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

General introductionSuSAv2-MEC implementation in MC event generators

Further works and Next steps

The relevance of neutrino-nucleus interactionmodels in T2K and SuperKamiokande

Guillermo D. MegiasRCCN, 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: [email protected] The relevance of ν-A interaction models in T2K and SK



1 General introductionState of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models

2 SuSAv2-MEC implementation in MC event generatorsImplementation of SuSAv2-MEC in MC event generatorsValidation of the implementation and Data comparisonFrom inclusive to semi-inclusive models

3 Further works and Next stepsLow-energy nuclear effects and extrapolation to other nucleiED-RMF vs. SuSAv2FSI effects, Cascade models and absorption




State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models

Contents








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 (axialstructure or strangeness content of the nucleons)

Astrophysical implications (supernovae, dark matter, sterile neutrinos)






















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 dataproduction to reduce systematics (mostly ν-A scattering and nuclear medium effects).





Long-baseline accelerator neutrino oscillation experiments

Neutrinos produced as secondary decay products of hadrons (π,K) generated in primaryreactions of p with nuclei ⇒ broad energy beam.

Experimental difficulties:

The neutrino flux: broad energy distribution around a maximum → True energy for a detectedevent 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 oscillationis 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-nucleuscross section measurements and on the ν flux at ND.





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/ν asymmetry, to improve hadron detection efficiency, the characterization of FS

particles or the extrapolation from the usual 12C target analysis to other nuclei (16O [T2K ND280 upgrade], 40Ar, etc.)





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/ν asymmetry, to improve hadron detection efficiency, the characterization of FS

particles or the extrapolation from the usual 12C target analysis to other nuclei (16O [T2K ND280 upgrade], 40Ar, etc.)





Challenges for nuclear models

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

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 allpossible FS.

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

4 Expressing these improvements of the nuclear model in terms thatcan be successfully incorporated in the simulation of neutrino eventsby neutrino event generators.





Inclusive vs. Semi-inclusive reactions

*Adapted from Bill Donnelly’s talk at ECT* 2018 workshop “Modeling neutrino-nucleus interactions”























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%).





Nuclear response in terms of the energy transfer




















Nuclear effects and disentangling of final state events

CCQE, CCQE-like, CC0π events and FSI effects

CC0π = CCQE-like without subtraction of π absorption background





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 of

finding a nucleon (p, Eb) within the nucleus. Semiphenomenological based on (e,e’p) data, mean-field calculations and LFG. Shell

model. Non relativistic. Implemented in NEUT.

Random Phase Approximation (RPA): can be added to the top of LFG/SF/HF/MF to incorporate NN correla-

tions. Very good description at low q0, Q2 but not relativistic.

Relativistic Mean Field (RMF, ED-RMF, SuSAv2): Fully relativistic shell model with accurate description

of nuclear dynamics and FSI effects. Bound nucleons: self-consistent Dirac-Hartree solutions, derived within a RMF Lagrangian

with 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.

0 1 2 3 410-7

10-5

10-3

10-1

FSI, RMF

Jastrown(p)

[fm

3 ]

p [fm-1]

CDFM

nLFD

RFG

HO

no FSI, projected

no FSI, RMF





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 of

finding a nucleon (p, Eb) within the nucleus. Semiphenomenological based on (e,e’p) data, mean-field calculations and LFG. Shell

model. Non relativistic. Implemented in NEUT.

Random Phase Approximation (RPA): can be added to the top of LFG/SF/HF/MF to incorporate NN correla-

tions. Very good description at low q0, Q2 but not relativistic.

Relativistic Mean Field (RMF, ED-RMF, SuSAv2): Fully relativistic shell model with accurate description

of nuclear dynamics and FSI effects. Bound nucleons: self-consistent Dirac-Hartree solutions, derived within a RMF Lagrangian

with 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 pre-dictions (lepton kin.). Main differencesfor hadron kin. due to nuclear effects.Semi-inclusive processes: Next step intheoretical ν interaction community.





Contents








Connection between ν-A and e-A reactions

l = e, µ, τ

Experimental conditions are different: (e, e′): Ee is well determined and different channels can be clearly identified by knowingthe 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 con-nected (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 whichare only sensitive to the vector response.

=⇒ Although not sufficient to fully constrain neutrino cross sections, electron scattering consti-tutes a necessary test and a solid benchmark for nuclear models.





Theoretical description: ν-A inclusive cross section

Double differential cross section χ = +(−) ≡ νµ(νµ)

[dσ

dkµdΩµ

]

χ

=|~kl |

|~kνl |

G2F

4π2ηµνW µν = σ0F2

χ ; σ0 =

(G2

Fcos θc

)2

2π2

(kµ cos

θ

2

)2

Nuclear structure information

F2χ = VLRL + VT RT + χ [2VT ′ RT ′ ]

VLRL = VCC RCC + 2VCLRCL + VLLRLL

RL = RVVL + RAA

L ; RT = RVVT + RAA

T ; RT ′ = RVAT ′

Nuclear responses RK can be calculated in terms ofthe single nucleon ones GK and the nuclear

dependence of the model ⇒ RK ≈ F (nuclear) · GK

Comparison with (e, e′) reactions[dσ

dkµdΩ

]= σMott

(vLRVV

L + vT RVVT

); σMott =

α2 cos2 θ/2

4Ei sin4 θ/2





Contents








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 solidbenchmark to test the validity of theoretical models for neutrino reactions as well as to studythe nuclear dynamics. The SuperScaling Approach exploits universal features of lepton-nucleusscattering 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) ∼σQE (nuclear

effects)

σsingle nucleon(no nucleareffects

)

f (ψ′) = kF

(d2σ

dΩe dω

)exp

σMott (vLGee′

L+ vT Gee′

T)

Good superscaling behavior at ψ′ < 0 (below QE peak). At

higher kinematics (ψ′), other contributions beyond QE and

IA (2p2h, ∆, etc.) can play an important role and scaling is

broken.


https://idus.us.es/xmlui/handle/11441/74826




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 solidbenchmark to test the validity of theoretical models for neutrino reactions as well as to studythe nuclear dynamics. The SuperScaling Approach exploits universal features of lepton-nucleusscattering 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 inthe T channel ⇒2p-2h MEC, corre-lations, ∆-resonance⇒ Mainly transverse


https://idus.us.es/xmlui/handle/11441/74826




RFG as a natural starting point to examinate the scaling concept

d2σ

dΩl dω= σ0F2

χ = σ0

(VLRVV

L + VCC RAACC + 2VCLRAA

CL + VLLRAALL + VT RT + χVT ′ RT ′

)

d2σ

dΩedω= σMott (vLRee′

L + vT Ree′

T )

RQEK ⇒ W µν =

3N M2N

4πk3F

∫d3p

E(p)E(p + q)× θ(kF − |p|)θ(|p + q| − kF )

×δ(ω − [E(p + q) − E(p)]) × W µνs.n.(Pi + Q,Pi)

RQEK =

1

kFfRFG(ψ′)

N

2κDR s.n.

K ≡1

kFfRFG(ψ′)GK , K = CC ,CL, LL,T ,T ′

fRFG(ψ′) =3

4(1 − ψ

′2)θ(1 − ψ′2)

ψ′

≡1√ξF

λ′ − τ ′

√(1 + λ′)τ ′ + κ

√τ ′(τ ′ + 1)

λ′

= ω′/(2MN ) , κ = q/(2MN )

ω′

= ω − Eshift , τ′

= κ2

− λ′2





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

RQEK

=1

kFfmodel (ψ

′)N

2κDUs.n.

K ≡1

kFfmodel (ψ

′)GK , K = CC ,CL, LL,T ,T ′

Scaling functions obtained from the cross section:

f QE (e,e′) = kF

d2σdΩe dω

σMott (vLGee′

L+ vT Gee′

T)

f QE (ν) = kF

d2σdΩl dω

σ0(VLGVVL

+ VCC GAACC

+ 2VCLGAACL

+ VLLGAALL

+ vT GT

+ χvT ′ GT ′

)

Specific scaling functions for the individual channels:

fK = kFRK

GK





Separate L/T scaling functions

fL = kF RL/GL

fT = kF RT /GT

Scaling violations inthe T channel ⇒2p-2h MEC, corre-lations, ∆-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)

It is experimentally observed f ee′

T ,exp> f ee′

L,exp(15-20%)





Testing SuperScaling for 12C(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 onRelativistic Mean Field (RMF) theoretical scaling functions (FSI) to reproduce nuclear dynamics.

RMF: Good description of the QE (e, e′) data and superscaling properties (f ee′

L,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.


http://journals.aps.org/prc/abstract/10.1103/PhysRevC.90.035501

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.94.013012




Inclusive 12C(e, e′) cross sections PRD 94, 013012 (2016)

0 0.1 0.2 0.3 0.4ω (GeV)

0

1000

2000

3000

4000

5000

d2σ/

dΩdω

(n

b/G

eV/s

r)

E=560 MeV, θ=60o, q

QE=508 MeV/c

0 0.1 0.2 0.3 0.4 0.5ω (GeV)

0

10000

20000

300002p-2h MECInelasticQETotal

E=680 MeV, θ=36o, q

QE=402.5 MeV/c

0.2 0.3 0.4 0.5ω (GeV)

0

100

200

300

400

500

d2σ/

dΩdω

(n

b/G

eV/s

r)

E=560 MeV, θ=145o, q

QE=795 MeV/c

0.4 0.6 0.8 1ω (GeV)

0

50

100

150E=3595 MeV, θ=25

o, q

QE=1640 MeV/c


http://arxiv.org/abs/1603.08396




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





Inclusive 16O(e, e′) and 40Ca(e, e

′) cross sections

0 0.1 0.2 0.3 0.4 0.5 0.60

5000

10000

15000

20000

25000

30000

16O, E

i=737MeV, θ=37.1

o

0 0.1 0.2 0.3 0.4 0.5 0.60

5000

10000

15000

40Ca, E

i=841MeV, θ=45.5

o

0 0.2 0.4 0.6 0.8ω (GeV)

0

5000

10000

15000

16O, E

i=1080MeV, θ=32

o

0 0.1 0.2 0.3 0.4 0.5ω (GeV)

0

5000

10000

15000

20000

QEInelastic2p-2hTotal

40Ca, E

i=560MeV, θ=60

o





(e, e′) JLab data vs. SuSAv2-MEC PRC99, 042501(R), 2019


https://journals.aps.org/prc/abstract/10.1103/PhysRevC.99.042501




Comparison with CC0π νµ-nucleus dataM

INE

Rν

Aνµ

-CH

T2K

CC

0πνµ

−C

8H

8

0 0.2 0.4 0.6 0.8 1 1.2 1.4pµ (GeV)

0

2

4

6

8

10

12dσ

/dp µd

cosθ

µ(10-3

9cm

2 /GeV

/nu

cleo

n)

0.85 < cosθµ < 0.90

0 1 2 3pµ (GeV)

0

2

4

6

8T2K

old

T2Kpreliminary, taken from C. Riccio at NuInt2018

2p2h1p1hTotal

0.94 < cosθµ < 0.98

0 0.5 1 1.5p

T (GeV/c)

0

5

10

15

20

d2 σ/d

p Td

p||

QE-like data

2p-2h MEC (θµ<20o)

QE (CH, θµ<20o)

TotalCCQE data

1.50 < p|| < 2.00

0 0.5 1 1.5p

T (GeV/c)

0

0.1

0.2

0.3

0.4

d2 σ/d

p Td

p||

10.00 < p|| < 15.00




Implementation of SuSAv2-MEC in MC event generatorsValidation of the implementation and Data comparisonFrom inclusive to semi-inclusive models

Contents








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: Imple-

mentation 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 Achannels).

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.

*Adapted from S. Dolan’s talk at GENIE Meeting (02/2019)36 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK

https://arxiv.org/abs/1905.08556




1p1h implementation: RMF and SuSAv2

1st step: Implementing SuSAv2 hadron tensor Wµν(q, ω) + LFG on the top and compar-ison with original SuSAv2 model

2nd step: Adding SuSAv2 formulas, parameters and parametrization of scaling functionsinto generators to speed up simulations and to allow reweighting (MQE

A, pF , Eb , etc.)

3rd step: Introducing RMF nucleon momentum distribution in generators to fully testfactorization approach.

4th step: Implement full RMF semi-inclusive model in generators

0 1 2 3 410-7

10-5

10-3

10-1

FSI, RMF

Jastrown(p)

[fm

3 ]

p [fm-1]

CDFM

nLFD

RFG

HO

no FSI, projected

no FSI, RMF





2p-2h MEC for (e, e′) and CC ν reactions PRD91, 073004 (2015)

The numerical evaluation of the hadronic tensor W µν2p2h

(R2p2hK

) is performed in the RFG model

in 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 (40Ar, 56Fe, 208Pb)

It is computationally non-trivial and involves 7D integrals of thousands of terms (+1 for

ν-flux) ⇒ High increase of the computing time of R2p2hK

⇒ Parametrization/Implementation

Accurate implementation of np/pp pairs for the 2p2h channel using separate hadron tensorsfor np and pp pairs.

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


http://journals.aps.org/prd/abstract/10.1103/PhysRevD.91.073004




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






Contents








SuSAv2-MEC implementation in GENIE: Validation plots (T2K CC0π)

T2K

CC

0πνµ

−12C

data

vs.

SuS

Av2

-ME

CG

EN

IE

χ2

=255.8

(67

bin

s)





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

T2K

CC

0πνµ

−12C

incl

usi

vedata

Nie

ves

SuS

Av2

-ME

C






SuSAv2-MEC in GENIE: Validation plots (T2K CC0πNp, 0p > 500 MeV)

T2K

CC

0πν

µ−

12C

sem

i-se

mi-

incl

usi

vedata

(0p>

500

MeV

)

χ2 S

uS

Av2

-ME

CG

EN

IE=

168.9

2(6

0bin

s)

χ2 R

MF

+G

EN

IE(S

usA

v2-2

p2h+

pi-

abs)

=171.8

7





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

T2K

CC

0πνµ

−12C

sem

i-se

mi-

incl

usi

vedata

(0p>

500

MeV

)

Nie

ves

SuS

Av2

-ME

C






Contents








CCQE ν inclusive cross sections with different modelsDifferent models can give similar inclusive CS but different semi-inclusive ones (more sensitiveto 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 compar-ison. 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.





Different models can give similar inclusive CS but different semi-inclusive ones (more sensi-tive 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 section χ = +(−) ≡ νµ(νµ)[dσ

dkµdΩµ

]χ

= σ0

(VCC RCC + 2VCLRCL + VLLRLL + VT RT + χ

[2VT ′ RT ′

])

Double differential semi-inclusive cross section χ = +(−) ≡ νµ(νµ)





Testing the factorization approach on CC0πNp T2K data

Comparison of RMF “semi-semi-inclusive” prediction and GENIE SuSAv2 implementa-tion 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 doesnot seem a bad approximationfor semi-semi-inclusive analysis(SuSAv2 + LFG on the top(Genie) vs. RMF code. To bedone with RMF on the top).

What about more semi-inclusive measurements?





Comparison of semi-inclusive T2K STV data with SuSAv2-MECGenie + BS π abs and Valenciamodel + BS π abs (arXiv:1905.08556). Goodness of fit: For δpT : χ2

SuSA= 20.5, χ2

Valencia= 27.1.

For δαT : χ2SuSA

= 45.3, χ2Valencia

= 31.4. For δφT : χ2SuSA

= 40.1, χ2Valencia

= 36.8.

Work in progressto test the factor-ization approach insemi-inclusive mea-surements when RMFmomentum distribu-tion is implemented.





Low-energy nuclear effects and extrapolation to other nucleiED-RMF vs. SuSAv2FSI effects, Cascade models and absorption

Contents








Why is the C to O extrapolation important?

T2K ND280 is primarily based on C8H8 (also containing H2O active target regions), whereasthe FD is water-based. ND measurements on C8H8 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 tofuture water-based atmospheric and LB experiments (HyperK) ⇒ ν−12C / ν−16O differenceswill 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 distor-tions, etc.

The implementation of 2p2h np and pp pairscan have an impact on this issue. 2p2h direct-exchange interference terms can imply a factor 2in the np/pp ratio with regard to other models⇒ Relevant for T2K and HyperK projects whereFS nucleon multiplicity is detected and for SK-Gdwhere Gd salts are added to the H2O target toimprove n detection and sensitivity to discoverCPV via ν/ν differences, since the latter pro-duce more neutrons.





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

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 0.2 0.4 0.6 0.8 1 1.2 1.4pµ (GeV)

0

0.1

0.2

0.3

0.4

0.5

dσ/d

p µ(10-3

9cm

2 /GeV

/nucl

eon)

0.850 < cosθµ < 0.900

0 2 4 6 8pµ (GeV)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

dσ/d

p µ(10-3

9cm

2 /GeV

/nucl

eon)

2p2hSuSAv2-GENIE

π-absGENIE

TotalGENIE

TotalRMF+GENIE

2p2h+π-abs

0.980 < cosθµ < 1.000

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






T2K CC0π νµ−H2O cross sections arXiv:1711.00771 [nucl-th] (2017)

0 0.5 1pµ (GeV)

0

5

10

15

20

dσ/d

pµd

cosθ

µ(10

-39cm

2/G

eV/n

ucl

eon)

T2K (16

O)SuSAv2-2p2hSuSAv2-1p1hSuSAv2-TotalRMF-1p1h

0.000 < cosθµ < 0.600

0 0.5 1 1.5 2 2.5pµ (GeV)

0

5

10

15

20

250.700 < cosθµ < 0.800

0 0.5 1 1.5 2 2.5pµ (GeV)

0

5

10

15

20

25

dσ/d

pµd

cosθ

µ(10

-38cm

2/G

eV/n

ucl

eon) 0.800 < cosθµ < 0.850

0 0.5 1 1.5 2 2.5pµ (GeV)

0

2

4

6

8

0.975 < cosθµ < 1.000

RMF + 2p2h

Good comparison with T2K-16Odata but some overstimations appearat very forward angles within theSuSAv2-MEC model ⇒ PossibleRMF scaling violations at low q0 ,q3 not completely included in theSuSAv2 formalism makes the modelquestionable at these kinematics.

Although RMF scaling functions arealmost identical for q3 & 400 MeV/c,at very low q3 they can differ (scal-ing is broken) ⇒ Solution: Determineand characterize low-q3 RMF scalingfunctions to be added in the SuSAv2formalism as well as in the implemen-tation.






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

Solid

lines

:12C

,D

ash

edlines

:16O

Blu

elin

es:

Su

SA

v2,

Bla

cklin

es:

RM

F,

Red

lin

es:

RP

WIA

0 0.5 1 1.5 2 2.5pµ (GeV)

0

5

10

15

20

25

30

d2 σ/dco

sθµ/d

p µ (10

-39 c

m2 /G

eV/n

eutr

on)

0.98 < cosθµ < 1.00

0 0.5 1 1.5 2 2.5pµ (GeV)

0

5

10

15

20

25

0.94 < cosθµ < 0.98

0 0.5 1 1.5 2 2.5pµ (GeV)

0

5

10

15

20

250.90 < cosθµ < 0.94

0 0.5 1 1.5 2 2.5pµ (GeV)

0

5

10

15

20

0.850 < cosθµ < 0.900

0 0.5 1 1.5 2pµ (GeV)

0

5

10

15

20

25dσ

/dp

µdco

sθµ(1

0-3

8cm

2/G

eV/n

ucl

eon) 0.800 < cosθµ < 0.850

0 0.2 0.4 0.6 0.8 1pµ (GeV)

0

5

10

15

20

250.700 < cosθµ < 0.800

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 RMFscaling functions to be added in the SuSAv2 formalism as well as in the implementation.





Contents








RMF, ED-RMF and SuSAv2 models arXiv:1904.10696

Scaling violations and low-energy effects present in RMF are not fully included in the SuSAv2-MEC 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 12C, 16O, 40Ar, etc.)

The ED-RMF model introduces an Energy-Dependent potential (based on SuSAv2) to theRMF that keeps the strength for slow nucleons but makes the RMF potential softer for increasingnucleon 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 for12C, 16O, 40Ar, etc.)

0

0.2

0.4

0.6

0.8

1

RMF (−− ) vs SuSAv2 (- - -)

scal

ing

func

tion

200100

RMF (−− ) vs SuSAv2 (- - -) 15001000

600300











The ED-RMF model introduces an Energy-Dependent potential (based on SuSAv2) to theRMF that keeps the strength for slow nucleons but makes the RMF potential softer for increasingnucleon momenta. See PRC 100, 045501 (2019),PRC 101, 015503 (2020) for details


0

0.2

0.4

0.6

0.8

1

RPWIA (−− ) vs SuSAv2 (- - -)

scal

ing

func

tion

200100

RPWIA (−− ) vs SuSAv2 (- - -) 15001000

600300











The ED-RMF model introduces an Energy-Dependent potential (based on SuSAv2) to theRMF that keeps the strength for slow nucleons but makes RMF potentials softer for increasingnucleon momenta. See PRC 100, 045501 (2019),PRC 101, 015503 (2020) for details


0

0.2

0.4

0.6

0.8

1

ED-RMF (−− ) vs SuSAv2 (- - -)

scal

ing

func

tion

200100

ED-RMF (−− ) vs SuSAv2 (- - -) 15001000

600300








ED-RMF, RMF, SuSAv2 for (e, e′)12C d2σ/dΩ/dω vs. ω

SuS

Av2

RM

F,

ED

-RM

F,

oth

ers

0

100

200

300

400

500

0 0.02 0.04 0.06 0.08 0.1 0.12

εi=320 MeV, θe=36 deg

(c)

ω (GeV)

RPWIAPB-RPWIA

RPWIA(pN>230)RMFMEC

0

5

10

15

20

25

30

35

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

εi=2500 MeV, θe=15 deg

(f)

ω (GeV)

RPWIAPB-RPWIA

RMFED-RMF

MEC

0 0.02 0.04 0.06 0.08 0.1 0.12ω (GeV)

0

50000

1e+05

1.5e+05

2e+05

2.5e+05

3e+05

3.5e+05E=320 MeV, θ=36

o

0 0.2 0.4 0.6 0.80

5000

10000

15000

20000

25000

30000

0 0.2 0.4 0.6 0.8

0.7

0.8

0.9

E=2500 MeV, θ=15o, q

QE=658.6 MeV/c





Contents








FSI effects for the ejected nucleon state: Cascade (generators) vs. Optical potentials (RMF)

RMF FSI effects: S+V real potentials ⇒ kinematical distor-tion 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 channelN(A,A′)N′, i.e. elastic N scattering, no more hadrons emitted⇒ imaginary potential is needed (or cascade effects) to subtractother processes: (νµ, µ−NN), (νµ, µ−Nπ), etc.

Semi-inclusive RMF predictions for16O(e, e′p)15N data at |Q2| ≤ 0.4

(GeV/c)2 [PRC 64, 024614 (2001)]





FSI effects: Cascade (generators) vs. Optical potentials (RMF)

RMF FSI effects: S+V real potentials ⇒ kinematical distortion of the outgoing nucleon (incland 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 Imaginary

0 1 2 3 4 5 6r(fm)

−400

−200

0

200

400

EDAIOEDAD1EDAD2EDAD3

0 1 2 3 4 5 6r(fm)

−200

−100

0

100

200

Vector

ScalarVector

Scalar

Cascade models in generators: N emmited ismoved step by step (mean free paths) until in-teracting with other nucleon or escaping fromthe nucleus. If N interacts ⇒ intranuclear ef-fects (absorption, (in)elastic, charge exchange,other particle productions) are simulated.

RMF model can be implemented with/withoutthe imaginary OP so can be compared withcascade effects⇒ No double-counting.





Summary and Conclusions

Neutrino-nucleus interactions are essential for ν oscillation experiments (T2K, SK), beingone 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 betweenexperiments, 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 determina-tion 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 providemore consistent theory-vs-data comparisons. Different models can give similar inclusive CS butprobably different exclusive ones.

Satisfactory comparison of SuSAv2-MEC with (e, e′) and (ν, l) inclusive and semi-inclusivedata for C, O and other nuclei makes them promising candidate for this purpose.






Documents

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