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Why is CSC Resolution Insensitive to Cross Talk? S. Durkin Nov. 10, 2009 A Theoretical Gatti Calculation using Maple. DAQMB/FEBs Readiness for First Beam. Jianui Gu The Ohio State University. Review. How to handle crosstalk in reconstruction?. - PowerPoint PPT Presentation
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1Stan Durkin CSC DPG November 10, 2009
DAQMB/FEBs Readiness for First Beam
Jianui GuThe Ohio State University
Why is CSC Resolution Insensitive to Cross Talk?S. Durkin Nov. 10, 2009
A Theoretical Gatti Calculation using Maple
2Stan Durkin CSC DPG November 10, 2009
Review
How to handle crosstalk in reconstruction?
Convolution for pulsed strip (black) and adjacent strip (blue) for a given layer in a ME2/2 chamber. The red curve is a fit to the peak.
Cross talk (blue) extracted from the data. Cross talk (red) was measured by fitting the Gatti distribution to test beam muon data. Notice the offset of about 3%
Reference: Determining the CSC Cross Talk using the Buckeye External Pulser.
S. Durkin, J. Gilmore, F. Geurts April 26, 2005
3Stan Durkin CSC DPG November 10, 2009
Yes, the Cross Talk is Treated CorrectlyQ
/(Q
L+Q
C+
QR
)
Hit Position (Strips)
Time Bin Peak-1 Time Bin Peak Time Bin Peak+1
Correct Cross Talk Correct Cross Talk
Gatti Formula
Cut on strip width: 0.85 to 0.95 cm
4Stan Durkin CSC DPG November 10, 2009
A Theoretical Gatti Calculation using Maple
Gatti Induced Charge Formula
ME3/2: r=h/w h=0.476 w=0.9
))(tanh1(
))(tanh1()(
2
2
23
2
1
rxK
rxK
KKxQ
563.03 K 1285.12 K
Step 1: Generate Charges on Strips as function of strip peak charge position x
)))(tanh(arctan())(tanh((arctan(
)(
)5.1(
23
)5.0(
23
5.0
5.1
r
x
r
x
L
x
x
L
peakpeak
peak
peak
KKKKConstQ
xxQQ
L-left M-middle R-right
MQ
RQ
5Stan Durkin CSC DPG November 10, 2009
Step 2: Apply Cross talk in three time bins
xt(1) xt(2) xt(3)
Time tpeak-50nsec tpeak tpeak+50nsec
Cross Talk 9.0% 5.75% -2.5%
sec138nt peak
Assumed same for all strips
)3()3())3(21()3(
)2()2())2(21()2(
)1()1())1(21()1(
xtQxtQxtQxq
xtQxtQxtQxq
xtQxtQxtQxq
MRLL
MRLL
MRLL
Bin 1Bin 2Bin 3unsmeared
Calculate Cross Talk Smearing
x(strips)
6Stan Durkin CSC DPG November 10, 2009
Pulse Charge as function of time (5 pole semigaussian) 44
44
*)(
et
etCtQ
peak
peakttStep 3: Add three time bins properly weighed as a function of time
w(1) w(2) w(3)
Time tpeak-50nsec tpeak tpeak+50nsec
Charge weight 0.704 1.000 0.808
Time Bin Charge Addition Weighting
))3()2()1((
))3(*)3()2(*)2()1(*)1((
www
xqwxqwxqwXQ LLL
L
Raw QCrossTalk XQ
x(strips)
7Stan Durkin CSC DPG November 10, 2009
Step 4: Calculate ratios used in RecHitD look-up table
The Answer
)(
)(
LM
LR
QQR
)(
)(
LM
LRR XQXQ
XQXQR
No Cross Talk: With Cross Talk:
x(strips)
x(strips)
RX
RR-RX
Maximum Difference 50 m
8Stan Durkin CSC DPG November 10, 2009
Qualitative Understanding
The Look-up Table Ratio (QR-QL)/(QM-QL) is Purposely Insensitive to Cross Talk:
QL QM QR QL QM QR
Center of Strip (x=0)
Between Strips (x=0.5)
QR=QL
XQR=XQL
QM=QR
XQM=XQR
Symmetry
R=RX=0 R=RX=1
Gatti Fitting is sensitive to shape while the Loop-up Table Method isn’t.
Both estimation methods have been shown to give the same resolution.
9Stan Durkin CSC DPG November 10, 2009
Bibliography
A paper describing this calculation include links to the maple scripts are available at:
http://www.physics.ohio-state.edu/~durkin/talks/CrossTalkSensitivityPaper.pdf
