Mikhail Batygov

1
A2 a new energy estimator

• Mikhail Batygov
• University of Tennessee

KamLAND Collaboration meeting at Toh-Gatta,
October 7-9, 2005
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Energy estimators Charge-based vs Hit-based

• Hit-based estimators (example Lindleys fitter
  from AKAT) have better resolution at lower
  energies
• Charge-based estimators (example first KAT
  energy estimator) have better resolution at
  higher energies
• Charge-based estimators are less prone to biases

Optimal approach

• Try to combine hit/no-hit and charge information
  within a single model, so that at lower energies
  the estimator behaves rather like hit-based, and
  at higher like charge-based, such that
  calibration is preserved while going across the
  energy scale

3
Dark count a trouble often underrated
Almost purely useful signal
Purely dark count
Mixed dark/useful
Hg-203 experimental pulse shape
4
Dark noise share in the whole hit budget
At Co-60 amplitude level (2.35 MeV Evis) 5 of
17 hits and 6 of 20 hits At Ge-68 amplitude
level (0.9 MeV Evis) 12 of 17 hits and 14
of 20 hits At Hg-203 amplitude level (0.2 MeV
Evis) 36 of 17 hits and 40 of 20 hits
At lowest energies (like Hg-203) dark noise
becomes the dominant factor in energy estimation
quality degradation. This concerns both the
resolution and the accuracy of the energy scale
5
The effect of dark count on energy reconstruction
quality
1. Resolution loss
2. Errors in dark rate estimation translate into
systematic distortion of energy scale
6
Hit timing a remedy for the dark count problem
KAT traditional approach
1. Sort hits by TOF-corrected arrival time 2.
Slide a 150-ns window over the sorted array to
select the best coverage (i.e. the largest
number of consecutive hits covered by this
window) 3. Disregard all hits that dont fit in
the window
A potentially more accurate (time filter)
approach
weight hits according to their probability not
to be dark ones, so that

• Weight is zero before the main pulse
• Weight is almost one near the peak
• Weight is some value between 0 and 1 in the tail
  of the signal

This requires an accurate estimation of the
origin time t0, but a vertex fitter can provide
one
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Hit, charge and time information employed
Writing the general likelihood of some
hit/charge/time configuration
where
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What is what
But what are fij(qi) ?
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Problem of individual charge probability
densities fij(qi)
We dont have charge distributions for strictly
2,3,4, photoelectrons, but it is possible to try
constructing them from SPE distributions
Note fij is indexed with the PMT number i to
reflect difference between 20 and 17 tubes
Suppose we know them. Then, for every PMT i we
have
Yet another problem here the sum is infinite.
Where to stop?
However, it turns out that the whole sum is more
accessible than its elements
Physically, ? is the conditional probability
density of charge, given ? - the expected number
of hits. But thats what we have directly from
source calibrations!
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Getting the necessary information from
calibrations
? can be varied by the selection of different
sources and their positions relative to a group
(ring) of PMTs ? is monitored by the ratio of
hits/no-hits through a simple relation Simultaneou
sly, the hit/no-hits ratio provides the bi
coefficients describing attenuation and shadowing
The only remaining trouble ? functions for high
higher ?s than are directly available from
calibrations
10 MeV source at 2 meters from PMT gives ?45
the highest ? one can reliably get from Co-60
calibrations is 5.
Current temporary solution scale the uppermost
available ?5 for all higher values of ?. Not
good but better than Gaussians. Work on MC
generations in progress.
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Likelihood maximization procedure
Full likelihood
Likelihood maximum condition
Leads to equation
First two terms taken alone constitute a generic
hit/no-hit energy fitter
This term accommodates charge information
(important for higher energies)
This term accommodates time information
(important for lower energies)
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How hit-based to charge-based transition works
Writing the likelihood maximum equation again
No hit term (positively defined)
Hit term (positively defined)
Charge term (no definite sign)
Time term (no definite sign)
Lowest energies No hit term large, positive,
taken with - Hit term large, positive,
taken with Charge term small Time term
significant correction that can be positive or
negative depending on E and hit time
configuration
Highest energies No hit term small Hit term
small (due to the exp.) Charge term relatively
large in magnitude but can have either sign or
made zero by selection of proper E Time term
small
Result hit-based energy fitter with time filter
compensating the impact of dark count
Result a charge-based fitter governed by the
condition of zeroing the third term
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Implementation
Maximum likelihood equation is solved with
modified Newton-Raphson method
Modification forbids energy go below 0, which
would lead to divergence Normally, 4-6 iterations
are enough to reach the accuracy to the 5-th
decimal place
Pulse shapes from V2 are used for time filter of
A2 without modification
Energy estimator does not exist and is not
planned to be implemented as a standalone energy
reconstruction program. Instead, A2 contains V2
vertex fitter and after calling it for vertex
reconstruction calls the energy estimation
subroutine. A user just calls A2 instead of V2
and gets x, y, z, t0 and E. Such a choice is
conditioned by the fact that the energy estimator
described here relies on t0 value which is
returned by the V2 vertex fitter.
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A2 performance resolution at medium energies
A2
KAT
?0.0983
?0.112
Evis, MeV
Evis, MeV
Reconstructed visible energy from Co-60 source
KAT
A2
?0.076
?0.061
Evis, MeV
Evis, MeV
Reconstructed visible energy from Zn-65 source
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A2 performance resolution at lower energies
A2
KAT
?0.059
?0.074
Evis, MeV
Evis, MeV
Reconstructed visible energy from Ge-68 source
A2
KAT
?0.023
?0.033
Evis, MeV
Evis, MeV
Reconstructed visible energy from Hg-203 source
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Lowest energies is where time filter comes into
play
A2 TF disabled
A2 normal
?0.098
?0.100
Time filter disabled on Co-60 2 resolution loss
A2 normal
A2 TF disabled
?0.023
?0.030
Time filter disabled on Hg-203 33 resolution
loss
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A more important benefit of time filter
Fidelity of energy scale at lower energies is
improved
Hg-203 peak position, MeV, depending on the dark
rate parameters put into the fit

• Time filter practically eliminates the
  dependence on hit time window estimation
• Time filter decreases the influence of dark rate
  estimation error by a factor of 3

Time filter doesnt abolish the necessity of dark
rate monitoring but minimizes the effect of
possible errors in its estimation
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Table of visible energies and energy resolutions
obtained with A2
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Energy scale reconstructed by A2
Zn-65
A2
Co-60
Ge-68
KAT
Hg-203
Lower ratio for Co-60 reconstructed by A2 is
associated with the omission of pulse shape
variations in the current version
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Speed of operation
Full A2 run for 35659 1MeV events (incl. vertex
reconstruction with V2) 49 sec gt Pure energy
reconstruction time is18 sec Standard Tohoku
energy estimator 90 sec for energy
reconstruction alone
Hardware 3.067 GHz Intel Xeon gcc 3.4.4, Linux
compiler options-O2 funroll-loops
fomit-frame-pointer marchpentium3
performance ratio on different platforms may
differ
Bottom line
The energy estimator included in A2 provides a
significant (more than 4-times) improvement of
speed compared to the current standard tool. Use
of the new reconstruction utilities (vertex and
energy) can cut the computation times by a factor
2 to 3.
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To do list

• Provide the correction for pulse shape variation
  similar to what is done in V2
• Perform extensive tests at different vertices
  and fine-tune the bi parameters in the whole
  volume
• Implement the correction for dead PMTs
• Extend the coverage with ?(q,µ) functions with
  MC to the occupancy ranges where direct
  calibrations are not available till it is safe to
  consider them Gaussian
• (If proves necessary) Include the discriminator
  misfire into the model

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Summary

• A new energy fitter algorithm has been developed
  and has passed preliminary testing.
• It accommodates hit, charge and time information
  through a common likelihood function, providing a
  natural and seamless transition from a purely
  hit-based estimator at lower energies to a mostly
  charge-based one at higher ones.
• A significant improvement in resolution,
  especially at low energies, is achieved.
• Dark rate filtering technique offers the
  improvement in the fidelity of energy scale at
  low energies.
• The speed of operation is substantially higher
  than that of the existing tools at the Tohoku
  University.
• Work in progress.