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.

$D^+ D^0$~mass distributions for selected candidates with the $D^0$ background subtracted. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the background-subtraction procedure.

Mass distributions for selected $D^+ D^+$ candidates with the $D^0$ background subtracted. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the background-subtraction procedure.

Mass distributions for selected $D^+ D^0 \pi^+$ candidates with the $D^0$ background subtracted. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the background-subtraction procedure.

Background-subtracted distributions for the multiplicity of tracks reconstructed in the vertex detector for $T_{cc}^+\to D^0 D^0 \pi^+$ signal, low-mass $D^0\bar{D}^0$ and $D^0D^0$ pairs. The binning scheme is chosen to have an approximately uniform distribution for $D^0\bar{D}^0$ pairs. The distributions for the $D^0\bar{D}^0$ and $D^0D^0$ pairs are normalised to the same yields as the $T_{cc}^+\to D^0 D^0 \pi^+$ signal. For better visualisation, the points are slightly displaced from the bin centres. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the background-subtraction procedure.

Background-subtracted transverse momentum spectra for $T_{cc}^+\to D^0 D^0 \pi^+$ signal, low-mass $D^0\bar{D}^0$ and $D^0D^0$ pairs. The binning scheme is chosen to have an approximately uniform distribution for $D^0\bar{D}^0$ pairs. The distributions for the $D^0\bar{D}^0$ and $D^0D^0$ pairs are normalised to the same yields as the $T_{cc}^+\to D^0 D^0 \pi^+$ signal. For better visualisation, the points are slightly displaced from the bin centres. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the background-subtraction procedure.

Mass distributions for selected $D^0 \bar{D}^0$ candidates with the $D^0$ background subtracted. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the background-subtraction procedure.

Mass distributions for selected $D^0 D^0$ candidates with the $D^0$ background subtracted. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the background-subtraction procedure.

Mass distributions for selected $\bar{D}^0D^0\pi^+$ candidates with the $D^0$ background subtracted. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the background-subtraction procedure.

Mass distributions for selected $D^0D^0\pi^+$ candidates with the $D^0$ background subtracted. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the background-subtraction procedure.

Mass distributions for selected $D^0D^-$ candidates with the $D^0$ background subtracted. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the background-subtraction procedure.

Mass distributions for selected $D^0D^+$ candidates with the $D^0$ background subtracted. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the background-subtraction procedure.

Distribution of $D^0 D^0 \pi^+$ mass where the contribution of the non-$D^0$ background has been statistically subtracted by assigning the a weight to every candidate.

Mass distribution for $D^0 \pi^+$ pairs from selected $D^0 D^0 \pi^+$ candidates with a mass below the $D^{*+}D^0$ mass threshold with non-$D^0$ background subtracted by assigning the a weight to every candidate.

$D^0 D^0$~mass distributions for selected candidates with the $D^0$ background subtracted by assigning the a weight to every candidate.

$D^+ D^0$~mass distributions for selected candidates with the $D^0$ background subtracted by assigning the a weight to every candidate.

Mass distributions for selected $D^+ D^+$ candidates with the $D^0$ background subtracted by assigning the a weight to every candidate.

Mass distributions for selected $D^+ D^0 \pi^+$ candidates with the $D^0$ background subtracted by assigning the a weight to every candidate.

Single-differential production cross-sections for nonprompt $J/\psi$ mesons as a function of $p_\text{T}$. The first uncertainties are statistical, the second are correlated systematic uncertainties shared between intervals, and the last are uncorrelated systematic uncertainties.

Single-differential production cross-sections for prompt $J/\psi$ mesons as a function of $y$. The first uncertainties are statistical, the second are correlated systematic uncertainties shared between intervals, and the last are uncorrelated systematic uncertainties.

Single-differential production cross-sections for nonprompt $J/\psi$ mesons as a function of $y$. The first uncertainties are statistical, the second are correlated systematic uncertainties shared between intervals, and the last are uncorrelated systematic uncertainties.

Fraction of nonprompt $J/\psi$ mesons (in \%) in ($p_\text{T},y$) intervals. The first uncertainty is statistical and the second is systematic.

Nuclear modification factor $R_{p\text{Pb}}$ for prompt $J/\psi$ mesons as a function of $y$. The first uncertainty is statistical and the second is systematic.

Nuclear modification factor $R_{p\text{Pb}}$ for nonprompt $J/\psi$ mesons as a function of $y$. The first uncertainty is statistical and the second is systematic.

Cross-section ratios between 8 TeV and 5 TeV measurements for prompt $J/\psi$ mesons as a function of $p_\text{T}$. The first uncertainty is statistical and the second is systematic.

Cross-section ratios between 8 TeV and 5 TeV measurements for prompt $J/\psi$ mesons as a function of $y$. The first uncertainty is statistical and the second is systematic.

Cross-section ratios between 13 TeV and 5 TeV measurements for prompt $J/\psi$ mesons as a function of $p_\text{T}$. The first uncertainty is statistical and the second is systematic.

Cross-section ratios between 13 TeV and 5 TeV measurements for prompt $J/\psi$ mesons as a function of $y$. The first uncertainty is statistical and the second is systematic.

Cross-section ratios between 8 TeV and 5 TeV measurements for nonprompt $J/\psi$ mesons as a function of $p_\text{T}$. The first uncertainty is statistical and the second is systematic.

Cross-section ratios between 8 TeV and 5 TeV measurements for nonprompt $J/\psi$ mesons as a function of $y$. The first uncertainty is statistical and the second is systematic.

Cross-section ratios between 13 TeV and 5 TeV measurements for nonprompt $J/\psi$ mesons as a function of $p_\text{T}$. The first uncertainty is statistical and the second is systematic.

Cross-section ratios between 13 TeV and 5 TeV measurements for nonprompt $J/\psi$ mesons as a function of $y$. The first uncertainty is statistical and the second is systematic.

Relative changes of cross-sections (in \%), for a polarisation of $\lambda_{\theta}=-0.2$ rather than zero, in ($p_\text{T},y$) intervals.

Relative changes of cross-sections (in \%), for a polarisation of $\lambda_{\theta}=-1$ rather than zero, in ($p_\text{T},y$) intervals.

Relative changes of cross-sections (in \%), for a polarisation of $\lambda_{\theta}=+1$ rather than zero, in ($p_\text{T},y$) intervals.

Nuclear modification factor for prompt charged particles at 5TeV with respect to pseudorapidity and transverse momentum in the forward region region. The pseudorapidity is expressed in the nucleon-nucleon center-of-mass system. First uncertainty is statistical, the second is systematic and the third is from the luminosity. Luminosity uncertainty is fully correlated among the different kinematic ranges.

Nuclear modification factor for prompt charged particles at 5TeV with respect to pseudorapidity and transverse momentum in the backward region region. The pseudorapidity is expressed in the nucleon-nucleon center-of-mass system. First uncertainty is statistical, the second is systematic and the third is from the luminosity. Luminosity uncertainty is fully correlated among the different kinematic ranges.

Correlation for the uncertainties of the differential cross-section of prompt inclusive production of long-lived charged particles.

Correlation for the uncertainties of the differential cross-section of prompt inclusive production of long-lived charged particles.

Correlation for the uncertainties of the differential cross-section of prompt inclusive production of long-lived charged particles.

$\Lambda_{b}^{0}$ production asymmetry in bins of $\Lambda_{b}^{0}$ $p_T$ for proton-proton collisions with $\sqrt{s} = 8$ TeV. The first uncertainty is statistical and the second represents the systematic uncertainty. The results in neighbouring intervals are correlated.

Covariance matrix of the statistical uncertainty on $\Lambda_{b}^{0}$ production asymmetry in bins of $\Lambda_{b}^{0}$ rapidity for proton-proton collisions with $\sqrt{s} = 7$ TeV.

Covariance matrix of the statistical uncertainty on $\Lambda_{b}^{0}$ production asymmetry in bins of $\Lambda_{b}^{0}$ rapidity for proton-proton collisions with $\sqrt{s} = 8$ TeV.

Covariance matrix of the systematic uncertainty on $\Lambda_{b}^{0}$ production asymmetry in bins of $\Lambda_{b}^{0}$ rapidity for proton-proton collisions with $\sqrt{s} = 7$ TeV.

Covariance matrix of the systematic uncertainty on $\Lambda_{b}^{0}$ production asymmetry in bins of $\Lambda_{b}^{0}$ rapidity for proton-proton collisions with $\sqrt{s} = 8$ TeV.

Measured, normalised distribution of $p_T, y$ from background-subtracted $\Lambda_{b}^{0}$ candidates for $\sqrt{s} = 7$ TeV. Distribution is not corrected for the detector efficiency. Darker areas correspond tp mpre densely populated regions.

Measured, normalised distribution of $p_T, y$ from background-subtracted $\Lambda_{b}^{0}$ candidates for $\sqrt{s} = 8$ TeV. Distribution is not corrected for the detector efficiency. Darker areas correspond tp mpre densely populated regions.

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.