}
 
 
\begin{figure}
\begin {center}
\epsfysize=19cm
\epsffile{tn35fig6.eps}
\end{center}
\caption{Details of muon decay positions}
\end{figure}
 
 
\begin{figure}
\begin {center}
\epsfysize=19cm
\epsffile{tn35fig7.eps}
\end{center}
\caption{Details of muon decay positions}
\end{figure}

\newpage
  
{\large \bf Notes on interpretation of Decay Distributions \\}

   Since the decay distributions are quite convoluted I have compiled
a list of the main features of each histogram and what they show.

{\bf        Figure 2: Pions}

   Top left:     This decay-in flight distribution looks exponential as expected.

                 Peak near -60 : proportional chambers

                 Peak at -300  : end of beampipe (some pions hit end-on - the simulation places them right next to the end of the pipe and they stop on the end wall). Whether this is actually present in reality or not is unclear, it could just be a bad extrapolation by GEANT of the beam rays.

   Top right:    Peaks correspond to the mylar foils of the dense stack.

   Bottom left:  Ring corresponds to a few pions stopping in pipe.
                 Propellor shape is shape of beam as it is being focussed.
                 Most decays occur near centre of beampipe.

   Bottom right: All decays in mylar foils occur near the main axis.


{\bf        Figure 4: Muons}

   Top left:     The decay distribution falls off towards -300. This is because the simulation does not simulate pions before -300cm, so there are no muons 
produced before -300cm, which means there are less muons stopping in the beampipe around -300cm.
 
                 Peak at -300cm : end of beampipe, as above. Maybe the stopped pions just here produce muons which immediately stop.

                 Discontinuity at -180 corresponds to the end of one pipe and
                  start of another.

   Top right:    Peaks correspond to the inner and outer faces of the yoke. Muons will
                  hit the side of the yoke and be stopped. Please note that 
                  this corresponds to an old  model for the yoke: the newest 
                  model locates these peaks at -158cm and -140cm.

   Bottom left:  Two rings correspond to the two pipes (one downstream of the
                  other). 
 
   Bottom right: Inner ring is PVC pipe; outer ring the start of the yoke.
                 Quite a few muons decay in the yoke as you can see.


{\bf        Figure 5: Muons}

   Top left:     More muons stopping in pipe in a complicated spectrum; the peak is probably due to being beyond the pion focus.

   Top right:    Peaks at -90, -70 and -68 are mylar foils.

                 Peak at -64 is the scintillator.

                 Peaks at -60 are proportional chambers mylar foils.

                 Beampipe stops at -70; downstream of this there is
                  no longer the continuous spectrum of muons stopping in the pipe.

   Bottom left:  Ring is the PVC pipe

   Bottom right: Ring is the pipe, decays in mylar foils are near axis though.


{\bf        Figure 6: Muons}

   Top left:     Spikes are mylar foils of drift chambers.

   Top right:    Large peak is at upstream side of target holder. 
                 Smaller peak is at target.        

   Bottom left:  Decays are centred in a region of about radius 10cm.

   Bottom right: More muons decay in the target holder than the actual
                  target itself.


{\bf        Figure 7: Muons}

   Top left:     Mylar foils of the downstream DCs.

   Top right:    Peaks correspond, from left to right, to the proportional
                  chambers, scintillator and a mylar foil.

   Bottom left:  Near axis.

   Bottom right: More diffuse. The magnetic field is less uniform in this region, this may scatter the muons.\\


{\large \bf Estimation of Backgrounds \\}

   The number of particle (by type) entering the detector from this pion beam
source where the pions or muons have not been seen by the scintillator 
are as follows. The percentage is relative to the number of pions at the 
focus (100 percent corresponds to 0.5 percent of the surface muon flux)

        Pions: 0.36 percent (about 0.09 particles/sec)

        Muons: 6.4 percent (about 1.6 particles/sec)

        Positrons: 10.1 percent (about 2.5 particles/sec)

   These figures are assuming a surface muon flux of 5000 particles/sec.

   The histograms above show only a very few pions stopping in the pipe
(of the order of a few parts in 10$^{-3}$ in the total pion flux) so
it seems a good assumption that the daughter muons from upstream pion decays will arrive at the same
point in the cycle as the pions. However the positrons seem to originate
from stopped muons (in the pipe and elsewhere) so their arrival will
be delayed by the muon lifetime, in effect we will have a continual background
of such positrons when the beam is incident on the apparatus.

   There is a possibility of calibration of parts of the detector system 
using these daughter muons and positrons; this is yet to be looked into.  \\

\begin{thebibliography}{10}

\bibitem{GEA} GEANT Version 3.21, CERN, Geneva 1993.

\bibitem{TN29} TN-29 E614 GEANT user's guide


\end{thebibliography}


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