Informations

1. Estimation of Systematic Error for   "R"   which Appear in the Formula,
     Exp._No.of.Ev._at_SK    =    R    *    Obs._No.of.Ev._at_near_det.
     (Error Induced by the Uncertainty of Flux_Ratio Only)

K2K Collaboration is using CHO Model as an estimator of Flux_Ratio;

Neutrino_Flux_at_SK   /   Neutrino_Flux_at_Near,

whose reliability is guaranteed by the Pion Monitor Measurement above 1GeV neutrino energy within Pion Monitor Measurement Error.

Here, systematic error of   R   induced by the uncertainty of   Flux_Ratio(it is the Pion Monitor Measurement Error) is calculated with taking into account energy dependent  Flux_Ratio  uncertainty as follows.
The   Exp._No.of.Ev._at_SK   is related to Neutrino Flux Ratio as follows.

Exp._No.of.Ev._at_SK
=      R      *      Obs._No.of.Ev._at_near_det.
=      t_ratio      *      SUM_OF_Neutrino_ENERGY_BIN[  n_near    *    f_ratio    *    c_ratio    *    e_ratio  ]

Where

t_ratio:      target mass ratio (far_det/near_det)
n_near:      No.of.Ev. at near det for this energy bin
f_ratio:      neutrino flux_ratio (far_det/near_det) for this energy bin
c_ratio:      neutrino cross section ratio (far_det/near_det) for this energy bin
e_ratio :     detection efficiency ratio (far_det/near_det) for this energy bin

As you see, this is an EXACT RELATION. Then   R   is explicitly written down as

R  =  ( 1  /  Obs._No.of.Ev._at_near_det. )     *      t_ratio   *   SUM_OF_Neutrino_ENERGY_BIN[ n_near * f_ratio * c_ratio * e_ratio ]

Estimation of systematic error for   R   is based on this formula.

Used numerical informations are

I) Error of  Flux_Ratio  estimated by the Pion_Monitor_Measurement as a function of neutrino energy. It is summarized in Table

Note:
a)Since there is no pion monitor estimation below 1GeV, Jim Hill's MC based error estimation for Flux_Ratio;
    0.0 GeV - 0.5 GeV           +5.1%   - 9.5%
    0.5 GeV - 1.0 GeV           +7.3%   - 2.5%
is used for this region.

b)In case of 0% detection efficiency (e.g. Scifi 0-0.5GeV), the Absolute_Neutrino_Flux information is necessary(not the Flux_Ratio).
    For this part,  number of expected at SK can't be done by usual   " near  *  far/near "   method.
    Thus the uncertainty is estimated by each near detector group as a  FLUX UNCERTAINTY separately for this part.
    Probably each near detector group had better to utilize its own different analysis thresholds for SK event analysis to minimize the systematic error.
    Though it is necessary to treat three different SK expected...

II) "  Flux   *   Cross_Section  "      Table      Prepared by Hayato

III)  Detection efficiency as a function of neutrino energy

Jun.'99
          0-0.5      0.5-1.0      1.0-1.5      1.5-2.0      2.0-2.5      2.5< (GeV)
1kt    24.8 %      58.8 %       71.5 %       75.7 %       81.5 %      83.1 %
Scifi   0.0 %         3.4 %      16.0 %       24.0 %       31.0 %       36.0 %
Mu     0.0 %       15.7 %      36.3 %       45.7 %       51.9 %       47.3 %
SK    54.9 %      70.1 %      78.8 %       82.3 %       82.2 %       80.3 %

Since Nov.'99
          0-0.5      0.5-1.0      1.0-1.5      1.5-2.0      2.0-2.5      2.5< (GeV)
1kt   23.3 %       58.9 %      70.9 %       77.7 %       82.7 %       83.1 %
Scifi   0.0 %         3.2 %      18.0%       30.0 %       37.0 %        40.0 %
Mu     0.0 %       16.0 %      36.5 %       45.7 %       52.0%        47.5 %
SK   54.4 %       70.1 %      78.8 %       82.3 %       82.1 %        80.2 %

IIII) Corresponding Fiducial Mass

Then systematic Error of   R   is calculated with adding the error for each energy region LINEARLY.

Finally here is a Result
(Uncertainty  of R.    Induced by the Uncertainty of Flux_Ratio Only.)

1kt           Jun.'99    +13.6%      -9.9%          Since Nov.'99    + 5.6%    -7.3%
Scifi         Jun.'99    +13.6%      -9.8%          Since Nov.'99    + 5.6%    -7.1%
Mu           Jun.'99    +13.6%      -9.8%          Since Nov.'99    + 5.6%    -7.1%

2. To be done in Future

I) Comparison of neutrino spectrum predicted by the Pion Monitor with measurement by each subdetector

1kt
Scifi
Muon_Chamber
(For Comparison, above about 1GeV information is necessary)

II) Extraction of more precise energy information (say 250Mev bin) from Pion Monitor Data

A) Figure in the 1st Paper

paper.ps

B) Estimated Neutrino Spectrum by the Pion_Monitor at Near (r=3.0m fiducial) and Far Detector with Beam M.C. Prediction

spect_jun.ps (Jun. Configuration)
spect_nov.ps (Nov. Configuration)

Upper for Near Detector and Lower for Far Detector
M.C. is normalized with Near Detector Data Entry above 1GeV
M.C. Error is for Statistical

<Message of This Figure>
The Shape of the Spectrum at Near and Far of Our MC is Guaranteed by the Pion Monitor Measurement above 1GeV (Absolute Flux is not Guaranteed by the Pion Monitor Measurement)

C) Estimated Far Near Neutrino Flux Ratio by the Pion_Monitor with Beam M.C. Prediction

ratio_jun.ps (Jun. Configuration)
ratio_nov.ps (Nov. Configuration)

M.C. Error is for Statistical

<Message of This Figure>
The Far/Near Ratio of Our MC is Guaranteed by the Pion Monitor Measurement above 1GeV

D) Centroid of Muons Measured at Muon Pit as a function of time from June '99 to June '00

aiming.ps

First Page for Ionization Chamber X(Horizontal)     Small Value Correspond to NORTH
Second Page for Ionization Chamber Y(Vertical)     Small Value Correspond to DOWN
Vertical Line indicate the end time of
June '99, Nov. '99, Jan.'00, Feb.'00, Mar.'00, May'00, June'00 data taking period.

<Message of This Figure>
Beam is Aimed to SK within about 1m rad Accuracy. This measurement is based on "SPILL by SPILL Information"  and "High Energy Muon
Information"

E) Stability of Muon Yield

stability.ps

Vertical Line indicate the end time of
June '99, Nov. '99, Jan.'00, Feb.'00, Mar.'00, May'00, June'00 data taking period.

<Message of This Figure>
The muon yield normalized to proton intensity measured by a current transformer is stable spill-by-spill within
a measurement uncertainty of 2%. This measurement is based on "SPILL by SPILL Information"  and "High Energy Muon
Information"

1) Cherenkov Light Distribution Measured by the Pion_Monitor at Various Refractive Indices(n)

demo.ps (Jun. Configuration)
demo_nov.ps (Nov. Configuration)

Pedestal Subtracted
PMT Relative Gain Correction Applied
Beam Intensity Correction Applied
PMT Saturation Correction Applied

2) Electromagnetic Activity (Background) which will be Subtracted are Indicated with Hatch

bkg.ps (Jun. Configuration) 2 figures are enclosed
bkg_nov.ps (Nov. Configuration) 2 figures are enclosed

n=1.00026 and n=1.00034 for Jun. Data
n=1.00024 and n=1.00041 for Nov. Data
are used for normalization(with Using MC. GCALOR), respectively.
Pedestal Subtracted
PMT Relative Gain Correction Applied
Beam Intensity Correction Applied
PMT Saturation Correction Applied

3) Cherenkov Light Distribution Measured by the Pion_Monitor at Various Refractive Indices(n) with Fitting Result

pimonfit_jun.ps (Jun. Configuration)
pimonfit_nov.ps (Nov. Configuration)

Pedestal Subtracted
PMT Relative Gain Correction Applied
Beam Intensity Correction Applied
PMT Saturation Correction Applied
ElectroMagnetic Background Subtracted

4) Estimated Pion Momentum/Angular Distribution by Fitting

pikine_jun.ps (Jun. Configuration) 2 figures are enclosed
pikine_nov.ps (Nov. Configuration) 2 figures are enclosed

Second Page is Estimated Error for Fitting

ElectroMagnetic Background Subtracted

5) Figure Shows you From which Decay Mode Neutrino Come. Based on CHO M.C.

flux_mode.ps

6) Expected Flux with Various Model. (Prepared by Wojciech Gajewski)

offspct15.ps

Explanation by Wojciech Gajewski:
Wang(67) is the result of the compilation of the measurements made by Lundy (13.4 GeV), Dekker (11.8 & 18.8 & 23.1 GeV), Baker (10.9 & 20.9 & 30.9 GeV) and Fitch (33.9 GeV) using Dekker's measurements for the normalization and 227 mb measured by Bullettini for the absorption cross section (Denisov measured it to be 206 mb @ 20 GEV). The results of this compilation are described by Yamamoto and used by him for a comparison with his measurements. Yamamoto's measurements agreed surprisingly well with this compilation.
"Cho" is the result of the measurements performed by Derrick's group few years later to resolve a question of low cross sections measured by Telegdi's group (Lundy) on the same proton beam at Argonne and have a better understanding of their neutrino beam. I talk to Derrick few years ago and he claimed that his measurements were correct. They seem to work pretty well for us.
I started the programs with the target size 50cm^2 @ 300m and 200cm^2 @ 2.5km (this flux is been rescaled by 10^4 to SK, which introduces an overestimate error of ~5%). Target radius is 1.5cm and Horn Current is 250kA

7) Summary of Systematic Error Estimation from Pion Monitor Analysis

syserr.ps 5 Pages

 

8) Typical Muon Profile Measured by Muon Monitors

mufit.ps

9) Typical Proton Profile at V39 and Target(Nov Configuration)

typ_proton_nov.ps

10) <Caution>These 3 Figures are Made by Dr.Noumi from Beam Channel Group. You need acknowledgement from him when you use it for presentation<Caution>

elv.epsSchematic View of Neutrino Beam Line
ts.eps Schematic View of Neutrino Beam Line
mussd.eps Schematic View of Muon Monitor

11) Schematic View of Pion and Muon Monitors

pimon.ps Schematic View of Pion Monitor
mumon.ps Schematic View of Muon Monitor(Ionization Chamber)
silicon.ps Schematic View of Muon Monitor(Silicon Pad Detector)

12) Schematic View of Beam Monitor Location

monitor_loc.ps

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