#### Transcript Talk given at November 2005 very large neutrino

Maximum likelihood reconstruction of events using waveforms Sean Grullon with Gary Hill Overview VLVnT2 November 8th-11th 2005 • Introduction & Motivation • Likelihood Formulation • waveform-loglikelihood-reco project in IceCube software framework • Preliminary Results using IceCube simulated Data • Current Development and Future Directions Sean Grullon w/ Gary Hill 2 Introduction & Motivation VLVnT2 • November 8th-11th 2005 All reconstruction algorithms in IceCube are ported from AMANDA. • Originally developed for AMANDA’s primary DAQ. – • • • • • • records Time over Threshold (TOT), the leading edge time (LE), and the Peak Amplitude. The Full waveform is not captured Incorporates Leading Edge time & peak amplitude information only. Uses the Pandel function which analytically parameterizes timing PDF in ice. Ice assumed to be homogeneous. Full detail regarding the AMANDA reconstruction algorithms can be found at Nuc. Ins. Meth. A 524 169(2004) Focus of talk is on the development of a new reconstruction aglorithm using the full waveform Sean Grullon w/ Gary Hill 3 IceCube waveforms VLVnT2 • November 8th-11th 2005 • • • Voltage (mV) • IceCube’s Analog Transient Waveform Digitizer (ATWD) captures and digitizes full waveform in situ with a ~ 420 ns time window Should prove powerful for high energy & non-contained events. FWHM of Waveform Depends linearly on the distance from the event to the optical module New algorithms need to be developed to take advantage of full waveform information A high priority since deployment has already begun. Sean Grullon w/ Gary Hill ATWD Sample # 4 Example Extracted waveform VLVnT2 November 8th-11th 2005 • Event generated by Nitrogen laser located at a depth of 1850 m in AMANDA Array. Pulse Shapes recorded at 3 distances from laser. (45m, 115m, and 167m) Sean Grullon w/ Gary Hill 5 Likelihood Formulation VLVnT2 November 8th-11th 2005 • How can you formulate a likelihood function with the full waveform at your disposal? • With the full waveform, we know: – arrival time distribution of the photons – the probability of these arrival times. • Given an expected distribution of photons μp(t), what is the probability of observing a waveform f(t)? – p(t) is normalized timing PDF, μ is the total number of expected photons, given either numerically or analytically. – f(t) is your observed waveform Sean Grullon w/ Gary Hill 6 Probability of f(t) given p(t)? VLVnT2 November 8th-11th 2005 •Suppose you bin the photon distributions into k time bins: f (t ) {ni } k n i 1 i N p (t ) {i } •The probability is given by Poisson statistics, as a product of Poisson probabilities over all the k bins: k P({ni } | {i }) i 1 Sean Grullon w/ Gary Hill i ni ni ! e i 7 This product turns into something useful…. VLVnT2 November 8th-11th 2005 k k P({ni } | {i }) i 1 i n i ni ni ! i 1 k n i k i e i 1 i 1 k P({ni } | {i }) N ! i 1 Sean Grullon w/ Gary Hill ni ! N! i ni N e 8 We have our Likelihood Function VLVnT2 November 8th-11th 2005 • Take the negative log of it i ni N k log P ({ni } | {i }) log N ! e i 1 ni ! N ! k k i 1 i 1 log N ! ni log i log ni ! N log log N ! k k i 1 i 1 ni log i log ni ! N log Sean Grullon w/ Gary Hill 9 Our likelihood function – cont. VLVnT2 November 8th-11th 2005 k log P({ni } | {i }) ni log pi N log i 1 •Likelihood minimized for every optical module Sean Grullon w/ Gary Hill 10 Where is this applicable? VLVnT2 November 8th-11th 2005 • 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. Sean Grullon w/ Gary Hill 11 IceCube software framework VLVnT2 November 8th-11th 2005 • The IceCube software framework is called IceTray. • unified object oriented C++ framework for handling online filtering and offline-software for reconstruction, analysis, and simulation. • IceTray modules operate on the IceCube data stream. • Modules perform specialized tasks such as reconstructions, calibrations, etc. • Uses boost C++ libraries for offline data. Data can be saved into a binary format or XML format. Sean Grullon w/ Gary Hill 12 IceCube data stream VLVnT2 November 8th-11th 2005 Sean Grullon w/ Gary Hill 13 Waveform loglikelihood reconstruction project VLVnT2 November 8th-11th 2005 • This likelihood reconstruction algorithm is currently implemented in IceTray. • Currently reconstructing electromagnetic cascades. • User has the option of selecting an analytical PDF (Pandel function) or a numerical PDF. • The numerical PDF in IceCube is Photonics, a numerical framework that simulates photon propagation in the ice. • Uses the SIMPLEX minimizer. • Uses calibrated ATWD waveform directly. Sean Grullon w/ Gary Hill 14 Preliminary Results VLVnT2 8th-11th November 2005 • 2500 cascade events with an energy of 100 TeV generated • Generated with a random vertex position and direction. • Full IceCube simulation used. • ~¼ of the events are not contained in the array (Up to 50 m away) • Free parameters of fit are the vertex, the energy, and the time. • Results compared to the AMANDA style cascade reconstruction algorithm. Sean Grullon w/ Gary Hill 15 VLVnT2 November 8th-11th 2005 Sean Grullon w/ Gary Hill 16 Preliminary Results Using Full Simulation: Vertex X VLVnT2 November 8th-11th 2005 RMS: 38.15 RMS: 49.62 •Accurate Vertex Reconstruction requires directional fit •Results not a final performance indication Sean Grullon w/ Gary Hill 17 Preliminary Results Using Full Simulation: Vertex Y VLVnT2 November 8th-11th 2005 RMS: 36.32 Sean Grullon w/ Gary Hill RMS: 48.62 18 Preliminary Results Using Full Simulation: Vertex Z VLVnT2 November 8th-11th 2005 RMS: 29.65 Sean Grullon w/ Gary Hill RMS: 51.23 19 Preliminary Results Using Full Simulation: Energy VLVnT2 November 8th-11th 2005 Sean Grullon w/ Gary Hill 20 Current Development and Future Directions VLVnT2 November 8th-11th 2005 • Currently testing new Photon tables with 3-D photon tracking as the PDF for reconstruction • Investigate reconstructing the cascade direction. • Make the project part of the official IceTray release. • Look at some sort of hit cleaning to improve results • Improve algorithm performance for noncontained events. • Look at other event types • Optimize the performance Sean Grullon w/ Gary Hill 21