# Presentation: 504466

## Muon ID Algorithm Development-Progress Report                                                           2/7/03-C. Milstene

- _Part of the  ____  ‘s_  below 5 GeV are lost with the actual algorithm.
-  We will try to broaden our acceptance toward low energy ’s .
- _The starting point_:
- (Tk-Hits)=4bins, (Tk-Hits)=2bin in the  Mu Detector
-                           bin= bin =21mrd
- (Tk-Hits)=3bins, (Tk-Hits)=1bin in the  HAD Calorimeter
- bin= bin =5.2mrd
- Nhits = 12 hits, in the Mu Detector
-  _The Goal_: Increase the Acceptance to Low Energy 
- By Improving the existing cuts
- By Including the EM Calorimeter into the ID package.

## Improving the Cuts

- The  low energy  ‘ s  are considerably bent by the 5 Tesla Magnetic
- Field  and replacing the fixed angle cut by a 1/p Angle Cut might
- be very useful.
- We will first define our 1/p cut in the Mu Detector, using the actual
- distributions of (Tk-Hits), (Tk-Hits) at  higher energy.
- The 20 GeV distributions shown in the next figure have been chosen.
- _The cuts_ :
- (Tk-Hits) =  Max( (2bins*20/Pmom),2bins)
- (Tk-Hits) =  Max( 1bin*(1+(20/Pmom) ) , 2bins)

## Distribution of (Tk-Hits) , (Tk-Hits) For 20 GeV  

## Distribution of (Tk-Hits) , (Tk-Hits)  continue1)

- _This corresponds to the cuts:_
- At 3GeV/c:  (Tk-Hits)   = 13 bins, (Tk-Hits) = 7bins
- At 4GeV/c:  (Tk-Hits)   = 10 bins, (Tk-Hits) = 6bins
- At 5GeV/c:  (Tk-Hits)   =   8 bins, (Tk-Hits) = 5bins
- At 10GeV/c:  (Tk-Hits)   = 4 bins, (Tk-Hits) = 3bins
- At 20GeV/c and Above : (Tk-Hits)   = 2 bins, (Tk-Hits) = 2bins
- There is a good agreement with those cuts, as shown at lower Energy as seen at 4 GeV/c in the next figure.

## Distribution of (Tk-Hits) , (Tk-Hits)4GeV/c - 

- Detail

- Detail

## Distribution of (Tk-Hits) , (Tk-Hits)  continue2)	

- _Applying those cuts_ _the ____ Acceptance rises:_
- At 3 GeV  from  4/5000  ~0.08%       to 1263/5000 
- At 4 GeV  from  3792/5000   to 4770/5000 
- t 5 GeV  the gain is negligible and above the cuts coincide with
- the previous constant cuts.
- _Remark_: At 2 GeV and below, the  ‘s curl in the magnetic field
- and don’t reach the Mu Detector
- In the next figure the m detection efficiency curve is represented
- With the new improved acceptances at low energies.

## Single Muon Efficiency  = F(Particle Momentum)

- In red are  represented the
- Points with (1/p) angle cut
- dependence
- The point at 3GeV/c which
- raised From 0.08% (x axis)
- Black triangle to 25.3%  and
- at 4GeV/c from ~75.8%
- to ~95.4% and tops the 5 GeV/c
- Points obtained in the previous
- algorithm.

## Examples of Events Which benefited the cuts

- The momenta dependant cuts did contribute a lot at low energy.
- It allowed to increase the number of Hits collected in the
-  Calorimeters Along the reconstructed track.
- A few Typical muons  are shown in the next figures with the
- improvement fron “Before” And “After” the  (1/p)  dependant
- cuts.
-  A Double Muons detected in b bbar  jets is also shown with the
- Number of hits collected each track.

## BEFORE-Mu 4GeV-MuDet 17Hits-Constant PhiCut &ThetaCut-Evt 6 Run 1   

- BEFORE-Mu 4GeV-MuDet 17Hits-Constant PhiCut &ThetaCut-Evt 6 Run 1

## AFTER-Mu 4GeV-MuDet 32Hits- PhiCut &ThetaCut= f(1/p)- Event 6-Run 1

## BEFORE Mu 4GeV-MuDet  14Hits-Constant PhiCut&ThetaCut - Event 7-Run 1

## AFTER-Mu 4GeV-MuDet 34Hits - PhiCut&ThetaCut = f(1/p)- Event 7-Run 1

## BB_bar 2 Detected  –(Show 31 Hits Both ’s)-Evt 135

## The Multiple Scattering

- The Effect of the multiple scattering on the TK-Hits)bins and
- (Tk-Hits)bins from layer 0 to the last layer  will be studied in some
- detail.
- The effect due to the material prior to the detector will be included.
- The multiple scattering in the EM Calorimeter will be calculated,
- then in the HAD Calorimeter, and the Mu Detector including all the
- Material in the way, e.g. ~10cm C in between the EM and the HAD,
- And the coil before the Mu Detector. DX0 will be calculated and
- (which depends on )  andevaluated for extreme cases.
- ___he bin size is_:
- For EM= 4mrd, for HAD=5.2mrd, for MuDet = 21 mrd.

## Sampling X0_EM- X0_HAD- X0_MuDet 

- EM:                     |
- W:0.25cm            | X0_EM=0.35*2=0.70cm
- other:0.25cm       |
- HAD:                   |
- Steel:3cm             |  X0_HAD=1.76*(4./3.)=2.34cm
- other:1cm            |
- MuDet:                |
- Steel:5cm             |  X0_MuDet=1.76*(6.5/5.)=2.29cm
- other:1.5cm            |

## DX0_EM, DX0_HAD, DX0_MuDet =F(Layer Number)

- The number of radiation length encountered by the particles
- depends in the number of layers gone through.
- X0=1/sqrt(3)*.014/p*sqrt(N*d/Xo) *N*d
-  p is the particle momentum GeV/c
-  N is the number of layers
-  d is the layer thickness in cm
- EM:        d/X0  =  0.5/0.7 ;    N = 0-29
- HAD:	   d/X0  =  4./2.34 ;    N = 0-33
- MuDet:   d/X0  =  6.5/2.29;   N = 0-31/48
- 	     (0-31 instrumented )

## X0_EM=F(Layer Number)

- X0_EM  at the highest at low energy and in the last layer

## DX0_EM, DX0_HAD, DX0_MuDet =F(Layer Number)(continue)

- Each of the calorimeters is part of the Detector and  as such the
- Particles experience Multiple Scattering in material before reaching the calorimeter. This  has not been accounted for yet.
- For the _HAD_ calorimeter, mostly the whole EM calorimeter:(~0.56/p)
- And ~10cm of Carbon left in between detectors(~0.059/p)
- Dx0_HAD_Deteco= sqrt( DX0_EM_Tot*DX0_EM_Tot +
- 			       DX0_C           *DX0_C            +
-                                            DX0_HAD*DX0_HAD )
- For _MuDet_ mostly EM(~0.56/p),HAD(~8.38/p ) the Carbon and the Coil(~2.39/p):
- DX0_MuDet_Deteco = sqrt(  DX0_EM_Tot*DX0_EM_Tot      +
- 				DX0_C           *DX0_C                 +
- 				DX0_HAD_Tot*DX0_HAD_Tot +
- 				DX0_Coil  *DX0_Coil                  +
- 				DX0_MuDet *DX0_MuDet   )

## X0_HAD=F(Layer Number)- HAD Calorimeter in SD_Detector

- The plots of DX0_HAD for HAD Calorimeter alone and after
- The EM Calorimeter are shown below.
- The smallest values are affected the most
-  e.g. 0.1882 instead of 0.0141 at 3GeV Layer 1
- ,but  2.7998 instead of 2.7934 at 3GeV Layer 33.
- By one order of magnitude higher in HAD than in EM

## X0_MuDet=F(Layer Number)- MuDet in SD_Detector

- The plots of DX0_MuDet for MuDet Calorimeter alone and inside
- the detector, with the particles multiple scattering in the _EM_ and _HAD_
-  calorimeters and the _Coil_.
- It appears clearly that the small values in the first layers are affected the most, the highest values which could increase the cuts staying almost unchanged , with a softer slope .
- Three times bigger in MuDet than in HAD calorimeter

## (continue1)

- _The cell in EM_ :
-   cell= /800 =4mrd
- _The cell in HAD_:
-   cell= /600 = 5.2 mrd
-  _Looking at each detector _
- As a separate entity the figures show
- _In the EM_ :
- R=R0+N*d, R0= 125cm
-   < 0.18/125 = 1.4 mrd smaller than the cell
- _In the HAD_ :
-  < 2.8/240 = 10.4 mrd smaller than 2 cells
- And  = 1/((R/X0 sin2)-ctg ) ranges
- from 0 to X0/R the size of the cell.

## (continue2)

- _The cell in MuDet_:
-   cell= /150 = 21 mrd
- _In the MuDet_ :
- R=R0+N*d, R0= 348.5cm , N = 32/48
- From the figure one get
-   < 6.08/348.5 ~ 17.5 mrd smaller than the MuDet cell
-   = 1/((R/X0 sin2)-ctg ) ranges from 0 to X0/R:
-  For a 3 GeV  in layer 33 mrd (see fig.)
- _Conclusion:_
- The Multiple Scattering is included in 1-2 cells of EM and 2-3
- Cells in the HAD as well as in MuDet. A 2-3  cells cut will include
-  the Multiple Scattering within 1 Standard deviation.

## Multiple Scattering (Conclusions)

- _Conclusion:_
- The multiple scattering is not a problem it is included within
- 1-2 bins in the EM , 2-3 bins in the HAD and within 1-2 bins
- Of the MuDet
- Therefore even at low energy it does not account for the larger
- Cuts needed.
- Looking at the distributions (Tk-Hits) and (Tk-Hits) without
- Taking the absolute value, one notices a clear asymmetry , next
- Figure, and it comes from the fact that the loss of Energy of the
- particle in the material  is not accounted for in the extrapolation
- of the track (Ron Cassell: the swimmer does not ).

## Asymmetry in (Tk-Hits)

## The Loss of energy through DeDx

- We will find out if the loss of energy through DeDx is accounting
-  for most of the (Tk-Hits),(Tk-Hits).
- The effect should be  stronger at lower energy, e.g, at 3 GeV/c
- than at 10GeV/c since a bigger proportion of energy is taken out.
-  At a given energy it increases the farther we go from the
- Interaction Point, e.g. the effect is stronger in MuDet than in
- EM Cal, and in MuDet stronger in layer 30 than in Layer 0 as
- can be seen in the next figures.
- This will be studied through the space angle:
- Space_angle =Sqrt((Tk-Hits)^2+(Tk-Hits)^2).
-                                                                                            Study with A. Para

## DeDx:Space_angle Study-at 3 GeV/c 

- In the EMCal, shown are layers 0,8,16,20,26 and 29

## DeDx:Space_angle Study-at 3 GeV/c(continue1)

- In HADCal bigger spread than EMCal where it is barely felt
- Sown in layer  0,8,16,20,26,33  it increases with the Layer Number.

## DeDx:Space_angle Study –at 3 GeV/c(cont.2)

- In My Det  bigger spread than HAD Calorimeter
- Shown In layers 0,4,8,12,16,20

## DeDx:Space_angle Study  at 10 GeVshown in EMCal layers 0,8,16,20,26,29 the spread barely change

## DeDx:Space_angle Study  at 10 GeV/cshown in HAD Cal layers 0,8,16,20,26,31 the spread barely change

## Next to come

- Include the DeDx in the track extrapolation
-       tight consequently the angle cuts in HAD Cal
-       and MuDet, using the information extracted
-       from Multiple Scattering studies.
- Take advantage of the information of EM Cal (low energy )
- Study of the energy repartition between detectors using
-       hadrons(especially between HAD Cal and MuDet)
-  Jet studies
-  And More to come (in discussion with G. Fisk)

## The  Multiple Scattering Contributions

- First the dependency on the layer number will be calculated
-         for each detector separately independently .
- 2)    Then, for the HAD calorimeter the contributions of the material
-         of the EM calorimeter, encountered by the particles which reach
-         the HAD calorimeter will be included.
- For the MuDet, for the same reasons the contributions of the material
-      of the EM , the HAD calorimeters as well as the Coil will be included.

## 

- As a result: Calorimeter hits
- will deviate from the track
- extrapolated from the tracker by
- an angle (.
- X0/R
- is calculated below
- 
- X0/sin() = r1/sin
-  r1 = R/sin)
- sin()/sin  = R/(X0 sin )
- sin  cos () + sin() cos /sin ()
- =R/(X0 sin 
-  sin ctg + cos  = R/(X0 sin 
-  ctg  =(1/sin)* ((R/X0 sin ) – cos 
-   ~tang () = 1/((R/X0 sin2)-ctg )

- X0

- 

- 

- r1

- r2

- R

- 