Soudan 2

Peter Litchfield

University of Minnesota

For the Soudan 2 collaboration

Argonne-Minnesota-Oxford-RAL-Tufts-Western Washington

Analysis of all contained and most partially contained events published last year (PR D68 (2003) 113004)

New data on uncontained single muons have been extracted

A preliminary oscillation fit including the new data has been performed

Reduced 90% allowed region, still in good agreement with Super-K

Probability of no oscillations reduced by a factor 10, now 5.3∙10-5

Soudan 2

Fine granularity detector, originally built to study proton decay

Low threshold

Good particle ID and two track resolution

Surrounded by an efficient veto shield to tag non-neutrino events produced by neutrals from cosmic ray muon interactions

Previous dataData taking stopped in June 2001 with a fiducial exposure of 5.9 kton-years

Analysis of contained and most partially contained events was published last year

Soudan 2 can observe and reconstruct individual particles at the production vertex, including protons in quasi-elastic interactions. Much improved resolution on L/E over just detecting the lepton

Data divided into 6 sub-sets depending on topology and resolution

The “high resolution” sample showed clear evidence of oscillations in the L/E distribution

Previous resultsBin-free Likelihood analysis of contained and partially contained events using the Feldman-Cousins prescription

No oscillation hypothesis probability 5.8∙10-4

Partially contained Last summer’s analysis did not include events with a single with its upper end contained and lower end exiting the detector

Mixture of upward going (upmu) from interactions below the detector and downward going (downmu) from interactions in the detector

The fine granularity of Soudan 2 allows these to be separated

Downward , scattering increases downwards, proton recoil at top

Upward , scattering increases upwards, decay at top

Data reduction

The standard Soudan 2 analysis chain, program filter, physicist scan and interactive graphics event reconstruction, was used

The physicist scan included an estimate of the track direction (up or down)

MC events for interacting in the detector were already included in the data as originally processed

New MC events for interacting in the rock below the detector and with a stopping in the detector were generated and processed though the analysis chain

Soudan 2 has no fast timing, throughgoing upward and produced in the detector which leave the top of the detector and have little or no hadronic shower cannot be distinguished from the overwhelming background of downward cosmic

Backgrounds

Because of the flat overburden at Soudan the number of incoming, stopping upgoing cosmic ray muons was estimated to be negligible

Upward going tracks in the detector can arise from cosmic ray muon interactions in the rock producing upward going pions

We expect the veto shield to register extra hits from other particles produced in the interactions

Data

MC

Number of veto shield hits

Eve

nts

Backgrounds

We expect hadronic tracks to have a maximum range before they interact

Plot range v Veto shield hits

Range (g/cm2)

Vet

o sh

ield

hit

s

Data

MC Require that all veto shield hits are associated with the muon track

After Veto shield cut

After Veto shield cuts data and MC agree

Range g/cm2

Vet

o sh

ield

hit

s

Data

MC

To be sure that no hadronic background remains require range > 2 interaction lengths

Range >260 gm/cm2

Check, hadronic eventsSome events have obvious hadronic scatters

Shaded events only have veto shield hits associated with the track

Most have downward zeniths

None pass VS and range cuts

Confirms that the hadronic background is small

Range g/cm2

Vet

o sh

ield

hit

s

Range g/cm2

Cos(zenith)

Event numbers

Assigned asNo oscillation MC truth

Datadownmu upmu

downmu 13.31.4 0.70.2 17

upmu 1.90.5 58.41.9 26

ambiguous 0.90.4 3.60.5 2

MC error is the error due to the MC statistics

A small number of events did not have a distinguishable direction and were labeled ambiguous

The separation of up and down going muons is good

The data and MC agree on the number of downmu. These come from downward going neutrinos which the previous analysis has shown are largely unoscillated

The data has only 50% of the expected MC rate for the upmus. These come from upward going neutrinos from the other side of the earth which the previous analysis has shown to be suppressed by oscillations

Downmu

Energy of the outgoing muon is estimated from the multiple scattering, shown in the previous analysis of partially contained events to be a reasonable estimator

Can calculate L/E, shown in plot

Shaded events are MC events assigned the wrong direction

Data agrees well with the MC with no oscillations

In the fit to be described these events are added to the partially contained events already included in the previous fit

UpmuTracks are at the end of their range, no information on the hadron shower, no measurement of energy

Only observable is zenith angle or equivalently distance traveled L

Upward events suppressed, some evidence for reduced suppression near horizontal

Azimuthal angle is flat

Cos(zenith)

Eve

nts/

0.1

Upward going muons

New Oscillation Analysis

A new analysis incorporating the new data has been carried out using the same formalism as that published in PR D68

Bin-free maximum likelihood analysis using the Feldman-Cousins prescription

Likelihood is calculated on a 15x80 grid of sin22θ23 x log10m2

Likelihood difference with the best likelihood point obtained

Best fit point in the grid square centered at m2=0.0052 eV2 and sin22θ23=0.97 but the Super-K best fit point is not much worse

log10m2

sin22θ

23

L

Comparison with data

Best fitNo oscillationsSaturated oscillations

2/data points

PCE UPMU All data

No oscillations 5.0/5 9.4/4 62.2/30

Best fit 4.1/5 0.9/4 32.5/30

Saturated oscillations 18.2/5 0.8/4 59.9/30

Limits calculationIf all errors were statistical the 90% confidence region would be defined by a likelihood rise of 2.3 from the minimum

BUT errors are NOT statistical

Effects of physical boundaries (sin22θ23<1.0)

Errors on L/E are not gaussian

Flux normalisation and background subtraction introduces nuisance parameters

Systematic errors on calibrations, fluxes and cross-sections

Calculate confidence regions using the Feldman-Cousins prescription

Confidence level contours are calculated by performing MC experiments at each grid square, including experimental statistical and systematic variations, and calculating the likelihood difference between that square and the best likelihood

90% confidence contours defined by the likelihood difference that contains 90% of the MC experiments

Confidence limitsM

C90

sin22θ

23

log10m2

90% likelihood surface

Comparisons

Effect of new data Comparison with Super-K and MACRO

Old analysis

This analysis

Probability of no oscillations

To calculate the probability of no oscillations MC experiments are generated in the lowest m2, sin22θ23 grid square

300,000 experiments generated, including all statistical and systematic effects

Difference between the lowest negative log likelihood and that in this square (LMC) plotted

16 MC experiments had a LMC greater than the data likelihood (16.02)

Probability of no oscillations 5.3∙10-5

Summary

The new uncontained single muon data reconfirm the oscillation picture first demonstrated by Super-K and confirmed by previous Soudan 2 analyses

Small, if any, oscillation suppression of downward

interactions

Large suppression of upward interactions

The bin-free likelihood analysis confirms and reduces the allowed region obtained earlier

The probability of no oscillations is 5.3∙10-5

All available Soudan 2 data has now been analysed for oscillation effects