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Brief Progress Report on 2km Studies

Brief Progress Report on 2km Studies. J. Burguet-Castell (Valencia) D. Casper (Irvine). Goals. Study relative sensitivity of experiment with and without 2km intermediate detector Create machinery for combined with systematics and far-near correlation matrix. Neutrino Beam and Event Spectrum.

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Brief Progress Report on 2km Studies

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  1. Brief Progress Reporton 2km Studies J. Burguet-Castell (Valencia)D. Casper (Irvine)

  2. Goals • Study relative sensitivity of experiment with and without 2km intermediate detector • Create machinery for combined with systematics and far-near correlation matrix

  3. Neutrino Beam and Event Spectrum • Used earlier version of Ichikawa beam MC • BNL horns • Generate and reconstruct MC events in SuperK • Reweight with modified fluxes

  4. Far-Near Correlation Matrix • Calculate far-near correlation matrix for: • 280 m detector to Super-K • 2km detector to Super-K • Note – beam MC was modified to account for correct position of 2km detector

  5. Study of Beam Systematics • We modified the beam MC to allow a variety of systematics • Horn spatial displacements • Horn angular displacements • Beam angular displacements • How well can the 280m and 2km detector predict the flux at SuperK? • Figure shows true spectrum at SK, and predicted spectrum from 280m and 2km

  6. Example of fit • Try fitting the oscillation parameters using: • No correction for beam systematics • 280m correction • 2km correction • No systematic terms included in fit (yet) • Bias of about 1 in best fit value without 2km correction

  7. From Flux to Events • Previous studies assumed the near (and/or intermediate detectors) measure the neutrino flux, which is used to predict the flux at Super-K • In reality, the near/intermediate detectors measure a spectrum of events, which must be used to predict the spectrum of events at SuperK

  8. What We Want the Method to Do • Include all information obtained from near/intermediate detectors • For appearance measurement, we want to predict not only the flux of  but also e • Would like to include identified 0 in close detectors • Would like to be able to allow uncertain cross-sections to vary (QE/non-QE) • Account for “cancellations” due to similar cross-sections and efficiencies

  9. The flux at the far detector is related to the flux at the near detector according to the correlation matrix

  10. Detector Response Matrix Response matrix forevents of type j indetector k True energy spectrumof events with type jin detector k Reconstructed energy spectrum of events of typej in detector k

  11. Cross-section and efficiency • The true spectrum of events with type j in detector k is determined by the flux, efficiency and cross-section:

  12. Reconstructed spectrum • Substituting in the expression for the reconstructed spectrum: True neutrinospectrum atdetector k Reconstructed spectrum ofevents of type j in detector k (not observable) Cross-section andefficiency Response matrix

  13. Summing over all channels • The observable quantity is the spectrum summed over all channels: We can rearrange the summations to get a more interesting result:

  14. The Weighted Response Matrix U • The newly defined matrix U is the weighted sum of response matrices for different channels: The inverse of this matrix U allows the true neutrino spectrum to be extracted from the reconstructed energy spectrum: Reconstructed(observed) spectrum True spectrum

  15. Predicting the SK Event Spectrum • We can again use the far-near correlation matrix to extrapolate the flux: And the corresponding matrix U’ (for SK efficiency and cross-section) transforms the flux into a reconstructed event spectrum: Predicted flux at SK(from near detector) Reconstructedspectrum (at SK)

  16. Summary • In the simplest case (one type of neutrino, no oscillation) the reconstructed neutrino energy spectrum at SK can be predicted from the near detector measurements Far-near flux correlationmatrix Observed reconstructedneutrino energyspectrum at near detector Predicted reconstructedneutrino energyspectrum at SK

  17. Conclusion • For more realistic cases, it becomes slightly more complicated: • Correlations between neutrino flavors • Additional samples (e.g. identified 0 momentum spectrum is relevant for appearance measurement) • Response matrix is not square – inverting the weighted response matrix becomes equivalent to doing a least-squares fit • Working out the math, code now

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