R. Porrata, Berkeley, March 2005

New Vertex Location and Energy Reconstruction Techniques

Using the Arrival Information of All Measured Photons

Rodín Porrata

UC Berkeley, Price Group

R. Porrata, Berkeley, March 2005

New Vertex and Energy Reconstruction Techniques for Cascades

Requirements: • Self-contained (no external minimizer) -> usable online• Very accurate vertex and energy reco -> usable offline

Some history: Spiesberger -> Vanderbrouke -> Porrata• Spiesberger: Passive acoustic location of marine fauna.

-> Basic SVD localization algorithm (assumes no delays).• Vanderbrouke: Use to locate EHE GZK acoustic signals? • Porrata: Adapt for use in environments where signal is scattered,

i.e., photons from cascades scattered by dust in ice.

Energy reconstruction obvious:• if allowed to use all photon info, e.g., DOMs, TWR,• if have very good vertex location.

R. Porrata, Berkeley, March 2005

Spiesberger’s SVD Porpoise Location Algorithm

For each of N hit OMs define the following N spherical wave equations:

Nonlinear in parameters.

Where:

Subtract the first equation from the rest, get N-1 paraboloid equations:

The i are time differences.The ti are the measured times assuming no scattering.The Ti are unscattered light propagation times.

These equations are linear in the 4 unknowns.

R. Porrata, Berkeley, March 2005

Spiesberger’s SVD Porpoise Location Algorithm

Have N-1 linear paraboloid equations and 4 unknowns.

Define: Where:

Perform the singular value decomposition of A:

Then the solution is given by:

As is, must use time of first hit only, as estimate of unscattered light propagation time.

R. Porrata, Berkeley, March 2005

Method of Energy Reconstruction

i = average number of photoelectrons expected.ni = measured number of photoelectrons.

Product of Poisson probabilities for seeing exactly n photoelectrons.

Take the derivative w.r.t. the energy. Set to zero. Solve.

Do not need 4800 separate quantities to calculate. One scalar vs position only!

The solution is trivial provided that (we can really count photoelectrons):1. DAQ response is linear.2. Feature extraction of waveforms is linear.3. Have a good model of photon propagation and through the ice.4. Have already obtained an accurate vertex location.

R. Porrata, Berkeley, March 2005

Simulation

Loop over events:• Obtain event position and energy• Loop over OMs:

Calculate number of photoelectrons, (d, ), according to diffusive approximation.

Poisson distribute to obtain nhits at OM.Distribute in time taking into account:

1. Un-scattered light propagation time, and2. Gamma distribution provides time delays due to scattering.

Write out hits• Write out EventEnd loop

•Vfid = 4.07 km3, •Vtrig (M=1) = 1.83 km3,

Simulated 1000 isotropic point source events at 100 TeV in dusty ice with a 4800 OM Ice3 array.

These studies indicative only!

R. Porrata, Berkeley, March 2005

Testing the Algorithm in Dust Free Ice

Cuts:• Ndir > 10• Chi2 < 10

Results (are ludicrous):• Veff = 1.5 km3

• E = 0.011 in log(E)• Fom = 136.0

R. Porrata, Berkeley, March 2005

Testing the Algorithm Blind

Dusty ice.

Cut: fit < 1 km

Results (so-so):• Veff = 2.28 km3

• E = 0.16 in log(E)• Fom = 14.25

R. Porrata, Berkeley, March 2005

1. Weight rows of A with:

2. Use variance of distribution and number of hits to estimate delay from direct time.

3. Subtract off estimated delay from measured time of first hit.

4. Require at least 4 photons to determine variance of the distribution.

Taking into Account the Distribution of the Photon Arrival Times in Dusty Ice

R. Porrata, Berkeley, March 2005

Taking into Account the Distribution of the Photon Arrival Times in Dusty Ice

1) Weighted ACuts:• Concentration > 25• fit < 600 m

Results:• Veff = 0.79 km3

• E = 0.11 in log(E)• Fom = 7.18

R. Porrata, Berkeley, March 2005

Taking into Account the Distribution of the Photon Arrival Times in Dusty Ice

1) Weighted A2) Subtracted estimated delay time.• N > 4• Concentration > 20• fit < 600 m

Results:• Veff = 1.07 km3

• E = 0.074 in log(E)• Fom = 14.5R. Porrata, Berkeley, March 2005

Energy Resolution = 0.074

R. Porrata, Berkeley, March 2005

Conclusions, Caveats and Outlook

• Will reach energy reconstruction specifications at “first guess”!

• Have not yet taken into account direction. Working on this.

• Method strongly depends on Ice3’s advertised ability to make sense of waveform information! Seckel’s method looks like it will produce the most physically meaningful photon times.

• Plan to code into IceRec software.

• Expect improvements as photon propagation is better modeled (see my earlier talk on photon propagation).

• Expect improvements when method is iterated.