Muon Energy reconstruction in IceCube and neutrino flux measurement Dmitry Chirkin, University of Wisconsin at Madison, U.S.A., MANTS meeting, fall 2009
Jan 19, 2016
Muon Energy reconstruction in IceCube and neutrino flux measurement
Dmitry Chirkin, University of Wisconsin at Madison, U.S.A.,MANTS meeting, fall 2009
Muon Energy reconstruction in IceCube
• parameterization of light pattern created by a muon
• fitting of event data to this light pattern
• calibration of the fitted parameter to get the muon energy
IceCube DOM
3 ATWD channels with gains ¼/2/16Up to 12 s combined waveform length
Up to 200-300 p.e./10 ns charge resolution
Number of photons vs. muon energyIn ice muon energy loss is dE/dx=a+bE with
a=0.26 GeV / mwe (1 mwe = 1/0.917 m of ice)b=0.36 10-3 / mwe
A bare muon generates Cherenkov photons
This is about 32440 Cherenkov photons per meter of muon track at visible wavelengths.
From Geant-based simulations each cascade left by a muon generates as much light as a bare muon with the length of track of
4.37 m E / GeV for electromagnetic cascades3.50 m E / GeV for hadronic cascades
For a typical muon the average is ~ 4.22 meters E/GeV
A typical cascade emits 4.2232440 = 1.37 105 photons/GeV for a muon track the “photon density parameter” isArea . Nc [m] = 32440 [m-1] (1.22+1.36 . 10-3 E/[GeV]) . 492.10 cm2 . F
= 2107.84 [m] (1.22+1.36 . 10-3 E/[GeV])
F=PMT efficiency, glass/gel transmission, etc.
Parameterization of the photon field left by a muon
The flux function: total expected number of photons μ arriving at each OM.
The parameterization of the flux function (as used by an icetray module MuE) is based on the following premises:
μ = Nl · μ0(d), where Nl is the average number of photons emitted per unit length of a muon track and d is the distance to the track. precise if the muon track is infinite and emits the same number of Cherenkov photons per unit length anywhere along its track.
In the immediate vicinity of the track:
Far:
We can stitch these together with
Other flux function parameterizations
• based on PDF evaluated by explicit photon propagation simulations with photonics, which take into account the exact ice structure
semi-infinite muon parameterization light saber (uniform cascades along track)
• the above treatment employs layered ice treatment as well, but through the average scattering and absorption approximations.
• fitting to decreasing amount of light along track• fitting to segments of the muon track• single OM energy estimates along track
Fitting data to the parameterized photon field
likelihood function for the track hypothesis used in event reconstruction is:
The total number of photons observed by an OM is:
the corresponding expectation is:
since
In the presence of systematic uncertainties in the flux function, expression above can be integrated over the possibilities allowed by the uncertainties, or one employs the 2 sum minimization instead, with errors accounting for both statistical and systematic uncertainties.
Energy calibration with simulation and resolution
Muon true (simulated) energy at the closest approach point to the center of gravity of hits in the event (weighted with charge)
Energy proxy: reconstructed number of cherenkov photons per unit length times effective area of the PMT
~ 0.3
dE/dx vs. number of Cherenkov photons
• reconstructing dE/dx: a convenient approximation number of Cherenkov photons is almost proportional to dE/dx
• final “calibrated” energy parameter is what is most convenient to one’s analysis: Rate of energy loss, or dE/dx: best, e.g., for muon bundles Muon energy at closest approach point to center-of-gravity of hits
Muon energy reconstruction
Conclusions:
• several light parameterization schemes exist
• various fitting algorithms are used
• Energy resolution of ~ 0.3 in log10(E [GeV]) is normally achieved
Neutrino energy spectrum unfolding
• event selection
• parameter distributions
• smearing/unfolding matrix
• summary of unfolding techniques
• verifying the unfolding algorithm
• measuring the neutrino spectrum
Event selection
8548
eve
nts
4492
eve
nts
854
8 e
ven
ts
449
2 e
ven
ts
2290
eve
nts
229
0 e
ven
ts
275.5 days of IceCube (22 strings) taken in 2007
My own framework for applying cuts: SBM (subset browsing method)
30 parameters identified to separate signal and backgroundStep 1: constructs surface separating signal from backgroundStep 2: additional requirements for similarity with simulated signal
atmospheric satmospheric s
(sim
ula
ted
s
and
s)
90 – 180o
90 – 120o
120 – 150o
150 – 180o
~90% 95% 99% purity
Muon energy resolution
Precision of the energy measurement: reconstructed vs. simulated true:
~ 0.3 in log10(E)
True (from simulation) muon energy distribution
reconstructed muon energy distribution
simulationdata
Parameter distributions
Reconstructed zenith angle distribution
datasimulation
datasimulation
Center of gravity (COG), or “average” event depth
Point-spread function (PSF):Median angular resolution is ~ 2o.
2400 2200 2000 1800 1600center of gravity depth [m]
horiz
onta
l
vert
ical
up
Neutrino energy from reconstructed muon energy
Transformation/unfolding matrix
What we have:
muon energy at detector with 0.3 in log10(E) resolution
and its zenith angle with ~1.5o resolution
What we want:
muon neutrino energy distribution
The transformation matrix is known from the simulation and relates muon and neutrino numbers:
m=An
Unfolding methods
Performance of the following unfolding methods was studied:
Simple inversion and no-regularization 2 and likelihood minimization
SVD (singular value decomposition):• regularizing with the 2nd derivative of the unfolded statistical weight• regularizing with the 2nd derivative of the unfolded log(flux)
This is the selected method as it has the best behavior for:constant spectral index regularization term goes to 0best identification of deviations from the given
spectrum• also added the likelihood term describing fluctuations in the unfolding matrix
Bayesian iterative unfolding:• with and without smoothing of the unfolding matrix
Statistical uncertainties
The following method is selected:
Expand the regularization term in the vicinity of the minimum: constant term sum of first derivatives, creating a bias for counts in each bin sum of second derivatives, which tightens the minimum
Introduce modified likelihood function by keeping the Poisson sum, and only the bias term from the regularization term (so that the minimum found during the unfolding does not change). However, do not include the sum of second derivatives of the regularization term.
Vary the unfolded counts in each bin (independently) till modified likelihood function increases by ½.
Testing for bias, diffuse E-2 flux
Testing for spectral index, charm contribution
rqpm
Errors from belt construction, ½-likelihood estimate
From 1000 simulations For a single representative simulation
Including fluctuations of the smearing matrix
Unfolded data For a single representative simulation
9938 15 4.6 2.1 0.3
cf. AMANDA-II 2000-3: ~ 1.2
1.9 0.5 0.1
preliminary
Unfolded data at 2 different quality levels
preliminary preliminary
Unfolded data with only events in the top or bottom
preliminary preliminary
Conclusions and Outlook
• Despite some residual problems in detector simulation, agreement with Barr. et al. (Bartol) muon neutrino flux is demonstrated
• Improving the simulation is actively pursued, and the result with reduced systematic (and smearing matrix statistical) uncertainties is forthcoming
preliminary