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What beamline group will supply for the (day-1) oscillation analysis

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### What beamline group will supply for the (day-1) oscillation analysis

### Followings are specific questions to beamline group and answers to them

A.K.Ichikawa

For T2K beamline group

Note

This is just a starting-point material for day-1 analysis. More discussion among the beamilne group is necessary.

This note will be modified when

more studies arises,

real data come,

or

statistic increases after day-1.

What beamline group will supply for the oscillation analysis

- Expected neutrino flux at the near detectors and far detector.
- Correlation between flux at the near detectors and that at the far detector, i.e. far-to-near ratio.
- Systematic errors for above quantities.

For the real data processing, refer Nakadaira-san’s presentation file at the last collaboration (pre) meeting.

Systematic errors to be taken into account for oscillation analysis

- Beam/horn miss-alignment
- Horn magnetic field
- Absolute field strength
- Distortion of the distribution
- Primary beam profile
- Primary hadron production
- Secondary hadron interaction
- Something which is not yet forseen.

How to propagate beam systematic errors for ND/SK spectrum fitting

- Correction function/vector for spectrum itself for each systematic errors.

Example: DF(Ei)=Dy*ci : Dy is proton beam mis-hit position

- Correlation matrix for systematic errors.
- Neutrino spectra itself will be re-weighted and fitted by near/far detector observations within the constraints of the systematic error matrix.

Q: Corresponding available data or measurements, internal T2K or external, available to constrain these parameter variations

- Beam/horn miss-alignment
- Survey during the installation
- Data from primary beam monitor, MUMON and INGRID
- Horn magnetic field
- Absolute field strength
- Field measurement
- Current Transformer at stripilne
- Distortion of the distribution
- Field measurement
- Indirectly, MUMON and INGRID
- Primary beam profile
- Data from primary beam monitor
- Primary hadron production
- Model comparison and reasonable assumption on the model discrepancy
- NA61 result
- ND280 off-axis measurement
- Secondary hadron interaction
- Same as the primary hadron production

Q: is reweighting possible?

- Yes, we will provide neutrino-energy- histogram based weighting for systematic errors

Q: effect of parameter on numu analysis, on nue analysis (this may be extracted from the global analysis) precision achievable on parameter from the data

- If beamline components including MUMON and INGRID work as expected, effect on the oscillation analysis from the beam related systematic errors will be sufficiently small compared to day-1 statistics and quite controllable except for the hadron production part.
- For the hadron production part, NA61 results will help a lot. Further MC study is necessary to evaluate the effect on the oscillation analysis from hadron production uncertainty either before NA61 and after NA61. And off course, ND280 off-axis detector is expected to put constraint on the numu and nue flux.

How will we feedback the data from the muon monitors, NGRID and even ND280 into the beam monte carlo (Jnubeam) to either adjust it, evaluate systematic errors, reweight or include it in a global fit of ND280 (which depends both on flux and cross-sections)?

- As written in previous pages, the information from MUMON and INGRID (and primay beam monitor) will be used to constrain the uncertainty of the beam/horn misalignment and probably asymmetric distortion of the horn fields. The correction function of the neutrino energy spectrum will be made from jnubeam. The actual correction is a product of a systematic error amplitude and corresponding correction function. The systematic error amplitude can be constraint by the information from MUMON and INGRID etc.
- On the other hand, the data from the ND280 off-axis detector will be used to put a constraint on the { flux (neutrino energy spectra) x cross section}. The far detector {flux x cross section} can be obtained by extrapolating the ND measurements.

1. how to establish the misalignments experimentally? Just as an example: one could think of taking initial runs with the beam monitors and the NGRID and operating e.g. no horn, then one horn at a time, etc.. to assess whether one can constrain the alignment of each of the horns individually (I believe this does not require high intensity)

- MUMON and INGRID !! (with Horn operation.)
- If horn-off running helps or not is not trivial. I’m afraid that profile is too broad with horn-off running to obtain useful information. But yes, we can and should do study with beam MC.

how will the feedback from the near detector (ND280) be done? (or what observations are more sensitive to flux and what are more sensitive to cross-section model?) I think this will involve some sort of global fit...

- Off-axis method gives numu flux which is rather independent on the hadron production. So it is expected that the ND280 off-axis measurement would be sensitive on the neutrino cross section. NA61 will further strength this direction.
- More beam MC study is necessary to evaluate how precisely we can predict the nue flux without NA61 nor ND280 off-axis measurement. Since the main contributor to nue at around the peak energy is muon decay, the uncertainty may be sufficiently small for the quantity nue/numu. But it is absolutely helpful if either NA61 Kaon or ND280 measurement (numu high energy tail or nue itself) is on time for day-1 analysis. (Note that high precision results are not necessary.)

as a related question to the previous one: how will the nue flux to SK be determined two methods are possible -- direct from nue events in ND280 -- indirect from numu events in ND280 constraining the nue prediction from JNUBEAM

- Yes, both methods seems possible. See the next slides. It is expected that the nue from muon has less uncertainty if nue/numu is used. While the Kaon uncertainty may be rather large, but this part may be constraint by numu high-energy tail measurement.

Red : Kaon contribution

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