Impact of neutrino interaction uncertainties in T2K Kei Ieki for the T2K collaboration 'Toward unified description of lepton-nucleus reactions from MeV to GeV region' 2014/2/9

Contents of this talk Results from T2K 𝜈-N interaction: How is it related to 𝜈 𝜇 →𝜈 𝑒 measurement? How big is the effect of the uncertainty in 𝜈-N interaction?

1. Results from T2K

The T2K experiment p Discovery of νμ  νe θ13, δCP Main goals We observed νμ  νe with 7.3σ significance in 2013! Precise measurement of νμ  νμ θ23, Δm232 Main goals J-PARC μ 295km π+ p νμ νe,μ,τ ~40m Near Detector (ND280) Far Detector (Super-Kamiokande) High intensity νμ beam & Giant water Cherenkov detector SK

Analyzed data Latest νμ→νe result Latest νμ→νμ result (will be updated soon) Latest νμ→νe result 1.2×1014 protons per pulse (world record)

Latest result (νμνμ, 3.01×1020 POT) Observed 58 νμ candidate events. Expected νμ events (no osc.): 205±17 events νμ energy spectrum |Δ 𝑚 32 2 | vs. sin22θ23 contour Best fit: |Δ 𝑚 32 2 | = 2.4 −0.15 +0.17 × 10 −3 eV2/c4 sin2θ23 = 0.514±0.082

Latest result (νμνe, 6.57×1020 POT) Observed 28 νe candidate events. Expected backgrounds: 4.9±0.6 events Electron momentum and angular distribution Best fit for normal (inv.) hierarchy: sin22θ13 = 0.136 −0.033 +0.044 ( 0.166 −0.042 +0.051 ) (sin2θ23 and Δ 𝑚 23 2 constrained by T2K νμνμ, δCP=0) Significance: 7.3σ “Discovery” of νμνe

Latest result (νμνe, 6.57×1020 POT) Combined with reactor measurement (sin22θ13=0.098±0.013 from PDG2012) δCP negative log likelihood curve 90% CL excluded region Normal hierarchy: 　　　0.604～2.509 Inverted hierarchy: 　 -3.142～-3.043, -0.132～3.142 Precision νμνe measurement is required for the observation of CP violation. 90% excluded regions

2. 𝜈-N interaction: How is it related to 𝜈 𝜇 →𝜈 𝑒 measurement?

νμνe measurement νe event selection: 1-ring e-like event Signal 𝜈 𝑒 ● 𝜈 𝑒 CCQE ( 𝜈 𝑒 + n → e- + p) 𝑒 − Signal 𝜈 𝜇 𝜈 𝑒 𝑊 𝑝 𝜈 𝑒 Main interaction mode in T2K (@ Eν~0.6 GeV) Eν can be reconstructed from pe and θe e- ● 𝜈 𝑒 CC1π ( 𝜈 𝑒 + N → e- + N + π) 𝑒 − 𝜈 𝜇 𝜈 𝑒 𝜋 𝑊 𝑁 Backgrounds ● νμ NC π0 events ● Contamination of 𝜈 𝑒 𝜈 𝜇 𝑒 − 𝜈 𝜇 𝜈 𝜇 𝑍 𝛾 𝜈 𝑒 𝜈 𝑒 𝑊 𝑝 𝛾 π 0

Fraction of events after νe event selection νμνe measurement νe event selection: 1-ring e-like ring ● 𝜈 𝑒 CCQE ( 𝜈 𝑒 + n → e- + p) 𝑒 − 68% 𝜈 𝜇 𝜈 𝑒 𝑊 𝑝 Fraction of events after νe event selection (assuming sin 2 2 𝜃 13 =0.1) Main interaction mode in T2K (@ Eν~0.6 GeV) Eν can be reconstructed from pe and θe ● 𝜈 𝑒 CC1π ( 𝜈 𝑒 + N → e- + N + π) 𝑒 − 𝜈 𝜇 𝜈 𝑒 𝜋 12% 𝑊 𝑁 4% 14% ● νμ NC π0 events ● Contamination of 𝜈 𝑒 𝜈 𝜇 𝑒 − 𝜈 𝜇 𝜈 𝜇 𝜈 𝑒 𝑍 𝛾 𝜈 𝑒 𝑊 𝑝 𝛾 π 0

Oscillation analysis (νμνe) In the analysis, we compare: Number of νe events Nνe Electron momentum and angular distribution (pe,θe) between data and MC prediction. e- θe νe ∝−sinδCP P(νμνe) = sin22θ13sin2θ23sin2 Δ m 31 2 4𝐸 +(CPV term)+… Leading term sin22θ13=0.1 ( 𝜈 𝑒 CCQE dominated) 𝑝 𝑒 (MeV/c) 400 800 1200 Expected Nνe 𝑝 𝑒 , 𝜃 𝑒 distribution Total sin22θ13=0.0, δCP=0 sin22θ13=0.1, δCP=0 sin22θ13=0.1, δCP=+π/2 17.2 sin22θ13=0.1, δCP=−π/2 25.7 4.9 𝑝 𝑒 (MeV/c) 400 800 1200 60 120 𝜃 𝑒 (degrees) 180 ±0.6(syst) sin22θ13=0.0 (BG only) 21.6 ±1.9(syst) (sin2θ23=0.5, normal hierarchy, 6.57×1020 POT) The uncertainty in ν-N interaction affects the prediction of Nνe and (pe,θe).

How we constrain the model ① 𝜈-N interaction, 𝜈 flux simulation ② Constraints from external data ③ Constraints from ND280 ④ SK 𝜈 𝑒 event selection MC Data Comparison of SK 𝜈 𝑒 events ⑤ Oscillation analysis

① ν-N interaction simulation in T2K NEUT event generator - CCQE: Llewellyn-Smith base model Smith-Moniz fermi gas model for nucleus - Single pion resonance production (CC/NC1π): Rein-Sehgal model - Deep Inelastic Scattering (DIS) and CC multi-π: 　 　 GRV98 PDF, Bodek-Yang correction - Final state interactions (FSI): Cascade model

② Constraints from external data We use effective parameters (MAQE, normalization parameters etc.) with uncertainties that span the base model and data, and allow the ND280 to constrain the model. Past measurements of MAQE CCQE MAQE (axial mass) 1.21±0.45 GeV/c2 CCQE norm 1±0.11

② Constraints from external data CC1π+ Resonant π production We use MiniBooNE 1π data (CC and NC) and fit to NEUT predictions. MARES (axial mass) 1.41±0.22 GeV/c2 CC1π norm 1.15±0.32 NC1π0 norm 0.96±0.33 NC1π0

③ Constraints from ND280 Measure the CC interactions to constrain the flux×cross section Fine Grained Detectors (FGD) ν interaction target Tracking & PID Finely segmented scintillator bars (CH) Time Projection Chambers (TPC) Gas 3D tracker Momentum measurement & PID 0.2T magnet

③ Constraints from ND280 μ + hadrons μ μ + π+ CC other CC0π CC1π+ We measure the muon momentum and angular distributions in three samples. CC other CC0π CC1π+ μ + hadrons μ μ + π+ TPC2 TPC1 TPC3 FGD1 FGD2 CC0π μ momentum CC other μ momentum CC1π+ μ momentum DIS RES CCQE DIS

CC0π μ momentum distribution ③ Constraints from ND280 The cross section parameters are constrained by fitting the muon momentum and angular distributions. CC0π μ momentum distribution After ND280 constraint MAQE 1.24±0.072 GeV/c2 MARES 0.96±0.068 GeV/c2 CCQE norm 0.97±0.076 CC1π norm 1.26±0.16 NC1π0 norm 1.14±0.25

3. How big is the effect of the uncertainty in 𝜈-N interaction?

Systematic errors in νμνe analysis Systematic error on predicted number of νe (sin22θ13=0.1, δCP=0, normal hierarchy) Error sources Error Neutrino flux & cross section (constrained by ND280) 2.9% Neutrino cross section (not constrained by ND280) 7.5% SK detector & Final state interaction & γ-N interaction 3.5% Total 8.8% 25.9% if there are no ND280 constraint Cross section systematic errors are important! Part of the errors are largely reduced thanks to ND280 constraint.

Systematic errors in νμνe analysis Systematic error on predicted number of νe (sin22θ13=0.1, δCP=0, normal hierarchy) Error sources Error Neutrino flux & cross section (constrained by ND280) 2.9% Neutrino cross section (not constrained by ND280) 7.5% SK detector & Final state interaction & γ-N interaction 3.5% Total 8.8% Error sources Error MAQE 3.1% MARES 1.0% CCQE norm 6.2% CC1π norm 2.0% NC1π0 norm 0.4% Anti-correlated with ν flux. Flux + cross section error is small.

Systematic errors in νμνe analysis Systematic error on predicted number of νe (sin22θ13=0.1, δCP=0, normal hierarchy) Error sources Error Neutrino flux & cross section (constrained by ND280) 2.9% Neutrino cross section (not constrained by ND280) 7.5% SK detector & Final state interaction & γ-N interaction 3.5% Total 8.8% Error sources Error CC other norm. 0.1% Spectral function 5.9% Fermi momentum CC coh. norm. 0.2% NC coh. norm. NC other norm. 0.5% σνe/σνμ 2.8% W-shape π-less Δ decay 3.6% Explained in the next page νμ/νe cross section difference 3% uncertainty applied according to Phys. Rev., D86, p. 053003, 2012. Disappearance of the resonance state without π emission 20% uncertainty applied according to Phys. Lett., Vol. B416, pp. 23-28, 1998

Systematic errors in νμνe analysis Systematic error on predicted number of νe (sin22θ13=0.1, δCP=0, normal hierarchy) Error sources Error Neutrino flux & cross section (constrained by ND280) 2.9% Neutrino cross section (not constrained by ND280) 7.5% SK detector & Final state interaction & γ-N interaction 3.5% Total 8.8%

Spectral function Spectral function (SF) is a sophisticated model which is known as better representation of the nuclear model compared to Fermi Gas model. Nucleon momentum distribution (Relativistic Fermi Gas) Electron scattering data SF shows better agreement with electron scattering data. SF defines the probability distribution of nuclear momenta and energies required to remove a nucleon. Currently we use RFG because SF is not implemented in NEUT yet. We apply the difference between RFG and SF as the error. SF will be implemented in NEUT soon.

Final state interaction (FSI) Pions are often absorbed by the nuclei before being detected.  CC1π events are misidentified as CCQE. Roughly half of the pions in the CC1π interaction are absorbed (ABS) or charge exchanged (CX, π++N→π0+N’) at Eν ~ 0.6 GeV. μ ABS, CX cross section νμ π ? p FSI is constrained by the π-N cross section measurements in the past. However, the cross section uncertainties are large. ΔσABS~25%, ΔσCX~50%

π-C ABS+CX cross section Constraint on FSI We measured the π-C cross section at TRIUMF π beamline to constrain the FSI uncertainty. ~5cm, 32 layers ~5cm, 32 fibers π+ π-C ABS+CX cross section Finely segmented scintillator fiber tracker is constructed for this measurement. ABS+CX cross section measured with the uncertainty improved by a factor of 2. FSI error will be improved by using this result.

Summary ν-N interaction systematic errors are important in the precision neutrino oscillation measurement. The dominant systematic errors in the oscillation measurement are the cross section parameters which are not constrained by ND280. Future improvements: Implementation of the models in the simulation (Spectral function etc.) Improved inputs from internal/external cross section measurements (ν-N cross section in T2K, π-N cross section)

Backup slides

Multi nucleon process There are some indications that multi nucleon interactions can consistently describe multiple datasets. Multi nucleon effects are often identified as CCQE.  Introduce a bias to the neutrino energy reconstruction.

MiniBooNE data