h.a.tanaka (slac/stanford) neutrino experiments

N E U T R I N O E X P E R I M E N T SH . A . TA N A K A ( S L A C / S TA N F O R D )

SFB 1044 Workshop on Electromagnetic Observables for Low Energy Nuclear Physics Johannes Gutenberg University, Mainz, Germany

O V E R V I E W:• Introduction to neutrino oscillation experiments

• How are neutrino oscillations measured?

• An overview of the current program and a survey of a few problems

• Some words about generators

• What is the role of relativity in neutrino-nucleus collisions?

• What new electron scattering measurements can be useful for this program?

• Yes!

• How can better theory be implemented in neutrino generators simulations?

• Yes!

!2

N E U T R I N O O S C I L L AT I O N• Neutrino come in three “flavor” eigenstates (νe, νµ, ντ)

• Determined by how their weak interaction properties

• Corresponding “antineutrinos” for each

• Likewise, neutrinos come in three mass eigenstates (ν1, ν2, ν3 )

• energy eigenstates which are stationary under time evolution

• The mass and flavor eigenstates “mix”

• Neutrinos are produced in flavor eigenstates (by weak interaction)

• Mass eigenstates evolve differently in time . . ..

• New flavor components appear . . . . . “neutrino oscillations”

• For a two neutrino species, a simple formula results

!3

P (⌫↵t�! ⌫�) = sin2 2✓ sin2 1.27

�m221(eV

2)

E(GeV)L(km)

energy difference(special relativity)transformation

properties

unit conversion “time”

e-, µ-, τ-

νe, µ, τ

W

|⌫↵i =X

i

U⇤↵i|⌫ii

e+, µ+, τ+

Wνe, µ, τ

✓⌫↵⌫�

◆=

✓cos ✓ sin ✓

� sin ✓ cos ✓

◆✓⌫1⌫2

◆

<latexit sha1_base64="abWpb/stxc6zpIFWQKryffRvx84=">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</latexit><latexit sha1_base64="abWpb/stxc6zpIFWQKryffRvx84=">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</latexit><latexit sha1_base64="abWpb/stxc6zpIFWQKryffRvx84=">AAAC0HicfVJLaxRBEO4Zo8bxkVWPXposSjy4zARBQYSgFy+BKNkksL0sNb01O016eobuGnEZV/Hqz/PmL8jfsGd3JK8lBQ1fPb6vqqs7rbRyFMd/g/DWxu07dzfvRfcfPHy01Xv85MiVtZU4lKUu7UkKDrUyOCRFGk8qi1CkGo/T049t/vgrWqdKc0jzCscFzIzKlATyoUnvTGjMaCcSKc6UacBamC8auYiEqScCdJUDF2LlpUgQCTTTriwSVs1yehm9j9artDLvfghZOkG5J3P+ggunTOd53VcXXJ87r1zb56ZZk/9j7q6lTnr9eBAvjV8HSQf6rLODSe+PmJayLtCQ1ODcKIkrGntZUlKjF64dViBPYYYjDw0U6MbN8kEW/LmPTHlWWn8M8WX0IqOBwrl5kfrKAih3V3NtcF1uVFP2dtwoU9WERq4aZbXmVPL2dflUWZSk5x6AtMrPymUOFiT5P9AuIbl65evgaHeQxIPk8+v+3oduHZvsGdtmOyxhb9ge+8QO2JDJYD9wwfdgEX4Jv4U/w1+r0jDoOE/ZJQt//wNP/N9m</latexit><latexit sha1_base64="abWpb/stxc6zpIFWQKryffRvx84=">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</latexit>

flavor mass

Mixing

flavor mass

Mixing

Note the importance of neutrino energy

M E A S U R I N G O S C I L L AT I O N S• Start with a beam in a (relatively) pure flavor state

• Observe oscillations at a fixed baseline (L) by:

• “Appearance”

• new flavor in the beam arising from oscillations

• “Disappearance”

• deficit of original flavor due to oscillations into new flavors

• In each case, we want to measure as a function of neutrino energy to obtain the probability as a function of Eν

!4

(GeV)νE0 0.5 1 1.5 2 2.5 3

νΦ

0

0.2

0.4

0.6

0.8

1

(GeV)νE0 0.5 1 1.5 2 2.5 3

osc

P

0

0.02

0.04

0.06

0.08

0.1

Initial neutrino flux with ~pure flavor (νµ)

Oscillation probability

(GeV)νE0 0.5 1 1.5 2 2.5 3

νΦ

0

0.2

0.4

0.6

0.8

1

initial flavornew flavorno oscillations

• More formally . . . we can predict the expected spectrum at the “far” detector (FD) as

• An essential strategy is also to observe the “same” neutrino beam with a “near” detector (ND)at L~0

x P(E;L)

x=0

“Far”

measure with near detector

NFD(⌫↵ ! ⌫� , Erec) =

ZdE⌫ �⌫↵(E⌫)⇥ �⌫↵(E⌫)⇥R⌫↵(E⌫ , Erec)⇥ P (⌫↵ ! ⌫� , E⌫)

<latexit sha1_base64="gDBQzxRslzaoX07BPtcR05qidsk=">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</latexit><latexit sha1_base64="gDBQzxRslzaoX07BPtcR05qidsk=">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</latexit><latexit sha1_base64="gDBQzxRslzaoX07BPtcR05qidsk=">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</latexit><latexit sha1_base64="gDBQzxRslzaoX07BPtcR05qidsk=">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</latexit>

P (⌫↵t�! ⌫�) = sin2 2✓ sin2 1.27

�m221(eV

2)

E(GeV)L(km)

NND(⌫↵, Erec) =

ZdE⌫ �⌫↵(E⌫)⇥ �⌫↵(E⌫)⇥R⌫↵(E⌫ , Erec)

<latexit sha1_base64="0Gjmsq4bPa5iAKnp3xiwBxvbv2w=">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</latexit><latexit sha1_base64="0Gjmsq4bPa5iAKnp3xiwBxvbv2w=">AAACd3icfVHLSgMxFM2M7/qqutOFwapUkDIjgoIIohZcSRWrQlOGO2nahmYyQ5IRyjC/4Me58z/cuDN9gE+8cOFwzrncV5gIro3nvTruxOTU9MzsXGF+YXFpubiyeq/jVFFWp7GI1WMImgkuWd1wI9hjohhEoWAPYe9ioD88MaV5LO9MP2HNCDqStzkFY6mg+HwdZNeXeZnINCAgki7s42qQKUbzPXyKCZcGt6qBlTE5waTW5UH26c3LQ2kPE8MjpjHRvBPBf47bP8TPjoWgWPIq3jDwb+CPQQmNoxYUX0grpmnEpKECtG74XmKaGSjDqWB5gaSaJUB70GENCyXYIZrZ8G453rFMC7djZdPuOWS/VmQQad2PQuuMwHT1T21A/qU1UtM+bmZcJqlhko4atVOBTYwHT8Atbtc1om8BUMXtrJh2QQE19lWDI/g/V/4N7g8qvlfxbw5LZ+fjc8yiDbSFyshHR+gMXaEaqiOK3px1p+RsO+/uprvrlkdW1xnXrKFv4fof8a29zw==</latexit><latexit sha1_base64="0Gjmsq4bPa5iAKnp3xiwBxvbv2w=">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</latexit><latexit sha1_base64="0Gjmsq4bPa5iAKnp3xiwBxvbv2w=">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</latexit>

R is what takes us from physics which depend on the “true” neutrino energy to what we actually observe (N, Erec)

R is a combination of neutrino interaction modeling (what comes out) and what the detector sees (efficiency, resolution, etc.)

N E U T R I N O E N E R G Y R E C O N S T R U C T I O N• Two basic approaches:

• Kinematic:

• Selection events which correspond to a “well defined” reaction and use the inferred kinematics

• e.g. target ν+n→μ+p interactions by selection pionless events and assume the kinematics:

•

• Calorimetric:

• Add up the energy of all the products detected in the neutrino reaction

• Issues:

• Kinematic:

• Reactions like “ν+n→μ+p” do not really exist on a nucleus

• Rely on modeling to predict the outgoing muon kinematics for events with targeted topology (e.g. “pionless”)

• Calorimetric

• Energy reconstruction depends on particle composition of outgoing particles (e.g. neutrons)

• Rely on modeling outgoing particles inclusively across all types of neutrino interactions that are selected

!5

ERec =mNEµ �m2

µ/2

mN � Eµ + |~pµ| cos ✓µ<latexit sha1_base64="lZ5Gu3TEkUc3K8g3M54ieSgBNnc=">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</latexit><latexit sha1_base64="lZ5Gu3TEkUc3K8g3M54ieSgBNnc=">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</latexit><latexit sha1_base64="lZ5Gu3TEkUc3K8g3M54ieSgBNnc=">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</latexit><latexit sha1_base64="lZ5Gu3TEkUc3K8g3M54ieSgBNnc=">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</latexit>

Reminder: R(Eν, Erec) tells us how a neutrino of energy Eν will be reconstructed to get Erec

N E U T R I N O B E A M S• With few exceptions (e.g. stopped meson beams), we are always presented with a spectrum of neutrinos

• For any observed neutrino interaction, we do not know its energy

• It must be inferred from the products emerging from the reaction

• Nuclear modeling is essential not only for predicting event rates, but the energy spectrum

• Whether in the near or far detector, what we observed is inherently flux-averaged

• ND inherently cannot tell you how a neutrino of Eν appears in the detector (i.e. R(Eν, Erec))

• This requires modeling

• The best it can do is tell you that your model of Rν agrees or disagrees in a flux averaged sense

• “Agrees” is necessary but not sufficient for “correct”

!6

NFD(⌫↵ ! ⌫� , Erec) =

ZdE⌫ �⌫↵(E⌫)⇥ �⌫↵(E⌫)⇥R⌫↵(E⌫ , Erec)⇥ P (⌫↵ ! ⌫� , E⌫)

<latexit sha1_base64="gDBQzxRslzaoX07BPtcR05qidsk=">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</latexit><latexit sha1_base64="gDBQzxRslzaoX07BPtcR05qidsk=">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</latexit><latexit sha1_base64="gDBQzxRslzaoX07BPtcR05qidsk=">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</latexit><latexit sha1_base64="gDBQzxRslzaoX07BPtcR05qidsk=">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</latexit>

NND(⌫↵, Erec) =

ZdE⌫ �⌫↵(E⌫)⇥ �⌫↵(E⌫)⇥R⌫↵(E⌫ , Erec)

<latexit sha1_base64="0Gjmsq4bPa5iAKnp3xiwBxvbv2w=">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</latexit><latexit sha1_base64="0Gjmsq4bPa5iAKnp3xiwBxvbv2w=">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</latexit><latexit sha1_base64="0Gjmsq4bPa5iAKnp3xiwBxvbv2w=">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</latexit><latexit sha1_base64="0Gjmsq4bPa5iAKnp3xiwBxvbv2w=">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</latexit>

T O Y E X A M P L E • For simplicity, assume:

• Monoenergetic source of να whose true energy is 600 MeV, but unknown to experiment

• cross section is known to be flat: σν(Eν) = c

• Δm2 is known (2.5x10-3 eV2)

• sin22θ = 0.5 but is unknown

• Near/Far Detectors respond identically

• But:

• True R(Eν, Erec) is “diagonal”: Erec=2/3 Eν

• Incorrect modeling: assume R(Eν, Erec) is Eν = Erec

• ~incorrectly assume events are QE when in fact they are Δ resonance

• Two ways to look at situation:

• Based on “correct” oscillation parameters predicted FD event rate is off from what it should.

• Observed rate indicates sin22θ = 0.75 (not 0.5)

• In either case, we are evaluating oscillation probability at the wrong Eν

!7

P (⌫↵t�! ⌫�) = sin2 2✓ sin2 1.27

�m221(eV

2)

E(GeV)L(km)

Near Far

Px →

x

Near Far

→

True

Reconstructed

P

observed

Expected based on true parameters

“ R E A L ” E X A M P L E F R O M N O VA

• Neutrino event rate vs. En is “corrected” by observed near detector spectrum

• Correction depends on R:

• Incorrect model gives incorrect parameters: systematic errors propagated by varying R

!8

183

Figure 12.20: The NOvA “reco-true-reco” strategy for extrapolating discrepanciesbetween near detector simulation and data to the far detector. This plot is explainedin detail in the text.

For comparison, the far-to-near is about 0.0006 at 2 GeV as shown in the bottom,third-to-left panel. This results in an un-oscillated prediction of the far detectorhistogram, f

truei

:

ftrue

i=

"’j

nrecoj,DCMP

nrecoj,MC

MNDji

#f

truei

ntruei

. (12.9)

Multiplying by an oscillation probability for the ⌫µ ! ⌫µ flavor transition, shown inthe bottom, fourth-from-the-left, the oscillated, constrained far detector event countin true energy, e

truei

, is

etruei=

"’j

nrecoj,DCMP

nrecoj,MC

MNDji

#f

truei

ntruei

Pµ!µ(E⌫) , (12.10)

where E⌫ is determined by the center of bin i. This is the distribution in the bottom,fifth-from-the-left.

After this, the last remaining step is to fold the true energy distribution back intoreconstructed energy bins using the migration matrix M

FDik

, shown in the bottomright. This gives us our expectation in each analysis bin, ek :

ek =’

i

"’j

nrecoj,DCMP

nrecoj,MC

MNDji

#f

truei

ntruei

Pµ!µ(E⌫)MFDik. (12.11)

This final prediction is shown on the top right. When performing a fit, the predictedspectra at several test oscillation parameters must be generated. To be compatiblewith this, for each flavor transition constraint, it is possible to predict the componentfor an arbitrary choice of oscillation parameters.

Eν

A N O T H E R A P P R O A C H ( T 2 K )

!9

𝜙ν σν• Fit model parameters to near detector

• “model” = flux, cross section, detector

• Updated model includes new parameter values and covariance matrix

• New model is “transported” to far detector prediction

• Some non-parametrized model variations are considered separately

ND DATA

ND DATA

FIT FITFIT

“ L O N G - B A S E L I N E ” E X P E R I M E N T S

• Accelerator-based neutrino beams have been sent to detectors hundreds of km away on three continents

• Key elements

• Precision measurements of neutrino mixing parameters

• CP violation, matter effects to resolve mass ordering

T2K and T2HKK (295 km)

NOvA (812 km)

!10

DUNE/LBNF: FNAL to Homestake: 1300 km

• Experiments require:

• O(MW) proton beams to produce neutrino beams

• O(101-2 kt) detectors situated hundreds of kilometers away

N E U T R I N O F L U X A N D I N T E R A C T I O N S• Accelerator-based neutrino beams produce O(GeV) neutrinos

• Pure νμ beams with O(1%) νe contamination from pion decays

• Likewise νμ beams can be produced

• At nucleon-level, we have:

• Quasi-elastic scattering

• Resonant pion producition

• Deep inelastic scattering

• Modeling relies heavily on “impulse approximation”

• Neutrinos interactions are inherently at the nucleon (or quark) level

• Initial state dynamics typically modeled with Relativistic Fermi Gas

• Final state dynamics via intranuclear cascade

• A few coherent processes considered

• Relativistic effects important for most processes

!11

E⌫ (GeV)0 1 2 3 4 5

�(E

⌫)/E

⌫(103

8cm

2nu

cleon�1GeV

�1)

0

0.5

1

1.5

2

⌫µ Flux (arbitrary norm.)GENIE 2.12.8, �⌫µch (E⌫)

CC-Total

CC-RES

CC 1p1h+2p2h

NC-Total

T2K: ND o↵-axis

NO⌫A: ND o↵-axis

DUNE CDR Ref.

MINER⌫A L.E.

FIG. 1. Neutrino fluxes, as a function of energy, of current and future accelerator-based neutrino

experiments. The fluxes relevant to neutrino interaction measurements are shown, from the T2K

experiment o↵-axis near detector (ND) [3], NOvA ND [4], and MINERvA (Low Energy configura-

tion only [5]). One future program, DUNE [6], is shown; the HK flux is very similar to the T2K

ND o↵-axis flux. Also overlaid are the total CC cross section divided by energy, according to the

GENIE 2.12.8 reference model (described in Appendix A).

the flavor of the charged lepton produced, the charge of which also distinguishes neutrinos

from anti-neutrinos. The main contributions to the CC cross section for the GENIE 2.12.8

reference model used throughout this review are also shown. The reference model is described

in Appendix A, and is an up to date Monte Carlo simulation used widely in the field. At

low E⌫ . 1 GeV, the cross section is dominated by the lowest energy transfer process,

charged-current quasi-elastic (CCQE) scattering ( ⌫(–)

l + A ! l�(+) + A0 + p(n)), which

is also called single nucleon knock-out, or 1p1h (one particle, one hole). There are also

significant contributions from multiple-nucleon knock-out (2p2h), where the interaction is

with more than one nucleon in the nucleus (⌫l+A(n, p) ! l�+A0+p+p and ⌫ l+A(n, p) !

l++A0+n+n2). At higher energy transfers, nucleon resonances (RES) can be excited, which

2 Note this is an approximation for illustration. There are significant questions about the proton, neutron

4

K. Mahn et al. arxiv: 1803.08848.

L O R E• The issue of neutrino-nucleus modeling is intimately coupled to how we use the near detector

• Some things I have heard:

• The purpose of the near detector is to measure the neutrino flux

• This is a useful thing for the near detector to do (via leptonic processes), but it is not sufficient

• n.b. measuring the neutrino flux at ND requires you to know the cross section (observable is φ x σ)

• What we need to know is the neutrino cross section versus energy

• This is a useful thing to know, but it is not sufficient in itself

• We need our models to also predict efficiencies and response

• We’re doing a counting experiment so shape doesn’t matter

• Still need true neutrino spectrum to calculate overall oscillation probability

• The near detector data agrees with our model hence the model must be correct

• Disagreement with the near detector indicates mismodeling

• But agreement does not mean the model is correct

• If the flux at ND/FD are the same, and the ND/FD detectors respond identically, systematic errors cancel

• ND/FD fluxes are not the same: we have oscillations at the FD

• Many systematics may cancel, but we must still know Eν (as opposed Erec) in order to predict the FD events correctly

!12

S. Zeller, JLAB Workshop, May 2015

Some of the Challenges 6

•  ν beams are not mono-energetic ! multiple processes contributing at a given Eν" (broad flux of neutrinos illuminating the detector)

•  σν’s are not particularly well-constrained in the region we care about

•  ν experiments use nuclear targets; nuclear effects significantly alter σν’s, f.s. particle topology/kinematics (all of this phyx has to go into generators)

•  at the end of the day, have to infer Eν from what we observe NOvA

DUNE &

CNGS T2K, BNB

M E A S U R E M E N T S

• Four primary channels:

• νμ disappearance: P(νμ→ νμ) (measures primarily θ23 and Δm231)

• νe appearance: P(νμ→νe)

• νμ disappearance: P(νμ→ νμ) ( measures primarily θ23 and Δm231)

• νe appearance: P(νμ→νe)

!13

29

cij º cos qijsij º sin qij

The leptonic mixing matrix U is —

ν1 ν2 ν3

Majorana phases

€

U =

c12c13 s12c13 s13e−iδ

−s12c23 − c12s23s13eiδ c12c23 − s12s23s13e

iδ s23c13s12s23 − c12c23s13e

iδ −c12s23 − s12c23s13eiδ c23c13

$

%

& & &

'

(

) ) )

×diag eiα1 2, eiα2 2,1( )

• CP odd phase δ can result in

• asymmetry of oscillation probabilities P(νµ→νe) ≠ P(νµ→νe)

• distortion of νe/νe appearance spectrum

• θ23 (as opposed to 2θ23) dependence allows “octant” resolution if θ23≠45°

• Mass hierarchy sensitivity through x: νe/νe enhanced in normal/inverted hierarchy

P (⌫µ ! ⌫e) ⇠ sin2 2✓13 ⇥ sin2 ✓23 ⇥sin2[(1�x)�]

(1�x)2

�↵ sin � ⇥ sin 2✓12 sin 2✓13 sin 2✓23 ⇥ sin� sin[x�]x

sin[(1�x)�](1�x)

+↵ cos � ⇥ sin 2✓12 sin 2✓13 sin 2✓23 ⇥ cos� sin[x�]x

sin[(1�x)�](1�x)

+O(↵2)

� ⌘ �m231L

4Ex ⌘ 2

p2GFNeE

�m231

↵ =

��m2

21

�m231

�� ⇠1

30

ν μ→ν e O S C I L L AT I O N P R O B A B I L I T Y

M. Freund, Phys.Rev. D64 (2001) 053003

!14All this must be disentangled!

A F E W N O T E S• Implicit in discussion is that modeling the signal is as important as modeling the background

• “discovery” phase of neutrino oscillations to precision phase

• CP violation in neutrinos is expected to be 30% in maximal cases

• Much better precision in oscillated expectation needed if CPV is non-maximal

• We also want to precisely measure the oscillation parameters, including δCP

• “2%”

• Three major nuclear targets/detector technologies

• H2O: water Cherenkov detectors (Super-Kamiokande, Hyper-Kamiokande)

• CH(2): plastic, liquid scintillator (NOvA, MIniBooNE)

• Ar: Liquid and gas argon time projection chambers (MicroBooNE, ICARUS, SBND, DUNE)

• Enormous investment now and into the future

• cf. US P5 Report

• Ongoing momentum on DUNE/LBNF in USA

• Recent “pre-approval” of Hyper-Kamiokande in Japan

!15

ν - A I N D U S T RY• NuINT:

• 12th Workshop since 2000

• Vibrant and growing!

• Also now a standard part of NuFACT and Neutrino conference series

• Review papers: (just a sample)

!16

FERMILAB-PUB-17-195-ND-TINT-PUB-17-020

NuSTECa White Paper: Status and Challenges ofNeutrino-Nucleus Scattering

L. Alvarez-Ruso,1 M. Sajjad Athar,2 M. B. Barbaro,3 D. Cherdack,4 M. E. Christy,5 P. Coloma,6

T. W. Donnelly,7 S. Dytman,8 A. de Gouvea,9 R. J. Hill,10, 6 P. Huber,11 N. Jachowicz,12

T. Katori,13 A. S. Kronfeld,6 K. Mahn,14 M. Martini,15 J. G. Morfın,6 J. Nieves,1 G. Perdue,6

R. Petti,16 D. G. Richards,17 F. Sanchez,18 T. Sato,19, 20 J. T. Sobczyk,21 and G. P. Zeller6

1Instituto de Fısica Corpuscular (IFIC), Centro MixtoCSIC-Universidad de Valencia, E-46071 Valencia, Spain

2Department of Physics, Aligarh Muslim University, Aligarh-202 002, India3Dipartimento di Fisica, Universita di Torino and INFN, Sezione di Torino, 10125 Torino, Italy

4Department of Physics, Colorado State University, Fort Collins, CO 80523, USA5Department of Physics, Hampton University, Hampton, Virginia, 23668 USA

6Fermi National Accelerator Laboratory, Batavia, IL 60510, USA7Center for Theoretical Physics, Laboratory for Nuclear Science, and Department of Physics,

Massachusetts Institute of Technology, Cambridge, MA 02139, USA8Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh PA 15260, USA

9Northwestern University, Evanston, IL 60208, USA10Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5 Canada

11Center of Neutrino Physics, Virginia Tech, Blacksburg, VA 24061, USA12Department of Physics and Astronomy,Ghent University, B-9000 Gent, Belgium

13Queen Mary University of London, London, UK14Department of Physics and Astronomy,

Michigan State University, East Lansing, MI 48824, USA15ESNT, CEA, IRFU, Service de Physique Nucleaire,

Universite de Paris-Saclay, F-91191 Gif-sur-Yvette, France16Department of Physics and Astronomy,

University of South Carolina, Columbia SC 29208, USA17Je↵erson Laboratory, Newport News, VA 23606, USA

18IFAE, Barcelona Institute Science and Technology, Barcelona, Spain19Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan

20J-PARC Branch, KEK Theory Center, KEK, Tokai, 319-1106, Japan21Institute of Theoretical Physics, University of Wroc law, Wroc law, Poland

(Dated: June 16, 2017)

The precise measurement of neutrino properties is among the highest priorities in fundamentalparticle physics, involving many experiments worldwide. Since the experiments rely on the interac-tions of neutrinos with bound nucleons inside atomic nuclei, the planned advances in the scope andprecision of these experiments requires a commensurate e↵ort in the understanding and modelingof the hadronic and nuclear physics of these interactions, which is incorporated as a nuclear modelin neutrino event generators. This model is essential to every phase of experimental analyses andits theoretical uncertainties play an important role in interpreting every result.

In this White Paper we discuss in detail the impact of neutrino-nucleus interactions, especiallythe nuclear e↵ects, on the measurement of neutrino properties using the determination of oscillationparameters as a central example. After an Executive Summary and a concise Overview of theissues, we explain how the neutrino event generators work, what can be learned from electron-nucleus interactions and how each underlying physics process—from quasi-elastic to deep inelasticscattering—is understood today. We then emphasize how our understanding must improve to meetthe demands of future experiments. With every topic we find that the challenges can be met onlywith the active support and collaboration among specialists in strong interactions and electroweakphysics that include theorists and experimentalists from both the nuclear and high energy physicscommunities.

aNeutrino Scattering Theory Experiment Collaboration http://nustec.fnal.gov

arX

iv:1

706.

0362

1v2

[hep

-ph]

15

Jun

2017

arX

iv:1

610.

0146

4v3

[nuc

l-th]

11

Apr

201

7

KEK-TH-1905, J-PARC-TH-0052

Towards a Unified Model of Neutrino-Nucleus

Reactions for Neutrino Oscillation Experiments

S.X. Nakamura1, H. Kamano2,3, Y. Hayato4, M. Hirai5,

W. Horiuchi6, S. Kumano2,3, T. Murata1, K. Saito7,3,

M. Sakuda8, T. Sato1,3, Y. Suzuki9,10

1 Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan2 KEK Theory Center, Institute of Particle and Nuclear Studies, KEK1-1, Ooho, Tsukuba, Ibaraki, 305-0801, Japan

3 J-PARC Branch, KEK Theory Center, Institute of Particle and Nuclear Studies,KEK and Theory Group, Particle and Nuclear Physics Division, J-PARC Center,203-1, Shirakata, Tokai, Ibaraki, 319-1106, Japan

4 Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo,Kamioka, Japan5 Nippon Institute of Technology, Saitama 345-8501, Japan6 Department of Physics, Hokkaido University, Sapporo 060-0810, Japan7 Department of Physics, Tokyo University of Science, Noda 278-8510, Japan8 Department of Physics, Okayama University, Okayama 700-8530, Japan9 Department of Physics, Niigata University, Niigata 950-2181, Japan10 RIKEN Nishina Center, Wako 351-0198, Japan

E-mail: [email protected]

September 30, 2016

Abstract. A precise description of neutrino-nucleus reactions will play a key role inaddressing fundamental questions such as the leptonic CP violation and the neutrinomass hierarchy through analyzing data from next-generation neutrino oscillationexperiments. The neutrino energy relevant to the neutrino-nucleus reactions spansa broad range and, accordingly, the dominant reaction mechanism varies across theenergy region from quasi-elastic scattering through nucleon resonance excitations todeep inelastic scattering. This corresponds to transitions of the effective degree offreedom for theoretical description from nucleons through meson-baryon to quarks.The main purpose of this review is to report our recent efforts towards a unifieddescription of the neutrino-nucleus reactions over the wide energy range; recent overallprogress in the field is also sketched. Starting with an overview of the currentstatus of neutrino-nucleus scattering experiments, we formulate the cross section tobe commonly used for the reactions over all the energy regions. A description of theneutrino-nucleon reactions follows and, in particular, a dynamical coupled-channelsmodel for meson productions in and beyond the ∆(1232) region is discussed in detail.We then discuss the neutrino-nucleus reactions, putting emphasis on our theoreticalapproaches. We start the discussion with electroweak processes in few-nucleon systemsstudied with the correlated Gaussian method. Then we describe quasi-elastic scatteringwith nuclear spectral functions, and meson productions with a ∆-hole model. Nuclear

arX

iv:1

403.

2673

v2 [

hep-

ph]

2 Se

p 20

14

Progress and open questions in the physics of neutrino cross sectionsat intermediate energies

L. Alvarez-Ruso,1 Y. Hayato,2 and J. Nieves1

1Instituto de Fısica Corpuscular (IFIC), Centro Mixto CSIC-Universidad de Valencia, E-46071 Valencia, Spain2University of Tokyo, Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan

New and more precise measurements of neutrino cross sections have renewed the interest in abetter understanding of electroweak interactions on nucleons and nuclei. This effort is crucial toachieve the precision goals of the neutrino oscillation program, making new discoveries, like theCP violation in the leptonic sector, possible. We review the recent progress in the physics ofneutrino cross sections, putting emphasis on the open questions that arise in the comparison withnew experimental data. Following an overview of recent neutrino experiments and future plans, wepresent some details about the theoretical development in the description of (anti)neutrino-inducedquasielastic scattering and the role of multi-nucleon quasielastic-like mechanisms. We cover notonly pion production in nucleons and nuclei but also other inelastic channels including strangenessproduction and photon emission. Coherent reaction channels on nuclear targets are also discussed.Finally, we briefly describe some of the Monte Carlo event generators, which are at the core of allneutrino oscillation and cross section measurements.

CONTENTS

I. Introduction 2

II. Recent and future oscillation and cross section experiments 2

III. Quasielastic and quasielastic-like scattering 6A. Quasielastic scattering on the nucleon 6B. Quasielastic scattering on nuclei 9

1. Electron scattering and the superscaling approach 122. Long-range RPA correlations 13

C. The role of 2p2h excitations 151. Multinucleon mechanisms and neutrino energy reconstruction 182. The high Eν > 1 GeV region 18

D. Quasielastic production of hyperons 20

IV. Weak pion production and other inelastic channels 20A. Introduction 20B. Pion production off nucleons 21C. Pion cross sections in nuclei and the MiniBooNE puzzle 23D. Other inelastic processes 26

1. Weak K and K production 262. NC photon emission 29

V. Weak coherent processes at intermediate energies 31A. Introduction 31B. CC and NC coherent π production reactions 33C. CC coherent kaon and antikaon production reactions 35D. NC coherent γ production reactions 36

VI. Montecarlo generators 38

VII. Concluding remarks 40

Acknowledgments 40

References 40

Comparisons and challenges of modern neutrino scattering experiments

(TENSIONS2016 report)

M. Betancourt,1 S. Bolognesi,2 J. Calcutt,3 R. Castillo,1 A. Cudd,3 S. Dytman,4 B. Eberly,5 A.P.Furmanski,6 R. Fine,7 J. Grange,8 L. Jiang,4 T. Katori,9 J. Kleckner,4 J. Kleyklamp,7 K. Mahn,3

B. Messerly,4 G. Perdue,1 L. Pickering,10 J. P. Stowell,11 J. Sobczyk,12 N. Suarez,4 H. Tanaka,13

R. Tayloe,14 R. T. Thornton,14 M. Wilking,15 C. Wilkinson,16 C. Wret,10 and G. P. Zeller1

1Fermi National Accelerator Laboratory, Batavia IL, USA2IRFU, CEA Saclay, Gif-sur-Yvette, France

3Michigan State University, Department of Physics and Astronomy, East Lansing, MI, 48824, USA4University of Pittsburgh, Department of Physics and Astronomy, Pittsburgh, PA 15260, USA

5SLAC National Accelerator Laboratory, Menlo Park, California, USA6University of Manchester, School of Physics and Astronomy, Manchester, UK

7University of Rochester, Department of Physics and Astronomy, Rochester, New York, USA8Argonne National Laboratory, Argonne, Illinois 60439, USA

9Queen Mary University of London, School of Physics and Astronomy, London, United Kingdom10Imperial College London, Department of Physics, London, United Kingdom

11University of She�eld, Department of Physics and Astronomy, She�eld, United Kingdom12University of Wroc law, Institute of Theoretical Physics, Wroc law, Poland

13University of Toronto, Department of Physics, Toronto, Ontario MSS 1A1, Canada14Indiana University, Bloomington, Indiana 47405, USA

15State University of New York at Stony Brook,Department of Physics and Astronomy, Stony Brook, New York, USA16University of Bern, Albert Einstein Center for Fundamental Physics,

Laboratory for High Energy Physics (LHEP), Bern, Switzerland(Dated: May 22, 2018)

Over the last decade, there has been enormous e↵ort to measure neutrino interaction cross sec-tions important to oscillation experiments. However, a number of results from modern experimentsappear to be in tension with each other, despite purporting to measure the same processes. TheTENSIONS2016 workshop was held at University of Pittsburgh July 24-31, 2016 and was sponsoredby the Pittsburgh High Energy Physics, Astronomy, and Cosmology Center (PITT-PACC). Thefocus was on bringing experimentalists from three experiments together to compare results in detailand try to find the source of tension by clarifying and comparing signal definitions and the analysisstrategies used for each measurement. A set of comparisons between the measurements using aconsistent set of models was also made. This paper summarizes the main conclusions of that work.

Corresponding Author: S. Dytman ([email protected])

CONTENTS

I. Introduction 3

II. Generator summary 5A. GiBUU overview 7B. GENIE overview 8C. NEUT overview 8D. NUANCE overview 9E. NuWro overview 10

III. QE-like measurements 10A. MiniBooNE 10B. MINERvA 11C. T2K 12D. QE-like measurement comparisons 13E. Model dependence 14F. QE-like generator considerations 18

arX

iv:1

805.

0737

8v1

[hep

-ex]

18

May

201

8

TOPICAL REVIEW

Neutrino-Nucleus Cross Sections for Oscillation

Experiments

Teppei Katori1

and Marco Martini2,3

1School of Physics and Astronomy, Queen Mary University of London, London, UK2ESNT, CEA, IRFU, Service de Physique Nucleaire, Universite de Paris-Saclay, F-91191Gif-sur-Yvette, France3Department of Physics and Astronomy, Ghent University, Proeftuinstraat 86, B-9000 Gent,Belgium

E-mail: [email protected], [email protected]

Abstract. Neutrino oscillations physics is entered in the precision era. In this contextaccelerator-based neutrino experiments need a reduction of systematic errors to the level ofa few percent. Today one of the most important sources of systematic errors are neutrino-nucleus cross sections which in the hundreds-MeV to few-GeV energy region are knownwith a precision not exceeding 20%. In this article we review the present experimental andtheoretical knowledge of the neutrino-nucleus interaction physics. After introducing neutrinooscillation physics and accelerator-based neutrino experiments, we overview general aspectsof the neutrino-nucleus cross sections, both theoretical and experimental views. Then, wefocus on these quantities in different reaction channels. We start with the quasielastic andquasielastic-like cross section, putting a special emphasis on multinucleon emission channelwhich attracted a lot of attention in the last few years. We review the main aspects of thedifferent microscopic models for this channel by discussing analogies and differences amongthem. The discussion is always driven by a comparison with the experimental data. Wethen consider the one pion production channel where data-theory agreement remains veryunsatisfactory. We describe how to interpret pion data, then we analyze in particular the puzzlerelated to the impossibility of theoretical models and Monte Carlo to simultaneously describeMiniBooNE and MINERvA experimental results. Inclusive cross sections are also discussed,as well as the comparison between the nµ and ne cross sections, relevant for the CP violationexperiments. The impact of the nuclear effects on the reconstruction of neutrino energy and onthe determination of the neutrino oscillation parameters is reviewed. A window to the futureis finally opened by discussing projects and efforts in future detectors, beams, and analysis.

Submitted to: J. Phys. G: Nucl. Phys.

Contents

1 Introduction 3

1.1 Neutrino oscillation physics . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Accelerator-based neutrino experiments . . . . . . . . . . . . . . . . . . . . 71.3 Neutrino fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Neutrino cross section generalities 14

2.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3 Matching Theory and Experiment . . . . . . . . . . . . . . . . . . . . . . . 22

arX

iv:1

611.

0777

0v1

[hep

-ph]

23

Nov

201

6

NS66CH08-Mosel ARI 14 September 2016 8:6

Neutrino Interactions withNucleons and Nuclei:Importance for Long-BaselineExperimentsUlrich MoselInstitut fur Theoretische Physik, Justus-Liebig-Universitat Giessen, Giessen D-35392,Germany; email: [email protected]

Annu. Rev. Nucl. Part. Sci. 2016. 66:171–95

First published online as a Review in Advance onJune 1, 2016

The Annual Review of Nuclear and Particle Scienceis online at nucl.annualreviews.org

This article’s doi:10.1146/annurev-nucl-102115-044720

Copyright c⃝ 2016 by Annual Reviews.All rights reserved

Keywordsneutrino, neutrino interaction, long-baseline experiments

AbstractThis article reviews our present knowledge of neutrino interactions withnucleons and discusses the interactions with nuclei, the target material of allpresently running and planned long-baseline experiments. I emphasize de-scriptions of semi-inclusive reactions and full descriptions of the final state;the latter are needed to reconstruct the incoming neutrino energy from final-state observations. I then discuss Monte Carlo generator and more advancedtransport-theoretical approaches in connection with experimental results onvarious reaction mechanisms. Finally, I describe the effects of uncertaintiesin the reconstruction of the incoming neutrino energy on oscillation param-eters. The review argues that the precision era of neutrino physics also needsprecision-era generators.

171

Ann

u. R

ev. N

ucl.

Part.

Sci

. 201

6.66

:171

-195

. Dow

nloa

ded

from

ww

w.a

nnua

lrevi

ews.o

rg A

cces

s pro

vide

d by

WIB

6097

- Jo

hann

es G

uten

berg

Uni

vers

ity o

f Mai

nz o

n 10

/02/

18. F

or p

erso

nal u

se o

nly.

From eV to EeV: Neutrino Cross-Sections Across Energy Scales

Joseph A. Formaggio⇤

Laboratory for Nuclear ScienceMassachusetts Institute of Technology,Cambridge, MA 02139

G. P. Zeller†

Fermi National Accelerator LaboratoryBatavia, IL 60510

(Dated: March 7, 2013)

Since its original postulation by Wolfgang Pauli in 1930, the neutrino has played aprominent role in our understanding of nuclear and particle physics. In the intervening80 years, scientists have detected and measured neutrinos from a variety of sources,both man-made and natural. Underlying all of these observations, and any inferenceswe may have made from them, is an understanding of how neutrinos interact withmatter. Knowledge of neutrino interaction cross-sections is an important and necessaryingredient in any neutrino measurement. With the advent of new precision experiments,the demands on our understanding of neutrino interactions is becoming even greater.The purpose of this article is to survey our current knowledge of neutrino cross-sectionsacross all known energy scales: from the very lowest energies to the highest that we hopeto observe. The article covers a wide range of neutrino interactions including coherentscattering, neutrino capture, inverse beta decay, low energy nuclear interactions, quasi-elastic scattering, resonant pion production, kaon production, deep inelastic scatteringand ultra-high energy interactions. Strong emphasis is placed on experimental datawhenever such measurements are available.

CONTENTS

I. Introduction 1

II. A Simple Case: Neutrino-Lepton Scattering 2A. Formalism: Kinematics 2B. Formalism: Matrix Elements 3C. Experimental Tests of Electroweak Theory 6D. Radiative Corrections and GF 7

III. Threshold-less Processes: E⌫ ⇠ 0� 1 MeV 8A. Coherent Scattering 8B. Neutrino Capture on Radioactive Nuclei 9

IV. Low Energy Nuclear Processes: E⌫ ⇠ 1-100 MeV 9A. Inverse Beta Decay 9B. Beta Decay and Its Role in Cross-Section

Calibration 10C. Theoretical Calculations of Neutrino-Deuterium

Cross-Sections 12D. Other Nuclear Targets 12E. Estimating Fermi and Gamow-Teller Strengths 14F. Experimental Tests of Low Energy Cross-Sections on

Nuclei 161. Hydrogen 162. Deuterium 163. Additional Nuclear Targets 18

G. Transitioning to Higher Energy Scales... 20

V. Intermediate Energy Cross Sections: E⌫ ⇠ 0.1� 20 GeV 21A. Quasi-Elastic Scattering 23B. NC Elastic Scattering 26

⇤ [email protected]† [email protected]

C. Resonant Single Pion Production 27D. Coherent Pion Production 31E. Multi-Pion Production 33F. Kaon Production 33G. Outlook 36

VI. High Energy Cross Sections: E⌫ ⇠ 20� 500 GeV 36A. Deep Inelastic Scattering 36

VII. Ultra High Energy Neutrinos: 0.5 TeV - 1 EeV 38A. Uncertainties and Projections 41

VIII. Summary 41

IX. Acknowledgments 42

References 42

I. INTRODUCTION

The investigation into the basic properties of the parti-cle known as the neutrino has been a particularly strongand active area of research within nuclear and particlephysics. Research conducted over the latter half of the20th century has revealed, for example, that neutrinoscan no longer be considered as massless particles in theStandard Model, representing perhaps the first signifi-cant alteration to the theory. Moving into the 21st cen-tury, neutrino research continues to expand in new direc-tions. Researchers further investigate the nature of theneutrino mass or explore whether neutrinos can help ex-plain the matter-antimatter asymmetry of the universe.At the heart of many of these experiments is the need

FERMILAB-PUB-12-785-E

Operated by Fermi Research Alliance, LLC under Contract No. De-AC02-07CH11359 with the United States Department of Energy.

15-19 October 2018 at Gran Sasso Science Institute!

I S S U E S I N K I N E M AT I C R E C O N S T R U C T I O N• Kinematic reconstruction:

• Observed as an “excess” of pionless ν-12C interactions at MiniBooNE

• Fits well with MA ~1.35 GeV CCQE interactions!

• Our understanding now is that these are ~3 things going on

• CCQE, MEC, pionless Δ excitation

• Kinematically different from single nucleon “quasi-elastic” interactions

• Modeling of these interactions is one of the biggest issues in T2K

• New kinematic handles, but still need modeling guidance

!17

S. Zeller, JLAB Workshop, May 2015

What Does This All Mean? 18

•  neutrino QE scattering is not so simple when scattering off nuclei - nuclear effects can significantly increase the interaction cross section at certain energies and for certain kinematics - idea that could be missing ~45% of σν in our simulations is a big deal

•  good news: expect larger event yields

•  bad news: need to understand the underlying physics

(1) impacts Eν determination

(2) effects will be different for ν vs. ν&   (at worse, could produce a spurious CP effect)" Lalakulich, Gallmeister, Mosel,1203.2935

ex: Ankowski et al., PRD 91, 033005 (2015); Nieves et al., 1310.7091, PRD 85, 113008 (2012); Mosel et al., 1204.2269; Martini et al. PRD 85, 093012 (2012); PRD 87, 013009 (2013); Lalakulich et al. PRC 86, 054606 (2012); Leitner/Mosel PRC 81, 064614 (2010)

leads to a reshaping of Eν"

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6Eν (GeV)

0

10

20

30

40

50

60

d(E ν,E

ν) (1

0-39 cm

2 /GeV

)

0.20.61.0

Eν (GeV)

FIG. 1: (Color online) The spreading function d(Eν , Eν) of Eq. (4) per neutron of 12C in the

case of electrons evaluated for three Eν values. The genuine quasielastic (dashed lines) and the

multinucleon (dotted lines) contributions are also shown separately.

III. APPLICATIONS

A. T2K

Here the situation is relatively simple as one deals with a long baseline experiment [10, 11]

with oscillation mass parameters already known to a good accuracy. We have pointed out

[4] the interest of the study for T2K of the muon events spectrum both in the close detector

and in the far detector since the two corresponding muonic neutrino beams have different

energy distributions. The study of the reconstruction influence on the electron events in

the far SuperKamiokande detector was performed in our Ref. [4], it is discussed again here

in our new reversed perspective. The two muon beams in the close and far detectors and

the oscillated electron beam at the far detector having widely different energy distributions,

the effect of the reconstruction is expected to differ in all three. The muon neutrino energy

distribution in the close detector, normalized with an energy integrated value of unity,

Φνµ(Eνµ) is represented in Fig. 2 as a function of Eνµ. At the arrival in the far detector it

is reduced by a large factor which depends on the oscillation parameters and its expression

8

-'.)*� "�� ;�� =9� ��"� � ��

�� '&�2��!�#(��

�� &�2��!�#(��'�� HI�� 4>6 � �� J�-� � 4K6�

��&�-�� )-��5�

�� ;.� ��

*�� *��-�*��&�

-'.)*� �� ;�� =9� ��"�� & ��*��

��&�� ;.� ��

�� &�

� �; ��'�� 4L6 ��

�� *��

�� !�$%�#�� 4;��&K6&�2��

�' �� 1�� 1�� ' �� E@��/��

��' � �� & � ��

5�� '��)-��*>��*��

�� 4E6�� $%��

��&�

�� ( ��-� ( � ��

� *�� -� B�5&>MF@&55�.�/�4;��&�E6�-�� '( � �� 1��

�� *��>E@��/�!��1 *�� #��

�� *��&�)��1��(�� 1�� *��

� �� "%�B�@(��N�(�� N��B�@&@O�F�@&%L�4;��&L6&

-'.)*� /�� !=�P=�#� � ��

�*�� $%�� (�

"%"�B�%��1��

�� & ��

�� 1��1��

��1�� &�

-'.)*��Q% ��

�� 1��'�� -�

*�� 5&>E(�5&%>(��5&@%�.�/&��Q%�*��%G&5(�%M&% � �� K5&> � � � � KM � �� !�J;#(�

��*��'&�� '�� 3��&

-'.)*� "�� ;�� =9� ��"� � ��

�� '&�2��!�#(��

�� &�2��!�#(��'�� HI�� 4>6 � �� J�-� � 4K6�

��&�-�� )-��5�

�� ;.� ��

*�� *��-�*��&�

-'.)*� �� ;�� =9� ��"�� & ��*��

��&�� ;.� ��

�� &�

� �; ��'�� 4L6 ��

�� *��

��

�� !�$%�#��

�� 4;��&K6&�2��

�' �� 1��

��1�� ' �� E@��/��

��' � �� & � ��

5�� '��)-��*>��*��

�� 4E6�� $%��

��&�

��

� � � �� ( ��-� ( � ��

� *�� -� B�5&>MF@&55�.�/�4;��&�E6�-�� '( � �� 1��

�� *��>E@��/�!��1 *��

�� #��

�� *��&�)��1��(��

��1�� *��

� �� "%�B�@(��N�(�� N��B�@&@O�F�@&%L�4;��&L6&

-'.)*� /�� !=�P=�#� � ��

�*�� $%�� (�

"%"�B�%��1��

�� & ��

�� 1��1��

��1�� &�

-'.)*��Q% ��

�� 1��'�� -�

*�� 5&>E(�5&%>(��5&@%�.�/&��Q%�*��%G&5(�%M&% � �� K5&> � � � � KM � �� !�J;#(�

��*��'&�� '�� 3��&

`M. Martini et al. Phys.Rev. D87 (2013) no.1, 013009

I S S U E S I N C A L O R I M E T R I C R E C O N S T R U C T I O N• Detectors react differently to different particles:

• Detection thresholds (tracking or particles below Cherenkov threshold

• neutrons (not detected or just “tagged” without energy reconstruction)

• Misidentified particles (e.g. π ↔ p)

• Electromagnetic showers (incomplete shower reconstruction)

• Particle content matters!

!18

Visible Energy in 𝜈 InteractionsX DUNE will see mixture of QE, RES, and DIS interactions

X Neutrino energy reconstruction via calorimetry (over kinematic reconstruction)

X Missing visible energy depends upon neutrino energy and is different for neutrino and antineutrino interactions

Lisa W. Koerner | CAPTAIN | 7/26/2017 7

• Large effect even for LAr

• “low thresholds”

• Fully active calorimetric target

L. Whitehead: CAPTAIN proposal to FNAL

18

will preferentially be the muon. When the muon and proton are collinear, use of dE/dx information mightallow the individual particles to be resolved. This information is not yet exploited by the pattern recognition,but is expected to yield improvements in the future.

Number of Hits210 310

Rec

onst

ruct

ion

Effic

ienc

y

0.0

0.2

0.4

0.6

0.8

1.0

µp

MicroBooNE Simulationp + −µ → Ar + µν

(a)

True Momentum [GeV]0 1 2 3

Rec

onst

ruct

ion

Effic

ienc

y

0.0

0.2

0.4

0.6

0.8

1.0

µp


(b)

[radians]p,µθ0 1 2 3

Rec

onst

ruct

ion

Effic

ienc

y

0.0

0.2

0.4

0.6

0.8

1.0

µp


(c)

Fig. 11: Reconstruction efficiencies for the target muon and proton in simulated BNB CC nµ quasi-elasticinteractions, (a) as a function of the numbers of true hits, (b) as a function of true momenta and (c) as afunction of the true opening angle between the muon and proton.

Figure 12 shows the completeness and purity of the reconstructed particles with the strongest matches tothe target muon and proton; the distributions strongly peak at one. Figure 12a shows that it is more difficult toachieve high reconstructed completeness for protons than for muons, as this can require collection of all hitsin complex hadronic shower topologies downstream of the main proton track. Figure 12b shows that there isa notable population of low purity protons, which are those that just satisfy the requirements to be matched tothe target proton, but which also track significantly into the nearby muon.

Figure 12c shows the displacement of the reconstructed neutrino interaction vertex from the true, generatedposition. It is found that 68% of events have a displacement below 0.74 cm. The 10.4% of events with adisplacement above 5 cm are mainly due to placement of the vertex at the incorrect end of one of the particletracks. This typically happens when there is a track of significant length with direction back towards thebeam source. The presence of decay electrons can also yield topologies where multiple, distinct particles areassociated with a specific point and can make the downstream end of the muon track appear to be a strongvertex candidate.

6.2 BNB CC resonance events: nµ +Ar ! µ�+ p+p+

The performance for three-track final states is studied using simulated BNB CC nµ interactions with resonantcharged-pion production. A specific subset of events is selected: those with one reconstructable muon, onereconstructable proton and one reconstructable charged pion in the visible final state. The true momentumdistributions for particles in selected BNB events peak at approximately 300 MeV for muons, 400 MeV forprotons and 200 MeV for charged pions. An example event topology is shown in Figure 13.

Table 2 shows that 95.1% of target muons, 86.8% of target protons and 80.9% of target pions result in asingle reconstructed particle; 70.5% of events are deemed correct, matching exactly one reconstructed particleto each target MCParticle. The performance for muons and protons is similar to that observed for the quasi-elastic events considered in Section 6.1. The fraction of muons with no matched reconstructed particles ishigher than for quasi-elastic events, because the muon and pion tracks can be merged into a single particle.The pions will sometimes interact, leading to a MCParticle hierarchy of a parent and one or more daughter,and this explains the frequency at which the target pion is matched to more than one reconstructed particle:if the parent and daughter are reconstructed as separate particles, with no corresponding reconstructed parent-daughter links, multiple matches to the target pion will be recorded.

20

As expected, target MCParticles are most likely to be merged into single reconstructed particles when thetargets are collinear. Figure 15 shows the completenesses and purities of the reconstructed particles with thestrongest matches to the target muon, proton and pion. The reported completeness is lowest for the target pionsbecause of the difficulty inherent in fully reconstructing the hierarchy of daughter particles, even when all theseparate particles are reconstructed.

Number of Hits210 310

Rec

onst

ruct

ion

Effic

ienc

y

0.0

0.2

0.4

0.6

0.8

1.0

µp

+π

MicroBooNE Simulation+π + p + −µ → Ar + µν

(a)

True Momentum [GeV]0 1 2 3

Rec

onst

ruct

ion

Effic

ienc

y

0.0

0.2

0.4

0.6

0.8

1.0

µp

+π


(b)

[radians])+π,p,µmin(θ0 1 2 3

Rec

onst

ruct

ion

Effic

ienc

y

0.0

0.2

0.4

0.6

0.8

1.0

µp

+π


(c)

Fig. 14: Reconstruction efficiencies for the target muon, proton and charged pion in simulated BNB CC nµinteractions with resonant pion production, (a) as a function of the numbers of true hits, (b) as a function oftrue momenta and (c) as a function of the true opening angles to the nearest-neighbour target MCParticle. Forinstance, for the muon in a given event, this would be the smaller of its true opening angles to the proton andthe charged pion.

Figure 15c shows the displacement of the reconstructed neutrino interaction vertex from the true, generatedposition. It is found that 68% of events have a displacement below 0.48 cm, whilst 7.3% of events have adisplacement above 5 cm. The vertex reconstruction performance is better than for the quasi-elastic eventsconsidered in Section 6.1. The presence of the pion track, whilst adding to the complexity of the events,provides additional pointing information indicating the position of the interaction vertex.

Completeness0.0 0.2 0.4 0.6 0.8 1.0

Frac

tion

of E

vent

s

4−10

3−10

2−10

1−10

1

µp

+π


(a)

Purity0.0 0.2 0.4 0.6 0.8 1.0

Frac

tion

of E

vent

s

4−10

3−10

2−10

1−10

1

µp

+π


(b)

R [cm]ΔVertex 0 1 2 3 4 5

Frac

tion

of E

vent

s

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14MicroBooNE Simulation

+π + p + −µ → Ar + µν

(c)

Fig. 15: Completeness (a) and purity (b) of the reconstructed particles with the strongest matches to the targetmuon, proton and charged pion in simulated BNB CC nµ interactions with resonant pion production and (c)the distance between generated and reconstructed 3D vertex positions.

μBooNE Eur.Phys.J. C78 (2018) no.1, 82 arxiv:1708.03135

T H O U G H T S O N G E N E R AT O R S• How can better theory be implemented in neutrino generators simulations?

• “Event generator”:

• Event generators do much more than calculate cross sections

• They must generate complete interactions

• We rely on them to evaluate detection efficiencies, misidentification of particles, etc.

• We can tailor analyses to focus on particular aspects (lepton kinematics) but we still need to model everything else

• “Frankenmodel”:

• We need to combine different models to give the “inclusive” model

• We have to ensure that the models are combined as consistently as possible (can be ugly!)

• Left and right hands can be different, but we can’t have two left hands

• New models need to find their place

• Because of topological migrations, etc. we cannot consider a model “in vacuo” to make contact with measurements

• Systematic Errors

• New models are as important for evaluating potential errors as they are for “improving” models

• A more realistic model may increase uncertainties!

!19

W H AT G O E S I N T H E G E N E R AT O R• Physics is not important

• traditionally, generators contain physics and calculate relevant cross sections

• It is not essential that they do this . . . .

• Some physics can be captured numerically (e.g. lookup table) or parametrized

• Some differential cross sections and other “corrections” can be reweighed

• the physics does not need to “live” in the generator

• Additionally, we need to be able to match data (particularly ND), not just new models

• If a new model is within reach of reweighting, etc. we can “incorporate” it this way.

• Physics is important

• We need a clear understanding of how a given model relates to everything else in the generator

• If we don’t, we need to account for that in the systematic error

• Physics guides systematic/modelling uncertainties

• How do we generate and propagate model variations through the generator?

!20

P R I S M * :• Neutrino energy spectrum steadily marches downs and narrows

as we go “off-axis” from the neutrino beam

• This variation gives us an independent handle on neutrino energy

• Data taken at different positions (spectra) can be combined (weighted and added, with oscillation probability!) to match far detector expectation

• Directly measured expected event properties (e.g. Erec)

• Pursued both from DUNE and Hyper-Kamiokande

• Pushes modeling uncertainties to higher order

• Need theoretical help:

• Keeping now “higher order” corrections small enough

• Probing robustness of method of this method and “traditional” approach

!21

(GeV)µν

E0 0.5 1 1.5

(Pea

k-no

rmal

ized

)Φ

0

0.5

1LBNF, Sept2017Engineered FHC

20 m Off axis

30 m Off axis

33 m Off axis

37 m Off axis

Fluxes Up to 35 m Off-Axis• Can still generally resolve bump below 2nd oscillation maximum for all values of

Δm322, although some fluctuations are seen in the ratio to the unoscillated fluxsin2θ23=0.4

Δm2 =

3.0x

10-3

Δm2 =

2.6x

10-3

Δm2 =

2.2x

10-3

sin2θ23=0.5 sin2θ23=0.6

*Precision Reaction Independent Spectrum Measurement

E L E C T R O N S C AT T E R I N G • e-A scattering is an essential test of models

• A few specific tests beyond the “general” program

• Tests of energy reconstruction

• Lepton-hadron (proton) Kinematics

• Outgoing hadron kinematics

• Final state interactions

• In each case, the techniques and tests should be performed with the generator in “e-A mode”

• Some generators fully support this

• Others may allow specific parts to be tested (e.g. FSI)

• 4 π spectrometer/detector

• It would be good to have a handle generally on all outgoing particles

• Matches closely the situation with neutrino detectors

• Comprehensive test of the model

!22

[MeV/c]+πp

210 310 410

[mb]

σ

10

210p+π

Total

QE Scatter

Inelastic

[MeV/c]-πp

210 310 410

[mb]

σ

0

20

40

60

80p-π

TotalQE ScatterInelasticSingle CX

FIGURE 2. p± on free proton scattering cross sections. Data from the PDG and fits by SAID [10].

Initial Momentum (MeV/c)+π0 200 400 600 800 1000 1200 1400 1600

(mb)

Rea

ctiv

eσ

0

500

1000

1500

2000

2500

3000

3500 1.2)×Pb (207 1.5)×Nb (93

1.5)×Fe (56 1.8)×Al (27

1.7)×O (16 C12

Initial Momentum (MeV/c)+π0 100 200 300 400 500 600 700

(mb)

Abs

orpt

ion

σ

0

200

400

600

800

1000

1200

1400 1.2)×Pb (207

1.5)×Nb (93

1.5)×Fe (56

1.8)×Al (27

1.7)×O (16

C12

FIGURE 3. Reactive (left) and absorption (right) cross sections for various target nuclei (tuned FSI).

(MeV)γE400 600 800

b/sr

)µ (

Ωdσd

20

40

60

80

100

120° = 28πγθ, +π →C 12γ

OldFSI

TunedFSI

(MeV)γE400 600 800

b/sr

)µ (

Ωdσd

20

40

60

80

100

120° = 44πγθ, -π →C 12γ

OldFSI

TunedFSI

FIGURE 4. Differential cross sections for p photoproduction off carbon, as a function of photon beamenergy. Data points from [11].

24

(GeV)T

pδ0.0 0.2 0.4 0.6 0.8 1.0

)-1

GeV

-1 N

ucle

on2

(cm

Tpδdσd

0123456789

1039−10×

0.0 0.2 0.4 0.6 0.8 1.0

40−10

39−10

38−10

NuWro 11qT2K Fit to Data

=23.12χ, N

SF w/2p2h=68.72χSF w/o 2p2h,

=172.32χ, N

RFG+RPA+2p2h=84.42χ,

NLFG+RPA+2p2h

(GeV)T

pδ0.0 0.2 0.4 0.6 0.8 1.0

Tpδdσd

σ1

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.0 0.2 0.4 0.6 0.8 1.0

2−10

1−10

1 T2K Fit to Data

=15.62χ, N

NuWro 11q SF+2p2h

=67.72χ), G

GiBUU 2016 (incl. 2p2h

=2.62χ, N

NEUT 540 LFG+2p2h

=36.32χ, N

NuWro 11q LFG+RPA+2p2h

(radians)Tφδ

0.0 0.5 1.0 1.5 2.0 2.5 3.0

)-1

radi

an-1

Nuc

leon

2 (c

mTφδdσd

0.00.51.01.52.02.53.03.54.04.55.0

39−10×

0.0 0.5 1.0 1.5 2.0 2.5 3.0

40−10

39−10

38−10NuWro 11q

T2K Fit to Data=13.52χ,

NSF w/2p2h

=48.92χSF w/o 2p2h, =85.52χ,

NRFG+RPA+2p2h

=77.32χ, N

LFG+RPA+2p2h

(radians)Tφδ

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Tφδdσd

σ1

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.0 0.5 1.0 1.5 2.0 2.5 3.0

2−10

1−10

1T2K Fit to Data

=9.72χ, N

NuWro 11q SF+2p2h

=46.22χ), G

GiBUU 2016 (incl. 2p2h

=6.42χ, N

NEUT 540 LFG+2p2h

=31.32χ, N


(radians)Tαδ0.0 0.5 1.0 1.5 2.0 2.5 3.0

)-1

radi

an-1

Nuc

leon

2 (c

mT

αδdσd

0.0

0.2

0.4

0.6

0.8

1.0

1.239−10×

NuWro 11qT2K Fit to Data

=18.02χ, N

SF w/2p2h=18.92χSF w/o 2p2h,

=57.52χ, N

RFG+RPA+2p2h=43.62χ,

NLFG+RPA+2p2h

(radians)Tαδ0.0 0.5 1.0 1.5 2.0 2.5 3.0

Tαδdσd

σ1

0.00

0.05

0.10

0.15

0.20

0.25T2K Fit to Data =16.62χ,

NNuWro 11q SF+2p2h

=33.72χ), G

GiBUU 2016 (incl. 2p2h =20.82χ, N

+2p2hNNEUT 5.4.0 LFG

=26.32χ, N


FIG. 15. The extracted di↵erential cross section as a function of the single transverse variables compared to: di↵erent initialstate models in the NuWro 11q simulation (left); shape only predictions from NuWro 11q and GiBUU 2016 (right). Althoughit is not shown the NEUT 5.3.2.2 SF prediction has an almost identical shape to the NuWro 11q SF prediction. The NuWro11q RFG+RPA prediction shown is similar to the NEUT model used as a starting point for T2K’s oscillation analyses. 2p2hN

indicates the Nieves et. al. model of Ref. [78] as implemented in NEUT or NuWro, while 2p2hG indicates an extrapolationfrom electron-scattering data implemented in the GiBUU 2016 simulation [82]. More details of these models can be found inSec. IVA. The inlays show the same comparisons on a logarithmic scale.

43

p (GeV)Δ0.5− 0.0 0.5 1.0 1.5

)-1 G

eV-1

Nuc

leon

2 c

m-3

9 (1

0 p

Δd σd

0

5

10

15

20

25

30

35

403−10×

0.5− 0.0 0.5 1.0 1.55−10

4−10

3−10

2−10

1−10

1

) < -0.6µθ-1.0 < cos(

p (GeV)Δ0.5− 0.0 0.5 1.0 1.5

)-1 G

eV-1

Nuc

leon

2 c

m-3

9 (1

0 p

Δd σd

05

101520253035404550

3−10×

0.5− 0.0 0.5 1.0 1.55−10

4−10

3−10

2−10

1−10

1

< 250 MeVµ

) < 0.0, pµθ-0.6 < cos(

p (GeV)Δ0.5− 0.0 0.5 1.0 1.5

)-1 G

eV-1

Nuc

leon

2 c

m-3

9 (1

0 p

Δd σd

0.000.010.020.030.040.050.060.070.080.090.10

0.5− 0.0 0.5 1.0 1.55−10

4−10

3−10

2−10

1−10

1

> 250 MeVµ

) < 0.0, pµθ-0.6 < cos(

p (GeV)Δ0.5− 0.0 0.5 1.0 1.5

)-1 G

eV-1

Nuc

leon

2 c

m-3

9 (1

0 p

Δd σd

0

10

20

30

40

50

603−10×

0.5− 0.0 0.5 1.0 1.55−10

4−10

3−10

2−10

1−10

1

< 250 MeVµ

) < 1.0, pµθ0.0 < cos(

p (GeV)Δ0.5− 0.0 0.5 1.0 1.5

)-1 G

eV-1

Nuc

leon

2 c

m-3

9 (1

0 p

Δd σd

0.000.050.100.150.200.250.300.350.400.450.50

0.5− 0.0 0.5 1.0 1.55−10

4−10

3−10

2−10

1−10

1

> 250 MeVµ

) < 0.8, pµθ0.0 < cos(

p (GeV)Δ0.5− 0.0 0.5 1.0 1.5

)-1 G

eV-1

Nuc

leon

2 c

m-3

9 (1

0 p

Δd σd

0

10

20

30

40

50

60

70

803−10×

0.5− 0.0 0.5 1.0 1.55−10

4−10

3−10

2−10

1−10

1

< 750 MeVµ

) < 1.0, 250 MeV < pµθ0.8 < cos(

p (GeV)Δ0.5− 0.0 0.5 1.0 1.5

)-1 G

eV-1

Nuc

leon

2 c

m-3

9 (1

0 p

Δd σd

0.000.010.020.030.040.050.060.070.080.090.10

0.5− 0.0 0.5 1.0 1.55−10

4−10

3−10

2−10

1−10

1

> 750 MeVµ

) < 1.0, pµθ0.8 < cos(

T2K Unfolded

=556.92χ, E

GENIE 2.12.4 BRRFG w/ 2p2h

=932.12χ, N

NuWro11q RFG+RPA w/ 2p2h

=454.42χ, N

NEUT 5.3.2.2 RFG+RPA w/ 2p2h

FIG. 29. The extracted di↵erential cross section as a function of the inferred and true proton momentum di↵erence in di↵erentmuon kinematic bins, within a restricted proton kinematic phase space, compared to GENIE 2.12.4, NuWro 11q and NEUT5.3.2.2 predictions which utilise an RFG or RFG+RPA nuclear model. GENIE’s RFG model also includes the empiricalcorrection from Bodek and Ritchie (BRRFG) [81]. The NEUT and GENIE predictions shown here are similar to those usedas a starting point for the T2K and NO⌫A experiment’s oscillation analyses respectively. More details of these models can befound in Sec. IVA. The 2p2h subscript indicates whether it is an implementation of the Nieves et. al. model of Ref. [78] (N)or the GENIE empirical 2p2h model (E). More details of these models can be found in Sec. IVA. Note that the first and lastbin in each plot is shortened for improved readability. The inlays show the same comparisons on a logarithmic scale.

C O N C L U S I O N S :• Current and upcoming neutrino oscillation continue to require better nuclear theory

• Numbers like “2%” are mentioned, but it is difficult to translate what that means

• Intimately coupled to near detector measurement strategy of at an oscillation experiment

• Strategy continues to evolve from past experiments . . . . ..

• Impressions:

• It’s great that theorists can engage both with e-A and ν-A calculations!

• ν-A:

• Community is still evolving how to report measurements, and this will continue to improve/evolve

• e-A:

• This is a very important area for more development

• specifically measurements that may be more directly applied towards ν-A issues

• Needless to say, the tightly controlled kinematics of e-A provide a much better probe for many nuclear effects

• A wide acceptance spectrometer can provide comprehensive tests of a model

• This kind of activity requires a convergence of particle and nuclear physicists . . . this seems like a good place!

!23

h.a.tanaka (slac/stanford) neutrino experiments

Documents