General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

The relevance of neutrino-nucleus interaction
models in T2K and SuperKamiokande
Guillermo D. Megias
RCCN, ICRR, University of Tokyo, Japan
University of Seville, Spain

ICRR Seminar, 10 February 2020
This project has received funding from the European Union’s Horizon 2020 researchand innovation programme under the Marie Sklodowska-Curie grant agreement No.
839481
1

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

2

1

General introduction
State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

2

SuSAv2-MEC implementation in MC event generators
Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

3

Further works and Next steps
Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Contents

3

1

General introduction
State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

2

SuSAv2-MEC implementation in MC event generators
Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

3

Further works and Next steps
Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption
G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Why ν-A interaction models are essential for oscillation experiments?
Discovery of neutrino oscillation → evidence for neutrino mass (mass hierarchy,
matter-antimatter asymmetry and CP violation processes)
Weak interaction → ν: probe to study hadronic and nuclear dynamics (axial
structure or strangeness content of the nucleons)
Astrophysical implications (supernovae, dark matter, sterile neutrinos)

4

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Why ν-A interaction models are essential for oscillation experiments?
Discovery of neutrino oscillation → evidence for neutrino mass (mass hierarchy,
matter-antimatter asymmetry and CP violation processes)
Weak interaction → ν: probe to study hadronic and nuclear dynamics (axial
structure or strangeness content of the nucleons)
Astrophysical implications (supernovae, dark matter, sterile neutrinos)

5

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Why ν-A interaction models are essential for oscillation experiments?
Discovery of neutrino oscillation → evidence for neutrino mass (mass hierarchy,
matter-antimatter asymmetry and CP violation processes)
Weak interaction → ν: probe to study hadronic and nuclear dynamics (axial
structure or strangeness content of the nucleons)
Astrophysical implications (supernovae, dark matter, sterile neutrinos)

6

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Why ν-A interaction models are essential for oscillation experiments?

Ample experimental program to characterize and determine ν oscillations
Long-Baseline accelerators: T2K, SK, HK (J-PARC), MINERνA, NOvA, DUNE (FermiLab).
Detection of neutrino oscillations in facilities at hundreds of kms from the neutrino source.
Main aims: direct measurement of oscillation parameters (mixing angles, CPV, NMH) or data
production to reduce systematics (mostly ν-A scattering and nuclear medium effects).

7

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Long-baseline accelerator neutrino oscillation experiments
Neutrinos produced as secondary decay products of hadrons (π, K ) generated in primary
reactions of p with nuclei ⇒ broad energy beam.

Experimental difficulties:➠ The neutrino flux: broad energy distribution around a maximum → True energy for a detected
event is unknown. Inaccuracy in the meson flux also affects the ν-flux prediction.
➠ To reduce flux uncertainties, two identical detectors are employed. Near Detector placednear the neutrino production region and Far Detector where a maximum/minimum oscillation
is expected. MonteCarlo simulations are also employed to reconstruct the neutrino energy foreach individual event detected.
➠ The reliability of ν-oscillation experiments depends on a precise determination of the ν-nucleus
cross section measurements and on the ν flux at ND.
8G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

T2K systematics today and needs for HyperK and DUNE
➠ Precise knowledge of ν properties require accurate ν-A interaction models.
➠ Global experimental systematics in T2K are around a 4% (7%) for νµ (νe ) reactions and are dominated by flux andcross section uncertainties (3%) ⇒ It is essential to improve description of neutrino interaction physics.
➠ Oscillation measurements in future experiments (HyperK, DUNE) aim to ∼ 1 − 3% systematic uncertainty anddetermine mass hierarchy and δCP violation phase.

➠ A reduction of 2% would improve CPV sensitivity from 5σ to 6σ while reducing by two experimental exposure.
➠ Need for development and implementation of sophisticated neutrino interaction models in event generators.
➠ This can help to understand ν/ν̄ asymmetry, to improve hadron detection efficiency, the characterization of FS
particles or the extrapolation from the usual 12 C target analysis to other nuclei (16 O [T2K ND280 upgrade], 40 Ar, etc.)
9

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

T2K systematics today and needs for HyperK and DUNE
➠ Precise knowledge of ν properties require accurate ν-A interaction models.
➠ Global experimental systematics in T2K are around a 4% (7%) for νµ (νe ) reactions and are dominated by flux andcross section uncertainties (3%) ⇒ It is essential to improve description of neutrino interaction physics.
➠ Oscillation measurements in future experiments (HyperK, DUNE) aim to ∼ 1 − 3% systematic uncertainty anddetermine mass hierarchy and δCP violation phase.

➠ A reduction of 2% would improve CPV sensitivity from 5σ to 6σ while reducing by two experimental exposure.
➠ Need for development and implementation of sophisticated neutrino interaction models in event generators.
➠ This can help to understand ν/ν̄ asymmetry, to improve hadron detection efficiency, the characterization of FS
particles or the extrapolation from the usual 12 C target analysis to other nuclei (16 O [T2K ND280 upgrade], 40 Ar, etc.)
9

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Challenges for nuclear models
Significant improvements of nuclear models by theorists are essential andshould include:10

1

The development of a unified model of nuclear structure giving theinitial kinematics and dynamics of nucleons bound in the nucleus.

2

Providing total kinematics of leptons and outgoing particles for all
possible FS.

3

Improving our understanding of the relevance of FSI (rescattering ofproduced hadrons in the nucleus) and initial nucleon-nucleon correlations.

4

Expressing these improvements of the nuclear model in terms thatcan be successfully incorporated in the simulation of neutrino eventsby neutrino event generators.
G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Inclusive vs. Semi-inclusive reactions*Adapted from Bill Donnelly’s talk at ECT* 2018 workshop “Modeling neutrino-nucleus interactions”
11

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Inclusive vs. Semi-inclusive reactions*Adapted from Bill Donnelly’s talk at ECT* 2018 workshop “Modeling neutrino-nucleus interactions”
11

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Inclusive vs. Semi-inclusive reactions*Adapted from Bill Donnelly’s talk at ECT* 2018 workshop “Modeling neutrino-nucleus interactions”
11

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Inclusive vs. Semi-inclusive reactions*Adapted from Bill Donnelly’s talk at ECT* 2018 workshop “Modeling neutrino-nucleus interactions”
11

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Nuclear effects in neutrino-nucleus reactions
Neutrino-nucleus interactions over the whole experimental range (of the order of 100sof MeV up to 10s of GeV) implies a large variety of nuclear effects: quasielastic (QE),
multinucleon excitations (2p-2h MEC), meson production via nucleon resonances (∆)
and deep inelastic processes. At these kinematics, charged-current quasielastic (CCQE)
ν-A scattering is the dominant interaction in oscillation experiments (& 40%).

12

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Nuclear response in terms of the energy transfer

13

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Nuclear response in terms of the energy transfer

14

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Nuclear response in terms of the energy transfer

15

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Nuclear response in terms of the energy transfer

16

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Nuclear effects and disentangling of final state events
CCQE, CCQE-like, CC0π events and FSI effects
CC0π = CCQE-like without subtraction of π absorption background17

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Neutrino-Nucleus Interaction Models in the market➠ Relativistic Fermi Gas (RFG): nucleus as a system of non-interacting on-shell nucleons. Bound nucleons below pF .
Too simple. Used for most 2p2h models. Easily extendable to all nuclei.

➠ Local Fermi Gas (LFG): RFG extension with local density approx (n(p) depends on nucleon position, nuclear finite
size effects). Used in NEUT and GENIE. Bad agreement with (e,e’) data.

➠ Spectral Function (SF): based on the factorization ansatz (σν−N · S(p, Eb )) where S represents the probability offinding a nucleon (p, Eb ) within the nucleus. Semiphenomenological based on (e,e’p) data, mean-field calculations and LFG. Shellmodel. Non relativistic. Implemented in NEUT.

➠ Random Phase Approximation (RPA): can be added to the top of LFG/SF/HF/MF to incorporate NN correlations. Very good description at low q0 , Q 2 but not relativistic.

➠ Relativistic Mean Field (RMF, ED-RMF, SuSAv2): Fully relativistic shell model with accurate descriptionof nuclear dynamics and FSI effects. Bound nucleons: self-consistent Dirac-Hartree solutions, derived within a RMF Lagrangianwith local relativistic potentials (S+V) fitted to saturation properties of nuclear matter, radii and nuclear masses. Valid for 1p1h
and SPP (π), easily extendable to all nuclei.
-1

10

FSI, RMF

RFG

n

3

n(p) [fm ]

-3

10

LFD

HO
Jastrow-5

no FSI,

10

RMF
no FSI,
projected

CDFM

-7

10

0

1

2

3

4

-1

p [fm ]

18

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Neutrino-Nucleus Interaction Models in the market➠ Relativistic Fermi Gas (RFG): nucleus as a system of non-interacting on-shell nucleons. Bound nucleons below pF .
Too simple. Used for most 2p2h models. Easily extendable to all nuclei.

➠ Local Fermi Gas (LFG): RFG extension with local density approx (n(p) depends on nucleon position, nuclear finite
size effects). Used in NEUT and GENIE. Bad agreement with (e,e’) data.

➠ Spectral Function (SF): based on the factorization ansatz (σν−N · S(p, Eb )) where S represents the probability offinding a nucleon (p, Eb ) within the nucleus. Semiphenomenological based on (e,e’p) data, mean-field calculations and LFG. Shellmodel. Non relativistic. Implemented in NEUT.

➠ Random Phase Approximation (RPA): can be added to the top of LFG/SF/HF/MF to incorporate NN correlations. Very good description at low q0 , Q 2 but not relativistic.

➠ Relativistic Mean Field (RMF, ED-RMF, SuSAv2): Fully relativistic shell model with accurate descriptionof nuclear dynamics and FSI effects. Bound nucleons: self-consistent Dirac-Hartree solutions, derived within a RMF Lagrangianwith local relativistic potentials (S+V) fitted to saturation properties of nuclear matter, radii and nuclear masses. Valid for 1p1h
and SPP (π), easily extendable to all nuclei.

➠ Most models give ∼ ν-A inclusive predictions (lepton kin.). Main differences
for hadron kin. due to nuclear effects.
Semi-inclusive processes: Next step intheoretical ν interaction community.

19

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Contents

20

1

General introduction
State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

2

SuSAv2-MEC implementation in MC event generators
Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

3

Further works and Next steps
Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption
G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Connection between ν-A and e-A reactionsl = e, µ, τExperimental conditions are different:➠ (e, e ′ ): Ee is well determined and different channels can be clearly identified by knowing
the energy and momentum transfer➠ CC(νl , l): Eν is broadly distributed in the neutrino beam and different channels andnuclear effects can contribute to the same kinematics of the outgoing lepton
From a theoretical framework, neutrino- and electron-nucleus scattering are obviously connected (CVC) to each other and a reliable model must be able to describe both processes.
Neutrinos can probe both the vector and axial nuclear responses, unlike electrons which
are only sensitive to the vector response.
=⇒ Although not sufficient to fully constrain neutrino cross sections, electron scattering constitutes a necessary test and a solid benchmark for nuclear models.
21

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Theoretical description: ν-A inclusive cross section
χ = +(−) ≡ νµ (ν̄µ )Double differential cross sectiondσ
dkµ dΩµ

=|~kl | GF2
e µν = σ0 Fχ2ηµν We|~kν | 4π 2

;

σ0 =

GF2 cos θc

l

χ

2π 2

2 

kµ cosθ̃
2

2

Nuclear structure information
Fχ2 = VL RL + VT RT + χ [2VT ′ RT ′ ]VL RL = VCC RCC + 2VCL RCL + VLL RLL
RL = RLVV + RLAA ; RT = RTVV + RTAA ; RT ′ = RTVA′
Nuclear responses RK can be calculated in terms of
the single nucleon ones GK and the nuclear
dependence of the model ⇒ RK ≈ F (nuclear ) · GK
Comparison with (e, e ′ ) reactions



22

dσ
dkµ dΩ

= σMott vL RLVV + vT RTVV

G. D. Megias: megias@icrr.u-tokyo.ac.jp

;σMott =

α2 cos2 θ/2
4Ei sin4 θ/2

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Contents

23

1

General introduction
State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

2

SuSAv2-MEC implementation in MC event generators
Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

3

Further works and Next steps
Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption
G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

SuperScaling Approach (SuSA)(see G.D. Megias’ Thesis for details)➠ The analysis of the large amount of existing (e, e ′ ) data at different kinematics is a solid
benchmark to test the validity of theoretical models for neutrino reactions as well as to study
the nuclear dynamics. The SuperScaling Approach exploits universal features of lepton-nucleus
scattering to connect the two processes.
In inclusive QE scattering we can observe:✰ Scaling of 1st kind (independence on q)✰ Scaling of 2nd kind (independence on Z )SuperScaling=⇒f (ψ) ≡ f (q, ω) ∼f (ψ′ ) = kF

σQE (nuclear )effects
σsingle nucleon (no nuclear )effects

d2σ
dΩe dω



exp

σMott (vL GLee + vT GTee )′′Good superscaling behavior at ψ ′ < 0 (below QE peak). At
higher kinematics (ψ ′ ), other contributions beyond QE andIA (2p2h, ∆, etc.) can play an important role and scaling isbroken.
24

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Separate L/T scaling functions(see G.D. Megias’ Thesis for details)➠ The analysis of the large amount of existing (e, e ′ ) data at different kinematics is a solid
benchmark to test the validity of theoretical models for neutrino reactions as well as to study
the nuclear dynamics. The SuperScaling Approach exploits universal features of lepton-nucleus
scattering to connect the two processes.
In inclusive QE scattering we can observe:✰ Scaling of 1st kind (independence on q)✰ Scaling of 2nd kind (independence on Z )=⇒SuperScaling

fL = kF RL /GL
fT = kF RT /GT
Scaling violations in
the T channel ⇒2p-2h MEC, correlations, ∆-resonance⇒ Mainly transverse

25

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models➠ RFG as a natural starting point to examinate the scaling concept


d2σ
AA
AA
AA
= σ0 Fχ2 = σ0 VL RLVV + VCC RCC+ 2VCL RCL+ VLL RLL
+ VT RT + χVT ′ RT ′dΩl dω
′′d2σ= σMott (vL RLee + vT RTee )dΩe dω

RKQE ⇒ W µν =Z

3N MN24πkF3d 3p× θ(kF − |p|)θ(|p + q| − kF )E (p)E (p + q)
µν
fs.n.
×δ(ω − [E (p + q) − E (p)]) × W(Pi + Q, Pi )RKQE =

1
N
1
fRFG (ψ ′ )RKs.n. ≡fRFG (ψ ′ )GK ,
kF
2κD
kF
fRFG (ψ ′ ) =

′

ψ ≡

1

p q
ξF

26

K = CC , CL, LL, T , T ′3(1 − ψ ′2 )θ(1 − ψ ′2 )4λ′ − τ ′p(1 + λ′ )τ ′ + κ

τ ′ (τ ′ + 1)

G. D. Megias: megias@icrr.u-tokyo.ac.jp′′

λ = ω /(2MN ) ,κ = q/(2MN )′τ =κ −λω = ω − Eshift ,

′

2

′2

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Scaling functions can be extracted from experimental data or different nuclear models.

RKQE =

N
1
1
fmodel (ψ′ )U s.n. ≡fmodel (ψ′ )GK ,
kF
2κD K
kF

K = CC , CL, LL, T , T ′Scaling functions obtained from the cross section:ff

QE (ν)QE (e,e ′ )d2σdΩe dω
= kF′′
σMott (vL GLee + vT GTee )d2σdΩl dω
= kF
AA + 2V G AA + V G AA + v G + χv ′ G )σ0 (VL GLVV + VCC GCC
CL CL
LL LL
T T
T
T′

Specific scaling functions for the individual channels:
fK = kF

27

G. D. Megias: megias@icrr.u-tokyo.ac.jp

RKGK
The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Separate L/T scaling functions
fL = kF RL /GL
fT = kF RT /GT
Scaling violations in
the T channel ⇒2p-2h MEC, correlations, ∆-resonance⇒ Mainly transverse

SuSA model: a semiphenomenological approach✪ Extracted from the (e, e ′ ) longitudinal scaling data
✪ Assumption fL (ψ) = fT (ψ) (as in most IA models)

′

′

ee
✪ It is experimentally observed fTee,exp > fL,exp(15-20%)28

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Testing SuperScaling for 12 C(e, e ′ ) in different nuclear models

The SuSAv2 model

PRC90, 035501 (2014)

PRD94, 013012 (2016)✪ SuSAv2 model: lepton-nucleus reactions adressed in the SuperScaling Approach and based on
Relativistic Mean Field (RMF) theoretical scaling functions (FSI) to reproduce nuclear dynamics.
′ee ).
✪ RMF: Good description of the QE (e, e ′ ) data and superscaling properties (fL,exp
RMF predicts fT > fL (∼ 20%) as a pure relativistic effect (FSI with the residual nucleus).
Strong RMF potentials at high q3 are corrected by RPWIA and q-dependent blending function.

29

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Inclusive 12 C(e, e ′) cross sectionso

PRD 94, 013012 (2016)oE=560 MeV, θ=60 , qQE=508 MeV/c

E=680 MeV, θ=36 , qQE=402.5 MeV/c

5000

2p-2h MEC
Inelastic
QE
Total

30000
d σ/dΩdω (nb/GeV/sr)

4000
3000

20000

2000

2

10000

1000
0
0

0.1

0.2
ω (GeV)

0.3

0
0

0.4

o

ω (GeV)

0.3

0.4

0.5

150

E=3595 MeV, θ=25 , qQE=1640 MeV/c

400
100
300
200
50

2

d σ/dΩdω (nb/GeV/sr)

0.2o

E=560 MeV, θ=145 , qQE=795 MeV/c

500

0.1

100
0

30

0.2

0.3
ω (GeV)

0.4

0.5

G. D. Megias: megias@icrr.u-tokyo.ac.jp

0
0.4

0.6

0.8
ω (GeV)1

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Inclusive 12 C(e, e ′ ) cross sections with different models (J.Sobczyk’s talk at NUINT18)

31

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

Inclusive 16 O(e, e ′) and 40Ca(e, e ′) cross sections
16

o

40

O, Ei=737MeV, θ=37.1

oCa, Ei=841MeV, θ=45.5

30000

15000

25000
20000

10000

15000
10000

5000

5000
0
0

0.1

0.2

0.3

0.4

16

0.5

0
0

0.6

0.1

o

0.2

0.3

0.4

40

O, Ei=1080MeV, θ=32

0.5

0.6

o

Ca, Ei=560MeV, θ=60

20000

QE
Inelastic
2p-2h
Total

15000
15000
10000
10000
5000

0
0

32

5000

0.2

0.4
ω (GeV)

0.6

0.8

G. D. Megias: megias@icrr.u-tokyo.ac.jp

0
0

0.1

0.2
0.3
ω (GeV)

0.4

0.5

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models(e, e ′) JLab data vs. SuSAv2-MEC

33

G. D. Megias: megias@icrr.u-tokyo.ac.jp

PRC99, 042501(R), 2019

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

dσ/dpµdcosθµ(10 cm /GeV/nucleon)

2

8
6

T2KoldT2Kpreliminary, taken from C. Riccio at NuInt2018
2p2h
1p1h
Total

8
6
4

4
2

2
0.2

0.4

1
0.6 0.8pµ (GeV)

1.2

0
0

1.4

1.50 < p|| < 2.00

0.4

QE-like datao2p-2h MEC (θµ<20 )o

QE (CH, θµ<20 )Total
CCQE datapµ (GeV)2

310.00 < p|| < 15.00

0.3

2

0.2

2

10

1

d σ/dpTdp||

0
0

15

d σ/dpTdp||

MINERνA ν̄µ -CH

0.94 < cosθµ < 0.98

10

20

0.1

5

0
0

34

0.85 < cosθµ < 0.90

12

-39

T2K CC0π νµ −C8 H8Comparison with CC0π νµ -nucleus data

0.5

pT (GeV/c)

1

G. D. Megias: megias@icrr.u-tokyo.ac.jp

1.5

0
0

0.5

pT (GeV/c)

1

1.5

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

Contents

35

1

General introduction
State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

2

SuSAv2-MEC implementation in MC event generators
Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

3

Further works and Next steps
Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption
G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

SuSAv2-MEC implementation in MC event generators arXiv:1905.08556➲ Implemented the SuSAv2 1p1h and 2p2h models in GENIEv3 for both (e, e ′ ) and CC νµ scattering. Next step: Implementation in NEUT.
➲ New 1p1h and 2p2h model calculated using pre-computed hadron tensors for (e, e ′ ) and CC ν reactions. The hadrontensor elements are stored in tables in terms of q0 and q3 in bins of 5 MeV between 0 and 2 GeV (no limits). Implementationof the hadron tensor components using the SuSA formalism (Rosenbluth-like decomposition: L and T components, V and A
channels).
➲ Global factor / lepton tensor are easily calculated - shared by other models➲ Use a GENIE’s bilinear interpolation function to evaluate specific q0 , q3 values➲ Hadron tensors are initially provided for a few targets (C and O so far, may add others). Can easily scale to other nuclei.

36

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevanceof ν-Atalkinteraction
in T2K
and SK*Adaptedfrom S. Dolan’s
at GENIEmodels
Meeting(02/2019)

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

1p1h implementation: RMF and SuSAv2◮ 1st step: Implementing SuSAv2 hadron tensor Wµν (q, ω) + LFG on the top and comparison with original SuSAv2 model◮ 2nd step: Adding SuSAv2 formulas, parameters and parametrization of scaling functions
into generators to speed up simulations and to allow reweighting (MAQE , pF , Eb , etc.)◮ 3rd step: Introducing RMF nucleon momentum distribution in generators to fully test
factorization approach.
◮ 4th step: Implement full RMF semi-inclusive model in generators-1

10

FSI, RMF

RFG

n

3

n(p) [fm ]

-3

10

LFD

HO
Jastrow-5

no FSI,

10

RMF
no FSI,
projected

CDFM

-7

10

0

1

2

3

4

-1

p [fm ]

37

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

2p-2h MEC for (e, e ′) and CC ν reactions

PRD91, 073004 (2015)µν✪ The numerical evaluation of the hadronic tensor W2p2h(RK2p2h ) is performed in the RFG modelin a fully relativistic way without any approximation. It can be easily extended to all nuclei.

✪ Separation into pp, nn and np pairs in the FS ⇒ also valid for N 6= Z (40 Ar, 56 Fe, 208 Pb)✪ It is computationally non-trivial and involves 7D integrals of thousands of terms (+1 forν-flux) ⇒ High increase of the computing time of RK2p2h ⇒ Parametrization/Implementation✪ Accurate implementation of np/pp pairs for the 2p2h channel using separate hadron tensors
for np and pp pairs.

Other 2p2h models neglect direct/exchange interference terms ⇒ strongly affects np/pp ratio
by a factor ∼ 2 (PRC94:054610,2016) ⇒ Implications in nucleon multiplicity and hadron Ereco
38

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

Comparison of SuSAv2-MECGenie with NievesGenie 2p2h

arXiv:1905.08556

Differences in np/pp separation are mostly related to the treatment of 2p2h direct/exchangeinterference terms (absent in Nieves model) → strongly affects np/pp ratio by a factor ∼2 (PRC94:054610,2016) ⇒ Implications in nucleon multiplicity and hadron Ereco
39

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

Contents

40

1

General introduction
State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

2

SuSAv2-MEC implementation in MC event generators
Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

3

Further works and Next steps
Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption
G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

41

χ2 = 255.8 (67 bins)

T2K CC0π νµ −12 C data vs. SuSAv2-MECGENIESuSAv2-MEC implementation in GENIE: Validation plots (T2K CC0π)

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

42

SuSAv2-MEC
NievesT2K CC0π νµ −12 C inclusive data

Comparison between 1p1h+2p2h models in generators arXiv:1905.08556

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

43

χ2= 171.87
RMF+GENIE(SusAv2-2p2h+pi-abs)

χ2= 168.92 (60 bins)
SuSAv2-MEC GENIE

T2K CC0π νµ −12 C semi-semi-inclusive data (0p>500 MeV)SuSAv2-MEC in GENIE: Validation plots (T2K CC0πNp, 0p > 500 MeV)

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

44

SuSAv2-MEC
NievesT2K CC0π νµ −12 C semi-semi-inclusive data (0p>500 MeV)

Comparison between 1p1h+2p2h models in generators arXiv:1905.08556

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

Contents

45

1

General introduction
State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

2

SuSAv2-MEC implementation in MC event generators
Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

3

Further works and Next steps
Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption
G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

CCQE ν inclusive cross sections with different models
Different models can give similar inclusive CS but different semi-inclusive ones (more sensitive
to nuclear-medium effects) ⇒ very different ν oscillation analyses (which relies on semi-inclusive predictions)
THE FUTURE IS SEMI-INCLUSIVE ⇒ Best way to produce consistent theory-vs-data comparison. Less dependency on simulations and deeper analysis of model nuclear effects.

PROBLEM: Current lack of full semi-inclusive models and proper implementation in generators.
Semi-inclusive ⇒ Inclusive (but not viceversa) ⇒ Factorization approach is questionable.
46

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

Different models can give similar inclusive CS but different semi-inclusive ones (more sensitive to nuclear-medium effects) ⇒ very different ν oscillation analyses (which relies on semi-inclusive predictions)
PROBLEM: Current lack of full semi-inclusive models and proper implementation in generators.
Semi-inclusive ⇒ Inclusive (but not viceversa) ⇒ Factorization approach is questionable.
- QE and 2p2h inclusive: We only need W µν (q, ω) or, equivalently, W µν (pµ , cos θµ )- QE semi-inclusive : 5D diff. CS (θµ , pµ , pN , θN , φN ) - 2p2h semi-inclusive: 9D diff. CS.
Double differential inclusive cross sectionhdσdkµ dΩµi= σ0χ = +(−) ≡ νµ (ν̄µ )Double differential semi-inclusive cross section

47



VCC RCC + 2VCL RCL + VLL RLL + VT RT + χ 2VT ′ RT ′

χ

G. D. Megias: megias@icrr.u-tokyo.ac.jpχ = +(−) ≡ νµ (ν̄µ )The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

Testing the factorization approach on CC0πNp T2K data
Comparison of RMF “semi-semi-inclusive” prediction and GENIE SuSAv2 implementation to T2K data (µ kinematics with restriction of pproton < 500 MeV/c).

Curves - theory
Histograms - GENIE
Blue: With cut in pproton
Dotted line - no FSI in GENIE
Factorization approach does
not seem a bad approximation
for semi-semi-inclusive analysis(SuSAv2 + LFG on the top(Genie) vs. RMF code. To bedone with RMF on the top).
What about more semiinclusive measurements?

48

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

Comparison of semi-inclusive T2K STV data with SuSAv2-MECGenie + BS π abs and Valencia
model + BS π abs (arXiv:1905.08556). Goodness of fit: For δpT : χ2SuSA = 20.5, χ2Valencia = 27.1.
For δαT : χ2SuSA = 45.3, χ2Valencia = 31.4. For δφT : χ2SuSA = 40.1, χ2Valencia = 36.8.

Workinprogressto test the factorization approach insemi-inclusive
measurements when RMF
momentum distribution is implemented.

49

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption

Contents

50

1

General introduction
State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

2

SuSAv2-MEC implementation in MC event generators
Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

3

Further works and Next steps
Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption
G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption

Why is the C to O extrapolation important?
➲ T2K ND280 is primarily based on C8 H8 (also containing H2 O active target regions), whereas
the FD is water-based.
➲ ND measurements on C8 H8 are essential to constrain flux and CS uncertainties, but C/Odifferences are not well constrained (one of the dominant remaining systematic uncertainties).
➲ Proper analysis of CC ν interactions on water are essential for T2K ND and FD but also to
future water-based atmospheric and LB experiments (HyperK) ⇒ ν−12 C / ν−16 O differences
will be carefully studied in this project for 1p1h and 2p2h.
RMF (1p1h) could reveal C/O differences due todifferent binding energy and shell effects, massof the residual nucleus, FSI and Coulomb distortions, etc.

The implementation of 2p2h np and pp pairs
can have an impact on this issue. 2p2h directexchange interference terms can imply a factor 2
in the np/pp ratio with regard to other models⇒ Relevant for T2K and HyperK projects where
FS nucleon multiplicity is detected and for SK-Gd
where Gd salts are added to the H2 O target to
improve n detection and sensitivity to discover
CPV via ν/ν̄ differences, since the latter produce more neutrons.

51

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption

Low-energy effects at T2K CC0π 0p >500 MeV/carXiv:1905.08556

dσ/dpµ(10 cm /GeV/nucleon)

0.850 < cosθµ < 0.900
0.5

2

0.3

2

0.2

-39

0.4

-39

dσ/dpµ(10 cm /GeV/nucleon)

Low-energy effects and scaling violations are only appreciable at very forward angles (low q3 , q0
values). RMF is more accurate than SuSAv2 at these kinematics.

0.1
0
0

0.2

0.4

1
0.6 0.8pµ (GeV)

1.2

1.4

0.08

0.980 < cosθµ < 1.000
2p2hSuSAv2-GENIE
π-absGENIE
TotalGENIE
TotalRMF+GENIE

0.07
0.06
0.05

2p2h+π-abs

0.04
0.03
0.02
0.01
0
0

2

4
pµ (GeV)68

Low-energy nuclear effects and its proper description can have an important effect in
the C to O extrapolation, which is essential for T2K and HK.
52

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption

dσ/dpµdcosθµ(10 cm /GeV/nucleon)

T2K CC0π νµ −H2 O cross sections
0.000 < cosθµ < 0.600

20

T2K ( O)SuSAv2-2p2h
SuSAv2-1p1h
SuSAv2-Total
RMF-1p1h2-390.700 < cosθµ < 0.800

25
16

15

10

dσ/dpµdcosθµ(10 cm /GeV/nucleon)

arXiv:1711.00771 [nucl-th] (2017)

20
15
10

5

5

0
0

1

0.5
pµ (GeV)000.800 < cosθµ < 0.850

25

1
1.5
pµ (GeV)

0.5

2

2.5

0.975 < cosθµ < 1.000
RMF + 2p2h8Although RMF scaling functions arealmost identical for q3 & 400 MeV/c,
at very low q3 they can differ (scaling is broken) ⇒ Solution: Determine
and characterize low-q3 RMF scaling
functions to be added in the SuSAv2
formalism as well as in the implementation.

6

15

-38

2

20

4

10

53

2

5
0
0

0.5

1
1.5
pµ (GeV)Good comparison with T2K-16 Odata but some overstimations appear
at very forward angles within the
SuSAv2-MEC model ⇒ Possible
RMF scaling violations at low q0 ,q3 not completely included in the
SuSAv2 formalism makes the model
questionable at these kinematics.

2

2.5

0
0

0.5

G. D. Megias: megias@icrr.u-tokyo.ac.jp

11.5
pµ (GeV)2

2.5

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption

2

cm /GeV/neutron)-39

0.98 < cosθµ < 1.00

30

20

20

15

15

15

10

10

5

5

5
0.5

1
1.5
pµ (GeV)20.850 < cosθµ < 0.900

25

20

1
1.5
pµ (GeV)

0.5

2

2.5

0.800 < cosθµ < 0.850

0.5

1
1.5
pµ (GeV)

2

2.5

0.8

1

0.700 < cosθµ < 0.800

20

15

15

10

10

-38

2

0
0

25

20

15
10
5
0
0

0
0

2.5

dσ/dpµdcosθµ(10 cm /GeV/nucleon)

000.90 < cosθµ < 0.94

25

20

10

2

0.94 < cosθµ < 0.98

2525

d σ/dcosθµ/dpµ (10Blue lines: SuSAv2, Black lines: RMF, Red lines: RPWIA

Solid lines: 12 C, Dashed lines: 16 O

Improvement of the SuSAv2-1p1h model at very low kinematics

0.5

1
1.5
pµ (GeV)

2

2.5

5

5

0
0

0
0

0.5

1
pµ (GeV)

1.5

2

0.2

0.4
0.6
pµ (GeV)

Although RMF scaling functions are almost identical for q3 & 400 MeV/c, at very low q3
they can differ (scaling is broken) ⇒ Solution: Determine and characterize low-q3 RMF
scaling functions to be added in the SuSAv2 formalism as well as in the implementation.
54

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption

Contents

55

1

General introduction
State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

2

SuSAv2-MEC implementation in MC event generators
Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

3

Further works and Next steps
Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption
G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

RMF, ED-RMF and SuSAv2 models

Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption

arXiv:1904.10696✪ Scaling violations and low-energy effects present in RMF are not fully included in the SuSAv2MEC model. Solution: Parametrize and introduce low-q RMF effects in SuSAv2✪ Strong q-dependence of RMF vector and scalar potentials at high kinematics is addressedin SuSAv2 with a blending function to introduce RPWIA (no FSI). To have a more consistentmodel and preserve orthogonality, unitarity and dispersion relations ⇒ Solution: ED-RMF (bothinclusive and semi-inclusive for 12 C, 16 O, 40 Ar, etc.)✪ The ED-RMF model introduces an Energy-Dependent potential (based on SuSAv2) to the
RMF that keeps the strength for slow nucleons but makes the RMF potential softer for increasing
nucleon momenta. See PRC 100, 045501 (2019),PRC 101, 015503 (2020) for details✪ SuSAv2 is a pure inclusive model. Solution: ED-RMF (both inclusive and semi-inclusive for
12 C, 16 O, 40 Ar, etc.)

scaling function

1
0.8

200
100

RMF (−− ) vs SuSAv2 (- - -)

0.6

1500
1000
600
300

0.4
0.2
0

56

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

RMF, ED-RMF and SuSAv2 models

Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption

arXiv:1904.10696✪ Scaling violations and low-energy effects present in RMF are not fully included in the SuSAv2MEC model. Solution: Parametrize and introduce low-q RMF effects in SuSAv2✪ Strong q-dependence of RMF vector and scalar potentials at high kinematics is addressedin SuSAv2 with a blending function to introduce RPWIA (no FSI). To have a more consistentmodel and preserve orthogonality, unitarity and dispersion relations ⇒ Solution: ED-RMF (bothinclusive and semi-inclusive for 12 C, 16 O, 40 Ar, etc.)✪ The ED-RMF model introduces an Energy-Dependent potential (based on SuSAv2) to the
RMF that keeps the strength for slow nucleons but makes the RMF potential softer for increasing
nucleon momenta. See PRC 100, 045501 (2019),PRC 101, 015503 (2020) for details✪ SuSAv2 is a pure inclusive model. Solution: ED-RMF (both inclusive and semi-inclusive for
12 C, 16 O, 40 Ar, etc.)

scaling function

1
0.8

200
100

RPWIA (−− ) vs SuSAv2 (- - -)

0.6

1500
1000
600
300

0.4
0.2
0

57

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

RMF, ED-RMF and SuSAv2 models

Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption

arXiv:1904.10696✪ Scaling violations and low-energy effects present in RMF are not fully included in the SuSAv2MEC model. Solution: Parametrize and introduce low-q RMF effects in SuSAv2✪ Strong q-dependence of RMF vector and scalar potentials at high kinematics is addressedin SuSAv2 with a blending function to introduce RPWIA (no FSI). To have a more consistentmodel and preserve orthogonality, unitarity and dispersion relations ⇒ Solution: ED-RMF (bothinclusive and semi-inclusive for 12 C, 16 O, 40 Ar, etc.)✪ The ED-RMF model introduces an Energy-Dependent potential (based on SuSAv2) to the
RMF that keeps the strength for slow nucleons but makes RMF potentials softer for increasing
nucleon momenta. See PRC 100, 045501 (2019),PRC 101, 015503 (2020) for details✪ SuSAv2 is a pure inclusive model. Solution: ED-RMF (both inclusive and semi-inclusive for
12 C, 16 O, 40 Ar, etc.)

scaling function

1
0.8

200
100

ED-RMF (−− ) vs SuSAv2 (- - -)

0.6

1500
1000
600
300

0.4
0.2
0

58

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption

ED-RMF, RMF, SuSAv2 for (e, e ′ )12 C
RMF, ED-RMF, others

500

35

εi=320 MeV, θe=36 deg300

εi=2500 MeV, θe=15 deg

30

RPWIA
PB-RPWIA
RPWIA(pN>230)
RMF
MEC

400

d 2 σ/dΩ/dω vs. ω
RPWIA
PB-RPWIA
RMF
ED-RMF
MEC

25
20
15

200

10
100

(c)

0

5

(f)

0
0

0.02

0.04

0.06
0.08
ω (GeV)

0.1

0.12

0

0.1

E=320 MeV, θ=36

3.5e+05

0.4 0.5
ω (GeV)

0.6

0.7

0.8

0.9

20000

2e+05
1.5e+05

15000

1e+05

10000

50000

5000

0
0

0.02

0.04

0.06 0.08
ω (GeV)

0.9

o

25000

2.5e+05

SuSAv2

0.3

30000

3e+05

59

0.2

E=2500 MeV, θ=15 , qQE=658.6 MeV/c

o

0.1

0.12

G. D. Megias: megias@icrr.u-tokyo.ac.jp

0
0

0.8

0.7
0.2

0.4

0.6

0.8

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption

Contents

60

1

General introduction
State of the art: Challenges and Open Questions
Connection between e − A and ν − A reactions
SuperScaling Approach: SuSAv2 and RMF models

2

SuSAv2-MEC implementation in MC event generators
Implementation of SuSAv2-MEC in MC event generators
Validation of the implementation and Data comparison
From inclusive to semi-inclusive models

3

Further works and Next steps
Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption
G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption

FSI effects for the ejected nucleon state: Cascade (generators) vs. Optical potentials (RMF)✪ RMF FSI effects: S+V real potentials ⇒ kinematical distortion of the outgoing nucleon (incl and semi-incl). Imaginary partof potential also needed for semi-incl to produce absorption, i.e.,flux lost into the unobserved channels.
✪ 1p1h semi-inc (νµ , µ− p) focuses on elastic channel
N(A, A′ )N ′ , i.e. elastic N scattering, no more hadrons emitted⇒ imaginary potential is needed (or cascade effects) to subtract
other processes: (νµ , µ− NN), (νµ , µ− Nπ), etc.

Semi-inclusive
16

RMF

predictions

O(e, e ′ p)15 N data at |Q 2 |(GeV/c)2 [PRC 64, 024614 (2001)]
61

G. D. Megias: megias@icrr.u-tokyo.ac.jp

for

≤ 0.4

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption

FSI effects: Cascade (generators) vs. Optical potentials (RMF)✪ RMF FSI effects: S+V real potentials ⇒ kinematical distortion of the outgoing nucleon (incl
and semi-incl). Imaginary part of potential also needed for semi-incl to produce absorption, i.e.,flux lost into the unobserved channels.
✪ 1p1h semi-inc (νµ , µ− p) focuses on elastic channel N(A, A′ )N ′ , i.e. elastic N scattering, nomore hadrons emitted ⇒ imaginary potential is needed (or cascade effects) to subtract otherprocesses: (νµ , µ− NN), (νµ , µ− Nπ), etc.
Imaginary part: phenomenological ED complex OP fitted to elastic p − A scattering data.
Real part: microscopic RMF real potentials ≡ phenom. real OP

Real

400

200

Vector

200

0

−200

−400

EDAIO
EDAD1
EDAD2
EDAD3

Scalar

0

1

2

3

r(fm)

62

Scalar100

0Cascade models in generators: N emmited is
moved step by step (mean free paths) until interacting with other nucleon or escaping fromthe nucleus. If N interacts ⇒ intranuclear effects (absorption, (in)elastic, charge exchange,other particle productions) are simulated.

Imaginary

4

5

−100
Vector

6

−200

0

1

2

3

4

r(fm)

G. D. Megias: megias@icrr.u-tokyo.ac.jp

5

6

RMF model can be implemented with/without
the imaginary OP so can be compared withcascade effects⇒ No double-counting.
The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption

Summary and Conclusions➲ Neutrino-nucleus interactions are essential for ν oscillation experiments (T2K, SK), being
one of the major sources of current systematics.
➲ The extrapolation to other nuclei (C, O, Ar) will be essential for future experiments suchas HyperK as well as to analyze nuclear-medium uncertainties and inconsistencies between
experiments, such as NOvA or MINERvA.
➲ Forthcoming measurements in water (T2K WAGASCI and NINJA experiments) will bevery useful to validate nuclear models already present in generators.
➲ Collaboration between experimentalists, generator developers and theorists is essential toreduce systematics, improve models in MC event generators and gain sensitivity to determination of oscillation parameters, CPV, NMH.
➲ Validation against (e, e ′ ) data is a solid benchmark for nuclear models in ν experiments.
Superscaling is a valuable tool to connect electron and neutrino scattering.
➲ Analysis of semi-inclusive reactions (more sensitive to nuclear model details) is essential forν oscillation experiments and will help to analyze physics of theoretical models and provide
more consistent theory-vs-data comparisons. Different models can give similar inclusive CS but
probably different exclusive ones.
➲ Satisfactory comparison of SuSAv2-MEC with (e, e ′ ) and (ν, l) inclusive and semi-inclusive
data for C, O and other nuclei makes them promising candidate for this purpose.
63

G. D. Megias: megias@icrr.u-tokyo.ac.jp

The relevance of ν-A interaction models in T2K and SK

General introduction
SuSAv2-MEC implementation in MC event generators
Further works and Next steps

64

G. D. Megias: megias@icrr.u-tokyo.ac.jp

Low-energy nuclear effects and extrapolation to other nuclei
ED-RMF vs. SuSAv2
FSI effects, Cascade models and absorption

The relevance of ν-A interaction models in T2K and SK