[PPT] - Cross Section Uncertainties in the NOvA Oscillation Analyses Aaron PowerPoint Presentation

SLIDE 1

Cross Section Uncertainties in  the NOvA Oscillation Analyses

Aaron Mislivec University of Minnesota

1

SLIDE 2

The NOvA Experiment

Off-axis, long-baseline neutrino

scillation experiment in the NuMI

neutrino beam at Fermilab

2

NOνA MINERνA

SLIDE 3

NOvA Physics Goals

– ν –

νμ ν

θ δ 𝜠𝒏𝟒𝟑

𝟑

𝑁𝑏𝑡𝑡 𝐼𝑗𝑓𝑠𝑏𝑠𝑑ℎ𝑧 θ θ 𝜠𝒏𝟓𝟐

𝟑

c

ν ν ν ν ντ νμ

NC Coherent Pion Production Measurement 𝜠𝒏𝟒𝟑

𝟑

𝜠𝒏𝟑𝟐

𝟑

Long Baseline Neutrino Oscillation Measurements:

νμ disappearance

νe appearance (±30% matter effect)

θ23, Δm232, δCP, Mass Hierarchy
NC disappearance
Sensitive to Sterile Neutrinos
θ24, θ34, Δm241

Non-Oscillation Measurements:

Cross sections (near detector)
Supernova detection
Exotic phenomena
Magnetic monopoles
Neutrino magnetic moment

3

SLIDE 4

NOvA Detectors

Functionally identical ND and FD

Same active materials and readout
No A-extrapolation between detectors
ND & FD correlations in cross sections,

event selection, and reconstruction

4

SLIDE 5

NOvA Detectors

Sampling Calorimeters (Near and Far)

PVC Extrusions filled with liquid scintillator -

mineral oil + 5% pseudocumene

WLS fiber collects and transports light to APD
Optimized for electron ID: Low-Z, 62% active
1 rad. length = 38cm (6 cell depths, 10 cell widths)

Far Detector

14 kton, 344k channels
810 km from source

Near Detector

0.3 kton, 20k channels
1 km from source

5

SLIDE 6

6

q (ADC)

10 102 3 10

νμ

e

νe ν

p μ p p π

γ γ 1m 1m

π0

NOvA Event Topologies

1 radiation length = 38cm (6 cell depths, 10 cell widths)

SLIDE 7

7

Event Selection

νe νμ ντ NC Cosmic

Learned varia+ons on the

riginal image

Input Image

Events classified with Convolutional Visual Network (CVN)

Events treated as images
Successive layers learn topological features
“Feed forward” neural network at end maps to event classes

νμ analysis identifies μ track using a kNN

Inputs: track length, dE/dx, scattering, fraction of non-track planes

JINST 11 P09001 (2016)

SLIDE 8

Energy Reconstruction

8

νe

Arbitrary units

(True - Reco)/True

1 − 0.5 − 0.5

A.U. (Area normalized) FD MC CC

µ

ν Bkgd. Total

NOvA Simulation

νe νμ

νμ CC:   Eν = Eμ + Ehad ΔEν ~ 9% Calorimetric (not kinematic) Eν reconstruction νe CC:   Eν = f(Ee, Ehad) ΔEν ~ 11%

SLIDE 9

NOvA Neutrino Event Generator

(GeV) True q

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Events

100 200 300 400 500

3

10 ×

GENIE QE (+RPA) Empirical MEC Valencia MEC GENIE RES

NOvA Simulation

9

(GeV)

had

Visible E

0.2 0.4 0.6 0.8 1

Events

20000 40000 60000

NOvA ND Data MEC QE RES DIS Other

P.O.T.

20

10 × 2.85

NOvA Preliminary

(GeV)

had

Visible E

0.2 0.4 0.6 0.8 1

Events

20000 40000 60000

NOvA ND Data QE RES DIS Other P.O.T.

20

10 × 2.85

NOvA Preliminary

GENIE 2.12.2 with the following modifications:

Addition of GENIE Empirical MEC scaled up 20%
Neutrino non-RES 1π scaled down 50% per

deuterium data

CC QE RPA from Valencia & R. Gran

(Phys. Rev. D 88, 113007) Non-RES 1π ✕ 0.5 First Analysis Second Analysis ND νμ CC ND νμ CC

SLIDE 10

Cross Section Uncertainties

Utilize GENIE’s standard systematics suite:

Primary process (e.g., CC QE, RES MA)
Hadronization
FSI

NOνA specific uncertainties:

5% on CCQE MA per deuterium data
CC QE RPA suppression & enhancement

(R. Gran, arXiv:1705.02932)

CC RES RPA f(Q2) off → on (R. Gran)
50% norm. uncertainty on DIS Nπ for

1.7 < W < 3.0 GeV

MEC…

10 Hadronic Energy Fraction

0.2 0.4 0.6 0.8 1

Events

0.02 0.04 0.06 0.08 0.1 0.12 0.14

6

10 × Simulated Selected Events Simulated Background Data

syst. range

σ Shape-only 1- MC mean: 0.31 GeV Data mean: 0.31 GeV POT

20

10 × ND area norm., 8.09

A Preliminary ν NO

ND νμ CC

DIS MEC

SLIDE 11

MEC Uncertainties

(GeV) True q

0.2 0.4 0.6 0.8 1 1.2

Arbitrary units

Empirical MEC QE q →

Emp. MEC q

RES q →

Emp. MEC q

NOvA Simulation

(GeV)

ν

E

2 4 6 8

`Shape' ratio to Empirical MEC

0.5 1 1.5 2 2.5 3

Nieves et al. MEC (GENIE) Martini et al. MEC (PRC 80, 065501) Megias et al. MEC (PRD 94, 093004) Uncertainty envelope

Eν shape from model comparisons
MEC q0 shape → QE, RES q0 shapes
Initial state np fraction from model comparisons:

València via GENIE vs. SuSA-MEC via PRC94, 054610

0.7 ≤

np np+nn ≤ 0.9

11

SLIDE 12

The MEC q0 shape is the largest cross section systematic in the 2017 νμ disappearance and  νe appearance results:

migrates events near νμ oscillation dip
effect on selection efficiency larger for νe than νμ

12 (GeV) True q

0.2 0.4 0.6 0.8 1 1.2

Arbitrary units

Empirical MEC QE q →

Emp. MEC q

RES q →

Emp. MEC q

NOvA Simulation

|

Δm

2 L

4 E |= π 2

sin

22θ

(GeV) True q

0.2 0.4 0.6 0.8 1

P.O.T.

20

10 × Events / 9

5000 10000 15000 20000 25000

Far Detector CC MEC only

µ

ν True All MEC uncertainties

NOvA Simulation

(GeV) True q

0.2 0.4 0.6 0.8 1

Ratio

1 2 3 4 5

Near Detector

MEC q0

SLIDE 13

13 (GeV) True q

0.2 0.4 0.6 0.8 1 1.2

Arbitrary units

Empirical MEC QE q →

Emp. MEC q

RES q →

Emp. MEC q

NOvA Simulation

|

Δm

2 L

4 E |= π 2

sin

22θ

(GeV) True q

0.2 0.4 0.6 0.8 1

P.O.T.

20

10 × Events / 9

5000 10000 15000 20000 25000

Far Detector CC MEC only

µ

ν True All MEC uncertainties

NOvA Simulation

(GeV) True q

0.2 0.4 0.6 0.8 1

Ratio

1 2 3 4 5

(GeV) True q

0.2 0.4 0.6 0.8 1

P.O.T.

20

10 × Events / 9

5 10 15 20 25

Far Detector CC MEC only

µ

ν True All MEC uncertainties

NOvA Simulation

(GeV) True q

0.2 0.4 0.6 0.8 1

Ratio

1 2 3 4 5

MEC q0

The MEC q0 shape is the largest cross section systematic in the 2017 νμ disappearance and  νe appearance results:

migrates events near νμ oscillation dip
effect on selection efficiency larger for νe than νμ

SLIDE 14

Near-to-Far Extrapolation

1. ND Data Eν Spectrum
2. ND Reco. → True Eν
3. FD / ND Event Ratio

in True Eν Bins

4. P(νx → νy)
5. FD True → Reco. Eν
6. FD Oscillated Prediction

Systematic shifts affect 2-6 1 2 3 4 6 5

14

SLIDE 15

Nfar(Ereco

ν

) = Posc(Etrue

ν

) × Φ(Etrue

ν

) × (Etrue

ν

, A) × R(Etrue

ν

) × ✏(...) Nnear(Ereco

ν

) = Φ(Etrue

ν

) × (Etrue

ν

, A) × R(Etrue

ν

) × ✏(...)

ND data + extrapolation leverages ND ↔ FD correlations in constraining the FD prediction

15

Near-to-Far Extrapolation

SLIDE 16

16

Reconstructed neutrino energy (GeV)

1 2 3 4 5

Ratio to nominal MC

0.8 0.9 1 1.1 1.2

extrap. ND shift in MaCCRES

σ ± FD shift MaCCRES σ ±

NOvA Simulation

Reconstructed neutrino energy (GeV)

1 2 3 4 5

Residual difference (%)

10 − 5 − 5 10

shift in MaCCRES FD minus ND σ + shift in MaCCRES FD minus ND σ

NOvA Simulation

Test Extrapolation: CC RES MA

Replace ND data with ND MC under CC RES MA shift
Extrapolate and compare with FD MC under same shift
Shifted ND MC + extrapolation accounts for most of the

shift’s effect in the FD

νμ CC Selection νμ CC Selection Residual

SLIDE 17

Reconstructed neutrino energy (GeV)

1 2 3 4 5

Ratio to nominal MC

0.7 0.8 0.9 1 1.1 1.2 1.3

extrap. ND shift in MEC q0 shape

σ ± FD shift MEC q0 shape σ ±

NOvA Simulation

Reconstructed neutrino energy (GeV)

1 2 3 4 5

Residual difference (%)

10 − 5 − 5 10

shift in MEC q0 shape FD minus ND σ + shift in MEC q0 shape FD minus ND σ

NOvA Simulation

17

Test Extrapolation: MEC q0 Shape

Replace ND data with ND MC under MEC q0 Shape shift
Extrapolate and compare with FD MC under same shift
Shifted ND MC + extrapolation accounts for most of the

shift’s effect in the FD

νμ CC Selection νμ CC Selection Residual

SLIDE 18

18

Resolution Binning

2017 νμ disappearance analysis extrapolates in bins of Ehad / Eν
Bins correspond to Eν resolution (ΔEμ ~ 3%, ΔEhad ~ 30%)
High-resolution bin helps resolve oscillation dip
Resolution binning further constrains FD prediction

100 200 300

3

10 ×

Reconstructed Neutrino Energy (GeV)

1 2 3 4 5

ν

/ E

had.

E

0.2 0.4 0.6 0.8 1

Quantile 1 Quantile 2 Quantile 3 Quantile 4

SLIDE 19

19

Reconstructed Neutrino Energy (GeV)

1 2 3 4 5

Events / 0.1 GeV

20 40 60

3

10 × Simulated Selected Events Simulated Background Data

syst. range

σ Full 1- POT

20

10 × ND POT norm., 8.09

A Preliminary ν NO

Reconstructed Neutrino Energy (GeV)

1 2 3 4 5

Events / 0.1 GeV

10 20 30 40 50

3

10 × Simulated Selected Events Simulated Background Data

syst. range

σ Full 1- POT

20

10 × ND POT norm., 8.09

A Preliminary ν NO

Reconstructed Neutrino Energy (GeV)

1 2 3 4 5

Events / 0.1 GeV

10 20 30 40

3

10 × Simulated Selected Events Simulated Background Data

syst. range

σ Full 1- POT

20

10 × ND POT norm., 8.09

A Preliminary ν NO

Reconstructed Neutrino Energy (GeV)

1 2 3 4 5

Events / 0.1 GeV

20 40 60

3

10 × Simulated Selected Events Simulated Background Data

syst. range

σ Full 1- POT

20

10 × ND POT norm., 8.09

A Preliminary ν NO

Resolution Binning

POT Normalized

Quantile 1 ΔEν ~ 6% Quantile 2 ΔEν ~ 8% Quantile 4 ΔEν ~ 12% Quantile 3 ΔEν ~ 10%

νμ CC νμ CC νμ CC νμ CC

SLIDE 20

20

Resolution Binning

Area Normalized

Reconstructed Neutrino Energy (GeV)

1 2 3 4 5

Events / 0.1 GeV

20 40 60

3

10 × Simulated Selected Events Simulated Background Data

syst. range

σ Shape-only 1- MC mean: 1.71 GeV Data mean: 1.71 GeV POT

20

10 × ND area norm., 8.09

A Preliminary ν NO

Reconstructed Neutrino Energy (GeV)

1 2 3 4 5

Events / 0.1 GeV

10 20 30 40

3

10 × Simulated Selected Events Simulated Background Data

syst. range

σ Shape-only 1- MC mean: 1.74 GeV Data mean: 1.73 GeV POT

20

10 × ND area norm., 8.09

A Preliminary ν NO

Reconstructed Neutrino Energy (GeV)

1 2 3 4 5

Events / 0.1 GeV

10 20 30 40

3

10 × Simulated Selected Events Simulated Background Data

syst. range

σ Shape-only 1- MC mean: 1.76 GeV Data mean: 1.75 GeV POT

20

10 × ND area norm., 8.09

A Preliminary ν NO

Reconstructed Neutrino Energy (GeV)

1 2 3 4 5

Events / 0.1 GeV

20 40 60

3

10 × Simulated Selected Events Simulated Background Data

syst. range

σ Shape-only 1- MC mean: 1.76 GeV Data mean: 1.77 GeV POT

20

10 × ND area norm., 8.09

A Preliminary ν NO

Quantile 1 ΔEν ~ 6% Quantile 2 ΔEν ~ 8% Quantile 4 ΔEν ~ 12% Quantile 3 ΔEν ~ 10%

νμ CC νμ CC νμ CC νμ CC

SLIDE 21

21

Replace ND data with ND MC under CC QE RPA shift
Extrapolate and compare with FD MC under same shift
Isolating cross section systematics in resolution (Ehad / Eν) bins in the

extrapolation further constrains the FD prediction

e.g. CC QE RPA in lowest Ehad / Eν bin (Quantile 1) above

Test Extrapolation: Resolution Binning

Reconstructed neutrino energy (GeV)

1 2 3 4 5

Ratio to nominal MC

0.8 0.9 1 1.1 1.2

extrap. ND shift in RPA shape: supp

σ ± FD shift RPA shape: supp σ ±

NOvA Simulation Q1

νμ CC Selection ND MC sample extrapolated as a whole Residual

Quantile 1

Reconstructed neutrino energy (GeV)

1 2 3 4 5

Ratio to nominal MC

0.8 0.9 1 1.1 1.2

extrap. ND shift in RPA shape: supp

σ ± FD shift RPA shape: supp σ ±

NOvA Simulation Q1

νμ CC Selection ND MC sample extrapolated in resolution bins Residual

Quantile 1

SLIDE 22

Signal uncertainty (%)

20 − 10 − 10 20 Statistical error Total syst. error Extrapolation Detector Response Beam Calibration Normalization Cross Sections ν

Background uncertainty (%)

30 − 20 − 10 − 10 20 30 Statistical error Total syst. error Beam Extrapolation Detector Response Normalization Calibration Cross Sections ν

)

3

10 × (

23

θ

2

Uncertainty on sin

50 − 50 Statistical error Total syst. error

CP

δ Value of Scintillation Model Scale

µ

Rel. E

Neutrino Flux

Rel. Calibration

Scale

µ

Abs. E

Normalization Cross Sections

Abs. Calibration

)

2

eV

3

10 × (

2 32

m ∆ Uncertainty on

0.05 − 0.05 Statistical error Total syst. error Scale

µ

Rel. E

Neutrino Flux Scintillation Model Scale

µ

Abs. E

Normalization

CP

δ Value of Cross Sections

Rel. Calibration
Abs. Calibration

Systematic Uncertainties

Largest cross section systematics for NOνA 2017 oscillation results: MEC q0 Shape, CC RES MA & MV, RES RPA

νμ νμ νe νe

22

SLIDE 23

Cross Sections and NOvA: Future

Cross section uncertainties becoming more important with

improvements to calibrations and detector simulation
test beam constraints on hadronic response

Continue to apply constraints from new cross section measurements, including those from NOνA In the process of binding alternate generators (NEUT, GiBUU) to NOvA software framework to study impact of models not in GENIE

23

SLIDE 24

Cross Sections and NOvA: Future

24

NOνA joint neutrino-antineutrino results planned for Summer 2018 Improvements to cross section tune and uncertainties for NOνA Summer 2018 results:

Separate neutrino and antineutrino tunes using FHC & RHC data
Tune MEC in (q0, |q|)
MEC (q0, |q|) shape uncertainty from re-tuning MEC with

QE, RES shifts

Apply RES RPA to central value
Currently implementing the MINERνA tune in the NOνA MC for

comparison

SLIDE 25

25

Thank You

NOνA Collaboration Austin, TX Feb 2018

SLIDE 26

νμ Data at the Far Detector

26

Total Observed 126 Best fit prediction 129 Cosmic Bkgd. 5.82 Beam Bkgd. 3.46 Unoscillated 763

SLIDE 27

23

θ

2

sin

0.4 0.5 0.6 0.7

)

2

eV

3

(10

32 2

m ∆

2 2.2 2.4 2.6 2.8 3 3.2

NOvA Preliminary

Normal Hierarchy 90% C.L. POT-equiv.

20

10 × NOvA 8.85 T2K 2016 MINOS 2014 Joint analysis

∆m2

32 = 2.444+0.079 −0.077 × 10−3 eV2

sin2 θ23 = ( UO: 0.558+0.041

−0.033

LO: 0.475+0.036

−0.044

νμ Disappearance Results

27

SLIDE 28

POT-equiv

20

10 × Events / 8.85

5 10 15 20

NOvA Preliminary

FD data Best Fit prediction Total Background Cosmic Background Low PID

Mid. PID

High PID

Core Peripheral

Reconstructed Neutrino Energy (GeV)

1 2 3 4 1 2 3 4 1 2 3 4 FD data Best Fit prediction Total Background Cosmic Background

νe FD Selected Sample

28

Total Observed 66 Signal Prediction 20-48 Cosmic Bkgd. 4.9 Beam Bkgd. 15.6 Unoscillated 20.5

SLIDE 29

CP

δ

23

θ

2

sin

0.3 0.4 0.5 0.6 0.7 2 π π 2 π 3 π 2

NOvA Preliminary

σ 1 σ 2 σ 3 Best Fit NH

CP

δ

23

θ

2

sin

0.3 0.4 0.5 0.6 0.7 2 π π 2 π 3 π 2

NOvA Preliminary

σ 1 σ 2 σ 3 IH

Joint νe Appearance Results

CP

δ ) σ Significance (

1 2 3 4 5 2 π π 2 π 3 π 2

NOvA Preliminary

NH Upper octant NH Lower octant IH Upper octant IH Lower octant*

POT equiv.

20

10 × 8.85 NOvA FD

IH at δcp = π/2 disfavored at

greater than 3σ.

Approaching IH rejection at 2σ.

29

SLIDE 30

Year

2016 2018 2020 2022 2024

)

2

χ ∆ = σ Significance (

1 2 3 4 5 =0.082

13

θ 2

2

, sin

2

eV

3

10 × =2.45

32 2

m ∆ =0.500

23

θ

2

/2, sin π =3

CP

δ Normal

and analysis improvements All projected beam intensity

NOvA Simulation

µ

ν +

e

ν NOvA joint Hierarchy CPV

Total events - neutrino mode

20 40 60 80

Total events - antineutrino mode

10 15 20 25 30

NOvA Simulation

= 0

CP

δ /2 π =

CP

δ π =

CP

δ /2 π = 3

CP

δ

2

eV

3

10 × 2.51 − =

2 32

m ∆ IH

2

eV

3

10 × 2.45 + =

2 32

m ∆ NH =0.082

13

θ 2

2

sin =0.47,0.56

23

θ

2

sin NOvA FD ) ν POT (

20

10 × 9.49 ) ν POT (

20

10 × 8.1 prediction 2017 best fit

First joint neutrino-antineutrino results planned for Summer 2018
Further probe Mass Hierarchy and δCP

NOvA Oscillation Results: Future

30

SLIDE 31

νe Appearance Backgrounds

31

Reconstructed Neutrino Energy (GeV)

20

10 × Events / 8.09

3

10

1 2 3 4 5

Low PID

Mid. PID

High PID

1 2 3 4 1 2 3 4 1 2 3 4

ND Data NC CC

µ

ν

e

ν Beam Uncorrected MC

Data-driven estimates of νe backgrounds at the ND:

π /K contributions to beam νe constrained by

contained & uncontained νμ CC events

NC-to-νμ CC ratio constrained by Michel electrons

SLIDE 32

32

Event Selection

tify muons in reconstructed tracks using a kNN

Track length, dE/dx, scattering, fraction of track-only planes

Quality and preselection cuts (analysis specific)

Quality: beam & detector
Contained and well-reconstructed
Eν range

νμ analysis identifies μ track using a kNN:

Track length
dE/dx
Scattering
Fraction of track-only planes

For both νμ and νe analyses, cosmics at FD reduced from ~106 to <10 by

Quality and preselection cuts
PID cut
BDT cut for comics

SLIDE 33

33

Comparison to Previous Results

97

23

θ

2

sin

0.4 0.5 0.6 0.7

)

2

eV

3

(10

32 2

m ∆

2 2.2 2.4 2.6 2.8 3 3.2

NOvA Preliminary

NOvA Normal Hierarchy, 90% C.L. POT-equiv.

20

10 × Joint Analysis, 8.85 Analysis, PRL.118.151802

µ

ν

Previous result: 2.6 σ exclusion of maximal mixing New simulation & calibration: ~1.8 σ

Expected small shift due to change in

energy resolution and scale.

Had larger than expected event migration
ut of the dip region. (3 vs. 0.5)

New selection & analysis: ~0.5 σ

Large changes possible due to new cosmic

rejection – we have a totally new set of background events.

Saw changes this size or larger in 5% of

pseudo-experiments.

New data: ~0.4 σ Final result: 0.8 σ

Includes FC corrections

SLIDE 34

34

Scintillator Model

Absorbed and re-emitted

Cherenkov light is a small but important component of our scintillator response.

– Particularly for low-energy protons in hadronic showers.

Was one of our largest

uncertainties, now reduced by an

rder of magnitude.

– Previously accounted for with second order terms in our scintillator model. – Those terms were unusual, so we placed large systematics.

Expected energy resolution for νμ

CC events increased from 7% to 9%.

99

SLIDE 35

35

Near-to-Far Extrapolation

νμ → νμ: extrapolate in resolution bins νμ → νe signal: extrapolate whole spectrum νe bkgd → νe bkgd: extrapolate components separately

SLIDE 36

NOvA Neutrino Event Generator

GENIE 2.12.2 with the following modifications:

Addition of GENIE Empirical MEC scaled up 20%
Neutrino non-RES 1π scaled down 50% per deuterium data
CC QE RPA from Valencia & R. Gran

(GeV) True q

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Events

100 200 300 400 500

3

10 ×

GENIE QE (+RPA) Empirical MEC Valencia MEC GENIE RES

NOvA Simulation

| (GeV) q Reco |

0.5 1 1.5 2

Events

20000 40000 60000

NOvA ND Data Non MEC With untuned Empirical MEC With tuned Empirical MEC

NOvA Preliminary

36

SLIDE 37

The MEC q0 shape is the largest cross section systematic in both the newest νμ disappearance and νe appearance results:

migrates events near νμ oscillation dip
effect on selection efficiency larger for νe than νμ

37 (GeV) True q

0.2 0.4 0.6 0.8 1 1.2

Arbitrary units

Empirical MEC QE q →

Emp. MEC q

RES q →

Emp. MEC q

NOvA Simulation

1 2 3 4

P.O.T.

20

10 × Events / 9

2000 4000 6000 8000

Near Detector CC MEC only

µ

ν True All MEC uncertainties

NOvA Simulation (GeV)

ν

True E

1 2 3 4

Ratio

0.5 1 1.5 2

MEC q0

|

Δm

2 L

4 E |= π 2

sin

22θ

SLIDE 38

1 2 3 4

P.O.T.

20

10 × Events / 9

50 100 150

3

10 ×

CC candidates

µ

ν All True MEC only

Near Detector All MEC uncertainties

NOvA Simulation (GeV)

ν

Reco E

1 2 3 4

Ratio

0.8 0.9 1 1.1 1.2

The MEC q0 shape is the largest cross section systematic in both the newest νμ disappearance and νe appearance results:

migrates events near νμ oscillation dip
effect on selection efficiency larger for νe than νμ

38 (GeV) True q

0.2 0.4 0.6 0.8 1 1.2

Arbitrary units

Empirical MEC QE q →

Emp. MEC q

RES q →

Emp. MEC q

NOvA Simulation

MEC q0

|

Δm

2 L

4 E |= π 2

sin

22θ