Mono-chromatic beams for PRISM Mark Hartz, Kavli IPMU/TRIUMF 1 - PowerPoint PPT Presentation

Mono-chromatic beams for ν PRISM Mark Hartz, Kavli IPMU/TRIUMF 1

Motivation We know that there are large uncertainties ❖ in the modeling of nuclear effects, especially in the CC0pi cross section around 1 GeV Nuclear effects introduce tails to ❖ reconstructed energy distribution away from the quasi-elastic peak - source of systematic uncertainty in oscillation measurements In electron scattering, these tails can be studied because the four momenta of the initial ❖ and final state leptons are measured If we know the initial neutrino energy, we can do similar measurements for neutrinos ❖ We can also directly study the energy dependence of the NC cross-sections ❖ Mono-energetic beams 2

Mono-chromatic widths How narrow should the mono-energetic beams be? ❖ The dominant np-nh effects are at ~300 MeV below the peak energy in the ❖ 700-1000 MeV neutrino energy range - We should have a resolution smaller than this In principle, it should be possible to have significantly better resolution ❖ Mono-energetic beams 3


 Study Procedure Use the coefficient fitting code to make mono-energetic beams at 600, 900 and ❖ 1200 GeV 60 bins of off-axis flux from 1 to 4 degrees 
 ❖ Apply the coefficients to the simulated nuPRISM interactions and evaluate flux ❖ systematic and statistical errors For now statistical errors are calculated as the sum in quadrature of the ❖ weights (including the coefficients) for each event in the bin. Will check against the poisson throwing method For the flux uncertainty, calculate a normalization and “shape” uncertainty ❖ Normalization uncertainty: spread of the integral of the linear ❖ combination event rate for each flux throw Shape uncertainty: spread on each bin after each flux throw has been ❖ renormalized to the nominal event distribution Using full MC stats, but statistical error bars are for 4.5e20 POT ❖ Mono-energetic beams 4

600 MeV Flux Fit Can achieve reasonable smoothness of the coefficients with a 70 MeV wide ❖ monoenergetic beam 9 10 × Arb. Norm. Coefficient Value 16 Linear Combination 0.2 14 2.5 Off-axis Flux ° 12 0.1 10 Gaussian: Mean=0.6, RMS=0.07 GeV 0 8 6 -0.1 4 2 -0.2 0 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 ( ) θ ° E (GeV) OA ν Here the fluxes are weighted by the energy to approximate the effect of the cross-section ❖ Haven’t completely studied the trade-off between beam width and flux & statistical ❖ errors (narrower beam may be possible) Mono-energetic beams 5

600 MeV Beam Event Rate (E ν ) Linear Combination, 0.6 GeV Mean Events/50 MeV 1 Ring Event Spectrum µ 10000 Absolute Flux Error Flux systematic variations: Shape Flux Error ❖ Statistical Error Norm: 11% RMS ❖ Gaussian Fit 5000 Fit Mean: 0.60 GeV Mean: 3 MeV RMS ❖ Fit RMS: 0.08 GeV Width: 5 MeV RMS ❖ 0 0.5 1 1.5 2 E (GeV) ν The flux normalization error is consistent with T2K cross section measurements ❖ The shape error is reduced near the peak, but not so much in the tails ❖ Mono-energetic beams 6

600 MeV Beam Event Rate (E rec ) Linear Combination, 0.6 GeV Mean Events/50 MeV 1 Ring Event Spectrum µ 6000 Absolute Flux Error Shape Flux Error Statistical Error 4000 NEUT QE NEUT Non-QE 2000 0 0.5 1 1.5 2 E (GeV) rec A significant excess due to non-QE at low reconstructed energy can be observed ❖ Should update the study using the Nieves model to have more non-QE events ❖ Mono-energetic beams 7

Comment on Flux Uncertainties All flux uncertainties Excluding absolute horn current uncertainty Linear Combination, 0.6 GeV Mean Linear Combination, 0.6 GeV Mean Events/50 MeV Events/50 MeV 1500 1500 1 Ring Event Spectrum 1 Ring Event Spectrum µ µ Absolute Flux Error Absolute Flux Error Shape Flux Error Shape Flux Error 1000 1000 Statistical Error Statistical Error Gaussian Fit Gaussian Fit Fit Mean: 0.60 GeV Fit Mean: 0.60 GeV 500 500 Fit RMS: 0.08 GeV Fit RMS: 0.07 GeV 0 0 0.5 1 1.5 2 0.5 1 1.5 2 E (GeV) E (GeV) ν ν A significant fraction of the flux uncertainty in the tails is coming from the horn absolute current ❖ uncertainty This error is made with regenerated nuPRISM fluxes at +5kA horn current ❖ Could this be a statistical effect? Need to investigate ❖ Mono-energetic beams 8

900 MeV Flux Fit Can achieve reasonable smoothness of the coefficients with a ~110 MeV wide ❖ monoenergetic beam 9 10 × 20 Coefficient Value Arb. Norm. Linear Combination 0.4 1.7 ° Off-axis Flux 15 Gaussian: Mean=0.9, RMS=0.11 GeV 0.2 10 0 -0.2 5 -0.4 0 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 θ ( ° ) E (GeV) OA ν Mono-energetic beams 9

900 MeV Event Rates All flux uncertainties Excluding absolute horn current uncertainty Linear Combination, 0.9 GeV Mean Linear Combination, 0.9 GeV Mean Events/50 MeV Events/50 MeV 1500 1 Ring Event Spectrum µ 1 Ring µ Event Spectrum Absolute Flux Error Absolute Flux Error 1000 Shape Flux Error Shape Flux Error 1000 Statistical Error Statistical Error Gaussian Fit Gaussian Fit Fit Mean: 0.90 GeV Fit Mean: 0.89 GeV 500 500 Fit RMS: 0.11 GeV Fit RMS: 0.11 GeV 0 0 1 2 3 1 2 3 E (GeV) E (GeV) ν ν The flux uncertainties (left) are rather larger around 600-700 MeV (the region of interest for nuclear effects) ❖ Turning of the horn current uncertainty (right) greatly reduces the error ❖ Once again, not sure if this is a statistical effect. For now, try choosing coefficients to spread out the ❖ contribution to the 600-700 MeV bins from multiple off-axis angles Mono-energetic beams 10

900 MeV Flux Fit, Take 2 0.3 Coefficient Value Coefficient Value 0.4 0.2 0.2 0.1 0 0 -0.2 -0.1 -0.4 1 1.5 2 2.5 3 3.5 4 -0.2 1 1.5 2 2.5 3 3.5 4 ( ) θ ° OA θ ( ° ) OA The coefficient distribution is ❖ 9 10 × Arb. Norm. 18 broader with smaller overall Linear Combination 16 14 magnitude 1.7 Off-axis Flux ° 12 Gaussian: Mean=0.9, RMS=0.12 GeV 10 At the cost of a slightly wider mon- ❖ 8 energetic beam 6 4 2 0 0 0.5 1 1.5 2 2.5 3 E (GeV) ν Mono-energetic beams 11

900 MeV Beam Event Rate (E ν ) Linear Combination, 0.9 GeV Mean Events/50 MeV 10000 1 Ring Event Spectrum µ Absolute Flux Error Shape Flux Error Flux systematic variations: ❖ Statistical Error 5000 Norm: 19% RMS Gaussian Fit ❖ Fit Mean: 0.88 GeV Mean: 15 MeV RMS Fit RMS: 0.14 GeV ❖ Width: 4 MeV RMS ❖ 0 1 2 3 E (GeV) ν The flux normalization error is rather larger compared to T2K cross section ❖ measurements The flux error in 600-700 MeV is improved ❖ Mono-energetic beams 12

900 MeV Beam Event Rate (E rec ) Linear Combination, 0.9 GeV Mean Events/50 MeV 1 Ring Event Spectrum µ 6000 Absolute Flux Error Shape Flux Error Statistical Error 4000 NEUT QE NEUT Non-QE 2000 0 0 1 2 3 E (GeV) rec We can clearly measure the feed-down contribution from non-QE processes ❖ The flux uncertainty relative to the peak is well controlled ❖ Mono-energetic beams 13

1200 MeV Flux Fit 6 10 × 0.04 Coefficient Value Arb. Norm. 4500 Linear Combination 0.03 4000 0.0 ° Off-axis Flux 0.02 3500 Gaussian: Mean=1.2, RMS=0.18 GeV 0.01 3000 0 2500 -0.01 2000 1500 -0.02 1000 -0.03 500 -0.04 0 1 1.5 2 2.5 3 3.5 4 0 1 2 3 4 5 ( ) θ ° E (GeV) OA ν 1200 MeV is about the limit of what we can achieve with a narrow band beam fit ❖ Even so, it is hard to completely reduce the high energy tail ❖ Mono-energetic beams 14

1200 MeV Beam Event Rate (E ν ) Linear Combination, 1.2 GeV Mean Events/50 MeV 2000 1 Ring Event Spectrum µ Absolute Flux Error 1500 Shape Flux Error Flux systematic variations: ❖ Statistical Error 1000 Gaussian Fit Norm: 11% RMS ❖ Fit Mean: 1.14 GeV Fit RMS: 0.21 GeV 500 Mean: 14 MeV RMS ❖ Width: 23 MeV RMS ❖ 0 1 2 3 4 E (GeV) ν Once again the error bars on the 500-600 MeV region are large. ❖ Mono-energetic beams 15

1200 MeV Beam Event Rate (E rec ) Linear Combination, 1.2 GeV Mean Events/50 MeV 1500 1 Ring Event Spectrum µ Absolute Flux Error Shape Flux Error Statistical Error 1000 NEUT QE NEUT Non-QE 500 0 1 2 3 E (GeV) rec The reconstructed distributions nicely shows the ability to observe the tail from nuclear ❖ effects The flux shape errors are smaller here (indicating it is statistical effect that is cancelled ❖ out in the smearing due to the reconstruction). Mono-energetic beams 16

Electron Scattering Variables In electron scattering, they are often measuring the energy transfer from the initial state ❖ lepton to the target If we know the initial state neutrino and final state muon four momentum, we can ❖ produce energy transfer plots for CC neutrino scattering as well Mono-energetic beams 17

Conclusion Mono-chromatic beams up to 1.2 GeV appear to work well ❖ Flux systematic errors are well controlled ❖ Need further investigation into the horn current systematic error ❖ around 500 MeV Statistical errors are not too large ❖ Preparing plots form the nuPRISM concept paper ❖ Mono-energetic beams 18