Partially contained $\nu_e$CC signal efficiency as a function of true neutrino energy. Each bin shows the fraction of Monte-Carlo $\nu_e$ CC events with true neutrino interaction vertex in the fiducial volume (3 cm inside the TPC active volume) which are selected in this channel.

Fully contained $\nu_e$CC true neutrino energy vs reconstructed neutrino energy. Each bin shows the relative number of selected fully contained Monte-Carlo $\nu_e$ CC events with true neutrino interaction vertex in the fiducial volume (3 cm inside the TPC active volume) which have the corresponding true neutrino energy and reconstructed neutrino energy values. Each axis has 60 bins covering an energy range from 0 to 3 GeV, corresponding to 0.05 GeV per bin.

Partially contained $\nu_e$CC true neutrino energy vs reconstructed neutrino energy. Each bin shows the relative number of selected partially contained Monte-Carlo $\nu_e$ CC events with true neutrino interaction vertex in the fiducial volume (3 cm inside the TPC active volume) which have the corresponding true neutrino energy and reconstructed neutrino energy values. Each axis has 60 bins covering an energy range from 0 to 3 GeV, corresponding to 0.05 GeV per bin.

Fully contained $\nu_\mu$CC true neutrino energy vs reconstructed neutrino energy. Each bin shows the relative number of selected fully contained Monte-Carlo $\nu_\mu$ CC events with true neutrino interaction vertex in the fiducial volume (3 cm inside the TPC active volume) which have the corresponding true neutrino energy and reconstructed neutrino energy values. Each axis has 60 bins covering an energy range from 0 to 3 GeV, corresponding to 0.05 GeV per bin.

Partially contained $\nu_\mu$CC true neutrino energy vs reconstructed neutrino energy. Each bin shows the relative number of selected partially contained Monte-Carlo $\nu_\mu$ CC events with true neutrino interaction vertex in the fiducial volume (3 cm inside the TPC active volume) which have the corresponding true neutrino energy and reconstructed neutrino energy values. Each axis has 60 bins covering an energy range from 0 to 3 GeV, corresponding to 0.05 GeV per bin.

Fully contained $\nu_e$CC data, signal, background, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The background includes neutral current events, $\nu_\mu$CC events, events with a true neutrino interaction vertex outside the fiducial volume (3 cm inside the TPC active volume), and cosmic ray backgrounds. The signal includes the remaining intrinsic $\nu_e$CC events. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

Partially contained $\nu_e$CC data, signal, background, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The background includes neutral current events, $\nu_\mu$CC events, events with a true neutrino interaction vertex outside the fiducial volume (3 cm inside the TPC active volume), and cosmic ray backgrounds. The signal includes the remaining intrinsic $\nu_e$CC events. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

Fully contained $\nu_\mu$CC data, signal, and background predictions. Events in the $\nu_e$CC or $\pi^0$ selections have been removed. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The background includes neutral current events, $\nu_e$CC events, $\nu_\mu$CC events with greater than or equal to one $\pi^0$, events with a true neutrino interaction vertex outside the fiducial volume (3 cm inside the TPC active volume), and cosmic ray backgrounds. The signal includes the remaining $\nu_\mu$CC events.

Partially contained $\nu_\mu$CC data, signal, and background predictions. Events in the $\nu_e$CC or $\pi^0$ selections have been removed. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The background includes neutral current events, $\nu_e$CC events, $\nu_\mu$CC events with greater than or equal to one $\pi^0$, events with a true neutrino interaction vertex outside the fiducial volume (3 cm inside the TPC active volume), and cosmic ray backgrounds. The signal includes the remaining $\nu_\mu$CC events.

Fully contained $\nu_\mu$CC$\pi^0$ data, signal, background predictions. Events in the $\nu_e$CC selection have been removed. Note that the rightmost bin is an overflow bin, containing all events with reconstructed $\pi^0$ kinetic energy greater than 1 GeV. The background includes neutral current events, $\nu_e$CC events, $\nu_\mu$CC events without a $\pi^0$, events with a true neutrino interaction vertex outside the fiducial volume (3 cm inside the TPC active volume), and cosmic ray backgrounds. The signal includes the remaining $\nu_\mu$CC$\pi^0$ events.

Partially contained $\nu_\mu$CC$\pi^0$ data, signal, and background predictions. Events in the $\nu_e$CC selection have been removed. Note that the rightmost bin is an overflow bin, containing all events with reconstructed $\pi^0$ kinetic energy greater than 1 GeV. The background includes neutral current events, $\nu_e$CC events, $\nu_\mu$CC events without a $\pi^0$, events with a true neutrino interaction vertex outside the fiducial volume (3 cm inside the TPC active volume), and cosmic ray backgrounds. The signal includes the remaining $\nu_\mu$CC$\pi^0$ events.

NC$\pi^0$ data, signal, and background predictions. Events in the $\nu_e$CC selection have been removed. Note that the rightmost bin is an overflow bin, containing all events with reconstructed $\pi^0$ kinetic energy greater than 1 GeV. The background includes $\nu_e$CC events, $\nu_\mu$CC events, neutral current events without a $\pi^0$, events with a true neutrino interaction vertex outside the fiducial volume (3 cm inside the TPC active volume), and cosmic ray backgrounds. The signal includes the remaining NC$\pi^0$ events.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.0), the standard prediction with no low energy excess. No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.1). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.2). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.3). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.4). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.5). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.6). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.7). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.8). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.9). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.0), the median unfolded MiniBooNE LEE under a $\nu_e$CC hypothesis. No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.1). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.2). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.3). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.4). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.5). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.6). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.7). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.8). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.9). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=2.0). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

Fully contained $\nu_e$CC $0pX\pi$ data, prediction, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

Partially contained $\nu_e$CC $0pX\pi$ data, prediction, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

Fully contained $\nu_e$CC $NpX\pi$ data, prediction, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

Partially contained $\nu_e$CC $NpX\pi$ data, prediction, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

Fully contained $\nu_\mu$CC $0pX\pi$ data, prediction, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

Partially contained $\nu_\mu$CC $0pX\pi$ data, prediction, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

Fully contained $\nu_\mu$CC $NpX\pi$ data, prediction, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

Partially contained $\nu_\mu$CC $NpX\pi$ data, prediction, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.0), the standard prediction with no low energy excess. No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.1). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.2). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.3). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.4). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.5). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.6). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.7). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.8). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.9). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.0), the median unfolded MiniBooNE LEE under a $\nu_e$CC hypothesis. No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.1). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.2). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.3). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.4). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.5). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.6). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.7). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.8). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.9). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=2.0). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

Data/MC ratio as a function of reconstructed $\pi^0$ momentum for the 2$\gamma$0p selection

Energy spectra for the 1$\gamma$1p selected events. The figure shows the unconstrained background prediction and breakdowns as a function of reconstructed shower energy.

Energy spectra for the 1$\gamma$1p selected events. This figure shows the total background prediction with systematic uncertainty both before and after the 2$\gamma$ constraint.

Energy spectra for the 1$\gamma$0p selected events. The figure shows the unconstrained background prediction and breakdowns as a function of reconstructed shower energy.

Energy spectra for the 1$\gamma$0p selected events. This figure shows the total background prediction with systematic uncertainty both before and after the 2$\gamma$ constraint.

The observed event rate for the 1$\gamma$1p event sample, and comparisons to unconstrained (left) and constrained (right) background and LEE model predictions.

The observed event rate for the 1$\gamma$0p event sample, and comparisons to unconstrained (left) and constrained (right) background and LEE model predictions.

The fractional systematic covariance matrix for the final selected 1$\gamma$1p, 1$\gamma$0p, 2$\gamma$1p, and 2$\gamma$0p event samples, in bins of reconstructed shower energy for the 1$\gamma$ distributions, and reconstructed $\pi^{0}$ momentum for the 2$\gamma$ distributions. The bin boundaries are defined in Sec. II in supplementary material. This covariance matrix is evaluated at central value prediction and all variances have been rounded to three significant digits.

The fractional systematic covariance matrix for the final selected 1$\gamma$1p, 1$\gamma$0p, 2$\gamma$1p, and 2$\gamma$0p event samples, in bins of reconstructed shower energy for the 1$\gamma$1p signal, 1$\gamma$1p background, 1$\gamma$0p signal and 1$\gamma$0p background distributions, and reconstructed $\pi^{0}$ momentum for the 2$\gamma$ distributions. The bin boundaries are defined in Sec. II in supplementary material. This covariance matrix is evaluated at central value prediction and variances have been rounded to three significant digits.

Dijet signal efficiencies as a function of the signal mass and lifetime for events satisfying all event and vertex requirements, with corrections based on systematic differences in the vertex reconstruction efficiency between data and simulation.

The distribution of $d_{\mathrm{BV}}$ for $\geq$5-track one-vertex events in data and three simulated multijet signal samples each with a mass of 1600 GeV. The production cross section for each signal model is assumed to be the lower limit excluded by CMS-EXO-17-018, corresponding to values of 0.8, 0.25, and 0.15 fb for the samples with $c\tau =$ 0.3, 1.0, and 10 mm, respectively. The last bin includes the overflow events. This bin includes one event in data with a vertex with large $d_{\mathrm{BV}}$ that appears to arise from tracks originating from separate pp interaction vertices, consistent with background.

Distribution of the $x$-$y$ distances between vertices, $d_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution $d_{\mathrm{VV}}^{\kern 0.15em\mathrm{C}}$ (blue continuous line) is constructed from one-vertex events in data, and is normalized to the number of two-vertex events in data with two 3-track vertices. The two vertical red dashed lines separate the regions used in the fit.

Distribution of the $x$-$y$ distances between vertices, $d_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution $d_{\mathrm{VV}}^{\kern 0.15em\mathrm{C}}$ (blue continuous line) is constructed from one-vertex events in data, and is normalized to the number of two-vertex events in data which have exactly one 4-track vertex and one 3-track vertex. The two vertical red dashed lines separate the regions used in the fit.

Distribution of the $x$-$y$ distances between vertices, $d_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution $d_{\mathrm{VV}}^{\kern 0.15em\mathrm{C}}$ (blue continuous line) is constructed from one-vertex events in data, and is normalized to the number of two-vertex events in data with two 4-track vertices. The two vertical red dashed lines separate the regions used in the fit.

Distribution of the $x$-$y$ distances between vertices, $d_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution $d_{\mathrm{VV}}^{\kern 0.15em\mathrm{C}}$ (blue continuous line) is constructed from one-vertex events in data, and is normalized using $\geq$5-track one-vertex event information. The two vertical red dashed lines separate the regions used in the fit.

Predicted yields for the background-only normalized template, predicted yields for three simulated multijet signals each with a mass of 1600 GeV, and the observed yield in each $d_{\mathrm{VV}}$ bin. The production cross section for each signal model is assumed to be the lower limit excluded by CMS-EXO-17-018, corresponding to values of 0.8, 0.25, and 0.15 fb for samples with $c\tau =$ 0.3, 1.0, and 10 mm, respectively. The uncertainties in the signal yields and the systematic uncertainties in the background prediction reflect the systematic uncertainties given in the text.

Observed 95% CL upper limits on the product of cross section and branching fraction squared for the multijet signals, as a function of mass and $c\tau$. The overlaid mass-lifetime exclusion curves assume pair-production cross sections for the neutralino (red) and gluino (purple) with 100% branching fraction to each model's respective decay mode specified. The solid black (dashed colored) lines represent the observed (median expected) limits at 95% CL. The thin black lines represent the variation of the observed limit within theoretical uncertainties of the signal cross section. The thin dashed colored lines represent the region containing 68% of the expected limit distribution under the background-only hypothesis. The observed limits from the CMS displaced jets search (CMS-EXO-19-021) are also shown in teal for comparison.

Observed 95% CL upper limits on the product of cross section and branching fraction squared for the multijet signals, as a function of mass and $c\tau$. The overlaid mass-lifetime exclusion curves assume pair-production cross sections for the neutralino (red) and gluino (purple) with 100% branching fraction to each model's respective decay mode specified. The solid black (dashed colored) lines represent the observed (median expected) limits at 95% CL. The thin black lines represent the variation of the observed limit within theoretical uncertainties of the signal cross section. The thin dashed colored lines represent the region containing 68% of the expected limit distribution under the background-only hypothesis. The observed limits from the CMS displaced jets search (CMS-EXO-19-021) are also shown in teal for comparison.

Observed 95% CL upper limits on the product of cross section and branching fraction squared for the multijet signals, as a function of mass and $c\tau$. The overlaid mass-lifetime exclusion curves assume pair-production cross sections for the neutralino (red) and gluino (purple) with 100% branching fraction to each model's respective decay mode specified. The solid black (dashed colored) lines represent the observed (median expected) limits at 95% CL. The thin black lines represent the variation of the observed limit within theoretical uncertainties of the signal cross section. The thin dashed colored lines represent the region containing 68% of the expected limit distribution under the background-only hypothesis. The observed limits from the CMS displaced jets search (CMS-EXO-19-021) are also shown in teal for comparison.

Observed 95% CL upper limits on the product of cross section and branching fraction squared for the dijet signals, as a function of mass and $c\tau$. The overlaid mass-lifetime exclusion curves assume pair-production cross sections for the top squark with 100% branching fraction to each model's respective decay mode specified. The solid black (dashed colored) lines represent the observed (median expected) limits at 95% CL. The thin black lines represent the variation of the observed limit within theoretical uncertainties of the signal cross section. The thin dashed colored lines represent the region containing 68% of the expected limit distribution under the background-only hypothesis. The observed limits from the CMS displaced jets search (CMS-EXO-19-021) are also shown in teal for comparison.

Observed 95% CL upper limits on the product of cross section and branching fraction squared for the dijet signals, as a function of mass and $c\tau$. The overlaid mass-lifetime exclusion curves assume pair-production cross sections for the top squark with 100% branching fraction to each model's respective decay mode specified. The solid black (dashed colored) lines represent the observed (median expected) limits at 95% CL. The thin black lines represent the variation of the observed limit within theoretical uncertainties of the signal cross section. The thin dashed colored lines represent the region containing 68% of the expected limit distribution under the background-only hypothesis. The observed limits from the CMS displaced jets search (CMS-EXO-19-021) are also shown in teal for comparison.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of mass for multijet signals, for a fixed $c\tau$ of 300um in the full Run-2 data set. The neutralino and gluino pair production cross sections are shown for the multijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of mass for dijet signals, for a fixed $c\tau$ of 300um in the full Run-2 data set. The top squark pair-production cross section is shown for the dijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of mass for multijet signals, for a fixed $c\tau$ of 1 mm in the full Run-2 data set. The neutralino and gluino pair production cross sections are shown for the multijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of mass for dijet signals, for a fixed $c\tau$ of 1 mm in the full Run-2 data set. The top squark pair-production cross section is shown for the dijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of mass for multijet signals, for a fixed $c\tau$ of 10 mm in the full Run-2 data set. The neutralino and gluino pair production cross sections are shown for the multijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of mass for dijet signals, for a fixed $c\tau$ of 10 mm in the full Run-2 data set. The top squark pair-production cross section is shown for the dijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of $c\tau$ for multijet signals, for a fixed mass of 800 GeV in the full Run-2 data set. The neutralino and gluino pair production cross sections are shown for the multijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of $c\tau$ for dijet signals, for a fixed mass of 800 GeV in the full Run-2 data set. The top squark pair-production cross section is shown for the dijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of $c\tau$ for multijet signals, for a fixed mass of 1600 GeV in the full Run-2 data set. The neutralino and gluino pair production cross sections are shown for the multijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of $c\tau$ for dijet signals, for a fixed mass of 1600 GeV in the full Run-2 data set. The top squark pair-production cross section is shown for the dijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of $c\tau$ for multijet signals, for a fixed mass of 2400 GeV in the full Run-2 data set. The neutralino and gluino pair production cross sections are shown for the multijet signals. For $m$ = 2400 GeV, the expected neutralino cross section is $\approx 8\times 10^{-5}$ fb and is not shown.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of $c\tau$ for dijet signals, for a fixed mass of 2400 GeV in the full Run-2 data set. The top squark pair-production cross section is shown for the dijet signals.

Data-to-simulation efficiency correction factors, shown for multijet and dijet signal topologies in several ranges of $c\tau$. Note that these correction factors account for the two long-lived particles in the simulated events, and are therefore the total correction factors used to scale event yields rather than the correction factors one would apply to individual vertices.

Distribution of the azimuthal angle between vertices, $\Delta\phi_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution (blue continuous line) is constructed from 3-track one-vertex events in data, and is normalized to the number of 3-track two-vertex events in data.

Distribution of the azimuthal angle between vertices, $\Delta\phi_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution (blue continuous line) is constructed from 4-track and 3-track one-vertex events in data, and is normalized to the number of two-vertex events in data which have exactly one 4-track vertex and one 3-track vertex.

Distribution of the azimuthal angle between vertices, $\Delta\phi_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution (blue continuous line) is constructed from 4-track one-vertex events in data, and is normalized to the number of 4-track two-vertex events in data.

Distribution of the azimuthal angle between vertices, $\Delta\phi_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution (blue continuous line) is constructed from $\geq$5-track one-vertex events in data, and is normalized using one-vertex event information. No $\geq$5-track two-vertex data events pass the selection.

CL$_{s}$ value as a function of the branching fraction of $B^{+} \rightarrow K^{+} \nu \bar{\nu}$ for expected and observed signal yields and the corresponding upper limits at 90% confidence level (CL). The expected limit is derived for the background-only hypothesis. The observed limit is derived from a simultaneous fit to the on-resonance and off-resonance data, corresponding to an integrated luminosity of 63 fb$^{−1}$ and 9 fb$^{−1}$, respectively.

Signal efficiency as a function of the dineutrino invariant mass squared $q^{2}$ for events in the signal region (SR) ($\rm{BDT}_{1} > 0.9$ and $\rm{BDT}_{2} > 0.95$). The error bars indicate the statistical uncertainty.

The number of data and fitted simulated events in each bin of the $|d_{0}^{\mu}|$ distribution in the $10<p_{\textrm{T}}^{\mu}<20$ GeV selection in the $\mu-\mu$ channel.

The number of data and fitted simulated events in each bin of the $|d_{0}^{\mu}|$ distribution in the $20<p_{\textrm{T}}^{\mu}<250$ GeV selection in the $e-\mu$ channel.

The number of data and fitted simulated events in each bin of the $|d_{0}^{\mu}|$ distribution in the $20<p_{\textrm{T}}^{\mu}<250$ GeV selection in the $\mu-\mu$ channel.

The measurement of the ratio of the rate of decay of W bosons to τ-leptons and muons, $R(\tau/\mu)=B(W\rightarrow\tau\nu_\tau)/B(W\rightarrow \mu\nu_\mu)$.

Integrated away-side $\gamma_{dir}$-h per-trigger $I_{AA}$ and $I_{dA}$ of Au+Au, d+Au, and p+p, as a function of $\xi$.

$I_{AA}$ vs $\xi$ for direct photon $p_{T}^{\gamma}$ of 5-7 GeV/$c$, 7-9 GeV/$c$, and 9-12 GeV/$c$.

$I_{AA}$ vs $\xi$ for direct photon $p_{T}^{\gamma}$ of 5-7 GeV/$c$, 7-9 GeV/$c$, and 9-12 GeV/$c$.

$I_{AA}$ vs $\xi$ for direct photon $p_{T}^{\gamma}$ of 5-7 GeV/$c$, 7-9 GeV/$c$, and 9-12 GeV/$c$.

$I_{AA}$ as a function of $\xi$ for direct photon $p_{T}^{\gamma}$ of 5-7, 7-9, and 9-12 GeV/$c$. Three away-side integration ranges are chosen to calculate the per-trigger yield and the corresponding $I_{AA}$, $|\Delta\phi-\pi|<\pi/2$, $|\Delta\phi-\pi|<\pi/3$, and $|\Delta\phi-\pi|<\pi/6$.

$I_{AA}$ as a function of $\xi$ for direct photon $p_{T}^{\gamma}$ of 5-7, 7-9, and 9-12 GeV/$c$. Three away-side integration ranges are chosen to calculate the per-trigger yield and the corresponding $I_{AA}$, $|\Delta\phi-\pi|<\pi/2$, $|\Delta\phi-\pi|<\pi/3$, and $|\Delta\phi-\pi|<\pi/6$.

$I_{AA}$ as a function of $\xi$ for direct photon $p_{T}^{\gamma}$ of 5-7, 7-9, and 9-12 GeV/$c$. Three away-side integration ranges are chosen to calculate the per-trigger yield and the corresponding $I_{AA}$, $|\Delta\phi-\pi|<\pi/2$, $|\Delta\phi-\pi|<\pi/3$, and $|\Delta\phi-\pi|<\pi/6$.

Ratios of $I_{AA}$ as a function of direct photon $p_T$ for three different away-side integration ranges.

Measured $I_{AA}$ for direct photon $p_T$ of 5-7, 7-9, and 9-12 GeV/$c$, as a function of $\xi$, are compared with theoretical model calculations.

Measured $I_{AA}$ for direct photon $p_T$ of 5-7, 7-9, and 9-12 GeV/$c$, as a function of $\xi$, are compared with theoretical model calculations.

Measured $I_{AA}$ for direct photon $p_T$ of 5-7, 7-9, and 9-12 GeV/$c$, as a function of $\xi$, are compared with theoretical model calculations.

Direct photon spectra(Nucl. Part. Phys. 23, A1 (1997)) normalized by $(dN_{ch}/d\eta)^{1.25}$ for in p+p at $\sqrt{s_{NN}}$= 63 GeV.

Direct photon spectra(Sov. J. Nucl. Phys. 51, 836 (1990)) normalized by $(dN_{ch}/d\eta)^{1.25}$ for in p+p at $\sqrt{s_{NN}}$= 63 GeV.

Direct photon spectra normalized by $(dN_{ch}/d\eta)^{1.25}$ for in Au+Au at $\sqrt{s_{NN}}$= 62.4 GeV.

Direct photon spectra normalized by $(dN_{ch}/d\eta)^{1.25}$ for in Au+Au at $\sqrt{s_{NN}}$= 39.0 GeV.

Direct photon spectra(Physical Review C91, 064904 (2015)) normalized by $(dN_{ch}/d\eta)^{1.25}$ for in Au+Au at $\sqrt{s_{NN}}$= 200 GeV.

Direct photon spectra(Physical Review Letters 104, 132301 (2010)) normalized by $(dN_{ch}/d\eta)^{1.25}$ for in Au+Au at $\sqrt{s_{NN}}$= 200 GeV.

Direct photon spectra(Physical Review Letters 109, 152302 (2012)) normalized by $(dN_{ch}/d\eta)^{1.25}$ for in Au+Au at $\sqrt{s_{NN}}$= 200 GeV.

Direct photon spectra(Physical Review C98, 054902 (2018)) normalized by $(dN_{ch}/d\eta)^{1.25}$ for in Cu+Cu at $\sqrt{s_{NN}}$= 200 GeV.

Direct photon spectra(Physics Letters B754 235 (2016)) normalized by $(dN_{ch}/d\eta)^{1.25}$ for in Pb+Pb at $\sqrt{s_{NN}}$= 2760 GeV.

Number of binary collisions N_{coll} vs. Charged particle multiplicity in Au+Au at various cm energies.

Charged particle multiplicity vs. centrality in Au+Au at various cm energies.

Number of binary collisions N_{coll} vs. centrality in Au+Au at various cm energies.

Integrated direct photon yield vs. Charged particle multiplicity in various systems at various cm energies.

Charged particle multiplicity vs. centrality in various systems at various cm energies.

Integrated direct photon yield vs. centrality in various systems at various cm energies.

Integrated direct photon yield vs. Charged particle multiplicity in various systems at various cm energies.

Charged particle multiplicity vs. centrality in various systems at various cm energies.

Integrated direct photon yield vs. centrality in various systems at various cm energies.

Integrated per-trigger yields as a function of associated particle angle relative to $\psi_2$ event plane $\phi^a - \psi_2$ integrated over the near side $|\Delta\phi|<\pi/4$.

Integrated per-trigger yields as a function of associated particle angle relative to $\psi_2$ event plane $\phi^a - \psi_2$ integrated over the away side $|\Delta\phi|<\pi/4$.

Integrated per-trigger yields as a function of associated particle angle relative to $\psi_2$ event plane for near-side $|\Delta\phi|<\pi/4$ and for away-side $|\Delta\phi|<\pi/4$.

Integrated per-trigger yields as a function of associated particle angle relative to $\psi_2$ event plane for near-side $|\Delta\phi|<\pi/4$ and for away-side $|\Delta\phi|<\pi/4$.

Per-trigger yields $Y(\Delta\phi)$ of dihadrons pairs measured in Au$+$Au collisions at $\sqrt{s_{_{NN}}}=200~{\rm GeV}$ after subtracting the underlying event model with several $p_T$ selections. Systematic uncertainties due to track matching are given.

Per-trigger yields $Y(\Delta\phi)$ of dihadrons pairs measured in Au$+$Au collisions at $\sqrt{s_{_{NN}}}=200~{\rm GeV}$ after subtracting the underlying event model with several $p_T$ selections. Systematic uncertainties due to track matching are given.

$\Psi_{2}$-dependent $C(\Delta\phi)$ for $2<p_{T}^{trig}<4$ GeV/c and $1<p_{T}^{assoc}<2$ GeV/c.

$\Psi_{2}$-dependent $C(\Delta\phi)$ for $2<p_{T}^{trig}<4$ GeV/c and $2<p_{T}^{assoc}<4$ GeV/c.

$\Psi_{2}$-dependent $C(\Delta\phi)$ for $4<p_{T}^{trig}<10$ GeV/c and $2<p_{T}^{assoc}<4$ GeV/c.

$\Psi_{3}$-dependent $C(\Delta\phi)$ for $2<p_{T}^{trig}<4$ GeV/c and $1<p_{T}^{assoc}<2$ GeV/c.

$\Psi_{3}$-dependent $C(\Delta\phi)$ for $2<p_{T}^{trig}<4$ GeV/c and $2<p_{T}^{assoc}<4$ GeV/c.

$\Psi_{3}$-dependent $C(\Delta\phi)$ for $4<p_{T}^{trig}<10$ GeV/c and $1<p_{T}^{assoc}<2$ GeV/c.

$\Psi_{2}$-dependent $Y(\Delta\phi)$ for $2<p_{T}^{trig}<4$ GeV/c and $1<p_{T}^{assoc}<2$ GeV/c.

$\Psi_{2}$-dependent $C(\Delta\phi)$ for $2<p_{T}^{trig}<4$ GeV/c and $2<p_{T}^{assoc}<4$ GeV/c.

$\Psi_{2}$-dependent $C(\Delta\phi)$ for $4<p_{T}^{trig}<10$ GeV/c and $2<p_{T}^{assoc}<4$ GeV/c.

$\Psi_{3}$-dependent $C(\Delta\phi)$ for $2<p_{T}^{trig}<4$ GeV/c and $1<p_{T}^{assoc}<2$ GeV/c.

$\Psi_{3}$-dependent $C(\Delta\phi)$ for $2<p_{T}^{trig}<4$ GeV/c and $2<p_{T}^{assoc}<4$ GeV/c.

$\Psi_{3}$-dependent $C(\Delta\phi)$ for $4<p_{T}^{trig}<10$ GeV/c and $2<p_{T}^{assoc}<4$ GeV/c.

$\Psi_2$-dependent C for 2 $< p_T^t <$ 4 and 1 $< p_T^a <$ 2 GeV/c.

$\Psi_2$-dependent C for 2 $< p_T^t <$ 4 and 2 $< p_T^a <$ 4 GeV/c.

$\Psi_2$-dependent C for 4 $< p_T^t <$ 10 and 2 $< p_T^a <$ 4 GeV/c.

$\Psi_2$-dependent Y for 2 $< p_T^t <$ 4 and 1 $< p_T^a <$ 2 GeV/c.

$\Psi_2$-dependent Y for 2 $< p_T^t <$ 4 and 2 $< p_T^a <$ 4 GeV/c.

$\Psi_2$-dependent Y for 4 $< p_T^t <$ 10 and 2 $< p_T^a <$ 4 GeV/c.

$\Psi_3$-dependent C for 2 $< p_T^t <$ 4 and 1 $< p_T^a <$ 2 GeV/c.

$\Psi_3$-dependent C for 2 $< p_T^t <$ 4 and 2 $< p_T^a <$ 4 GeV/c.

$\Psi_3$-dependent C for 4 $< p_T^t <$ 10 and 2 $< p_T^a <$ 4 GeV/c.

$\Psi_3$-dependent Y for 2 $< p_T^t <$ 4 and 1 $< p_T^a <$ 2 GeV/c.

$\Psi_3$-dependent Y for 2 $< p_T^t <$ 4 and 2 $< p_T^a <$ 4 GeV/c.

$\Psi_3$-dependent Y for 4 $< p_T^t <$ 10 and 2 $< p_T^a <$ 4 GeV/c.

Fourier fit coefficients for CNT-MPCN ($d$-going) correlations, as a function of collision system and $\pi^0$ $p_T$: (a) the negative of the dipole coefficient, $-c_1$; (b) the quadrupole coefficient $c_2$; (c) the ratio ${-c_2}/{c_1}$.

Fourier fit coefficients for CNT-MPCN ($d$-going) correlations, as a function of collision system and $\pi^0$ $p_T$: Fractional systematic uncertainty on the quadrupole coefficient $c_2$ for $d$+Au.

Fourier fit coefficients for CNT-MPCN ($d$-going) correlations, as a function of collision system and $\pi^0$ $p_T$: Fractional systematic uncertainty on the quadrupole coefficient $c_2$ for $d$+Au and $p$+$p$.

System centrality dependence of correlation coefficients $-c_1$, $c_2$, and the ratio ${-c_2}/{c_1}$ as a function of $N_{part}$.

System centrality dependence of correlation coefficients $-c_1$, $c_2$, and the ratio ${-c_2}/{c_1}$ as a function of $N_{part}$.