1. 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

2. 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

3. Previous data  Data 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

4. Previous results  Bin-free Likelihood analysis of contained and partially contained events using the Feldman- Cousins prescription  No oscillation hypothesis probability 5.8∙10 -4

5. 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

6. 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 

7. 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 Events

8. Backgrounds  We expect hadronic tracks to have a maximum range before they interact  Plot range v Veto shield hits Range (g/cm 2 ) Veto shield hits Data MC  Require that all veto shield hits are associated with the muon track

9. After Veto shield cut  After Veto shield cuts data and MC agree Range g/cm 2 Veto shield hits Data MC  To be sure that no hadronic background remains require range > 2   interaction lengths Range >260 gm/cm 2

10. Check, hadronic events  Some 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/cm 2 Veto shield hits Range g/cm 2 Cos(zenith)

11. Event numbers Assigned as No oscillation MC truth Data downmuupmu downmu 13.3  1.40.7  0.2 17 upmu 1.9  0.558.4  1.9 26 ambiguous 0.9  0.43.6  0.5 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

12. 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

13. Upmu  Tracks 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) Events/0.1 Upward going muons

14. 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 sin 2 2θ 23 x log 10  m 2  Likelihood difference with the best likelihood point obtained  Best fit point in the grid square centered at  m 2 =0.0052 eV 2 and sin 2 2θ 23 =0.97 but the Super-K best fit point is not much worse log 10  m 2 sin 2 2θ 23 LL

15. Comparison with data Best fit No oscillations Saturated oscillations  2 /data points PCEUPMUAll data No oscillations5.0/59.4/462.2/30 Best fit4.1/50.9/432.5/30 Saturated oscillations18.2/50.8/459.9/30

16. Limits calculation  If 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 (sin 2 2θ 23 <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

17. Confidence limits MC90 sin 2 2θ 23 log 10  m 2 90% likelihood surface

18. Comparisons Effect of new data Comparison with Super-K and MACRO Old analysis This analysis

19. Probability of no oscillations  To calculate the probability of no oscillations MC experiments are generated in the lowest  m 2, sin 2 2θ 23 grid square  300,000 experiments generated, including all statistical and systematic effects  Difference between the lowest negative log likelihood and that in this square (  L MC ) plotted  16 MC experiments had a  L MC greater than the data likelihood (16.02)  Probability of no oscillations 5.3∙10 -5

20. 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