1 INGRID Analysis Technical Note

2 Masashi Otani 3 Akira Murakami 4 Christophe Bronner 5 for INGRID group

6 January 11, 2011

7 Abstract

8 In this note we summarize the INGRID analysis results with 2010a data. We 9 measured the neutrino event rate, the beam profile center and these stability 10 for the confirmation and support of 2010a oscillation analysis. We select the 11 neutrino interaction, mainly charged current interaction, at each module and 12 reconstruct the neutrino beam profile. We compare some distributions between 13 data and MC and found good agreement. We get the data/MC ratio for the 14 event rate to be 1.074 ± 0.001(stat.) ± 0.040(syst.). The center of the neutrino 15 beam profile found to be 0.2 ± 1.4(stat.) ± 9.2(syst.) cm for X profile and 16 -6.6 ± 1.5(stat.) ± 10.4(syst.) cm for Y profile. Finally the off-axis angle is 17 measured to be 2.52 degrees with the error of 0.37 mrad.

18 Contents

19 1 Introduction 3

20 2 Monte Carlo simulation 5

21 3 Neutrino event selection 11 22 3.1 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 23 3.2 Basic distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 24 3.3 Vertex resolution of tracking . . . . . . . . . . . . . . . . . . . . . 19 25 3.4 Detection efficiency to neutrino interaction events . . . . . . . . . 20

26 4 Event rate measurements 22 27 4.1 Data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 28 4.2 Event rate stability . . . . . . . . . . . . . . . . . . . . . . . . . . 22 29 4.3 The data/MC ratio . . . . . . . . . . . . . . . . . . . . . . . . . . 23 30 4.4 Systematic error of event rate . . . . . . . . . . . . . . . . . . . . 28

31 5 Measurements of beam profile 32 32 5.1 Stability of beam center . . . . . . . . . . . . . . . . . . . . . . . 32 33 5.2 The systematic error of beam center . . . . . . . . . . . . . . . . 33

34 6 Measurement of beam direction 34

35 7 Conclusion 36

36 Chapter 1

37 Introduction

38 INGRID is on-axis near detector which consists of identical 14 modules ^{1} to 39 monitor the beam stability. Each module has a sandwich structure made of the 40 iron plates and the scintillator trackers. INGRID module consists 11 tracking 41 planes which consists 2 layers. Each layer has 24 scitillator bars and the direction 42 of scitillator is perpendicular each other layer. 43 We count the number of neutrino interactions, mainly CC interaction, oc-44 curred inside the module. Based on the number of selected events for each 45 module, the beam profile is reconstructed. Fig.1.1 shows a typical event in an 46 INGRID module. Detector coordinates are shown in Fig.1.2. INGRID uses a 47 right-handed Cartesian coordinate system in which the z axis is the beam di-48 rection and the y axis is the vertical upward direction. With this definition the 49 INGRID module number is decided from horizontal modules. 50 In this note, we describe the measurements of

51 (1) neutrino event rate and its stability

52 (2) neutrino beam center and its stability

53 (3) neutrino beam direction

54 for the data taken from January to June 2010 (2010a data set). 55 This article is organized as follows. Chapter 2 explains the overview of Monte 56 Carlo simulation.Chapter 3 explains the neutrino event selection. Finally the 57 result of the event rate measurement, beam profile measurement and beam 58 direction are shown in Chap. 4, Chap. 5 and Chap. 6, respectively.

1Additional two off-center modules and a proton module are installed after 2010a data taking.

Figure 1.1: The typical neutrino event

Figure 1.2: INGRID coordinates and the definition of the number of an INGRID module

60 Monte Carlo simulation

61 Three MC simulation programs are used : JNUBEAM, NEUT and a INGRID 62 dedicated dedetector simulation code (Fig.2.1).

63 • Neutrino flux prediction : JNUBEAM (version 10d tuned ver. 2)

64 • Neutrino interaction to materials : NEUT (version 5.0.6.)

65 • Detector response simulation based on Geant4 ^{1}

Figure 2.1: INGRID MC overview

66 Neutrino flux prediction

67 The neutrino flux at INGRID are predicted by JNUBEAM version 10d. For the 68 detailed description of JNUBEAM, see Ref.[1]. Figure 2.2 shows the neutrino 69 energy spectrum at the INGRID detector location. The estimated integrated 70 neutrino flux at the INGRID center module is 5.94×10^{14} cm^{−2}10^{−21}POT (POT 71 means ”# of protons on the target ”. The flux at INGRID is dominated by 72 muon neutrinos (95%). Figure 2.3 and 2.4 show the flux energy spectrum at the 73 INGRID center module and horizontal edge module, and the Super-Kamiokande 74 detector, respectively. Because each INGRID module covers the different off-75 axis angle, the neutrino energy spectrum is slightly different at each module. 76 Table 2.1 shows the average neutrino energy at each module and the average 77 energy is different for about 0.2 GeV between the center module and the edge 78 module.

1This INGRID MC is not the software of ND280 software packages

Table 2.1: Average energy of neutrino flux at each horizontal modules and SK. The module # 3 is center module. The average energy at INGRID is larger than one at SK

module# 0 1 2 3 4 5 6 SK
Average energy[GeV] 1.08 1.20 1.29 1.32 1.29 1.21 1.09 0.61

79 Neutrino interaction simulation

80 Neutrino interactions with the iron plate (Fe) in the INGRID detector is sim-81 ulated by the NEUT program libraries. INGRID modules include the iron 82 targets and the scintillator targets. Currently, all the neutrino interactions at 83 INGRID module are assumed the interactions with iron at the whole of module 84 (the difference of the cross section is neglected). The neutrino interactions with 85 scintillator target is under preparation. The neutrino interaction at support 86 material is neglected. The mass ratio of the support material to INGRID mod-87 ule is about 1 %, its effect should be small. Simulation with correct material is 88 under preparation. For a detailed description of NEUT, see Ref.[2].

89 Detector response simulation

90 The detector response to the generated particles from the neutrino interaction 91 is simulated by the simulator based on Geant4. The x and y vertex position 92 of the neutrino interaction is obtained from JNUBEAM flux file. The vertex z 93 is uniformly generated in the iron plate and the scintillator tacker taking into 94 account the mass ratio of iron planes (99.54 ton) to scintillator planes (3.74 95 ton). 96 Detector response simulation includes following effects.

97 • The conversion factor from energy deposit to the number of photon in MC 98 simulation is tuned by adjusting the peak photoelectron (PE) of beam 99 related sand muon. Tthe quenching effect of scintillator, attenuation of 100 photon propagating in the fiber and MPPC response model based on [3] 101 are also included. Figure 2.5 shows the typical PE distribution of the 102 beam related sand muons after these MC tuning. The peak PE is well 103 reproduced.

Figure 2.2: Neutrino flux energy spectrum predicted by JNUBEAM at the INGRID center module

Figure 2.3: Neutrino flux energy spectrum predicted by JNUBEAM at the INGRID center module (#3) and edge module (#0)

Figure 2.4: Neutrino energy spectrum predicted by jnubeam at the SK detector location 104 • Although the inefficiency resulted from the photoelectron statistics (light 105 yield is ∼ 20 PEs at peak and the TDC threshold is 2.5 PEs) is expected 106 to be less than 0.1%, each channel has 1 ∼ 2% inefficiency resulted from 107 the gap between scintillator bars. This is studied by cosmic-ray data. In 108 Fig.2.6, black line shows the tracking inefficiency as a function of the angle 109 with respect to z-axis. Because the particle with small angle has more 110 probability to go through the gap, the inefficiency becomes larger for a 111 smaller angle track. We changed the cross-section of the scintillator bar in 112 MC (from the simple square one to the octagon-shaped one) by reference 113 to the real geometry (Fig.2.7) to reproduce the angular dependence of the 114 inefficiency in data. The blue and red points in Fig.2.6 show the angular 115 dependence of the tracking inefficiency in the MC simulation before and 116 after the tuning, respectively. The angular dependence of the tracking 117 inefficiency is well reproduced in MC.

118 • Accidental hits by MPPC dark noise result in miss reconstruction of the 119 track and miss identification of the vertex position. As a consequence the 120 selection efficiency is influenced by the MPPC dark noise. In MC, the 121 MPPC noise hits are generated to reproduce the number of PE, timing, 122 and noise rate of data. Figure 2.8 shows the timing distribution for data 123 during the beam-off period and MC. Because the accumulation of the 124 charge due to MPPC noise smaller than TDC threshold is increase with 125 respect to time, the number of hits increase with respect to time. The 126 distribution is well reproduced.

Figure 2.5: PE distribution of beam related sand muon. Left plot is MC simulation and right one is data.

Figure 2.6: Tracking inefficiency as a function of angle of the reconstructed track. Data is cosmic data.

Figure 2.7: Photo of the cross-section of the scintillator bar (left) and the crosssection in MC (right)

Figure 2.8: The timing distribution of MPPC noise. Left is data and Right is MC.

128 Neutrino event selection

129 3.1 Event selection

130 The events at INGRID include not only neutrino events but also back ground 131 events, for example accidental events due to MPPC noise, cosmic events, and 132 sand muons events. The neutrino events have to be selected in those events. At 133 this time, the long track of charged particle whose vertex is within the fiducial 134 volume of an INGRID module is selected as the neutrino event. The beam data 135 shown in Chap.?? and the MC simulation corresponded to 100 × 10^{21} pot are 136 used for analysis. To select neutrino events and reject back ground events, some 137 event selections are applied to the beam data and MC. These selections are as 138 following :

139 (1) Time clustering

140 (2) Number of active planes cut

141 (3) PE/(number of active layers) cut

142 (4) Tracking

143 (5) Track matching

144 (6) Beam timing cut

145 (7) Upstream VETO cut

146 (8) Fiducial volume cut

147 Theres selections are applied to a event at each module and each bunch 148 one by one. The detail of these selections is explained in this section. In this 149 analysis, channels having a ADC signal larger than 2.5 PE are defined as ”hit”.

150 Time clustering

151 Hits are clustered with the following criteria : If there are more than 3 hits within 152 100 nsec, all the hits within ± 50 nsec from the average time are classified into 153 a cluster. By this clustering, the random MPPC noise hits are expected to be 154 rejected. Other event selections (#2〜#8) are applied to each cluster. In the 155 following, one cluster is called one event.

156 Number of active layers cut

157 The planes with at least one coincidence hit in both x and y layers are called 158 active planes. Figure 3.1 shows the distribution of the number of active planes. 159 The event which has more than 2 active planes are select as the signal and the 160 back ground events due to the random MPPC noise are expected to be rejected.

161 PE/(number of active layers) cut

162 Figure.3.2 shows total PE of all hits in the active layer divided by the number of 163 active layers (PE/(number of active layers)) after the selection with the number 164 of active planes > 2. The events with more than 6.5 PE/(number of active 165 layers) are selected as signal.

166 Tracking

167 Next is the explanation of the tracking method. The hits in the most down-168 stream active x and y layer are adopted as a end-point of the track. Looking at 169 the hits in the next upstream plane in order, the hit is selected as the track if the 170 difference of the slope calculated from the straight line is less than 2 channels. 171 The selected hits are fitted to a straight line by a least square method to get 172 the angle of the reconstructed track. In this tracking, the longest track should 173 to be selected. If there are two hits in the most downstream layers, the tracking 174 is processed at each hit, and then select the longer reconstructed track.

175 Track matching

176 After reconstruction of the track some badly fitted tracks are rejected by con-177 sidering the difference of the start point z of a 2-D track in x view and y view. 178 Fig.3.3 shows the distribution of the difference of the start point z of the track 179 between 2-D track in x view and y view. We require the difference smaller than 180 2 planes. Figure 3.4 shows the angular distribution of the reconstructed track 181 after following track matching selection.

182 Beam timing cut

183 To reject background events such as cosmic-ray on beam off timing, the events 184 within ± 100 nsec from the expected timing of each bunch are selected (Fig.3.5).

Figure 3.1: Number of active planes(left:DATA, right:MC normalized by area)

Figure 3.2: PE/(number of active layers) after the selection with the number of active planes > 2 (Left:DATA, Right:MC normalized by area)

Figure 3.3: Difference of the start point z of the track in x view and y view (Left:DATA, Right:MC normalized by area)

Figure 3.4: Angular distribution of the reconstructed track after all selections after the track matching selection (Left:DATA, Right:MC normalized by area)

Figure 3.5: Time residual plot after the track matching selection 185 Upstream VETO cut & Fiducial volume cut

186 Two selections are applied to reject the incoming particles produced by the 187 neutrino interaction in upstream materials (for example the wall of the neutrino 188 hall).

189 First one is the upstream VETO cut. If the VETO plane has a hit at 190 the upstream position extrapolated from the reconstructed track, the event is 191 rejected. Figure 3.6 shows the example of the event rejected at this selection.

192 After the VETO cut, fiducial volume cut is applied. The fiducial volume is 193 the cubic volume which is defined as ± 50 cm^{2} transverse area from the center 194 of an INGRID module and from 2 to 8-th tracker(Fig.3.7). The position of most 195 upstream hit associated with the reconstructed track is defined as the vertex 196 of the neutrino event. The vertex is required to be within the fiducial volume 197 (Fig.3.8 and 3.9).

Figure 3.6: The event rejected by upstream VETO selection Figure 3.7: The definition of fiducial volume Figure 3.8: vertex x after the upstream VETO cut (Left:DATA, Right:MC normalized by area)

Figure 3.9: vertex y after the upstream VETO cut (left:DATA, right:MC normalized by area)

198 Event selection summary

199 The number of events and the selection efficiencies at each selection step is 200 summarized in Tab.3.1. We obtained 493813 neutrino event candidates among 201 2010a data set.

Table 3.1: Summary of the event selection. Data and MC are normalized by POT

selection  Data selection eff.  MC  selection eff.
1 # of active planes > 2 1906146  1.97 × 10^{6}
2 PE / active layers > 6.5 1906078  (1.00)  1.97 × 10^{6}  (1.00)
3  Tracking  1804786  (0.95)  1.83 × 10^{6}  (0.93)
4  Track matching  1749548  (0.97)  1.77 × 10^{6}  (0.97)
5  Beam timing  1747181  (0.99)  1.77 × 10^{6}  (1.00)
6 Upstream VETO cut  745912  (0.43)  7.34 × 10^{5}  (0.42)
7  Vertex in fiducial  493813  (0.66)  4.73 × 10^{5}  (0.66)

202 3.2 Basic distribution

203 In this section, some distributions of the selected events are showed. In each plot 204 the distribution of MC simulation is normalized by the area of the distribution 205 of data. The data/MC ratio is found to be few percents at each plot.

Figure 3.10: number of active planes  Figure 3.11: DATA/MC

Figure 3.12: Vertex X  Figure 3.13: DATA/MC

Figure 3.14: Vertex Y  Figure 3.15: DATA/MC

Figure 3.16: Reconstructed track angle  Figure 3.17: DATA/MC

206 3.3 Vertex resolution of tracking

207 Vertex resolution is checked by MC simulation to compare the reconstructed 208 value and the MC true information. The results of vertex X, Y and track angle 209 are shown in Fig.3.18, Fig.3.19 and 3.20, respectively. Their r.m.s. for CCQE 210 events are 2.7 cm for X, 2.8 cm for Y and 3.8 degree, respectively.

Figure 3.18: Vertex resolution in the X direction Figure 3.19: Vertex resolution in the Y direction

Figure 3.20: Angular resolution of reconstructed track

211 3.4 Detection efficiency to neutrino interaction 212 events

213 The event selection efficiency as a function of the true neutrino energy is esti-214 mated by MC. The efficiency is showed in Fig.3.21 and 3.22. The definition of 215 this efficiency is the ratio of the number of selected events to that of the events 216 generated inside the fiducial volume. Figure 3.23 shows the selection efficiency 217 for CC interactions as a function of the muon angle. The muon angle depen-218 dence to the neutrino energy (Fig.3.24). The acceptance for the muon angle is 219 restricted due to the event selections, especially at large angle. The efficiency for 220 CC interaction depends on the neutrino energy. Figure 3.25 shows the efficiency 221 for the muons with all angle and less than 15 degrees. The selection efficiency 222 for the muon with small angle is almost 100% and the rising edge around 0.3 223 GeV corresponds to the minimum energy of the muon to penetrate the 2 iron 224 plates and 3 scintillator trackers. 225 Table 3.2 shows the selection efficiency for each module. Because the en-226 ergy spectrum of the beam neutrino is slightly different module by module, the 227 selection efficiency is also different.

Figure 3.21: Neutrino event selection efficiency Figure 3.22: Selection efficiency for CCQE and CC others.

module Efficiency[% ]
0  51.7
1  54.0
2  55.1
3  55.1
4  55.0
5  54.2
6  51.2

Table 3.2: Efficiency of each module Figure 3.23: The selection efficiency for CC interactions as a function of the muon angle.

Figure 3.24: The neutrino energy VS. the muon angle generated from CC interactions. Black rectangle shows the mean energy at each angular bin.

Figure 3.25: The selection efficiency for CC interactions for the muon with all angle and less than 15 degree

229 Event rate measurements

230 4.1 Data set

231 We analyze the beam data from January to June, 2010. Data taking period, 232 number of good spills and number of INGRID good spills are summarized in 233 Tab.4.1. Data taking efficiency for entire period is 99.9%, and total number of 234 protons recorded at INGRID is 3.255 × 10^{19}. The MC simulation corresponds 235 to an equivalent of 100 × 10^{21} pot.

236 4.2 Event rate stability

237 We measured the event rate of the neutrino event candidates and the beam 238 related dirt muon candidates with all fourteen modules. Here the dirt muon 239 candidate is defined as the event rejected at upstream VETO selection or the 240 fiducial volume cut. Figure 4.1 and Fig.4.2 show the daily pot and number of the 241 neutrino event candidates, and number of dirt muon candidates, respectively. 242 Figure 4.3 and Fig.4.4 show daily event rate normalized by pot. We succeeded 243 to measure the daily event rate of neutrino event candidate and dirt muon

MR run #  Period  Good spills INGRID good spills Protons at CT05
29  Jan. 23 - Feb. 5  26813  26813  0.32 × 10^{18}
30  Feb. 24 - Feb. 28  59256  59070  1.12 × 10^{18}
31  Mar. 19 - Mar. 25  86980  86935  1.97 × 10^{18}
32  Arp. 14 - May. 1  237350  236647  7.64 × 10^{18}
33  May. 9 - Jun. 1  350079  350012  1.22 × 10^{19}
34  Jun. 7 - Jun. 26  246504  246410  9.30 × 10^{18}
Total  1006982  1005887  3.26 × 10^{19}

Table 4.1: Summary of data sets 244 candidate with about 1.7% and 1.1% statistical error each day. The chi-squares 245 calculated from the average rate are 86 and 82 for 76 degrees of freedom. It is 246 concluded that the beam events is stable within statistical error.

247 4.3 The data/MC ratio

248 To obtain the number of events in the fiducial volume, we need to do following 249 corrections.

250 (1) Iron mass 251 In INGRID most of the neutrino interactions occur in the 9 iron targets 252 of each module. During their fabrication, there was a tolerance on the 253 thickness of those iron planes. This results in iron planes having slightly 254 different volumes, and as a consequence different masses. The maximal 255 variation from design mass is 2.15 % from the given tolerance on thickness. 256 The mass of each iron plane was measured at the end of the fabrication 257 process, so we can deduce correction factors for the expected number of 258 events for each module, by using the fact that 95.2 % of interactions in 259 one module occur in the iron.

260 (2) Accidental MPPC noise 261 Another correction on the number of observed events comes from noise 262 hits in the detector. Those noise hits reduce the number of reconstructed 263 events compared to the case when there is no noise. To correct this effect, 264 we use the following procedure:

265 · Measure noise in data

266 · Create a noise simulation to reproduce those measurements

267 · Use Monte Carlo simulation to compare the number of reconstructed 268 events with and without adding noise

269 · Deduce from the simulation correction factors and systematic errors

270 Noise is measured in beam data. We measure the rate of noise hits, which 271 are defined as hits occuring in the detector when no particles are actually 272 going through the detector. To find such hits, we look at cycles where 273 beam spills are not coming (INGRID records data on 23 integration cycles, 274 but beam spills only arrive during 6 of them), and perform regular event 275 selection to make sure there is no cosmic particle in the detector. We then 276 measure a noise rate for each channel of the detector, as well as light yield 277 and timing distribution.

278 Noise is then simulated with a given probability for each channel. Timing 279 for the noise hits is simulated using the distribution measured in data. 280 Light yield is then simulated using a measured light yield distribution for 281 the corresponding timing.

Figure 4.1: daily pot and number of neutrino event candidates Figure 4.2: daily pot and number of dirt muon candidates Figure 4.3: daily event rate of neutrino event candidate

Figure 4.4: daily event rate of dirt muon candidate 282 Monte Carlo simulation is then used to measure the variation of number 283 of reconstructed events due to noise. We first reconstruct events on Monte 284 Carlo files which do not include noise hits, then add noise hits to those 285 files and perform reconstruction again. We then compare the number of 286 reconstructed events in each case. The simulation is using jnubeam 10c. 287 From this simulation we have for each module a noise rate and the vari-288 ation of number of reconstructed events due to noise. There is a linear 289 relation between them as can be seen on Fig.4.5. We will use this lin-290 ear relation to make corrections on the number of observed events. This 291 relation is: 292 Variation of number of events [%] = -0.9585 * < noise rate > 293 Those corrections are made for each module, and each subset of events we 294 are considering. In each case we measure the noise rate, and then from 295 the linear relation deduce the variation of number of reconstructed events 296 which should be used as a correction factor.

Figure 4.5: Variation of number of reconstructed events as a function of noise rate

297 (3) Beam related background 298 We estimated the contamination fraction of beam related background with 299 background MC in which the neutrino flux and the neutrino interaction 300 is generated in upstream dirt ( 10 x 10 x 5 m^{3}). 301 Almost all contaminations come from short track induced neutron (∼ 302 50%) or gamma (∼ 40%) and dirt muon (∼ 10%) which is not detected 303 accidentally due to scintillator inefficiency.

304 In background MC, number of generated interactions is normalized so that 305 the number of rejected events at upstream VETO selection, which consists 306 dirt muon mainly, is equal to DATA. The difference from POT expectation 307 is 35% and it is considered as systematic error. Finally contamination 308 fraction is estimated to be 0.4% and it is applied as one of the correction 309 factor.

310 The correction factors are summarized in Tab.4.2 run by run and module by 311 module. In this table the corrected number of selected events (N^{cor.}) is calcu-312 lated with N^{cor.} = N^{sel.} × \frac{1}{1+C}, where N^{sel.} is the number of selected events and 313 C is the correction factor. The final result is summarized in Table 4.3. Finally 314 we obtain DATA/MC to be 1.074 ± 0.001 (stat.).

module 29,30 31  32  33  33  34

number of selected events 0 1054 1548 5956 4119 5425 6962

1  1526 2033 7827 5432 7122 9520
2  1875 2476 9360 6492 8555 11622
3  1882 2570 10133 6795 9078 12191
4  1831 2459 9627 6636 8683 11651
5  1524 2176 7876 5421 7217 9588
6  1058 1585 5837 4172 5421 7285
7  1229 1717 6636 4509 5826 8100
8  1588 2187 8351 5819 7620 10270
9  1884 2562 9770 6632 8766 11946
10  1949 2681 10305 6987 9373 12473
11  1908 2520 9771 6713 8897 11871
12  1561 2133 8146 5512 7193 9822
13  1218 1659 6263 4327 5815 7734
correction factor 0 -3.3 -3.3 -4.3 -4.0 -3.9 -3.9
1  -2.6 -2.6 -2.6 -2.4 -2.4 -2.4
2  -2.0 -2.0 -2.0 -1.7 -1.7 -1.7
3  -2.3 -2.3 -2.3 -2.0 -1.9 -1.9
4  -1.8 -1.8 -1.8 -1.6 -1.5 -1.5
5  -1.9 -1.9 -1.9 -1.6 -1.5 -1.4
6  -2.3 -2.3 -2.8 -2.5 -2.4 -2.3
7  -2.7 -2.7 -2.5 -3.5 -3.3 -3.1
8  -2.2 -2.2 -2.0 -3.0 -2.8 -2.6
9  -2.1 -2.1 -2.7 -4.1 -3.8 -3.6
10  -4.2 -4.2 -4.1 -5.4 -5.2 -5.0
11  -1.9 -1.9 -1.8 -2.9 -2.7 -2.6
12  -4.9 -4.9 -4.7 -6.2 -6.0 -5.9
13  -2.5 -2.5 -2.5 -3.4 -3.2 -3.0

corrected number of

selected events 0 1090 1601 6224 4292 5647 7242

1  1567 2087 8037 5565 7298 9756
2  1913 2526 9551 6606 8703 11822
3  1927 2632 10374 6934 9255 12422
4  1865 2504 9804 6741 8817 11825
5  1553 2218 8028 5509 7328 9697
6  1083 1622 6002 4278 5552 7453
7  1263 1765 6803 4674 6024 8360
8  1624 2237 8520 6001 7838 10545
9  1925 2617 10040 6912 9110 12391
10  2035 2800 10742 7385 9883 13130
11  1945 2569 9951 6914 9143 12183
12  1641 2242 8550 5878 7653 10435
13  1250 1702 6421 4478 6005 7976

Table 4.2: Correction factors

Number of selected events  493813
Corrected number of events  508511
Number of selected events in MC 4.733e5

Table 4.3: Number of events before and after corrections

315 4.4 Systematic error of event rate

Table 4.4 shows the systematic errors.

Item  Error[%]
Iron mass  0.1
Accidental MPPC noise  0.7
Beam related background  0.2
Fiducial selection  1.1
Hit efficiency  1.8
Tracking efficiency  1.4
Track matching selection  2.7
Not beam-related background  <0.1
p.e./active layer selection  <0.1
Beam timing selection  <0.1
Total  3.7

Table 4.4: Systematic error table

316

317 Iron mass

318 Before construction of INGRID the mass of each iron plate was measured with a 319 precision of 1 kg, which corresponds to 0.13 % of the mass of one iron plate. We 320 will use this figure as the systematic error on this correction factor. We might 321 need to increase this systematic error in the future, as the correction factors 322 are calculated using the mass of the whole iron plate, when we actually use a 323 fiducial cut in analysis, only interactions in the central part of the iron plates 324 are kept.

325 Accidental MPPC noise

326 The effect of MPPC noise is studied with MC as discussed at previous chapter. 327 Two sources of systematic errors are considered. First one comes from the error 328 on the linear fit. To get this systematic error, we multiply the fit error by the 329 maximal measured noise rate. Second one comes from the measurement of noise. 330 Correction factors are calculated using the average noise rate measured on one 331 period. But this noise rate fluctuates in time (probably due to temperature 332 variations). So we measure the maximal difference between average noise rate 333 and noise rate measured at different times during one period, and using the 334 linear relation between noise rate and variation of number of events we get the 335 systematic error. The quadratic sum of these two errors is 0.7 %.

336 Beam-related background

337 We estimated the contamination fraction of beam related background with wall 338 neutrino Monte Carlo. The fraction is estimated to be 0.4% , in which the 339 number of interactions of background is normalized to compare the number of 340 dirt muon in DATA and MC. There is a 35% difference from POT expectation, 341 which is considered as one of the source of the systematic error. We considered 342 20% neutrino flux uncertainty and 20% cross section uncertainty as other sources 343 of the systematic error. Finally 0.2% (=\sqrt{0.35^{2} + 0.2^{2} + 0.2^{2}}) is applied as the 344 systematic error.

345 Fiducial selection

346 To estimate the uncertainty of fiducial selection and the effect of non uniformity 347 of iron plate, we divided fiducial in several horizontal slices and checked the 348 difference between DATA and MC. Table 4.5 shows the result. The maximum

absolute value, 1.1%, is applied as systematic error.

selection  DATA MC |DATA - MC|
<50 cm from center(nominal selection) 100.0 100.0  0.0
<25 cm  25.6 25.2  0.4
25 ∼ 40 cm  39.9 39.3  0.6
40 ∼ 50 cm  34.4 35.5  1.1
Systematic error ( Maximum absolute )  1.1

Table 4.5: DATA-MC for several sub fiducial volume

349

350 Hit efficiency

351 We estimated the relation between hit efficiency and number of selected events 352 with MC. Fig. 4.6 shows the result from which the systematic error of hit effi-353 ciency is estimated to be 1.8% because hit efficiency has 1.1% uncertainty. ^{1}

354

355 Track matching selection

356 In the neutrino event selection, after reconstruction of XZ track and YZ track we 357 require track start point matching. To estimate the uncertainty of the selection, 358 we changed the tolerance for the matching and checked the difference of the

10.5% of the measurement error of hit efficiency, 1.0% of the tuning of hit efficiency in MC

Figure 4.6: hit efficiency V.S. number of selected events

359 number of selected events between DATA and MC. Table 4.6 shows the result. The maximum absolute value, 2.7%, is applied as systematic error.

Vertex Z of XZ track - Vertex Z of YZ track DATA MC |DATA - MC|
-1, 0, +1 (nominal selection)  100.0 100.0  0.0
0  83.0 85.7  2.7
-2, -1, 0, +1, +2  104.0 103.0  1.0
Systematic error ( Maximum )  2.7

Table 4.6: DATA-MC for several tolerance of track matching.

360

361 Tracking efficiency

362 To check the difference of the tracking efficiency between DATA and MC, the 363 tracking efficiency is compared with several sub-sample selected by number of 364 active planes. Table 4.7 shows the result. The maximum absolute value, 1.4%, 365 is applied as systematic error.

366 Not beam-related background

367 The off-bunch data (cycle 17 ∼ 22 where as on-bunch cycle is 4 ∼ 9) are analyzed 368 with same procedure and only 93 events are selected whereas the number of 369 signal is 493813. It is negligible.

370 PE/active layer selection

371 To estimate the uncertainty of PE/active layer selection, we changed the cut 372 value and checked the difference of number of selected events from one with

number of active planes  DATA MC |DATA - MC|
3  87.6 86.9  0.7
4  93.2 91.8  1.4
5  94.7 94.3  0.5
6  95.6 96.2  0.6
7  96.2 96.6  0.4
8  96.7 96.8  0.1
9  98.7 97.9  0.8
10  99.1 99.0  0.1
Systematic error ( Maximum )  1.4

Table 4.7: The tracking efficiency of DATA and MC with several sub sample

373 nominal cut. The result is the difference is less than 0.01% and its uncertainty 374 is negligible.

375 beam timing selection

376 To estimate the uncertainty from neutrino beam timing, we changed the cut 377 value and checked the difference of number of events from nominal cut. The 378 difference is less than 0.01% and it is negligible.

380 Measurements of beam 381 profile

382 We measured the beam profile on a monthly basis, which corresponds to MR run 383 number. Fig.5.1 shows horizontal and vertical beam profile with RUN 32 data. 384 We fit the profile with gaussian function with least square method and fitted

center and sigma are applied as beam center and beam width, respectively.

Figure 5.1: Horizontal profile(left) and vertical profile(right)

385

386 5.1 Stability of beam center

387 Figure 5.4 shows the monthly x center and Fig.5.5 show the monthly beam y 388 center. We succeeded to measure the profile center with about 4.2 cm statistical 389 error for each month. The chi-square calculated from the average rate are 4.1 390 for 5 degrees of freedom for x beam centers and 3.8 for 5 degrees of freedom for 391 y beam centers. It is concluded that the beam center is stable within statistical 392 error.

Figure 5.2: Horizontal profile center.  Figure 5.3: Vertical profile center

393 5.2 The systematic error of beam center

394 We estimated the systematic error using the toy profile MC simulation in which 395 the number of events at each module is varied with 3.7% from original profile 396 made by all the beam data. 100’000 profiles are generated and the beam center 397 is measured with same method as the data analysis. Figure 5.4 and Fig.5.5 show 398 the x center distribution and y center distribution, respectively. The RMS is 399 applied as the systematic error. The result shows 9.2 cm for x center and 10.4 400 cm for y center.

Figure 5.4: Fitted Horizontal center with 100’000 profiles Figure 5.5: Fitted Vertical center with 100’000 profiles

402 Measurement of beam 403 direction

404 The beam direction is measured as a direction from the proton beam target 405 to the beam center measurements summarized in Tab.6.1. Table 6.2 shows the 406 result of survey of the positions of proton beam target, the center of INGRID 407 horizontal modules and vertical modules (based on the result put on [4]). With 408 these measurements we calculate the beam direction and result is shown in Tab. 409 6.3; Depression angle is 3.651 ± 0.0216 degrees and direction angle is 270.475 410 ± 0.0190. Table 6.3 shows also the result of survey of the angle between the 411 target and the SK detector. Finally the off-axis angle is obtained to be 2.519 ± 412 0.021 degrees (43.96 ± 0.37 mrad).

Table 6.1: Summary of beam center measurements

X center  Y center
Measurement +0.2 ± 9.3 -6.6 ± 10.5

Table 6.2: The position with the NEUT coordinate system

X[m]  Y[m]  Z[m]
Target  0  0.30603  -4.62
INGRID H center -0.000863 -17.55557 277.36844
INGRID V center -0.038371 -17.38257 273.35956

Table 6.3: Direction from the proton beam target and SK

Depression[degree] Direction[degree] Angle from SK[degree]
SK  1.260  270.475  -
INGRID center  3.637  269.681  2.506
INGRID measurement  \begin{matrix}3.651 \\ ± 0.0216 \end{matrix}  \begin{matrix}270.475 \\ ± 0.0190 \end{matrix}  \begin{matrix}2.519 ± 0.0213 \\ (43.96±0.37 mrad) \end{matrix}

414 Conclusion

415 In this note we have presented the measurement of the neutrino event rate, pro-416 file center in INGRID during and beam direction with 2010a data. We selected 417 the neutrino interactions to reconstruct the long track started within fiducial 418 volume. The results have been compared to MC and found good agreement 419 with DATA. Finally DATA/MC of the event rate and beam profile centers have 420 been evaluated with an associated systematic error:

R_{DATA/MC} = 1.074 ± 0.001(stat.) ± 0.040(syst.)
Xcenter = +0.2 ± 1.4(stat) ± 9.2(syst.)cm
Ycenter = −6.6 ± 1.5(stat.) ± 10.4(syst)cm
offaxis angle = 2.519 ± 0.021degrees
= 43.96 ± 0.37mrad

421 Bibliography

422 [1] will be put the name of jnubeam tech. note 423 [2] will be put the name of NEUT doc. 424 [3] the report by Calibration group of ND280 working group put

425  on  http://www.t2k.org/nd280/calib/Meetings/Jan10Workshop/
426  MPPClinearity/at download/filet2k.org).
427 [4] http://www.t2k.org/beam/NuFlux/GeometryInformation