Observed event yields and estimated backgrounds in the low- and high-mass control regions. The uncertainty in the background yield is the sum in quadrature of the statistical and systematic uncertainties.

Summary of the relative systematic uncertainties in heavy Majorana neutrino signal yields and the background from prompt same-sign leptons, both estimated from simulation. The relative systematic uncertainties assigned to the data-driven backgrounds for the misidentified lepton background and mismeasured charge background are also shown. The uncertainties are given for the low-mass selections.

Summary of the relative systematic uncertainties in heavy Majorana neutrino signal yields and the background from prompt same-sign leptons, both estimated from simulation. The relative systematic uncertainties assigned to the data-driven backgrounds for the misidentified lepton background and mismeasured charge background are also shown. The uncertainties are given for the high-mass selections.

Summary of contributions to the systematic uncertainty related to the prompt same-sign leptons background, misidentified lepton background, and mismeasured charge background on the total background uncertainty for the case of $m_{\rm N}$ = 100 and 500 GeV.

Observed event yields and estimated backgrounds after the application of all selection, except for the final optimization. The background predictions from prompt same-sign leptons (Prompt bkgd.), misidentified leptons (Misid. bkgd.), mismeasured charge (Charge mismeas. bkgd.) and the total background (Total bkgd.) are shown together withthe number of events observed in data. The uncertainties shown are the statistical and systematic components, respectively.

Dielectron channel results after final optimization. The background predictions from prompt same-sign leptons, misidentified leptons, and mismeasured charge are shown along with the total background estimate and the number of events observed in data. The uncertainties shown are the statistical and systematic components, respectively.

Electron-muon channel results after final optimization. The background predictions from prompt same-sign leptons and misidentified leptons are shown along with the total background estimate and the number of events observed in data. The uncertainties shown are the statistical and systematic components, respectively.

$\Upsilon$(nS) polarization parameter $\tilde\lambda$ in the HX frame for $p_T$ of 10 to 15 GeV. The global uncertainties, independent of state and $N_{ch}$ bin, are also indicated.

$\Upsilon$(nS) polarization parameter $\lambda_\vartheta$ in the HX frame for $p_T$ of 15 to 35 GeV. The global uncertainties, independent of state and $N_{ch}$ bin, are also indicated.

$\Upsilon$(nS) polarization parameter $\lambda_\varphi$ in the HX frame for $p_T$ of 15 to 35 GeV. The global uncertainties, independent of state and $N_{ch}$ bin, are also indicated.

$\Upsilon$(nS) polarization parameter $\lambda_{\vartheta\varphi}$ in the HX frame for $p_T$ of 15 to 35 GeV. The global uncertainties, independent of state and $N_{ch}$ bin, are also indicated.

$\Upsilon$(nS) polarization parameter $\tilde\lambda$ in the HX frame for $p_T$ of 15 to 35 GeV. The global uncertainties, independent of state and $N_{ch}$ bin, are also indicated.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

95% CL intervals on the double ratio of measured yields, $(N_{\psi\mathrm{(2S)}} / N_{J/\psi})_{\mathrm{PbPb}} / (N_{\psi\mathrm{(2S)}} / N_{J/\psi})_{pp}$, as a function of pT, for the forward rapidity analysis bin.

Double ratio of measured yields, $(N_{\psi\mathrm{(2S)}} / N_{J/\psi})_{\mathrm{PbPb}} / (N_{\psi\mathrm{(2S)}} / N_{J/\psi})_{pp}$, as a function of centrality, for the midrapidity analysis bin.

95% CL intervals on the double ratio of measured yields, $(N_{\psi\mathrm{(2S)}} / N_{J/\psi})_{\mathrm{PbPb}} / (N_{\psi\mathrm{(2S)}} / N_{J/\psi})_{pp}$, as a function of centrality, for the midrapidity analysis bin.

Double ratio of measured yields, $(N_{\psi\mathrm{(2S)}} / N_{J/\psi})_{\mathrm{PbPb}} / (N_{\psi\mathrm{(2S)}} / N_{J/\psi})_{pp}$, as a function of centrality, for the forward rapidity analysis bin.

95% CL intervals on the double ratio of measured yields, $(N_{\psi\mathrm{(2S)}} / N_{J/\psi})_{\mathrm{PbPb}} / (N_{\psi\mathrm{(2S)}} / N_{J/\psi})_{pp}$, as a function of centrality, for the forward rapidity analysis bin.

Double ratio of measured yields, $(N_{\psi\mathrm{(2S)}} / N_{J/\psi})_{\mathrm{PbPb}} / (N_{\psi\mathrm{(2S)}} / N_{J/\psi})_{pp}$, integrated over centrality, for the midrapidity and forward rapidity analysis bins.

95% CL interval on the double ratio of measured yields, $(N_{\psi\mathrm{(2S)}} / N_{J/\psi})_{\mathrm{PbPb}} / (N_{\psi\mathrm{(2S)}} / N_{J/\psi})_{pp}$, integrated over centrality, for the midrapidity and forward rapidity analysis bins.

Interpretation of results in the T1tttt model. The colored regions show the upper limits (95\% CL) on the production cross section for $pp\rightarrow \tilde{g}\tilde{g},\tilde{g}\rightarrow t\bar{t}\tilde{\chi}^0_1$ in the $m_{\tilde{g}}$-$m_{\tilde{\chi}^0_1}$ plane.

Interpretation of results in the T1tttt model. The colored regions show the upper limits (95\% CL) on the production cross section for $pp\rightarrow \tilde{g}\tilde{g},\tilde{g}\rightarrow t\bar{t}\tilde{\chi}^0_1$ in the $m_{\tilde{g}}$-$m_{\tilde{\chi}^0_1}$ plane. The curve shows the observed limit on the corresponding SUSY particle masses obtained by comparing the excluded cross section with theoretical cross sections.

Interpretation of results in the T1tttt model. The colored regions show the upper limits (95\% CL) on the production cross section for $pp\rightarrow \tilde{g}\tilde{g},\tilde{g}\rightarrow t\bar{t}\tilde{\chi}^0_1$ in the $m_{\tilde{g}}$-$m_{\tilde{\chi}^0_1}$ plane. The curve shows the observed limit on the corresponding SUSY particle masses obtained by comparing the excluded cross section with $+1\sigma$ theoretical cross sections.

Interpretation of results in the T1tttt model. The colored regions show the upper limits (95\% CL) on the production cross section for $pp\rightarrow \tilde{g}\tilde{g},\tilde{g}\rightarrow t\bar{t}\tilde{\chi}^0_1$ in the $m_{\tilde{g}}$-$m_{\tilde{\chi}^0_1}$ plane. The curve shows the observed limit on the corresponding SUSY particle masses obtained by comparing the excluded cross section with $-1\sigma$ theoretical cross sections.

Interpretation of results in the T1tttt model. The colored regions show the upper limits (95\% CL) on the production cross section for $pp\rightarrow \tilde{g}\tilde{g},\tilde{g}\rightarrow t\bar{t}\tilde{\chi}^0_1$ in the $m_{\tilde{g}}$-$m_{\tilde{\chi}^0_1}$ plane. The curve shows the expected limit on the corresponding SUSY particle masses obtained by comparing the excluded cross section with theoretical cross sections.

Interpretation of results in the T1tttt model. The colored regions show the upper limits (95\% CL) on the production cross section for $pp\rightarrow \tilde{g}\tilde{g},\tilde{g}\rightarrow t\bar{t}\tilde{\chi}^0_1$ in the $m_{\tilde{g}}$-$m_{\tilde{\chi}^0_1}$ plane. The curve shows the expected limit on the corresponding SUSY particle masses corresponding to a $+1\sigma$ variation of the experimental uncertainty.

Interpretation of results in the T1tttt model. The colored regions show the upper limits (95\% CL) on the production cross section for $pp\rightarrow \tilde{g}\tilde{g},\tilde{g}\rightarrow t\bar{t}\tilde{\chi}^0_1$ in the $m_{\tilde{g}}$-$m_{\tilde{\chi}^0_1}$ plane. The curve shows the expected limit on the corresponding SUSY particle masses corresponding to a $-1\sigma$ variation of the experimental uncertainty.

Observed excluded region (95\% CL), shown in blue, in the $m_{\tilde{g}}$-$m_{\tilde{\chi}^0_1}$ plane for a model combining T5tttt, gluino pair production, followed by gluino decay to an on-shell top squark, together with a model for direct top squark pair production. The top squarks decay via the two-body process $\tilde{t}\rightarrow t\tilde{\chi}^0_1$. The neutralino and top squark masses are related by the constraint $m_{\tilde{t}} = m_{\tilde{\chi}^0_1} + 175$ GeV.

Expected excluded region (95\% CL), shown in blue, in the $m_{\tilde{g}}$-$m_{\tilde{\chi}^0_1}$ plane for a model combining T5tttt, gluino pair production, followed by gluino decay to an on-shell top squark, together with a model for direct top squark pair production. The top squarks decay via the two-body process $\tilde{t}\rightarrow t\tilde{\chi}^0_1$. The neutralino and top squark masses are related by the constraint $m_{\tilde{t}} = m_{\tilde{\chi}^0_1} + 175$ GeV.

The particle-level di-jet differential cross section. The systematic uncertainty on the data contains contributions from track finding efficiency, track transverse momentum resolution, calorimeter energy resolution, and unfolding uncertainties. For the theory, values are given for the underlying event and hadronization (UEH) correction uncertainty and the quadrature sum of the UEH and theoretical uncertainties. Both the UEH and theoretical uncertainties include contributions from factorization and renormalization scale uncertainties and PDF uncertainties. An 8.8% uncertainty common to all points due to the integrated luminosity determination is also present, but not included in the systematic values quoted below.

Values of gluon X1 and X2 obtained from the PYTHIA detector-level simulation for the same-sign di-jet topology compared to the gluon X distribution for inclusive jets. The inclusive distribution has been scaled down by a factor of 20 compared to the di-jet distributions.

Values of gluon X1 and X2 obtained from the PYTHIA detector-level simulation for the opposite-sign di-jet topology compared to the gluon X distribution for inclusive jets. The inclusive distribution has been scaled down by a factor of 20 compared to the di-jet distributions.

Di-jet A_LL asymmetry vs parton-level invariant mass for the same-sign di-jet topology. The systematic uncertainty on the mass includes contributions from jet energy scale, the correction to parton-level, and the difference between NLO and PYTHIA cross sections. The systematic uncertainty on the asymmetry includes contributions from trigger and reconstruction bias and residual transverse beam polarization components. A 6.5% uncertainty common to all points due to uncertainty on the measured beam polarizations is also present, but not included in the uncertainties quoted below.

Theoretical predictions for the di-jet A_LL asymmetry for the same-sign topology using the DSSV14 and NNPDFpol1.1 polarized PDF sets. The DSSV14 prediction is presented without uncertainty while the systematic uncertainty on the NNPDFpol1.1 prediction contains contributions from factorization and renormalization scale uncertainties and PDF uncertainties.

Di-jet A_LL asymmetry vs parton-level invariant mass for the opposite-sign di-jet topology. The systematic uncertainty on the mass includes contributions from jet energy scale, the correction to parton-level, and the difference between NLO and PYTHIA cross sections. The systematic uncertainty on the asymmetry includes contributions from trigger and reconstruction bias and residual transverse beam polarization components. A 6.5% uncertainty common to all points due to uncertainty on the measured beam polarizations is also present, but not included in the uncertainties quoted below.

Theoretical predictions for the di-jet A_LL asymmetry for the opposite-sign topology using the DSSV14 and NNPDFpol1.1 polarized PDF sets. The DSSV14 prediction is presented without uncertainty while the systematic uncertainty on the NNPDFpol1.1 prediction contains contributions from factorization and renormalization scale uncertainties and PDF uncertainties.

Inclusive Jet Cross Section for 1.5 < |y| < 2.0 as a function of the jet transverse momentum. The (sys) error is the total systematic error, including the luminosity uncertainty of 4.4%.

Inclusive Jet Cross Section for 2.0 < |y| < 2.5 as a function of the jet transverse momentum. The (sys) error is the total systematic error, including the luminosity uncertainty of 4.4%.

Inclusive Jet Cross Section for 2.5 < |y| < 3.0 as a function of the jet transverse momentum. The (sys) error is the total systematic error, including the luminosity uncertainty of 4.4%.

Inclusive Jet Cross Section for 3.2 < |y| < 4.7 as a function of the jet transverse momentum. The (sys) error is the total systematic error, including the luminosity uncertainty of 4.4%.