1. A different cc/nc oscillation analysis Peter Litchfield  The Idea:  Translate near detector events to the far detector event-by-event, incorporating oscillations  Process and fit nc and cc events simultaneously, incorporating near/far differences in reconstruction and selection  Produce predicted far detector nc and cc energy distributions based on the near detector data  Compare with far detector data and produce a summed likelihood difference plot for the nc and cc events as a function of the oscillation parameters  Do a Feldman-Cousins style error analysis  Based on the analysis of Soudan 2 atmospheric neutrino data

2. Flow diagram Reconstructed Near detector data event Reconstructed Near detector MC event Truth Near detector MC event Truth Far detector MC event Reconstructed Far detector MC event Reconstructed Far detector data event Oscillation parameters near-far beam differences Compare

3.  How to do event by event association:  Given the data event parameters;  nc/cc  total observed energy  measured y for cc events  Look for similar reconstructed events in the near detector MC  Smear the MC event parameters with a normalised gaussian Associating events  Apply a weight to each MC event given by the value of the gaussian at the distance of the data event parameter from the MC  Ideally the MC should be flat in all parameters, using the MDC Monte Carlo, apply another weight to flatten the generated distributions MC event Smeared MC event weight Data event

4. Associating events  For each reconstructed near detector MC event, look up its truth.  Look for similar events in the far detector in truth nc/cc, energy, y  Make a similar gaussian smearing and weight for the far detector truth event  Make a weight to flatten the far detector truth MC distributions  Add an oscillation weight depending on the truth energy and  m 2, sin 2 2   Add a weight for the near-far beam energy spectrum difference based on the near-far truth MC spectra.  For each near detector data event we now have a set of far detector MC events each with a weight that depends on how close it is in parameter space and on the oscillation parameters and beam difference parameters.

5. Reconstructed energy distributions  Using the reconstruction of the far detector MC event, define the far detector event as nc or cc and find the reconstructed energy.  Sum the weights to produce a predicted far detector nc/cc event energy distribution corresponding to the near detector event.  Sum all near detector events with appropriate near/far normalisation to produce predicted far nc anc cc energy distributions.  Compare with the far detector data nc and cc energy distributions and calculate a likelihood surface as a function of  m 2, sin 2 2 .

6. Does it work?  Very much preliminary, work in progress  Using the MDC release 1.12 long ntuples  Very crude nc/cc separation just based on track length  Using the CINT interpreter, rather slow, not using the full statistics  Currently just using normalised near/far spectra, need to sort out the absolute normalisation  Rather coarse  m 2, sin 2 2  grid  BUT it seems to do reasonable things.

7. Likelihood plots CC NC log 10  m 2 sin 2 2  LL NC+CC Very Preliminary Low Statistics Coarse parameter bins Shape only 0.003 0.001

8. CC Energy plots Predicted from near Far data  m 2 =.001,sin 2 2  =0.6  m 2 =.001,sin 2 2  =1.0  m 2 =.0032,sin 2 2  =1.0  m 2 =.0022,sin 2 2  =1.0 Best fit Total energy (GeV) 0 10 20 30 40

9. nc energy plots Predicted from near Far data  m 2 =.001,sin 2 2  =0.6  m 2 =.001,sin 2 2  =0.1  m 2 =.0032,sin 2 2  =1.0  m2=.0022,sin 2 2  =1.0 Total energy (GeV) 0 10 20 30 40

10. Energy plots Predicted from near Far data nc cc nc cc Best fit  m 2 =0.0022, sin 2 2  =1.Least oscillations  m 2 =0.001, sin 2 2  =0.6 Events Energy (GeV) 0 1 2 3 4 5 6

11. Advantages  To first order the method is independent of the neutrino interaction physics.  Near detector data events are reproduced in the far detector, the physics is the same.  Only truth is compared near-far, reconstructed events are compared near-near and far-far.  Less dependent on software reconstruction differences.  Simultaneously fits nc and cc.  Less dependent on nc/cc separation algorithms.  Naturally incorporates oscillations on the truth, event by event.  Easily extendable to incorporate sterile neutrinos.  Naturally lends itself to a Feldman-Cousins style error analysis

12. Disadvantages  Currently rather slow.  For each near detector data event it loops over all near MC events and for each near MC event all far MC events.  Currently using the CINT interpreter, reputed to be very slow.  Haven’t carefully studied optimising the code, including storing more calculated quantities.  In principle only needs doing with the full statistics once.

13. Feldman-Cousins error analysis  The method naturally lends itself to a Feldman-Cousins style error analysis  MC experiments comparable to the actual experiment are generated and analysed at each  m 2, sin 2 2  point to produce an expected likelihood distribution for that truth.  That  m 2, sin 2 2  point is within the (e.g)90% confidence region if the data likelihood at that point is within the 90% region of the generated likelihood distribution.  Systematic effects (beam parameters, physics parameters, reconstruction variations….) are included in the generated experiments, NOT the MC.  No complicated fitting of parameters!!  It is going to be slow  The MC doesn’t change and can be calculated once.  Good for running on a multi-node farm each doing one experiment.

14. Next steps  Use R16 MAD ntuples with better nc/cc separation  Sort out absolute normalisation  Get the code to compile and make it faster  Extend and optimise the association parameters, e.g. add W for cc events, other parameters for nc?  Extend to sterile neutrinos  Set up the F-C analysis  Rewrite the code from C -- to C ++  Others can try it