NEUT model improvements and external data fits Tom Feusels for T2K Collaboration University of British Columbia NuFact 2015 Rio de Janeiro Aug 13, 2015 T. Feusels (UBC) External data fits 13/08/2015 1 / 27
Table of Contents Introduction 1 NEUT 2 Spectral Function Nieves 2p2h RPA External Data Fits 3 CCQE fits CC1pi fits FSI fits Summary and Outlook 4 T. Feusels (UBC) External data fits 13/08/2015 2 / 27
Table of Contents Introduction 1 NEUT 2 Spectral Function Nieves 2p2h RPA External Data Fits 3 CCQE fits CC1pi fits FSI fits Summary and Outlook 4 T. Feusels (UBC) External data fits 13/08/2015 3 / 27
T2K Oscillation Analysis Overview NEUT External Data - MiniBooNE - CCQE - Miner ν A - pion production model parameters priors - ANL - CC coherent & covariance matrix - BNL - FSI cascade model - π - C scattering - ... - ... ND280 Data Near Detector Fit Neutrino Anti-Neutrino With covariance matrix: - CC0 π - Detector systematics - CC1track - CC1 π - CCNtrack - Flux systematics - CCother see Talk K. Mahn (Tue Aug 11) extrapolation to Super-K Super-K Data Oscillation - 1 Ring e-like Analysis - 1 Ring mu-like + Super-K detector systematics see Talk K. Duffy (Tue Aug 11) T. Feusels (UBC) External data fits 13/08/2015 4 / 27
Table of Contents Introduction 1 NEUT 2 Spectral Function Nieves 2p2h RPA External Data Fits 3 CCQE fits CC1pi fits FSI fits Summary and Outlook 4 T. Feusels (UBC) External data fits 13/08/2015 5 / 27
The NEUT Neutrino Generator Default (NEUT < 5.3.2) Llewellyn-Smith model for 1p1h CCQE interactions. Rein-Sehgal model for resonant and coherent pion production. BBBA05 form factor with default M A of 1.21 GeV/c 2 for CCQE and resonant production. GRV94/GRV98 pdfs with Bodek-Yang corrections for DIS. Relativistic Fermi Gas (RFG) from Smith-Moniz with Pauli-blocking as initial state nuclear model. Latest improvements (NEUT 5.3.2): Initial state nuclear model: Spectral function model by Benhar et al. implemented. 2p2h model of Nieves implemented. Random Phase Approximation (RPA). More realistic pion form factors from Graczyk and Sobczyk ( Phys. Rev. D 77 , 053001 (2008)). T. Feusels (UBC) External data fits 13/08/2015 6 / 27
Spectral Function Spectral Function in nucleon momentum and removal energy by Benhar et al. ( Phys. Rev. C 62 , 034304 (2000)). Standard Impulse Approximation used. Available for C, O and Fe. Pauli-blocking with hard cut-off. Effective Spectral Function by Bodek et al. recently added to NEUT but not yet candidate model for T2K. T. Feusels (UBC) External data fits 13/08/2015 7 / 27
Nieves 2p2h model Interaction with pair of short range correlated nucleons. Use pre-calculated tables based on Nieves et al. ( Phys. Rev. C 83 , 045501 (2011)). Only lepton kinematics predicted, hadronic part through Sobczyk model. High energy extension based on Gran et al. ( Phys. Rev. D 88 , 113007 (2013)). T. Feusels (UBC) External data fits 13/08/2015 8 / 27
Random Phase Approximation (RPA) ν ¯ ν Nuclear screening effect due long range nucleon-nucleon correlations. NEUT implementation depends on Q 2 and E ν , based on Nieves et al. ( Phys. Rev. C 83 , 045501 (2011)). Assumes Local Fermi Gas, but also valid for Relativistic Fermi Gas. No Spectral Function RPA correction. T. Feusels (UBC) External data fits 13/08/2015 9 / 27
Table of Contents Introduction 1 NEUT 2 Spectral Function Nieves 2p2h RPA External Data Fits 3 CCQE fits CC1pi fits FSI fits Summary and Outlook 4 T. Feusels (UBC) External data fits 13/08/2015 10 / 27
CCQE Fit procedure and datasets Procedure: Float model parameters (M A , 2p2h normalization, p F ) and MiniBooNE normalization in χ 2 1 fit within each model. Test agreement of complete dataset with model through standard Pearson χ 2 Goodness of 2 Fit test. Use Parameter Goodness of Fit (PGoF) test for consistency between datasets within each 3 model. Rescale parameter errors to span differences between datasets according to PGoF test. 4 Apply PGoF procedure to an ND280 data fit and external data fits to ensure prior errors 5 cover both the external fit results and ND280 data at 1 σ . Datasets: d 2 σ MiniBooNE: dT µ d cos θ µ for ν and ¯ ν (CCQE-corrected data from Phys. Rev. D 81 , 092005 (2010) and Phys. Rev. D 88 , 032001 (2013)) d σ MINER ν A: QE for ν and ¯ ν with restricted phase space θ µ ≤ 20 ◦ , including dQ 2 cross-correlations ( Phys. Rev. Lett. 111 , 022502 (2013) and Phys. Rev. Lett. 111 , 022501 (2013)) Models: RFG + RPA + MEC vs SF + MEC . T. Feusels (UBC) External data fits 13/08/2015 11 / 27
Neutrino CCQE fits: MiniBooNE and MINER ν A 9 SF+MEC θ θ θ 7 -1. < cos < 0.0 0.0 < cos < 0.3 0.3 < cos < 0.6 µ 10 µ µ χ 2 = 37.1 (97.5) 8 6 7 8 /GeV) 5 6 RFG+RPA+MEC 5 6 4 χ 2 = 37.9 (97.8) 4 3 2 4 cm 3 2 2 2 -39 1 DATA 1 × -39 10 10 0 0 0 ) 2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 /GeV 16 RFG+RPA+MEC × θ θ θ 25 θ χ 20 0.6 < cos < 0.7 22 0.7 < cos < 0.8 25 0.8 < cos < 0.9 0.9 < cos < 1.0 2 = 26.8 (97.8) ( µ µ µ µ 14 µ 20 18 θ 2 18 20 12 SF+MEC dcos (cm 16 20 χ 16 2 = 20.6 (97.5) σ 10 14 2 14 d 15 12 15 2 8 µ 12 /dQ 10 DATA dT 10 6 8 10 10 8 σ 4 6 d 6 4 5 5 4 2 2 2 0 0 0 0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 2 2 Q (GeV ) T (GeV) µ QE MiniBooNE MINER ν A χ 2 is from each dataset while total χ 2 in brackets. Dashed line: without MiniBooNE normalization terms. Even though much more bins for MiniBooNE, fit not dominated by MiniBooNE data. T. Feusels (UBC) External data fits 13/08/2015 12 / 27
Anti-Neutrino CCQE fits: MiniBooNE and MINER ν A 0.22 0.7 SF+MEC θ θ θ -1. < cos < 0.0 0.0 < cos < 0.3 0.3 < cos < 0.6 µ 1.4 0.2 µ µ χ 2 = 27.5 (97.5) 0.6 0.18 1.2 0.16 /GeV) 0.5 1 0.14 RFG+RPA+MEC 0.4 0.12 0.8 χ 2 = 25.2 (97.8) 0.1 0.3 2 0.6 cm 0.08 0.06 0.2 0.4 0.04 -39 0.1 0.2 DATA × 0.02 -39 10 10 0 0 0 ) 2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 /GeV 14 RFG+RPA+MEC 10 × θ 6 θ θ θ χ 4 0.6 < cos < 0.7 0.7 < cos < 0.8 0.8 < cos < 0.9 14 0.9 < cos < 1.0 2 = 14.5 (97.8) ( µ µ µ µ 12 µ θ 3.5 8 12 5 2 SF+MEC dcos (cm 10 3 χ 2 = 13.8 (97.5) σ 10 4 2 8 6 d 2.5 2 8 µ /dQ 2 3 6 DATA dT 4 6 1.5 σ 4 2 d 4 1 2 2 1 2 0.5 0 0 0 0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 2 2 Q (GeV ) T (GeV) µ QE MiniBooNE MINER ν A χ 2 is from each dataset while total χ 2 in brackets. Dashed line: without MiniBooNE normalization terms. Even though much more bins for MiniBooNE, fit not dominated by MiniBooNE data. T. Feusels (UBC) External data fits 13/08/2015 13 / 27
Fit results χ 2 /DOF Fit type M A (GeV) MEC (%) p F (MeV) Rel. RPA 97.8/195 1.15 ± 0.03 27 ± 12 223 ± 5 Non-rel. RPA 117.9/195 1.07 ± 0.03 34 ± 12 225 ± 5 SF + MEC 97.5/196 1.33 ± 0.03 0 (at limit) 234 ± 4 Best fit χ 2 good for both RFG + Rel. RPA + MEC and SF + MEC , but no MB correlations so Gaussian statistics invalid. D χ 2 := χ 2 χ 2 i , where χ 2 Parameter Goodness of Fit: ¯ tot − � i is the result of an individual fit i =1 to Dataset i . D � Number of degrees of freedom: P PGoF := P i − P tot . i =1 Test compatibility between datasets in framework of model ( Phys. Rev. D 65 , 014011 (2001)) If different datasets favour different parameter values, model cannot describe all the data consistently. T. Feusels (UBC) External data fits 13/08/2015 14 / 27
PGoF tests: RFG + RPA + MEC χ 2 / DOF χ 2 / DOF Datasets Goodness of Fit(%) PGoF (%) All 97.8/195 100.00 17.9/6 0.66 MINER ν A ( ν vs ¯ ν ) 23.4/13 3.74 1.0/3 79.03 MiniBooNE ( ν vs ¯ ν ) 58.3/179 100.00 2.0/3 58.69 ν (MB vs MIN) 62.6/127 100.00 16.1/3 0.11 ¯ ν (MB vs MIN) 38.5/65 99.64 6.1/3 10.75 MINER ν A vs MiniBooNE 97.8/195 100.00 15.9/3 0.12 ν vs ¯ ν 97.8/195 100.00 -3.3/3 100.0 Largest tension between MINER ν A and MiniBooNE neutrino results. Note: PGoF test requires uncorrelated datasets, so result for MINER ν A’s PGoF for ν vs ¯ ν is too good. T. Feusels (UBC) External data fits 13/08/2015 15 / 27
PGoF tests: SF + MEC χ 2 / DOF χ 2 / DOF Datasets Goodness of Fit(%) PGoF (%) All 97.5/196 100.00 41.1/4 0.0 MINER ν A ( ν vs ¯ ν ) 12.6/13 47.75 1.0/2 59.87 MiniBooNE ( ν vs ¯ ν ) 50.2/180 100.00 6.5/2 3.85 ν (MB vs MIN) 54.8/128 100.00 25.1/3 0.0 ¯ ν (MB vs MIN) 34.1/65 99.64 8.5/2 1.40 MINER ν A vs MiniBooNE 97.5/196 100.00 34.6/2 0.12 ν vs ¯ ν 97.5/196 100.00 8.5/2 1.39 Largest tension between MINER ν A and MiniBooNE neutrino results. SF + MEC model finds much worse agreement between datasets. ⇒ Choose RFG+RPA+MEC as default T2K model. T. Feusels (UBC) External data fits 13/08/2015 16 / 27
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