Proposal for the study to define what is really necessary and what is not when the data from beam, ND and SK are combined A.K.Ichikawa 2008/1/17

Prediction of flux at SK with error matrix by beam MC Simple parameterization or modeling is the key for success, I believe. The errors/perturbation on the flux can be categorized in two types. A. Beam-axis Symmetrical effect Mainly (p,  ) distribution at the  /K production is a dominant source. Example : Uncertainty of Hadron production, (symmetrical) primary beam profile before the target, horn current B.Beam-axis Asymmetrical effect Mainly optics transfer matrix for  /K is affected asymmetrically. Example : Horn misalignment “A” can be constrained by NA61 and ND280 It’s O.K. if we find that the ND280 off-axis is very insensitive to A because it would mean that Super-K is also very insensitive. But by going back to (p,  ) distribution, we can make a reasonable error matrix even before NA61. “B” can be constrained by MUMON and INGRID. How? How much needed?

Far/Near or Not? If ND280 information is used only for neutrino flux, Far/Near ratio method would work. Especially when the neutrino cross section uncertainty is large, it will not make sense to put constraint on the Far/Near ratio from ND measurement. But, in general, its better to put constraints on original  /K distribution and make modified expected flux at Super-K if possible. Especially, this time, error on the off- axis angle is directly affect SK spectrum and that can be constraint by ND on-axis measurement. Also Far/Near seems too sensitive for a small shift of the peak position with this narrow neutrino spectrum. So for a moment, let’s take latter method. An alternate method may be the matrix transfer.

Symmetrical effect Proposed parameterization for this study 2 nd order perturbation on the Hadron production (p,  ),where r1, r2, r3 stand for the perturbation at low, high and middle momentum/anglar region, respectively. r~30%?, 50%?, 100%? Very conservative constraint from energy conservation. MUMON can constrain? Can this parametrization fit different hadron model distr. (MARS, FLUKA etc.)? Does z (along beam axis) on the target surface need special treatment?

Measurement at ND Parameters to be fitted  CCQE,  CC-nonQE –How to treat energy dependence? Once we neglect the energy dependence of the cross section, spectrum shape will be fitted just by the hadron production part? Or  CC-noQE /  CCQE will give some constraint on the hardness of the hadron production? Introduce 2 nd -order energy-dependent perturbation to the cross section as an approximation like r1,r2,r3 in the previous page? K/ e will be constrained significantly even without direct e measurement.? Then, lets get the flux expectation at Super-K with an error matrix.

Asymmetrical Effect For example, mis-alignment of the horns or beam hit position seem to cause asymmetric angle deflection of  /K’s and hence to change “effective” off-axis angle. Proposed parameterization 1 st or 2 nd order polynomial (a, b) to approximate  ND (E )/  0ND (E ),  SK (E )/  0SK (E ). If there is strong correlation between these two, that would reduce systematic error. How to implement? (Far/Near is smart?) Make (a, b) for unit displacement on each parameter and assume that those are lineally depend on that displacement. a beam (  x)=a0beam*  x bbeam(  x)=b0beam*  x Although there are many displacement parameters such as  xbeam,.  ybeam,  xhorn2,…, those which give same tendency on  ND (E )/  0ND (E ),  SK (E )/  0SK (E ) should be merged as much as possible. Ideally just one set of (a,b). But perhaps, different set of (a,b) for  and K. Then MUMON and INGRID measurement would make constrant on (a,b) and we can make Super-K expected flux as a function of (a,b) with error matrix on (a,b)

4 (GeV) ratio black: default red : beam 3mm off-center

Oscillation analysis using expected spectrum Use existing ntuple files. For  disappearance, systematic errors to be included Energy scale  CCQE,  CC-nonQE (correlated to ND measurement) Fiducial volume/normalization  CC /  NC and statistical error at Super-K For e appearance, systematic errors to be included Background estimation. Number and distribution? And 1.Make table for final sensitivity/precision values with each errors on beam, ND, Super-K only. 2.Get  m 2 and  23 for start from different hadron production model than actually used.

Direct Outcome of this study is estimate on the systematic errors which are sensitive to the physics outcome and define what measurement is really necessary. And then, the strategy will become clear.

Contribution of syst. errors on spectrum Total Spec.nQE/QESpec.+nQE/QE F/N  SK SK Escale Kobayashi, K2K seminar

To Do List Let’s review K2K analysis -general and fitting details - Let’s review MINOS analysis Let’s review Dean/Alysia proposal Let’s make necessary codes for beam, ND fitting and oscillation parts. –Beam Symmetrical systematics Compare (p,  ) of GFLUKA, latest FLUKA, MARS. Compare  of GFLUKA, latest FLUKA, MARS. Find good parameterization (Or give up this approach?) Estimate constraint and make error matrix? –Beam Asymmetrical systematics Find good parameterization (Or give up this approach?) Estimate constraint (by MUMON, INGRID) and make error matrix Or neglect them if we find that they are small enough. –ND fitting Find good parameterization for energy dependent cross section uncertainty Make fitting code –SK oscillation analysis Make code based on K2K program? –Final plots By the way, for the beam MC part, following issues are remaining. –geometry update, especially horn striplines. –Hadron production model, how to implement NA61 result –output format ntup ｌ e -> root one run statistics is limited by zebra capacity. –computer server? –  /K production vector may have bug? Check needed. –Some minor decay mode of Kaons –Someday, Geant4?