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HighLAND
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In this section the different systematics used in ND280 are explained
There are a number of categories of possible pile up, but only the
effect of sand muons is significant for the \(\nu_\mu\) analyses. For vertex
selection in FGD1, events with TPC1 activity are rejected by the
external veto cut because, in most cases, TPC1 activity is due to tracks
from interactions upstream of the detector (sand muons) or outside the
tracker fiducial volume. A quick study of MC events rejected due to the
TPC1 veto indicates that the majority are not true CC interactions.
Since sand muons are not included in the standard NEUT simulation, the
Monte Carlo does not include the effect of events that are rejected due
to coincidence with a~sand muon and a correction must be made.
For vertex selection in FGD2, an analagous cut is made to veto events
with TPC2 activity. Therefore, the pileup correction and systematic is
evaluated in an identical manner for TPC1 and TPC2, with TPC1 pileup
applicable to selections with FGD1 vertices and TPC2 pileup applicable
to selections with FGD2 vertices.
For vertex selection in FGD2, an analagous cut is made to veto events
with TPC2 activity. Therefore, the pileup correction and systematic is
evaluated in an identical manner for TPC1 and TPC2, with TPC1 pileup
applicable to selections with FGD1 vertices and TPC2 pileup applicable
to selections with FGD2 vertices.
Evaluation of this correction is made in an identical procedure to the
2013 analysis (as described in T2K-TN-152~\cite{TN-152}). The correction
is evaluated for each data set (Run~1, 2, 3b, 3c, 4, 5ab, 5c) separately
for P0D water-in and water-out using the relevant MC samples for each
period. (Note sand muons simulations are only available for water-out).
The procedure is to count the number of TPC1 (TPC2) events \(NTPC_s\) in
a separate sand muon Monte Carlo sample which relates to a fixed PoT,
\(POT_s\). The data intensity \(I_{d} = POT/nSpills\), is then derived from
the data sample and used to calculate the effective number of spills and
hence the sand TPC1 (TPC2) events/bunch for that data set, where \(N_b\) is
the number of bunches per spill (6 for Run 1, 8 otherwise). Flux tuning
is applied using the 13a tuning from the
nd5_tuned13av1.0_13anom_runX files.
Since the pile up is not taken into account in the Monte Carlo, the
number of selected events should be reduced in the Monte Carlo. To do
so, we re-weight the Monte Carlo with the following reduction factor,
\[
w_{c} = (1-C_{s})
\]
where \(C_{s}\) is the correction to be applied and defined as
\[
C_{s} = \frac{NTPC_s\times I_{d}}{POT_s\times N_b}
\]
Since there is an uncertainty in the sand muon simulation of 10\% (for
neutrinos, 30\% is taken for antineutrinos) and there are possible
differences between the data and Monte Carlo arising from differences in
the actual and simulated beam intensity and different material
descriptions for side-band materials, there is a~systematic uncertainty
on this pile-up contribution. The uncertainty is evaluated through
a~data-MC comparison of the number of TPC1 (TPC2) events/bunch, with the
sand muon contribution added to the MC. Explicitly, the data-MC
difference is
\[
\Delta_{\rm data:MC} = C_d - (C_{MC}+C_s)
\]
where
\[
C_{d}=\frac{NTPC_d}{nSpills\times N_b}
\]
\[
C_{MC}=\frac{NTPC_{MC}\times I_{d}}{POT_{MC}\times N_b} .
\]
The same procedure is applied to evaluate the number of
TPC1 (TPC2) events per bunch for data and MC (MC is also weighted by the
data intensity) and the \(\Delta_{\rm data:MC}\) value can then be taken
as the uncertainty. However, the sand muon uncertainty means that there
is a 10\% uncertainty (30\% for antineutrinos) in the correction factor,
but combining the two uncertainties is double counting so the procedure
is to take either \(\Delta_{\rm data:MC}\) or \(0.1\times C_{s}\)
(\(0.3\times C_{s}\) for anti-neutrinos), whichever is larger, as
\(\sigma_{\rm pileup}\). This systematic error is then propagated as the
normalization error using Eq. eq_normsyst
\[
w_{pileup} = 1+\alpha \cdot \sigma_{\rm pileup}
\]
where \(\alpha\) is the random variation.
This systematic is treated in detail in T2K-TN-222 \cite{TN-222}. The study has been performed using tracks that cross multiple TPCs, whose redundancy allows building a fully reconstructed observable (no truth info needed) sensitive to the intrinsic TPC resolution. The ultimate goal of this analysis is to compare the TPC and global momentum resolutions of data and MC, and in the case they differ, to find the smearing factor that makes them similar. This smearing factor would be the systematic parameter to be propagated in any event selection. The use of tracks crossing at least two TPCs allows to compute the difference between the momentum reconstructed using the two TPC segments of the same global track. Using the inverse of the transverse momentum to the magnetic field, \(1/p_t\), the distribution of its difference corrected by energy loss in the intermediate FGD \(\Delta 1/p_t\) is approximately Gaussian and centered at zero, with a standard deviation having as main contribuitor the intrinsic resolution of the TPCs involved. The resulting \(\Delta(1/p_t)\) distribution can be fitted to a Gaussian function in order to obtain the standard deviation, \(\sigma_{\Delta 1/p_t}\), for different kinematic ranges (\(p_t\), angle, position, etc). \(\sigma_{\Delta 1/p_t}\) contains multiple contributions, among which the one related to the momentum resolution should be extracted.
1.8.13