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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
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
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
2 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
Contents
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
3 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling 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 (axialstructure or strangeness content of the nucleons)
Astrophysical implications (supernovae, dark matter, sterile neutrinos)
4 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling 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 (axialstructure or strangeness content of the nucleons)
Astrophysical implications (supernovae, dark matter, sterile neutrinos)
5 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling 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 (axialstructure or strangeness content of the nucleons)
Astrophysical implications (supernovae, dark matter, sterile neutrinos)
6 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling 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 dataproduction to reduce systematics (mostly ν-A scattering and nuclear medium effects).
7 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
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.
8 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling 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/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.)
9 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling 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/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.)
9 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
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.
10 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling 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: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling 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: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling 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: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling 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: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling 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: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
Nuclear response in terms of the energy transfer
13 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
Nuclear response in terms of the energy transfer
14 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
Nuclear response in terms of the energy transfer
15 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
Nuclear response in terms of the energy transfer
16 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling 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 background
17 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling 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 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
18 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling 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 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.
19 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
Contents
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
20 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
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.
21 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF 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
22 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
Contents
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
23 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling 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 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.
24 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling 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 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
25 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
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
26 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
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
27 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
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%)
28 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
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.
29 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
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
30 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
Inclusive 12C(e, e′) cross sections with different models (J.Sobczyk’s talk at NUINT18)
31 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
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
32 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
(e, e′) JLab data vs. SuSAv2-MEC PRC99, 042501(R), 2019
33 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
State of the art: Challenges and Open QuestionsConnection between e − A and ν − A reactionsSuperScaling Approach: SuSAv2 and RMF models
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
34 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Implementation of SuSAv2-MEC in MC event generatorsValidation of the implementation and Data comparisonFrom inclusive to semi-inclusive models
Contents
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
35 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Implementation of SuSAv2-MEC in MC event generatorsValidation of the implementation and Data comparisonFrom 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: 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
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Implementation of SuSAv2-MEC in MC event generatorsValidation of the implementation and Data comparisonFrom inclusive to semi-inclusive models
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
37 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Implementation of SuSAv2-MEC in MC event generatorsValidation of the implementation and Data comparisonFrom inclusive to semi-inclusive models
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
38 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Implementation of SuSAv2-MEC in MC event generatorsValidation of the implementation and Data comparisonFrom 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: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Implementation of SuSAv2-MEC in MC event generatorsValidation of the implementation and Data comparisonFrom inclusive to semi-inclusive models
Contents
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
40 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Implementation of SuSAv2-MEC in MC event generatorsValidation of the implementation and Data comparisonFrom inclusive to semi-inclusive models
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)
41 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Implementation of SuSAv2-MEC in MC event generatorsValidation of the implementation and Data comparisonFrom inclusive to semi-inclusive models
Comparison between 1p1h+2p2h models in generators arXiv:1905.08556
T2K
CC
0πνµ
−12C
incl
usi
vedata
Nie
ves
SuS
Av2
-ME
C
42 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Implementation of SuSAv2-MEC in MC event generatorsValidation of the implementation and Data comparisonFrom inclusive to semi-inclusive models
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
43 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Implementation of SuSAv2-MEC in MC event generatorsValidation of the implementation and Data comparisonFrom inclusive to semi-inclusive models
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
44 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Implementation of SuSAv2-MEC in MC event generatorsValidation of the implementation and Data comparisonFrom inclusive to semi-inclusive models
Contents
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
45 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Implementation of SuSAv2-MEC in MC event generatorsValidation of the implementation and Data comparisonFrom inclusive to semi-inclusive models
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.
46 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Implementation of SuSAv2-MEC in MC event generatorsValidation of the implementation and Data comparisonFrom inclusive to semi-inclusive models
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)
47 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Implementation of SuSAv2-MEC in MC event generatorsValidation of the implementation and Data comparisonFrom inclusive to semi-inclusive models
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?
48 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Implementation of SuSAv2-MEC in MC event generatorsValidation of the implementation and Data comparisonFrom inclusive to semi-inclusive models
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.
49 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Low-energy nuclear effects and extrapolation to other nucleiED-RMF vs. SuSAv2FSI effects, Cascade models and absorption
Contents
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
50 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Low-energy nuclear effects and extrapolation to other nucleiED-RMF vs. SuSAv2FSI effects, Cascade models and absorption
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.
51 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Low-energy nuclear effects and extrapolation to other nucleiED-RMF vs. SuSAv2FSI effects, Cascade models and absorption
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.
52 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Low-energy nuclear effects and extrapolation to other nucleiED-RMF vs. SuSAv2FSI effects, Cascade models and absorption
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.
53 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Low-energy nuclear effects and extrapolation to other nucleiED-RMF vs. SuSAv2FSI effects, Cascade models and absorption
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.
54 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Low-energy nuclear effects and extrapolation to other nucleiED-RMF vs. SuSAv2FSI effects, Cascade models and absorption
Contents
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
55 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Low-energy nuclear effects and extrapolation to other nucleiED-RMF vs. SuSAv2FSI effects, Cascade models and absorption
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
56 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Low-energy nuclear effects and extrapolation to other nucleiED-RMF vs. SuSAv2FSI effects, Cascade models and absorption
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
RPWIA (−− ) vs SuSAv2 (- - -)
scal
ing
func
tion
200100
RPWIA (−− ) vs SuSAv2 (- - -) 15001000
600300
57 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Low-energy nuclear effects and extrapolation to other nucleiED-RMF vs. SuSAv2FSI effects, Cascade models and absorption
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 RMF potentials 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.)
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ED-RMF (−− ) vs SuSAv2 (- - -)
scal
ing
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tion
200100
ED-RMF (−− ) vs SuSAv2 (- - -) 15001000
600300
58 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Low-energy nuclear effects and extrapolation to other nucleiED-RMF vs. SuSAv2FSI effects, Cascade models and absorption
ED-RMF, RMF, SuSAv2 for (e, e′)12C d2σ/dΩ/dω vs. ω
SuS
Av2
RM
F,
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-RM
F,
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ers
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0 0.02 0.04 0.06 0.08 0.1 0.12
εi=320 MeV, θe=36 deg
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RPWIAPB-RPWIA
RPWIA(pN>230)RMFMEC
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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
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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
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3.5e+05E=320 MeV, θ=36
o
0 0.2 0.4 0.6 0.80
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E=2500 MeV, θ=15o, q
QE=658.6 MeV/c
59 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Low-energy nuclear effects and extrapolation to other nucleiED-RMF vs. SuSAv2FSI effects, Cascade models and absorption
Contents
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
60 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Low-energy nuclear effects and extrapolation to other nucleiED-RMF vs. SuSAv2FSI 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 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)]
61 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Low-energy nuclear effects and extrapolation to other nucleiED-RMF vs. SuSAv2FSI 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 (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)
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EDAIOEDAD1EDAD2EDAD3
0 1 2 3 4 5 6r(fm)
−200
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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.
62 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Low-energy nuclear effects and extrapolation to other nucleiED-RMF vs. SuSAv2FSI effects, Cascade models and absorption
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.
63 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK
General introductionSuSAv2-MEC implementation in MC event generators
Further works and Next steps
Low-energy nuclear effects and extrapolation to other nucleiED-RMF vs. SuSAv2FSI effects, Cascade models and absorption
64 G. D. Megias: [email protected] The relevance of ν-A interaction models in T2K and SK