# Sean Grullon w/ Gary Hill Maximum likelihood reconstruction of events using waveforms.

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Sean Grullon w/ Gary Hill Maximum likelihood reconstruction of events using waveforms

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill2 Overview Introduction & Motivation Likelihood Formulation wf-llh-reco project in IceTray Results using Simulation V01-00- 04 Current Development and Future Directions Discussion

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill3 Introduction & Motivation All reconstruction algorithms in IceRec are ported from AMANDA. –Were originally developed for the Muon- DAQ… (TOTs, LEs, Peak Amp.) Need new algorithm(s) to take advantage of the full waveform information Icecube provides. Full Waveform information should prove powerful for high energy & non-contained events. A high priority since deployment has already begun.

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill4 Likelihood Formulation How can you formulate a likelihood function with the full waveform at your disposal? Given an expected distribution of photons μp(t), what is the probability of observing a waveform f(t)? –p(t) is normalized timing probability, μ is the total number of expected photons, given either numerically (Photonics) or analytically (e.g. Pandel) – f(t) is your observed waveform

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill5 Probability of f(t) given p(t)? Suppose you bin the photon distributions into k bins:

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill6 Probability of {n i } | {μ i } ? The probability is given by Poisson statistics, as a product of Poisson probabilities over all the k bins:

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill7 This product turns into something useful….

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill8 … Namely a multinomial distribution, the probability of arranging exactly N events into k bins, multiplied by the Poisson probability of these N events occurring.

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill9 This product turns into..

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill10 We have our Likelihood Function Take the negative log of it

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill11 Our likelihood function – cont.

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill12 Where is this applicable? We assumed we knew the photon arrival times precisely, or have a waveform made from the superposition of many photons. If we have a non-delta function time response, this form is still applicable as long as our PDF is slowly varying over the region described by the OM time response. Should be the case for our optical modules, typical pulse widths are narrow relative to the scale of expected photon arrival time distribution.

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill13 wf-llh-reco module The icetray implementation of this likelihood reconstruction. Currently looking at (non-directional) cascades. Uses UPandel for the timing PDF. Uses the SIMPLEX minimizer in ROOT’s TMinuit class. Uses calibrated ATWD waveform directly and not the output of the Feature Extractor Module in the sandbox area of SVN, named wf-llh-reco.

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill14 Preliminary Results using Simulation V01-00-04 1000 100 TeV simple cascade events were generated locally in Madison by Paolo Desiati. Cascades were generated with a random vertex position and direction. Full IceCube simulation used layered photonics tables. Wf-llh-reco project results compared to cscd-llh project

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill15 Preliminary Results Using Simulation V01-00-04: Vertex X RMS: 38.15RMS: 49.4

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill16 Preliminary Results Using Simulation V01-00-04: Vertex Y RMS: 36.32RMS: 48.62

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill17 Preliminary Results Using Simulation V01-00-04: Vertex Z RMS: 29.65RMS: 51.23

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill18 Preliminary Results Using Simulation V01-00-04: Energy

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill19 Scatterplot of Z resolution vs. MC Z

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill20 Preliminary Results for an initial study of non-contained events 500 JULIET Toy Cascades simulated with layered photonics tables. Cascades simulated from 1PeV to under 10EeV All cascades non-contained, randomly distributed from just outside full Icecube array to 0.5 km away.

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill21 Non contained EHE events: Preliminary Energy Resolution

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill22 Non contained EHE cascades: Preliminary vertex resolution

IceCube Collaboration Meeting – Imperial College September 27th, 2005 September 2005 Sean Grullon w/ Gary Hill23 Current Development and Future Directions Currently implementing Photonics as the PDF for reconstruction Investigate reconstructing the cascade direction Move project from SVN sandbox to the IceRec meta-project. Look at some sort of hit cleaning to improve results Improve algorithm performance for non- contained events. Look at other event types Optimize the performance

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