Event Selections

The selection of the signal and control regions has as main goal enlarge the phase space of the muon kinematics. In previous analysis the selection criteria has been optimised to select forward going muons originating from FGD1 and leaving more than 18 clusters in TPC2. The acceptance has been increased using all the ND280 sub-detectors and the time of flight (TOF) of the particles between different sub-detectors which gives informa-tion about the sense of the track.

For the selection of particles that enter the TPCs, the standard TPC PID is per-formed, while to identify particles that do not enter the TPCs, ECal PID is used if there is an associated ECal segments. ECal PID helps in the improvement of the muon purity reducing the shower-like contamination. Furthermore the ratio between the track length and the electromagnetic energy associated to the track reduce the proton contamination.

Finally, the momentum in that selection is reconstructed from the total length of the track (measured by range), so it is require to stop either in ECAL or SMRD.

In both selections is used the TOF between PØD, BrECal and FGD1-FGD2. The first two are fundamental to tag backward going particles starting in FGD1.

The other two are used to reduce the out of fiducial volume contamination in the selection of forward going tracks.

All the FGD1 thickness in the direction Z has been used for these selection in order to have a common fiducial volume between the ν_µ and ¯ν_µ selection. Nonetheless at recon-structed level events starting in the first and last layer are rejected.

In the following sections are described the selection criteria of signal regions and sidebands.

Selection of the ν_µ CC-0π events

The target for the ν_µ interactions is the FGD1 which is used also as tracker along with TPC1 or TPC2, ECal and SMRD. First ν_µ charged current events are selected following the criteria described in Chap. 4. The only difference is the definition of FGD1FV: the cut along the x and y direction are the same, while all the thickness along z has been considered. These cuts has been extended to include muons which have segment only

in FGD or in FGD and in BrECAL or SMRD. Using all the ND280 sub-detectors along with the timing information between them allows the selection of backward going and high-angle muons improving the angular acceptance.

The proton selection is performed both by looking for particle reconstructed as positive track in the TPC with a vertex in the FGD1 FV which passes the TPC track quality cut and a PID criteria, and for tracks that stop in FGD and are compatible with proton hypotheses. Anyway also events without reconstructed proton are also included, thus the cross-section is fully inclusive with respect to the presence of a proton. More details about this selection can be found in [155]. The selected events are divided in five signal regions:

I region characterized by events with only one muon candidate in one of the TPCs (TPC2 if the muon is going forward and TPC1 if is going backward) and with one muon and more than one proton in FGD or TPC,

II region event with one muon candidate in one of the TPCs and one proton candidate in TPC2

III region event with one muon candidate in one of the TPCs and a proton candidate in FGD1,

IV region event with one muon candidate in FGD1 that reach the ECAL or SMRD and with one proton in TPC2 or more than one in FGD1 or TPC2,

V region event with only one muon candidate in FGD1, that reach the ECAL or SMRD or one muon plus any number of proton.

The kinematics of the muon candidate in each selection regions for the CC-0π signal and the various backgrounds are shown in Fig. 5.2. The signal regions where the muon is reconstructed in the TPC (regions I-II-III) have very similar momentum distributions, although events with a reconstructed proton tend to have muons at slightly larger angles, while the regions with the muon in the FGD and the proton in the TPC (regions IV-V) have muons with much smaller momenta and larger angles. In order to better show the contribution from the different backgrounds, the MC is broken down by the following true topologies: ν_µ CC-0π, ν_µ CC-1π⁺, ν_µ CC-Other, ¯ν_µ CC-0π, ¯ν_µ CC-1π⁻, ¯ν_µ CC-Other, NC, ν_e, ¯ν_e, out of FV.

The ν_µCC-0π cross section is extracted adding the contribution from all the regions, but it is important to keep separated the events with and without a proton reconstructed in the analysis because they are affected by different systematics and backgrounds.

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Figure 5.2. Distribution of ν_µ events in the different signal regions as function of the reconstructed muon momentum (left column) and scattering angle (right column). Dif-ferent colors indicate difDif-ferent topologies. The legend show also the purity for each true topology.

Selection of the ¯ν_µ CC-0π events

The ¯ν_µ CC-0π selection has as purpose the identification of events with one positive muon and no pion in the final state, even if the experimental signature of the CCQE anti-neutrino interactions is characterized only by one positive muon since the neutron is not visible. This choice of the signal definition is supported by the goal of the model independence, since being more inclusive, also event with more that one nucleon in the final state are taken into account.

This selection is based on ν_µ charged current selection described in [192]. The main difference are the charge requirement and the TPC PID. Indeed the muon candidate is identified as the highest-momentum positively-charged track, while the PID cut is the same described in Ref. [176] and has been optimized for the ¯ν_µcharged current selection.

The muon candidate can be selected in one of the three following selections: forward (FWD), backward (BWD) and respectively high angle forward (HAFWD) and backward (HABWD). In the FWD/BWD selections, the muon candidate must have more than 18 clusters in TPC, while tracks with short or without TPC segment are used in the HAFWD/HABWD. The cuts are summarized in Tab. XXII.

FWD BWD HAFWD HABWD

Cut name Cut description

Event quality Only good beam spills are used (see Chap.4) Track

multiplicity One or more FGD1 segments must exist

Track quality

Low angle Positively-charged

NT P C−Cluster>18 vertex in FGD1

High angle NT P C−Cluster618

vertex in FGD1 end position in ECal or SMRD Track

direction z_start< z_end z_start> z_end z_start< z_end z_start> z_end Backgroud

veto

z_veto− zµ>−100 mm

or p^veto/p^µ< 0.8 no cut applied z_veto− zµ>−150 mm

or p^veto/p^µ< 0.9 no cut applied

Muon PID

0.1 <Lµ< 0.7 and Lp<500 M eV /c

M IP > 0.9 reject particles stopping in FGD2

ECal PID

Lµ> 0.1 and Lp<500 M eV /c

M IP > 0.7

ECal PID

TABLE XXII. Summary of the selection criteria.

Compared with the selection discussed in Chap. 4, the FGD2 and ECal informations have been used. Since most of the tracks stopping in FGD2 are pions, they are rejected. ECal PID helps in the rejection of the electromagnetic and hadronic component.

Then thanks to the pion tagging developed for the ν_µ multiple pion selection described before it is possible to tag pion-less events in all the selections. The kinematics of the muon candidate for the signal regions are shown in Fig. 5.3. In the ¯ν_µ sample the ν_µ contamination is not negligible in particular in the high momentum region where the ν_µ

flux is higher that the ¯ν_µ, as already explained in Chap. 4. Then protons and positive pions produced in ν_µ interactions can be misidentified as muon constituting an irreducible background. Moreover in HA selection the charge is not reconstructed, then also negative muons are selected. The selection of backward-going muons results in a high background due to out FV events. This happen because the veto cut is not applied to avoid rejection of muon candidate. Anyway, the ¯ν_µcross section it is very low in the backward region, for this reason the number of event is very low. This aspect will be taken under consideration in the discussion on the binning choice in Sec. 5.3.4.

In order to better show the contribution from the different backgrounds, the MC is broken down by the following true topologies: ν_µ CC-0π, ν_µ CC-1π⁺, ν_µ CC-Other, ¯ν_µ CC-0π, ¯ν_µCC-1π⁻, ¯ν_µ CC-Other, NC, ν_e, ¯ν_e, out of FV. As it will be shown in Sec. 5.3.5, an increment of the efficiency is achieved with this selection in high angle region, while for the selection of backward tracks is rather small. The ¯ν_µ CC-0π cross section is extracted adding the contribution from all the selections.

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Figure 5.3. Distribution of ¯ν_µ events in the different signal regions as function of the reconstructed muon momentum (left column) and scattering angle (right column). Dif-ferent colors indicate difDif-ferent topologies. The MC is normalized for POT in data. The legend show also the purity for each true topology.