Neutrino Interaction Physics for Oscillation Analyses

Transcription

1 Neutrino Interaction Physics for Oscillation Analyses Patrick Stowell on behalf of the T2K Neutrino Interactions Working Group NuIntUK 20th July 2015

2 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 1 / 16 Introduction Oscillation experiments have been a large driving force in measurement of neutrino cross-sections. Accurate neutrino energy reconstruction required for high precision neutrino oscillation measurements. Reconstruction relies on the choice of interaction cross-section and nuclear model. Near detector fits can constrain flux and cross-section uncertainties. Fits to external datasets can help to further constrain cross-section. 90 % CL limit contours around best fit mixing parameters in the sin 2 2θ 13 δ CP plane produced when using different choices for the nuclear model in a toy experiment. ( Importance of nuclear effects in the measurement of neutrino oscillation parameters, E. Fernandez-Martinez, et. al., arxiv: )

3 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 2 / 16 Neutrino Oscillations Study of neutrino oscillations requires measurement of event rates at far detectors. Probability of oscillation requires accurate reconstruction of Neutrino Energy, E ν. ( ) 1.27 m P(L, E ν) = 1 sin 2 2θ sin 2 2 (ev)l(km) (1) E ν(gev) Some oscillation experiments are moving into a regime dominated by systematic uncertainties. Different experiments run over different energy regimes 1. Solar: 0 < E ν < 20.0 MeV 2. Reactor: 0 < E ν < MeV 3. Accelerator: 0.1 < E ν < GeV 4. Atmospheric: 0.1 < E ν < 10 6 GeV Importance of cross-section model varies between experiments.

4 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 3 / 16 Energy Reconstruction E ν must be reconstructed from the final state particles usually the lepton. ν µ = 2M ne µ (M n 2 + mµ 2 Mp) 2 2 ( M n E µ + ) (2) Eµ 2 mµ 2 cos θµ E QE Effective nucleon mass given by M n = M n ɛ B (ɛ B = +34 MeV for carbon) Quasi-elastic E ν reconstruction process itself is model dependent. Choice of nuclear model can change the reconstructed energy distributions. The MC generator treatment of FSI effects also changes these distributions. Difference in reconstructed Eν QE event rates for two different event generators in a toy experiment similar to T2K ( Neutrino-nucleus interaction models and their impact on oscillation analyses, P. Coloma et. al., arxiv: )

5 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 4 / 16 Near to Far Detector Extrapolation Most of the uncertainties in the cross-section and flux could be cancelled if: Near and Far detectors are the same build Near and Far analysis cuts have the same acceptance Near and Far detectors see the same flux Disappearance experiments can attempt to cancel the flux and cross-section uncertainties using ratios from near and far detectors. This is not as easy for appearance experiments hoping to measure δ CP.

6 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 5 / 16 Uncertainties and Model Choices Number of competing models currently available makes it difficult to evaluate systematic uncertainties. Choice in nuclear model could bias a fitted mixing result if neglected in an oscillation analysis. T2K accounts for this by looking at shifts/biases in fitted results with respect to changes in the nuclear interaction models. The effect moving between the RFG and Martini-Marteau MEC model can have on fitted mixing parameters. ( Revisiting the T2K data using different models for the neutrino-nucleus cross sections, D. Meloni et. al., arxiv: ).

7 T2K External Data Fits

8 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 7 / 16 Selected CCQE external Data sets First time external data sets have been used to constrain central values on priors. MiniBooNE 2D T µ cos θ µ neutrino (Target: CH 2 ) arxiv: MiniBooNE 2D T µ cos θ µ antineutrino (Target: CH 2 ) arxiv: MINERvA 1D Q 2 QE neutrino θµ < 20 (Target: CH) arxiv: MINERvA 1D Q 2 QE antineutrino θµ < 20 (Target: CH) arxiv:

9 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 8 / 16 NEUT CCQE MC Models Fitted three separate models to data: 1. RFG + Relativistic RPA + MEC Model. 2. RFG + Non-relativistic RPA + MEC Model. 3. SF + MEC Model. The Nieves model used to handle 2p-2h Meson Exchange Currents (MEC) and Random Phase Approximation (RPA) in MC simulations. The axial mass, M A, fermi momentum, p F, and the MEC Normalisation were treated as effective free parameters in the fit.

10 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 9 / 16 CCQE Fit Procedure Method 1. Compare model MC predictions to selected CCQE external datasets. 2. Minimise the χ 2 Total from a joint fit by varying model parameters. 3. Determine models agreement with all datasets using PGoF calculation. 4. Rescale errors to cover model disagreements when fitting individual datasets. Notes The MiniBooNE datasets were fit with uncorrelated shape-only errors and the normalisation parameters were floated as nuisance parameters in the fit. Parameter Goodness-of-Fit (PGoF) test was used to check how well the model could describe all datasets in the joint fit. Relativistic RPA was preferred by the datasets over Non-relativistic RPA, this model is labelled as RFG+RPA+MEC from now on.

11 Fitted Distributions 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 10 / 16

12 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 11 / 16 Fitted CCQE Parameters The RFG+RPA+MEC Model was found to have the best PGoF from the joint fit results and was selected as the new cross-section parametrisation (see slide 29). Model M A p F MEC χ 2 /NDOF RFG + RPA + MEC 1.15 ± ± 5 27 ± /195 SF + MEC 1.33 ± ± 4 0 (at limit) 97.46/196 Chosen model combinations had difficulty recreating both MINERvA and MiniBooNE measurements simultaneously in the joint fit. An error rescaling factor of 2.3 was chosen to inflate the errors to cover the model s poor PGoF statistic. Additional rescaling was chosen so MEC errors covered 100% normalisation for the Nieves model.

13 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 12 / 16 NEUT Resonant Models NEUT uses the Rein-Seghal model to simulate pion production. Graczyk and Sobczyk updated form factors (arxiv: ) were used with the Rein-Seghal model. Non-resonant background is purely I = 1/2. Final state interactions of pions produces a significant modification to measured resonance cross-section on heavier nuclear targets since the interaction probabilities of pions in the nucleus are large.

14 1 ANL and BNL data used the flux correction method shown in arxiv: (Callum Willkinson) 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 13 / 16 Resonant Model Fit Procedures The T2K Resonant model was tuned to bubble-chamber data where pion FSI effects are negligible. ANL (CCπ +, CCπ 0 ) 1 BNL (CCπ +, CCπ 0 ) 1 BEBC 90 (CCπ +, CCπ 0 ) FNAL 78 (CCπ + ) BEBC 86 (CCπ + ) The resonant axial mass, M A, C A 5 (0) and I 1/2 non-resonant background scale were floated as free parameters in the fit. Final comparisons were used to compare model parameters fitted on deuterium with the later MiniBooNE pion production measurements.

15 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 14 / 16 Fitted Pion Production Parameters Fitted distributions from the resonance tuning to bubble chamber data Parameters M A (GeV) C5 A (0) I 1/2 Bg Scale Tuned Values (by eye) 0.95 ± ± ± 0.20

16 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 15 / 16 Problems and Future plans Model combinations have trouble fitting to MINERvA and MiniBooNE measurements simultaneously Looking at moving to use CCQE-like measurements. No RPA uncertainties were evaluated for the RFG models Uncertainties in our current RPA parametrisation are currently being investigated No joint tuning was performed on pion production FSI parameters Joint Resonance and FSI parameter fits currently underway.

17 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 16 / 16 Conclusions The large uncertainty in cross-section models is a problem for neutrino oscillation experiments. Fitting to external datasets allows for additional constraints to be placed on the cross-section that may not be possible with the near detectors. Problems faced in the external data fits have helped us identify problems in our current MC model parametrisation.

18 Backup Slides

19 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 18 / 16 Sterile Neutrinos Experiments that have weak constraints on their un-oscillated event rate need a cross-section model. Fitted results will however be strongly correlated with the cross-section model chosen. Point to consider when comparing sterile neutrino disappearance fits. (Left) Effect changing the nuclear model has on a sterile disappearance search using MINERvA CCQE data [arxiv: ]. (Right) Difference between sterile disappearance fit result when M A is fitted sequentially or simultaneously in a sterile disappearance search with MiniBooNE cross-section data [arxiv: ].

20 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 19 / 16 CCQE Tuning: Energy and Q 2 Reconstruction The neutrino energy can be reconstructed from the final state lepton. ν = 2M i E µ (M i 2 + mµ 2 Mf 2 ) 2 ( M i E µ + ) (3) Eµ 2 mµ 2 cos θµ E QE M 2 i is the effective mass of the bound nucleon, M 2 i = M i ɛ B. On carbon ɛ B = +34MeV for neutrinos, and ɛ B = +30MeV for antineutrinos. Q 2 QE is then calculated using Q 2 QE = 2E QE ν (E µ p µ cos θ µ) m 2 µ (4)

21 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 20 / 16 CCQE Tuning: PGoF Scaling Parameter Goodness of Fit (PGoF) method used to determine tensions where the model cannot describe every dataset. [M. Maltoni, T. Schwetz, Phys. Rev. D68, (2003)] D χ 2 PGoF,min = χ 2 tot,min χ 2 i,min (5) i=1 D n PGoF = n tot n r (6) r=1 Statistic used to rescale the parameter errors in the current CCQE priors by a scaling factor φ χ 2 PGoF = χ 2 PGoF /ndof PGoF = φ (7)

22 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 21 / 16 CCQE Tuning: χ 2 calculation Joint Fit χ 2 Total for data, D, and MC, T, defined by: χ 2 = 16 (D i T i )M 1 ij (D j T j ) MINERvA (8) i,j ( ) D k (T k /λ MB ( ν ) 1 λ MB ) 2 ν + k σ shp + ɛ MB k ν MiniBooNE Neutrino (9) k ( D l (T l /λ MB ν ) σ shp l ) 2 + ( 1 λ MB ) 2 ν ɛ MB MiniBooNE Antineutrino (10) ν Published cross-correlations between MINERvA CCQE ν and ν were used in the fit. MiniBooNE data lacked bin-to-bin correlations. Published uncorrelated shape-only errors and total normalisation errors were used in the fit. Soon to be updated hopefully! Possible correlations between MINERvA and MiniBooNE datasets were unknown and hence were neglected in the fit.

23 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 22 / 16 CCQE Tuning: MINERvA θ µ < 20 sample MINERvA published two sets of CCQE data. 1. Full angular acceptance of muons. 2. Limited angular acceptance with θ µ < 20. Limited angular acceptance excludes events where MINOS cannot be used to tag muons making it a less model dependent measurement. The limited angular acceptance sample was chosen for the T2K CCQE data fits. ) 2 /GeV 2 (cm MINERvA Neutrino Full MINERvA Neutrino θ < 20 ) 2 /GeV 2 (cm MINERvA Antineutrino Full MINERvA Antineutrino θ < 20 dσ/dq 2 12 dσ/dq Q 2 (GeV ) QE Q 2 (GeV ) QE

24 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 23 / 16 CCQE Tuning: MINERvA Cross-correlations MINERvA provide cross-correlations between their neutrino and anti-neutrino datasets. These were used in the CCQE cross-section fits.

25 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 24 / 16 CCQE Tuning: SF vs RFG 1. Relativistic Fermi Gas: All momentum states are filled unto a fixed Fermi-momentum cut-off. Nucleons have a fixed binding energy and Pauli-blocking is strong. 2. Spectral Function: Omar Benhar Spectral Function is currently implemented in NEUT. [ Benhar, A. Fabrocini, Phys. Rev. C62, (2000)] 2D Distribution in momentum and removal energy. Contains a high momentum tail from correlated pairs of initial state nucleons.

26 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 25 / 16 CCQE Tuning: Relativistic/Non-relativistic RPA Random Phase Approximation (RPA) is a nuclear screening effect due to long range correlations between nucleons. [J. Nieves, I. R. Simo, M. J. V. Vacas, Phys. Rev. C 83, (2011)] Can be calculated in a relativistic or non-relativistic regime. Causes an observable suppression of the cross-section at low Q 2. NEUT implementation is a 2D function of Q 2 and E ν.

27 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 26 / 16 Nieves MEC Model Nieves multi-nucleon interaction model is implemented in NEUT to handle MEC. [ J. Nieves, I. R. Simo, M. J. V. Vacas, Phys. Rev. C 83, (2011)] Includes a cut on q 3 to allow extensions upto high E ν. [R. Gran, J. Nieves, F. Sanchez, M. Vicente Vacas, Phys. Rev. D88, (2013)] No hadronic kinematic information is provided by the model, this is calculated using Jan Sobczyk s multi-nucleon ejection model. [Jan T. Sobczyk, Phys. Rev. C86, (2012)]

28 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 27 / 16 Final CCQE Fit Parameters The fit parameters after each stage of error rescaling the CCQE fit parameters are shown below.

29 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 28 / 16 Correlation Matrices Fitted correlation matrix between CCQE parameters for the RFG+RPA+MEC model.

30 CCQE Tuning: RFG vs SF PGoF 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 29 / 16

31 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 30 / 16 BANFF + CCQE Rescaling external data sets < T2K data. Using T2K data has a lot of extra event by event information not available to us in external data sets. All cross-section measurements made at ND280 are fit to the NEUT model with no external constraints to produce pulls. external fits including ND280 CCQE pulls used to rescale errors on parameter values. Creates an effective de-weighting of the constraints from external data if they don t agree with ND280 data

32 CCQE-like Measurements MiniBooNE subtract a CCQE-like data tuned background signal to produce a CCQE-corrected sample. This includes subtraction of pion-less delta decay (PDD). Current implementation of the Nieves multi-nucleon interaction model contains large PDD contribution in NEUT. This problem can be solved by fitting CCQE-like instead of CCQE-corrected samples. This means we must fit contributions from CCQE-like backgrounds from other channels (mainly resonances) No. Events CCQE 2p/2h Nieves CC1π + on p CC1π 0 on n CC1π + on n CC1γ Multi π (1.3 < W < 2.0) CC1η 0 on n Percentage of Events Mode Neutrino Anti-neutrino True CCQE MEC RES Other Q QE Number of CCQE-like events separated by NEUT interaction mode from preliminary tunings to MiniBooNE CCQE-like neutrino cross-section data. 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 31 / 16

33 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 32 / 16 Resonance Tuning: NEUT FSI Pion Final State Interactions model in NEUT was tuned to a series of pion scattering data. Data from Absorption, Charge Exchange, Inelastic and Reactive scattering channels were considered in the fits. (T2K Tech Note 33)

34 20th July 2015 Neutrino Interaction Physics for Oscillation Analyses 33 / 16 Pion Model Comparisons to MiniBooNE Model tuned on free nucleons was only compared to data on nuclear targets. Fits for FSI to MiniBooNE datasets performed but not passed to oscillation analysis. MiniBoonE pion production data compared to the NEUT model tuned to free nucleon data.