Sci Fi Performance

Malcolm Ellis MICE Collaboration Meeting Feburary 11 th 2005 1

Outline

      Reconstruction status Data production since last collaboration meeting Miscellaneous studies:  Momentum resolution vs Magnetic Field  Helium gas versus Vacuum Emittance calculation and correction Tracker performance    Resolution (X,P X , etc...) Transverse (4D) Emittance resolution Longitudinal (2D) Emittance resolution Conclusions 2

Reconstruction Status

    Problems were found in the field map implemented since November meeting. For the moment, the field is still assumed to be constant in the Reconstruction.

Navigation bug in Kalman found and temporary fix applied to remove error in calculation of MCS covariance matrix.

dE/dx model tuned, but still far from optimal.

Results presented are from a stable, tested version, but do not represent the ultimate physics performance possible, hence show the worst-case. Future improvements will likely improve the performance by a small amount.

3

Data Production

 One large and numerous smaller productions run since November:   10 million events – matched beams (narrow P Z ) transverse emittance between 0.5 and 9.5 p mm rad.

1 million events – matched 2.5 studies.

p mm rad beam, with 510 ns and 25 MeV RMS longitudinally – used for tracker performance and longitudinal emittance   0.5 million events – various matched beams at different tracker solenoid fields ~250k – studies for global PID and matching, He gas vs vacuum, varying physics processes to study pulls, etc...

4

Momentum Resolution vs B

   Prediction by John Cobb that for a matched beam, the resolution in P would go approximately as 1/sqrt(B).

Two separate beams were simulated each at 2T, 3T, 4T, 5T and 6T:    One beam matched for the particular field (red points) Another beam that is matched at 4T (blue points).

In both cases the beam is 2.5 p mm rad.

Conclusion:  No strong effect in P T resolution, however P Z resolution does improve with increasing B...

5

Beams vs B

Red points

: beams matched to the particular magnetic field 2T, 3T, etc.

Blue points

: beams matched for 4T but simulated going through 2T, 3T, etc.

6

Resolution vs B

Red points

: beams matched to the particular magnetic field 2T, 3T, etc.

Blue points

: beams matched for 4T but simulated going through 2T, 3T, etc.

7

Tracker Performance Specification

  In order to determine if a given tracker can measure the emittance with sufficient precision, a figure of merit has been determined based on the resolution of the tracker in each measured parameter and the RMS of the true parameter.

If, in the i th beam is s i variable, the RMS spread of the true and the RMS resolution of the tracker is s i res . The RMS spread of the measured distribution is then given by:



s

i

meas 2

    

i i

2 8

Specification continued

  The uncertainty in the measurement causes a bias in the measured width of the beam.

To estimate the size of this bias, the previous equation can be re-arranged, and using the binomial expansion: s

i

meas  s

i

true 1     s

i

res s

i

true    2  s

i

true   1  1 2    s

i

res s

i

true    2   9

Specification from Bias

 In order that the bias induced by the measurement error be less than 1%, it follows that: s

i

res  1 s

i

true 7  14 %   The figure of merit chosen, that the ratio above be less than 10%, thus satisfies this condition.

In this analysis, correlations between measurement uncertainties and the measured values have been ignored as have correlations between the measured parameters themselves.

10

Correcting the Emittance

    A measurement of emittance will always be biased by the measurement error, the amount depending on the resolution of the tracker.

In 2 x n dimensions, the true normalised emittance is given by:

V

2 true

n

is the true covariance matrix of the 2n the mass of the muon.

V

  2

n ij

  2

n



w N i

 

w i

1

m

  

w

2

n j



V w

2

j

true

n

 11

Measurement Error

  

V

  2

n ij

The measured value m i relation:

w

Where d i of a true value w i 

m i

 d

i

has the The expression for V true can then be written in terms of the measured parameters:  

m i



m i

 

m j



m j

  

m i



m i

  d

j

 d

j

   d

i

 d

i

 

m j



m j

   d

i

 d

i

  d

j

 d

j

    The covariance matrix of the errors on the measured track parameters can be defined: And the correlation matrix between the measured coordinates and the errors in the measurements:

R ij

 

m i



m i

  d

j

 d

j



C ij

  d

i

 d

i

  d

j

 d

j

V true can then be written:

V

true 2

n



V

meas 2

n



R



R T



C

 12

Transverse (4D) Emittance

  The transverse emittance is determined from the four track parameters (X,P X ,Y,P Y ).

 4

N

 1

m

 4

V

4 The resolution of the tracker as a ratio of the RMS of the beam at equillibrium (2.5 p mm rad) is presented, followed by the results from the emittance calculation.

13

X Position

14

Y Position

15

X Momentum

16

Y Momentum

17

Transverse Resolution

  The difference between the resolution in X and Y momentum is partially due to the addition of the dE/dx correction necessary for accurate reconstruction of the total momentum. This correction needs further work (hence my earlier comment about this being a “worst case” presentation).

All measured parameters are better than 14% RMS/RMS and only one is (just) outside the 10% criteria.

18

Uncorrected 4D Emittance

19

Corrected 4D Emittance

20

21

Cooling Measurement

22

Longitudinal (2D) Emittance

 The longitudinal emittance  2

N

 1 2

V

2   In the absence of a mature simulation and reconstruction of the TOF and matching to the SciFi tracker, the resolution in time at the tracker reference surface was varied from 30 ps to 110 ps by smearing the Monte Carlo truth times with a gaussian distribution.

Reminder: the longitudinal characteristics of the beam are s E = 25 MeV and s t = 510 ps.

23

E

24

Uncorrected Emittance:

s

t = 50 ps

Downstream Tracker – 50k Events per bin Upstream Tracker – 50k Events per bin

25

Bias vs Resolution

26

Corrected Emittance:

s

t = 50 ps

Downstream Tracker – 50k Events per bin Upstream Tracker – 50k Events per bin

27

Emittance Resolution vs

s

t

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Tracker Performance Table

Simulation at equillibrium emittance with 510 ps RMS in time and 25 MeV RMS in Energy

X Y PX PY E

PT PZ X’ Y’ T’ RMS of the Monte Carlo truth distribution

21.0

21.0

17.9

17.9

25.2

11.7

28.8

0.0954

0.0953

0.0527

RMS of the (Reconstructed – Monte Carlo truth) distribution

0.543

0.442

2.05

1.52

3.49

1.81

4.58

0.0102

0.00735

0.00967

Ratio of the RMS of the (Reconstructed – truth) distribution to the RMS of the Monte Carlo truth distribution

2.58 % 2.10 % 11.5 % 8.52 % 13.8 %

15.5 % 15.9 % 10.7 % 7.72 % 18.3 % RMS of the (Reconstructed – Monte Carlo truth) distribution if the tracker volume contains He gas 0.542

0.440

2.05

1.52

3.48

1.814

4.60

0.0102

0.00731

0.00982

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He gas vs Vacuum

    Simulation of tracker changed to replace vacuum with 1 atm He.

Tracker performance compared with baseline case, results included in summary table.

Conclusion:  no significant difference in tracker performance.

Next steps:  What are the safety/engineering implications for the rest of MICE?

 Review the implications for the tracker (the tracker group will review this at the end of March in KEK).

30

Summary

   RMS/RMS for parameters used in emittance calculation (X,P X ,Y,P Y ,E) is greater than 10% in some cases, but less than 14%.

A correction procedure has been developed and shown to:   remove bias give resolution better than 0.1% for 200k events Issues:     Understand use/resolution of TOF Derive correction matrices from “data” in MICE III He vs Vacuum Study station spacing 31

Conclusions

 The tracker group feels that the spirit (if not the exact letter) of the tracker validation requirements have now been met.

32

Tracker Performance Plots for parameters not directly used in the emittance calculations

33

P

T 34

P

Z 35

X’

36

Y’

37

T’

38