Proposal%20for%20the%20study%20to%20define%20what%20is%20really%20necessary%20and%20what%20is%20not%20when%20the%20data%20from%20beam,%20ND%20and%20SK%20are%20combined

1
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

2
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,q) distribution at the p/K production
  is a dominant source.
• Example Uncertainty of Hadron production,
  (symmetrical) primary beam profile before the
  target, horn current
• Beam-axis Asymmetrical effect
• Mainly optics transfer matrix for p/K is affected
  asymmetrically.
• Example Horn misalignment
• A can be constrained by NA61 and ND280
• Its 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,q) distribution, we can make a
  reasonable error matrix even before NA61.
• B can be constrained by MUMON and INGRID.
• How? How much needed?

3
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 p/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, lets take latter method.
• An alternate method may be the matrix transfer.

4
Symmetrical effect

• Proposed parameterization for this study
• 2nd order perturbation on the Hadron production
  (p,q)
• ,where r1, r2, r3 stand for the perturbation at
  low, high and middle momentum/anglar region,
  respectively.
• r30?, 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?

5
Measurement at ND

• Parameters to be fitted
• sCCQE, sCC-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 sCC-noQE/sCCQE
  will give some constraint on the hardness of the
  hadron production?
• Introduce 2nd-order energy-dependent perturbation
  to the n cross section as an approximation like
  r1,r2,r3 in the previous page?
• K/ne will be constrained significantly even
  without direct ne measurement.?
• Then, lets get the flux expectation at Super-K
  with an error matrix.

6
Asymmetrical Effect

• For example, mis-alignment of the horns or beam
  hit position seem to cause asymmetric angle
  deflection of p/Ks and hence to change
  effective off-axis angle.
• Proposed parameterization
• 1st or 2nd order polynomial (a, b) to approximate
  FND(En)/F0ND(En), FSK(En)/F0SK(En). 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.
• abeam(Dx)a0beamDx
• bbeam(Dx)b0beamDx
• Although there are many displacement parameters
  such as Dxbeam,.Dybeam, Dxhorn2,, those which
  give same tendency on FND(En)/F0ND(En),
  FSK(En)/F0SK(En) should be merged as much as
  possible. Ideally just one set of (a,b). But
  perhaps, different set of (a,b) for p 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)

7
4
black default red beam 3mm off-center
(GeV)
ratio
8
Oscillation analysis using expected spectrum

• Use existing ntuple files.
• For nm disappearance, systematic errors to be
  included
• Energy scale
• sCCQE, sCC-nonQE (correlated to ND measurement)
• Fiducial volume/normalization
• sCC/sNC
• and statistical error at Super-K
• For ne appearance, systematic errors to be
  included
• Background estimation. Number and distribution?
• And
• Make table for final sensitivity/precision values
  with each errors on beam, ND, Super-K only.
• Get Dm2 and q23 for start from different hadron
  production model than actually used.

9
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.
10
Contribution of syst. errors on spectrum
Kobayashi, K2K seminar
Spec.
nQE/QE
Spec.nQE/QE
Total
SK Escale
eSK
F/N
11
To Do List

• Lets review K2K analysis -general and fitting
  details -
• Lets review MINOS analysis
• Lets review Dean/Alysia proposal
• Lets make necessary codes for beam, ND fitting
  and oscillation parts.
• Beam Symmetrical systematics
• Compare (p,q) of GFLUKA, latest FLUKA, MARS.
• Compare F 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