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Aart Heijboer ● ORCA * catania workshop
sep 2009
1
statistical power of mass hierarchy measurement(with ORCA)Aart Heijboer, Nikhef
![Page 2: statistical power of mass hierarchy measurement (with ORCA) Aart Heijboer, Nikhef](https://reader035.vdocuments.us/reader035/viewer/2022062803/568147a3550346895db4dbe6/html5/thumbnails/2.jpg)
Aart Heijboer ● ORCA * catania workshop
sep 2009
2
Computing oscillations probabilities
2
3
4
56
F = U V
6 V
5 V
4 V
3 V
2 V
1 U-1
The product of transition matrices computedfor a matter of constant density
i.
Oscillation probability given by Pab
= |Fab
|2
with F the transition matrix is the flavour basis
several options to compute exp in practice Cayleigh-Hamilton formalism (hep-ph/9910546) Diagonalize H power series for exp.
Cross-checked with published plots and 'Globes' package.all methods agree
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Aart Heijboer ● ORCA * catania workshop
sep 2009
3
note allowed ranges are not identical for NH and IH → taken into account in the following plots
assumed zero
taken from most recent global-data fit Arxiv:1205.5254
Inputs for oscillations probabilities
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Aart Heijboer ● ORCA * catania workshop
sep 2009
4
Oscillation probability ( → ) for straight up
beware: there are also plots around which accidentally exaggerate the NH/IH difference by comparing the central value or NH with a IH curve at the ~1 sigma edge of the allowed global fit.
NH/IH difference largely degenerate with change in m2
large
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Aart Heijboer ● ORCA * catania workshop
sep 2009
5
Other zenith angles...
effect is fairly large, but... almost opposite for anti-neutrinos will be washed out by E- and angle
resolutions
next step: compute realistic event rates
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Aart Heijboer ● ORCA * catania workshop
sep 2009
6
Interaction rates : ingredients
cross-sections
neutrino fluxes (Bartol), include e
cross-sections from integrating DIS formula (approximates to ~20% genie and measurements)
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Aart Heijboer ● ORCA * catania workshop
sep 2009
7
Interaction rates
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Aart Heijboer ● ORCA * catania workshop
sep 2009
8
Adding detector effects
This is where the guess-work starts; all results depend crucially on these assumptions
assume zenith angle muon is measured perfectly. resolution comes for angle between and
Neutrino energy resolution: assume 25% requires reconstruction of muon and hadronic shower
Acceptance: neutrino vertex inside instrumented volumerequire 15 hits (educated guess: need direction, E-resolution,
rejection of atm. muons.).
geant4 simwith full photon
tracking
assumed detector:(100m)3 =1Mton
6x6 strings20 oms/string
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Aart Heijboer ● ORCA * catania workshop
sep 2009
9
Effect of detector on oscillogram: NH
![Page 10: statistical power of mass hierarchy measurement (with ORCA) Aart Heijboer, Nikhef](https://reader035.vdocuments.us/reader035/viewer/2022062803/568147a3550346895db4dbe6/html5/thumbnails/10.jpg)
Aart Heijboer ● ORCA * catania workshop
sep 2009
10
Effect of detector on oscillogram: IH
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Aart Heijboer ● ORCA * catania workshop
sep 2009
11
difference between NH(central values fromglobal fit) and IH (central values fromglobal fit)
after accounting for assumed detector resolutions: maximum rate difference between NH and IH ~10% to be compared to other uncertainties
(e.g. on mixing angles and masses → next slide).
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Aart Heijboer ● ORCA * catania workshop
sep 2009
12
effect of parameter uncertainties : NHeach plot compares central values with +1 sigma variation in each parameter
→ cannot be neglected: need to deal with these (nuisance) parameters
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Aart Heijboer ● ORCA * catania workshop
sep 2009
13
(Optimal) analysis to distinguish NH and IH
Optimal observable to distinguish between NH and IH hypotheses = Maximum likelihood rato
So this means, for each pseudo-experiment (data):1. assume NH and find by maximizing (this involves computing many smeared-oscillograms for NH)2. do the same for IH3. compute
The likehood contains a gaussian constraint representing the current knowledge from the global fit m2
21 and
21 are fixed in the fit to gain speed
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Aart Heijboer ● ORCA * catania workshop
sep 2009
14
Results of parameter fit on (NH) peudo-experiments
true value drawn from global-fit-allowed range
fitted
va
lue
ORCA can improve the current uncertainty for m2
large &
23
already with 1 year of data
13
) still dominated by other data
(via Gaussian constraint in the likelihood)after 10 Mtonyr → ORCA not very sensitive to it.
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Aart Heijboer ● ORCA * catania workshop
sep 2009
15
likelihood ratio distribution...
...for toy experimentsin which the truehierarchy is normalor inverted.
remember: resultsdepend cruciallyon assumptionson resolution anddetector layour andacceptance
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Aart Heijboer ● ORCA * catania workshop
sep 2009
16
likelihood ratio distribution
for toy experimentsin which the truehierarchy is normalor inverted.
remember: resultsdepend cruciallyon assumptionson resolution anddetector layour andacceptance.
expressed in sigma's,separation betweenNH and IH = 3 sigmawith 10 Mton x year.
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Aart Heijboer ● ORCA * catania workshop
sep 2009
17
Conclusions / thoughts
Full toy analysis set up, including oscillation fitgood sensitivity to m2
large &
23 before we can do MH
Determining MH is not an easy measurementFor assumed detector performance, need 10 Mton x year for 3 sigmaOf course, assumptions could be pessimisticStill several sources of systematic to be accounted for
(earth density, rate normalization, cross-sections,....)
Determining the mass hierarchy with this type of detector requires Large instrumented volume (1 Mton is not enough )
When we have full simulation and reconstruction, we should investigate sparse (or variable-density ) detectors
( But demands on (energy) reconstruction quality are very high )