CORSIKA Follow Up to Vetoing
Atmospheric Neutrinos In High
Energy Telescopes
Kyle Jero
What’s The Big Deal Anyway?
• Typical methods for high energy
astrophysical neutrino detection
rely on using the Earth to shield
from cosmic ray muons or
detecting a different spectra than
observed in cosmic rays.
• A new method proposed by
Schönert et al. exploits a property
of atmospheric showers that
assists in distinguishing between
muon neutrinos of atmospheric
and astrophysical sources
The Idea
• Atmospheric neutrinos come almost exclusively from
charged pions and kaons decays
• 99.99% of pions and 63.4% of kaons decay into a muon and
muon neutrino
• The created muons have a “guaranteed” energy which
can be calculated with relativistic kinematics and are
nearly collinear with the neutrino
• The result is that muon neutrinos from air showers
always have at least one accompanying muon which can
penetrate to the depth of IceCube if the muon’s energy
is large enough to survive the trip through the ice
• Muons need ~300 GeV of energy to survive
• This makes it relatively easy to find astrophysical
neutrinos with IceCube since astrophysical neutrinos
may interact within the detector volume leaving no
energy at the detector’s edge while atmospheric
neutrinos with an accompanying muon will almost
always leave energy at the detector’s edge
Kinematics
𝑖 = π 𝑜𝑟 𝐾
𝑐=1
𝐸𝑖 > 𝑠𝑒𝑣𝑒𝑟𝑎𝑙 𝐺𝑒𝑉
𝑚𝑎𝑘𝑒𝑠 β~1
In CM Frame
𝑃𝑖 = 𝑚𝑖 , 0,0,0
Boosting Into Lab Frame
𝑃μ = 𝐸μ , 𝒑𝝁
𝑃ν = 𝐸ν , 𝒑𝝂
𝑝ν𝑥 𝐶𝑀 = 𝒑𝑪𝑴 cos θν
𝑃𝑖 = 𝑃μ + 𝑃ν → 𝑃ν = 𝑃μ − 𝑃𝑖
𝑃ν 2 = 𝑃μ − 𝑃𝑖
2
2
𝑃ν = 0
2
𝑚
+ 𝑚μ
𝑖
0 = 𝑚μ 2 + 𝑚𝑖 2 − 2𝑚𝑖 𝐸μ → 𝐸μ =
2𝑚𝑖
𝑚𝑖 2 + 𝑚μ
𝐸ν = 𝐸𝑖 − 𝐸μ = 𝑚𝑖 −
2𝑚𝑖
𝑚𝑖 2 − 𝑚μ
𝐸ν =
2𝑚𝑖
2
𝑝μ𝑥 𝐶𝑀 = 𝒑𝑪𝑴 cos( θν − π) = − 𝒑𝑪𝑴 cos θν
→ 𝑃ν 2 = 𝑃μ 2 + 𝑃𝑖 2 −2𝑃μ 𝑃𝑖
𝑃μ 𝑃𝑖 = 𝐸𝑖 𝐸μ − 𝒑𝒊 𝒑𝝁 = 𝑚𝑖 𝐸μ
2
𝐸μ = γ(𝐸μ 𝐶𝑀 + β𝑝𝜇𝑥 𝐶𝑀 ) 𝐸ν = γ(𝐸ν 𝐶𝑀 + β𝑝ν𝑥 𝐶𝑀 )
2
𝐸ν = γ 𝒑𝑪𝑴 (1 + cos θν )
2
𝐸μ = γ 𝒑𝑪𝑴
𝑚𝑖 2 + 𝑚μ
(
2 − cos θν )
2
𝑚𝑖 − 𝑚μ
𝐼𝑛 𝑡ℎ𝑒 𝑤𝑜𝑟𝑠𝑡 𝑐𝑎𝑠𝑒 cos θν = 1
𝐸ν = 2γ 𝒑𝑪𝑴
𝐸μ ≥ 𝐸ν (
𝐸μ = 2γ 𝒑𝑪𝑴 (
𝑚μ 2
2
𝑚𝑖 − 𝑚μ
2)
𝑚μ 2
2
𝑚𝑖 − 𝑚μ
2)
Kinematics
𝐸μ ≥ 𝐸ν (
𝑚μ 2
2
𝑚𝑖 − 𝑚μ
𝐸μ ≥ 1.342 𝐸ν 𝑓𝑜𝑟 π
2)
𝐸μ ≥ 0.048 𝐸ν 𝑓𝑜𝑟 𝐾
• Can also show that the neutrino and muon deviate less
than 1m (10m) over a 10 km path for neutrino energies
greater than 1 TeV originating from a pion (kaon) decay
• These calculations prove that a nearly collinear muon with
at least 1.342 TeV (48 GeV) in energy is created for almost
all atmospheric muon neutrinos with energy over 1 TeV
which originated from pion (kaon) decays
What Can Be Done With This Information?
𝑥
𝑘𝑚.𝑤.𝑒
2.8
• Using 𝐸μ,𝑚𝑖𝑛 𝑥 = 0.73𝑇𝑒𝑉 × (𝑒
− 1) from Muon Monte
Carlo to give an estimate of the muon’s energy at depth one can
produce the plot below
• The plot shows that for neutrino energies above ~104 GeV and zenith
angles less than ~55⁰ there exists a region where an atmospheric
muon neutrino will have an
accompanying muon
• To find events one searches
for events that are starting
tracks above a certain
energy and below a certain
zenith angle
• This is the basis for the
search done by Nathan and
Claudio
What Else Can Be Done?
• Verify the result with air shower simulation
• Simulation would allow for the properties of the
entire shower to be studied rather than just the
single decay and provide answers to questions like
– Do we gain something from the additional muons
created in other branches of the shower?
– Do electron neutrinos in air showers also have this
property?
• The results can also help calculate the significance
of events found by starting track analyses
Analysis Overview
Cosmic Ray Spectrum
Model after observed spectrum
Air Shower Simulation
Produce and propagate particles created in primary interaction
and subsequent interactions/decays
Muon Propagation
Track muons through the ice with proper energy losses
Analysis
What are the properties of the surviving muons and neutrinos?
Cosmic Ray Spectrum and CORSIKA
• Use a five component version of Hörandel’s Poly-Ganato model
•
•
•
Poly-Ganato is a phenomenological model of cosmic ray energies that fits well to
the measured spectrum
Five components means the primary can be a H, He, N, Al, or Fe nucleus
Uses weighting to represent the frequency with which a randomly generated
primary naturally occurs
• Use CORSIKA to generate a primary
•
Randomly select an energy between 10 TeV and 10 EeV sampled from a power law
spectrum for the primary particle
•
•
E-2 and E-1 power laws used with 2.625x106 files generated for each
Randomly select a zenith and azimuth sampled uniformly from 0 - 89 degrees and
0 - 360 degrees respectively
• QGSJET-1C high energy cross-section model chosen for it’s charm treatment
• Set magnetic field and atmospheric model based on measurements taken from
the South Pole
• Stop tracking particles when they can no longer produce neutrinos of energy
>1TeV and muons of energy >100 GeV
• Track all surviving particles in the shower to the surface of the ice
Propagation and Analysis
• MMC simulates the interactions that occur as a muon passes through
matter (ice) and tracks the energy losses associated with the interactions
• Initial energy and the overburden and are fed into MMC
• MMC determines if the muon survived for the specified overburden and if
so what it’s final energy was
• The surviving muons in each
shower are treated as an
accompanying buddle for every
neutrino in the shower
• If the energy of the bundle is
above 1 TeV such an event is
said to trigger IceCube
• With information on each
neutrinos energy and zenith one
can make a plot for comparison
to the original paper
• White line gives veto probability ≅ 1 from the Schönert et al. plot
which corresponds to a passing rate of 0
• Simulation agrees with the predicted results and indicates a factor
of 4-5 is gained from including other parts of the shower
• Below 104 GeV is still being populated and is subject to change
• Simulation shows a similar region exists for electron neutrinos. However, charm
interactions can give a large amount of the primary energy to an electron and electron
neutrino, leaving little energy for muons to be produced in other branches of the shower.
This means that electron neutrinos without accompanying muon bundle energy greater
than 1 TeV are more likely to occur for electron neutrinos than muon neutrinos. These are
represented by the regions with a passing rate of 1 (red) surrounded by passing rates near
zero (blue)
• Below 104 GeV is still being populated and is subject to change
Fin