PHY310: Lecture 16 Analyzing Data Road Map Step One: Defining the Data Set Where it came from Understanding the background physics What are the measured variables Second Topic Third Topic 1
Example Analysis We will be analyzing Super-Kamiokande Two Ring Data Measure the π mass We'll use it to understand some of the systematic errors Place limit on Sterile Neutrino Oscillations Done by C. Mauger as a doctoral thesis. Place limit on proton decay lifetime Look at neutron decays to a neutrino and a π While preparing this lecture, I realized SK has not published this lifetime (2007) We're doing original research 2
The Detector: Super-Kamiokande I A Water Cherenkov Detector Split into Inner Detector: The main active volume for physics measurements Water Total: about 32 kilotons 32,000 cubic meters 38 m Fiducial: about 22.5 kilotons 11046 photo multiplier tubes Outer Detector: Active shielding from entering particles, identify exiting particles Water Total: about 20 kilotons 2000 photo multiplier tubes 34 m 3
What is Fiducial Volume Jargon Alert Fiducial (Webster's): 1. Taken as a standard of reference 2. Founded on faith or trust 3. Having a nature to be trusted Fiducial Volume (Particle Physics): 2m 1. The volume used to make physics measurements 2. The volume where the detector is assumed to be well understood Super-Kamiokande Inner Detector Volume Super-Kamiokande Fiducial Volume 4
The SK Inner Detector The main volume used to make physics measurements About 40 meters tall and 35 meters in diameter 5
The SK Outer Detector Identify entering and exiting particles About 2 meters thick Notice how incredibly clear the water is. The bottom is 40 m deep 6
Events In Super-Kamiokande Ring Imaging Water Cherenkov Detectors Cherenkov Radiation: An EM bow wave cos c = 1 n index of refraction in water is n = 1.32 dn 1 2 sin c 1 2 dx n Measure light Tank of Water (all Active) light direction 7
Particles Seen in SK Super-Kamiokande can image charged particle β > 1/n, or about 0.75 That means relativistic γ > 1.5 Since energy loss is proportional to 1/β2, if we see a particle β 1 θc 45 Since everything is going the speed of light Often it's easier to measure time in distance, cτ 1 ns 30 cm 8
Atmospheric Neutrinos Created by cosmic rays Pass through earth to hit detector Path length between 10 km and 13000 km Geometry means up-down symmetric! Flux is easy to predict Upward neutrinos go a long ways Downward neutrinos don't 9
Atmospheric Neutrino Production proton Air + π νμ Junk μ+ π+ 1 νμ 1 anti-νμ 1 νe νμ e+ μ+ νe anti-νμ 10
Particle Zoology Lump particles and anti-particles together Hadrons Leptons Electrons Protons Charge: ±1 (lump electrons and positrons together) Charge: +1 Neutrons Unstable outside of nucleus Photons (γ) π± Charge: ±1 Lifetime: 26 ns (7.8m) Decays to a muon and muon neutrino π Charge: 0 Lifetime: 0.08 fs (femto = 10-15) Decays to two photons cτ = 24 nm Muons Charge: ±1 (lump muons and antimuons together) Lifetime: ~2.2 μs Decays to an electron, an electron neutrino, and a muon neutrino Electron Neutrino Charge: 0 Invisible Muon Neutrino Charge: 0 Invisible 11
Neutrino Interactions Neutrinos (mostly) don't interact, but when they do... Charged Current Interactions Changes a neutrino into a lepton (l is a muon or electron) Quasi-Elastic: νl + n l- + p, ˉνl + p l+ + n Single Pion Production: νl + N l + N + π±, νl + N l + N + π Neutral Current Interactions Neutrino in, Neutrino Out Single Pion Production: ν + N ν + N + π±, ν + N ν + N + π 12
Neutrino Oscillations in SK The elephant in the room for atmospheric neutrino analysis 2 2 2 P = sin 2 cos 1.27 m L E You don't need statistics to see that data doesn't fit no oscillations Model in Red, Data as Points, Best Fit in Green 13
Understanding the Oscillation Effect C.R. have same energies in North and South so do neutrinos L E up L E down Up-going neutrinos oscillate, down-going neutrinos don't Up-going neutrinos go much further than down-going 14
Our Data Samples Atmospheric Neutrino Data Exposure 1490 days June 1996 to April 2001 Atmospheric Neutrino Simulation Simulated Exposure 36500 days (100 years) Preselection Event Energy < 1335 MeV Exactly two reconstructed rings In the detector fiducial volume i.e. more than 2 m from the inner detector wall 15
Getting Started Create an Analysis Log Two Options Traditional: A paper binder where you write notes, and tape in any plots that you make. Electronic: A document (ooffice, msoffice) that you write notes and paste any plots that you make In either case: Note what you did Formulas used Derivations done Techniques applied Names of data files used Names of data files created Names of figure files created 16
The Data The data is in eventdata.txt Total Events: 48322 Data: 1739 Simulation: 46583 Notice the name is not good. You should rename it to tell you were you got it, and make notes in your analysis log Row Definitions: First Row: Number of variables Second Row: Names of Variables Rest of File: the Data Field Definitions All Events: Energy, invariant mass, momentum, decay times, zenith angle, track1 type, track1 energy, track2 type, track2 energy, event type Only MC: neutrino type, neutrino energy, neutrino zenith angle 17
Event Energies The visible energy in MeV data (type 0): all events MC (type 1 and 2): all simulated events. 18
The Event Energy Estimated assuming that all particles in the event are either electrons or photons Proportional to the total amount of charge collected from the PMTs 19