FLUCTUATIONS OF MUON ENERGY LOSSES Newt & Paolo Original method developed by Peter Steffan

ENERGY LOSS Energy loss vs. muon energy: There are two kinds of processes: Continuous: ionization Stochastic: Pair production, bremstrahlung, photonuclear interactions Above the critical energy (600 GeV in water) stochastic losses dominate. Very important that this plot only shows the average muon energy loss and no mention of fluctuations

Multiple Muon Events Each muon in a bundle of muons follows its own energy loss procedure depending on the energy of that muon and the energy loss recorded will be over several muons

ENERGY LOSS OF A SIMULATED MULTIPLE MUON EVENT(20TeV) Fluctuations due to stochatic losses A minimum ionisation loss component “Wild” fluctuations every where

FLUCTUATIONS DISTRIBUTION The peak occurs at the ionization losses level and all the other fluctuations are due to stochastic losses.In particular the ratio of variance to mean of this distribution seems high Large spread

SINGLE MUON EVENT(60TeV) There is a Certain degree of Consistency in These fluctuations A minimum ionisation loss component

MULTIPLE MUON EVENT 2 Energy=20TeV

MULTIPLE MUON EVENT 3 Energy=5TeV,5muons

SINGLE MUON EVENT 2 Energy=10TeV

SINGLE MUON EVENT 3 Energy=20TeV

Ice Properties The problem with studying this variable where we observe fluctuation of energy released(amplitude) is that ice properties themselves introduce some fluctuations into the observed amplitude

Reconstructed Errors B A Dust Dust True track Δθ Reco Track Clear Ice Large Amplitude Seen when lower is expected from reco track hypothesis B Dust Δθ Reco Track Clear Ice A Dust Small Amplitude Seen when large is expected from reco track hypothesis As photons get scattered in dust they run out of steam ; This process inherently introduces fluctuations

NEW ESTIMATORS y = σ B/<B> An estimator1 is defined, based on a comparison between the light produced by the muon and the light it would have produced if it was a minimum Ionizing muon: An estimator2 is derived from estimator 1 and is y = σ B/<B> B=Number of Observed Photon/Number of Photons expected from MIM

HIT AND EVENT SELECTION To overcome some of these problems partly I choose only direct hits(-15ns to 75 ns)(less effected by ice properties) Use hits with in 50m radius cylinder around the track(less scattered) Require the event to have at least 6 direct hits(more direct hits means more information to study the fluctuations ) Criteria on Track length and chi square to improve reconstruction quality Take only hits with amplitude greater 3.0 P.E for reconstruction.(No noise hits which will introduce some systematic fluctuations)

SIGNAL-BACKGROUND DISTRIBUTIONS Singles Multiples Keep These Sigma/average Sigma/average Linear scale Log scale Done with Reconstructed track(Con Pandel)

SIGNAL-BACKGROUND DISTRIBUTIONS Singles Multiples Keep These Sigma/average Sigma/average Lin scale Log scale Done with true track

SIGNAL-BACKGROUND DISTRIBUTIONS Singles When all hits are chosen Notice what happens? Any possible separation Of signal and background Through this parameter is masked out by the fluctuations Of ice properties Multiples Keep These Done with all hits (not just direct hits)

Correlation With Energy Keep these Keep These Y VS Nhits(Energy estimator) Y VS Nhits(Energy estimator) Single muon Events Multiple muon Events

Correlation With Muon Multiplicity No great correlation with multiplicity and pass rate is approximately same at all multiplicities think why? Depends on how the total energy is split among muons and sometimes muons end up with approximately same energies Keep these Y Vs Muon Multiplicity

Multiple Muon Event-1

Multiple Muon Event-2

Single Muon Event-1