6 on ?An Update on the 2000-2003 Diffuse Muon Neutrino Analysis

Jessica Hodges

Friday, December 16th

6 observed on ?Status: The analysis was unblinded several months ago and 6 events passed all cuts, including the final energy-dependent cut, Nch>=100.

Background Prediction: At the time of unblinding, the assumed background was composed of conventional atmospheric neutrinos using the Lipari weighting scheme. Overall normalization of 0.887 matched the Monte Carlo to the data. This led to a background prediction of 9.8 events.

Consider new neutrino flux predictions instead of Lipari (which is older and 1-dimensional)

Instead, consider two more recent calculations based on more up-to-date observations(use the values for Bartol and Honda from the NeutrinoFlux class developed by Alessio – summer 2005)

* BARTOL 2004* HKKM 2004

Differences in the Neutrino Spectrum arise from different ways to characterize:

1 – CR flux from different elements (H, He, heavier components)

2 – hadronic interactions, particularly kaon flux at high energy

(Ek) = K ( E

k + b e -C (Ek)0.5

)-

Honda and Bartol use similar, but not identical, values for the parameter for protons and the heavier elements.

However, the values are so close that the primary

cosmic ray spectra from Bartol and Honda are

identical to within 1%.

Four parameters are used to characterize the cosmic ray flux for each element.

pink solid line = HKKM 2004

dashed green line = BARTOL 2004

short dashed green line = old HKKM

taken from HKKM 2004 paper

HERE YOU CAN SEE THE DIFFERENCES BETWEEN THE BARTOL AND HONDA PROTON FLUXES

Despite small differences in the individual element inputs.....

For the all-nucleon cosmic ray spectrum, Bartol and Honda are the same to within 1%.

Since the CR all-nucleon inputs are roughly the same, any differences in the neutrino flux that arise between Bartol and Honda are from hadronic interactions.

old Bartol

Bartol 2004Honda 2004

Consider the red line only.(blue line still needs to be checked with higher statistics)

plot made by Teresa Montaruli

15%25%

Bartol 2004 and Honda 2004 are 15% different at 103 GeV = 1 TeV 25% different at 104 GeV = 10 TeV

Honda and Bartol are 25% different in their predicted NEUTRINO flux. Considering both of these models in my final result should encompass the range of uncertainty in the hadronic interaction model.

peak energy of atmospheric before energy cut103 GeV = 1 TeV

peak energy of atmospheric after energy cut104 GeV = 10 TeV

Neutrino energy is roughly a factor of 10 less than the CR primary energy

my atmospheric neutrinos come from this part of the CR spectrum

Change the spectral index of the neutrinos. Reweight events with: (Trueen[2] )-0.0X

In my region of interest, the lines are nearly parallel. Hence, changing the spectral index acts as a change in overall normalization.

This is because my events are very high energy and I am pivoting about a very low energy point.

Region of Interest

log10

E

Espectru

m

Thus far, I have explored these ways of changing my background prediction:

1) Changing the flux model.Bartol and Honda atmospheric neutrinos have different shapes

because they use different hadronic interaction models.

2) Changing the neutrino slope and hence the up/down normalization of the flux.

What other parameters can I study that might alter the number of events I predict as my background? * Need to check detector effects like OM sensitivity.

Assume that every OM has had its absolute sensitivity modified by +- 30%.

* Use 2003 nusim and data files (prepared identically in Zeuthen).

* Perform a 2-bin analysis like in Zeuthen.

Sensitivity Vertical Bin Horizontal Bin

70

100

130

The data ratio is 1.125. This indicates that at this cut level, the best fit to the OM sensitivity must be roughly between 110 and 120.

Does the optimal sensitivity change with cuts?

Zeuthen followed essentially the same procedure and found that the best fit sensitivity for their analysis was 92% +/- 10%.

So, YES, optimal OM sensitivity varies with the cuts.

--->>> Next, check my different cut levels and see what OM sensitivity is the best fit.

Look at the plots of sensitivity vs ratio.

Quickly eyeballing where the best fit OM sensitivity:

level 1 75-95level 2 100-115level 3 125-135level 4 135-145level 5 115-125level 6 110-120level 7 110-120level 8 150??level 9 105-125

level1

Note that these values are all over the place!

Is 115% consistent with 92%?

With this 2-bin zenith procedure, the value indicated for the OM sensitivity changes greatly with cut level.

Since Zeuthen's cuts are different than mine, given what I just told you, it seems natural that they would measure a best fit to the OM sensitivity that is different than mine.

Hence, it is difficult (read impossible with our current knowledge) to pinpoint the OM sensitivity to one single value that is independent of any given analysis.

The range of possible OM sensitivities is still wide open.

How to Proceed

1. Consider ALL of the possible models across the range of possible OM sensitivities.

2 hadronic interaction models (BARTOL, HONDA)

7 neutrino spectrum power laws (+0.4, +.02, +.01, 0, -.01, -.02, -.03)

2. Choose a subset of these scenarios as the “best fit” or “most likely” scenarios.

3. Find out how many events are predicted for Nch>=100 for these “best fit” scenarios. Choose the largest and smallest as the range of possible background events.

Consider low energy data: Nch < 100 Data = 186 events. The 1 sigma range is 172 to 200 events.

Choose combos which cause the atmospheric neutrino prediction to fall within 1 sigma of the measured data value.

All of these combinations satisfy the condition that the number of low energy atmospheric neutrinos predicted falls within 1 sigma of the measured data value.

Count the number of events in the “best fit” scenarios for Nch>=100.

Average these numbers for table made with the Bartol flux. Repeat for Honda.

These two values will be input as the high and low range of the atmospheric neutrino background.

Next, need a prediction for how the signal behaves.

Is the signal affected differently by the OM sensitivity?

Yes, because higher energy events are not as affected by threshold effects.

Threshold effectsDramatically increasing the OM sensitivity pushes many low energy events into the survival region.

Ratio of number of events for 130% Lipari / 70% Lipari

Ratio of number of events for 130% Signal / 70% Signal

Consider the entire range, 70% to 130%, and the number of signal counts.

70% sensitivity: 15.7 counts in 2003100% sensitivity: 20.1 counts in 2003130% sensitivity: 25.8 counts in 2003

Hence, suppose that the signal should fluctuate by 25% in either direction from the value I predicted for the 4-year analysis.

For 2000-2003, I predicted 68.4 signal events after the energy cut. This could fluctuate to 51.3 or 85.5.

Final Steps

Take the range of predicted signal and background events and use these to smear out the confidence belt used to compute the limit.

Find the new limit with systematic errors.

Write a paper.

Be happy. :-)

The top pink proton fit is the BARTOL proton fit that you saw on the last page.

ATIC filled in the gap between 100 and 10000 GeV