statistical power of mass hierarchy measurement (with ORCA) Aart Heijboer, Nikhef

Aart Heijboer ● ORCA * catania workshop

sep 2009

1

statistical power of mass hierarchy measurement(with ORCA)Aart Heijboer, Nikhef


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


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


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


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


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)


sep 2009

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Interaction rates


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


sep 2009

9

Effect of detector on oscillogram: NH


sep 2009

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Effect of detector on oscillogram: IH


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).


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


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


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.


sep 2009

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likelihood ratio distribution...

...for toy experimentsin which the truehierarchy is normalor inverted.

remember: resultsdepend cruciallyon assumptionson resolution anddetector layour andacceptance


sep 2009

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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.


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 )

statistical power of mass hierarchy measurement (with ORCA) Aart Heijboer, Nikhef

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