Neut
Yoshinari Hayato(Kamioka, ICRR, Univ. of Tokyo )Contents• Brief History ~ Requirements• Neutrino interactions above ~100MeV• Procedure of the neutrino event generation• Used models for each neutrino interaction mode
• Nuclear effects ( Final state interactions of hadrons )• Remaining issues

0. Before starting this talk
ニュートリノー核子・原子核反応シミュレーションの重要性
大気ニュートリノ観測実験 + 核子崩壊探索実験
長基線ニュートリノ振動実験
ニュートリノの直接観測はできない
検出器内で発生した
ニュートリノー核子・原子核散乱による生成粒子を観測する。
主として用いられる反応
Charged current interactions with nucleus
ν + N → l + N’ ( + X )N, N’: nucleusl: charged leptonX: hadrons ( π, K, Ω, nucleons etc… )ニュートリノー核子・原子核散乱の正確な理解が必要

1. Introduction
Example 1: 加速器を用いたニュートリノ実験の場合
ニュートリノの方向は既知

Case 1: Eν = 100 ~ 1 GeV
Select charged current quasi-elastic scattering events
ν + N → l + N’

生成した荷電レプトンの運動量及び方向を用いてニュートリノのエネルギーを再構成
反応種別の同定が必要→ Selection efficiency や purity / background contamination
は、シミュレーションを用いて評価する。
Case 2: Eν > several GeV
Charged current deep inelastic scattering events dominate.
ν + N → l + N’ + hadrons

ニュートリノエネルギーの再構成には
生成荷電レプトンの運動量と方向、ならびに検出器において観測されたハドロンのエネルギーを用いる。
Precise knowledge of the primary neutrino interactions
and the secondary hadron interactions is important.

1. Introduction
Example 2: 大気ニュートリノ観測実験
大半の解析においては、観測されたレプトンの運動量及び方向を用いる。
ニュートリノ振動パラメータは、観測データと振動を考慮にいれたシミュレーションを用いることで決定される。
Example 3: 核子崩壊探索実験
陽子崩壊の主要なモードと予言されるp → e+ π0では、
single π productionが主要なバックグラウンドとなる。
（終状態の粒子が同一である）
ニュートリノ反応や核子崩壊によって、原子核中で生成したπ粒子などは、原子核中で散乱・吸収されることもしられている。.
( π+ n → π0 p etc. )Precise knowledge of the primary neutrino interactions
and the secondary hadron interactions is important.

1. Brief History
Minimal SU(5) GUT predicts nucleon decay.
Major decay mode of proton is p → e+ + π0
• Ring imaging water Cherenkov detector has high efficiency
in reconstructing electrons and low momentum π0s.
• Possible to build massive detector
to search for the nucleon decay
predicted by the theory.
But π0 may interact in nucleus
if the proton in Oxygen decays.

Study of interaction of π in Oxygen is important for the analysis.
Need simulation program
to determine the event selection criteria
and to estimate the detection efficiency.

1. Brief History
Ring imaging water Cherenkov detectors
Japan

1983 : Kamiokande( 3,000 ton, ~ 1,000 20inch PMTs )1996 : Super-Kamiokande ( 50,000 ton, ~12,000 20inch PMTs )*) Also in US, IMB experiment started in 1982.
( 7,000 ton tank, ~ 2,000 5(8)inch PMTs )Detect relativistic particles
running through the detector medium ( water )using the Cherenkov light.
• Number of the Cherenkov rings= Observed number of particles• Energy ( momentum ) is reconstructedusing the total charge of the ring.
• Direction is reconstructedusing the image of the ring.
• Particle type is identified
using the shape of the ring.
• Electron / gamma• Muon etc.

: Diffused: Sharp

Neut was initially developed for the Kamiokande experiment.

1. Brief History
The major background in searching for the nucleon decay
is caused by the atmospheric neutrinos.
One of the neutrino interaction
in a few GeV region
Single pion production

Atmospheric neutrino flux

νe + p → e+ + n + π0νe + n → e- + p + π0 etc..
Basically, the electron ( positron ) and π0from primary neutrino interaction
have different energy/momentum
from nucleon decay products.
But re-scattering of π in Oxygen changes its charge or momentum.
Need precise simulation program to estimate the background.
• Primary neutrino interaction with water( = neutrino interaction with Oxygen or proton )• π re-scattering in Oxygen1. Brief History
Indication of neutrino oscillationfrom the observation of solar and atmospheric neutrino
Super Kamiokande• Super-Kamiokande
Massive ( 50kt ) Water Cherenkov detector~30 times larger statistics
High precision observation.
1998 Evidence of neutrino oscillation

50kt• Accelerator based neutrino experiment
K2K ~ SciBooNE
Beam experiment ~ High statistics @ near detectors.
Several types of the detectors
with various target material

Water Chrenkov detector
Water target tracking detector
Scintillator detector
Iron target muon range detector

Need much more precise neutrino interaction simulation program.
New experimental data and models make various improvements possible.

2. Neutrino interactions
Charged current quasi-elastic scattering
Neutral current elastic scattering
Single π,η,K resonance productions
Coherent pion productions
Deep inelastic scattering

νμ+ N →ν + N
νμ+ N →l + N’ + π (η,K)νμ+ X →l + X’ + πνμ+ N →l + N’ + mπ(η,K)(l : lepton, N,N’ : nucleon, m : integer)

Cross-sections
Total (NC+CC)
σ/E (10-38cm2/GeV)

νμ+ n →μ- + p

Cross-sections

CC Total
CC Total

CC quasi-elastic
DIS
CC single π
NC single π0Eν (GeV)DIS (CC)3. Procedure of the neutrino event generation( Event generator )• 反応エネルギーの決定
最終的な事象のエネルギー分布がneutrino flux ( φ (E) ) と total cross-section ( σtotal (E) )の積の分布を再現するように。
• 反応モードの決定
各反応モード毎の散乱断面積を用いて、反応種別を決定。
（各反応の散乱断面積が計算できていることが必要）• 素過程ニュートリノ反応のシミュレーション
生成粒子数を決定、各粒子の粒子種別及び運動量（方向）を決定。
• 生成粒子の原子核中での散乱シミュレーション（必要なら）原子核中で発生した各粒子（ハドロン）の核内での散乱をシミュレーションし、各粒子が原子核から出た時の状態を決定。
（吸収・散乱・粒子生成・荷電変換反応などがおこりうる）

3. Procedure of the neutrino event generation
1) Fix the energy of neutrino
Energy distribution of neutrino should obey
the distribution determined byneutrino flux ( φ (E) ) x total cross-section ( σtotal (E) )example)Atmospheric neutrino( Angular distribution is also taken into account in the actual simulation. )neutrino flux ( φ (E) ) x Cross-sections

CC Total

DIS (CC)3. Procedure of the neutrino event generation
2) Fix the interaction mode
Interaction mode is selectedby using the each individual interaction cross-section.
（In order to select one of the interactions
it is necessary to know the cross-sections for each mode.）
Example ) picked up energy in the previous step was 2.5GeV

σ/E (10-38cm2/GeV)

Cross-sections
Total (NC+CC)
CC TotalDIS
CC single π
CC quasi-elastic
NC single π0Eν (GeV)3. Procedure of the neutrino event generation
3) Simulate primary interaction
Fix the number of particles in the finals state
Fix the types and 4-momenta ( direction ) of each particle.
Example ) single π production
Input : Use fixed neutrino energy and direction in step 1).

μνμinitial particles

πfinal particlespn4) Simulate secondary interaction in nucleus
Simulate the interaction in the target nucleus
and fix the properties of each particle
outside of the target nucleus.
Example ) π charge exchange interaction
in nucleus
Trace generated hadrons in nucleus
until the particles exit from the nucleus.

π+
n

π0
p

4. Introduction of NEUT ~ What NEUT does
• Neutrino energy range : ~ 100MeV to ~ TeV• Target nucleus :primarily proton and Oxygen.
Rather well tested with Carbon ( at K2K, SciBooNE )*) Possible to specify heavier or lighter target nucleus.
But additional approximations are used to simulate.

• Provide cross-sections to estimate the interaction rates
or to select the interaction mode.
• Simulates primary neutrino interaction
with nucleon and nucleus targets.
Simulate emission of gamma from the excited state.
( only for Oxygen at this moment )• Simulates meson interactions in the target.
Especially in detail for the low momentum pions.
• Simulates nucleon re-scattering in the target nucleus.

Before going to detaill (El, pl)νN(Eν, pν)q2
Resonance N*(EN*, pN*)

(Eν, pν)q2 : 4 momentum transfer
q2 ≡ (El - Eν)2 - (pl - pν)2 (= -Q2)
W : Invariant Mass of N*

W≡ E

2
N*

−p

2
N*

4. Introduction of NEUT
~ Summary of the interaction models• QE– Llewellyn-Smith, Smith&Moniz– MA is 1.1 or 1.2GeV/c• Resonance production– Rein & Sehgal– MA is 1.1 or 1.2GeV/c– Recently Δ Æ Nγ decay is considered.
– Recently lepton mass effects in CC single-π is considered.

• Coherent-π– Rein & Sehgal( recently lepton mass correction is included. )• DIS– GRV94 pdf with Bodek-Yang correction– GRV98 pdf with Bodek-Yang correction

Charged current quasi-elastic
μ

νμ
n
p

Major interaction in the low energy region
Useful interaction mode to reconstruct incident neutrino energy~ used to measure the spectrum shape of the neutrino flux
Only the charged lepton is observed
if the momentum of recoil nucleon is below 1GeV
with the water Cherenkov detector.

5. Charged Current Quasi elastic scatteringν + N Æ l + N’

Cross-section calculations
Free nucleon : C.H.L. Smith(Phys. Rep. 3,261(1972))-1.267(MV=0.84GeV/c)

In the original article, both vector and axial-vector form factors
are assumed to be dipole. Also, GEn is set to 0.
Recent precise electron scattering experiments suggests
deviation from the dipole assumption for vector form factor.

Still, dipole form factor is used in NEUT.
MA = 1.1 or 1.2 GeV/c2

5. Charged Current Quasi elastic scatteringν + N Æ l + N’

Cross-sections ( Neut )νμ + n Æ μ - + p

νμ + p Æ μ + + n

MA=1.21MA=1.21

Cross-section differences ( dipole and non-dipole vector form factors )Black: Non-Dipole( BBBA07 )Red : Dipole

Solid
Dottedneutrino
anti neutrino

MA=1.05

Black: Non-Dipole( BBBA07 )Red : Dipole

MA=1.21

5. Charged Current Quasi elastic scattering
Quasi-elastic scattering with nucleon in nucleus
Nucleons are bound in nucleus.
Eν > 100MeV
Fermi gas model is a good ( first-order ) approximation.
• Nucleon is moving in the Fermi sea.
• Nucleon is bound in the nucleus. ( “binding energy” )• Pauli blocking is required.
( Outgoing nucleon required to have larger momentum
than Fermi surface momentum. )
p

νμ

μ
n

Eν + En + B = Ep + Eμ
pp > Fermi momentum

To obtain the cross-section of CCQE for bound nucleons,relativistic Fermi-gas calculation by Smith and Moniz is used.
(Nucl.Phys.B43 605(1972),erratum-ibid.B101 547(1975),with additional correction. )5. Charged Current Quasi elastic scattering
Assuming the simplest Fermi gas model,
Target nucleus is determined by Fermi momentum and potential

Black
Red

Free
Bound

νμ + n Æ μ - + p

νμ + p Æ μ + + n

Cross-section difference
Fermi momentum dependence~ A dependenceσ ( 10-38 cm2)

Cross-section difference( Free vs. bound )

Green
Red
Blue
PurpleCyan

205 MeV / c
225 MeV / c
245 MeV / c
265 MeV / c
285 MeV / c

Oxygen ~ 225 MeV / c
Iron~ 250 MeV / c
GeV5. Charged Current Quasi elastic scatteringνe + p Æ e+ + n

Blue
PurpleFree proton
Bound proton in Oxygen.

Area normalized.

GeV / cq2 ( momentum transfer )Arbitrary scale ( linear )Arbitrary scale ( linear )Outgoing lepton momentum

Area normalized.

(GeV/c2)2

Clearly the small momentum transfer regionis suppressed due to Pauli Blocking and binding energy.
In the determination of the kinematics,
NEUT uses the classical ( simple ) energy and momentum conservations.

5. Charged Current Quasi elastic scattering
There are several recent models
Here is a coparison with the model by Nieves et al.
νe + 16O Æ e‐ + X

νμ + 16O Æ μ‐ + X

NEUT(Smith‐Moniz)
Nieves et al.
solid: ν, dashed: νNieves model is lower thanS‐M by 10% at 500MeV
for both in ve,vμRatio ( Nieves to S‐M ) is
within +/‐25% above 200MeV.
Currently, this model is applicable
up to 500MeV,
and not used in neut.
Authors are trying to extend
the energy range up to ~1GeV.

5. Charged Current Quasi elastic scattering
Comparison between the models
Smith-Moniz and Nieves et al.

νμ + n Æ μ- + p
Angular distribution of μ
cm2)

0.2

dσ/dQ 2 (x10

−38

0.15

6

−38

NEUT (Smith‐Moniz)
Nieves et al.

dσ/cosθ (x10cm2/GeV 2)

Differential cross-section dσ/dq2

0.1

NEUT (Smith‐Moniz)
Nieves et al.

4

2

0.05
0

0.2

0.4

0.6
2
Q (GeV2)

0
−1

−0.5

0

0.5

More detailed model by Nieves et al. shows
larger suppression in small q2 region.
Forward going particles are suppressed.

1cosθ

Single pion production
μ

νμ
π

n
p

Major background of the nucleon decay
Particles in the final state are same as the ones from nucleon decay.

Major background of the νe appearance search at T2K

γ from asymmetric decay of π0
might be misidentified as νe appearance signal.

Major contamination to the energy spectrum measurement.
If pions are absorbed,
event shape is similar to the CCQE
in the water Cherenkov detector.
Without the detection of the recoil-nucleon track,
it is difficult to discriminate single pion and CCQE.

6. Single meson production via resonancesν + N Æ l + N’ + π (K ,η)Based on D.Rein, and L.M.Sehgal, Ann. of Phys. 133(1981)
ν + N Æ l + Δ (N*)Δ(N*) Æ π + N’
Resonances up to 2GeV are taken into account.
In NEUT, only Δ absorption and Pauli blocking
are also considered( Effect : Delta absorption ~ 20%
Pauli blocking ~ a few % )ν μ + p Æ μ - + p + π+1

ν μ + n Æ μ - + n + π+

10 Eν (GeV)

1

10Eν (GeV)Δ++ (1232) dominant

first order :determined by resonance masses

Arbitrary scale ( linear )W

momentum of π

Arbitrary scale ( linear )ν p → l- p π +ν p → l- p π +GeV / c2

ν p → l- p π +pπArbitrary scale ( linear )Invariant massof resonance ( W )Arbitrary scale ( linear )6. Single meson production via resonances

MeV / cν n → l- n π +W

GeV / c2

ν n → l- n π +pπ

MeV / c

7. Single meson production via resonances
K and the other meson productions via resonances
Used to estimate the background of nucleon decay.
Basically same for the π production.
ν + N Æ l + N*
Δ(N*) Æ K + Λ
Use appropriate resonances and branching ratios.

etc.

In NEUT, we use upper limit of each branching ratio.
( for the background estimation )ν + N Æ l- + K + Λ

ν+NÆν+K+Λν + n Æ l- + p + η

ν+NÆν+N+η

8. Δ Æ Nγ decay
Δ resonance can decay into gamma (Br ~<0.5%)
This branching ratio is small,but NC ΔÆNγ can be backgroundin searching for the νμÆνe appearance.
This mode is added to NEUT, assuming– Kinematics are basically same as ΔÆNπ
ν + N Æ l + Δ (N*)Δ(N*) Æ γ + N’
– Three reactions are considered• CC : ν + n Æ l- + p + γ• NC : ν + n Æ ν + n + γ• NC : ν + p Æ ν + p + γ

γ
n

Δ+

8. Δ Æ Nγ decayEγ(GeV)

Arbitrary scale ( linear )Arbitrary scale ( linear )CC : ν + n Æ l‐ + p + γ

ν

γ
cosθγ

cosθγ

Eγ(GeV)

Arbitrary scale ( linear )Arbitrary scale ( linear )NC : ν + n Æ ν + n + γ

cosθγ

Eν is randomly selected between 200MeV and 3000MeVDeep inelastic scattering
Dominant interaction in the high energy region ( > several GeV )Understood as neutrino quark interaction.
Parton distribution function of nucleon is obtained
from the high energy lepton nucleon ( nucleus ) scattering experiments.

Thus, important in estimating the energy of neutrino
above several GeV.
( measure momentum of lepton
together with the total energy deposit
to estimate the energy of neutrino. )9. Deep Inelastic scatteringν + N Æ l + hadrons
Dominant interaction in the high energy region (> several GeV )νμW
Hadrons

N
Parton distribution functions ( F2 and xF3 )are extracted from the accelerator experiments.
However, major parton distribution functions
can not be used not applicable in the small W or q2 region.
( If we use the PDF as-is,
excess was observed in the small q2 region. )1) Use experimental results of neutrino scattering in that region.
2) Apply corrections to the parton distribution functions.

9. Deep Inelastic scatteringν + N Æ l + hadrons

Avoid double counting : the resonance region to the DIS region
W < 2GeV : Restrict # of mesons to be larger than 1
Exclude 1 meson production
by using multiplicity function <n>(W)Because non-resonant background is already includedin the single π production.
Multiplicity is determined based on the experimental result.
Current version: S. J. Barish et al. Phys. Rev D.17,1 (1978)( There are recent reports from CHORUS collaboration.
Eur.Phys.J.C51:775-785,2007 )W > 2GeV : Use PYTHIA to generate vectors.
# of π = 1

W < 2GeV

W > 2GeV

Rein & Sehgal

PDF + Custom kinematics( Bodek & Yang Corr. )# of π > 1

Use PDF + PYTHIA Use PDF + PYTHIA( Bodek & Yang Corr. )( Bodek & Yang Corr. )As for the parton distribution function,
we use the correction suggsted by Bodek and Yang.

9. Deep Inelastic scattering

Bodek and Yang ( For GRV98 )1. Modified scaling variable

2. Correction factor for the PDF ( K-factor ) to describe low q^2

3. Correction to Callan-Gross relation

A = 0.419
B = 0.223
C1v = 0.544
C2v = 0.431
Csea = 0.380
R: Fitted function

4. d/u ratio

9. Formation zone
In determining the location of the interaction,
the simple Woods-Saxon density function is used.
In order to pick up the location of the production pointof hadrons,
Formation Zone is taken into account.
The idea of formation zone:
Hadronization does not occur at the interaction point
Distance from the neutrino interaction point
to the production point of hadronis proportional to the momentum of hadron.
Actual interaction position
Generated position of hadron

Formation Zone (L) is defined as follows:
L = p / μ2
p : Momentum of hadron
μ2: fitted constant = 0.08 ± 0.04 GeV2

Ammosov et al.

9. Deep Inelastic scattering( G. Mitsuka )νμ Charged current cross sections

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

arbitrary unit ( linear )σ/Eν (10

-38

2

-1

cm GeV )muon neutrino and anti neutrino CC TOTAL Cross Srction
GRV94DI (original)
GRV94DI (bodek)
GRV98LO (original)
GRV98LO (bodek)

νμνμ
CCFR 90
CDHSW 87
GGM-PS 79

0

10

CHARM 88
BNL 80
CRS 8020

BEBC-WBB 79
IHEP-JINR 96
IHEP-ITEP 79

CCFRR 84
SKAT

30 50

100

200

Eν

(GeV)

150

GRV94
GRV94 (with correction)
GRV98
GRV98 (with correction)

250

Eν(GeV)q2 distribution ( atmospheric ν flux )GRV98
GRV98 (with correction)
With the correction,Eν<5GeVcross-section is suppressed
5<Eν<20GeV
andsmall q2 region is also suppressed.

q2(GeV2/c2)

9. Deep Inelastic scattering
Two examples of basic distributions( Atmospheric neutrino flux was used as input )Hadron multiplicity vs. Eν

Arbitrary scale ( log )Arbitrary scale ( linear )Invariant mass ( W ) vs. Eν

E

ν (G

eV
)

2

ass
m
t
n
ia
Invar

eV/c
G
)
(W

Hadr
on m
ultipl
ic

)
V
e
G
(

ity

Eν

(

)

10. Coherent pion productions ν + X Æ ν + X + π0()

π production without breaking the target nucleusνModel by Rein & Sehgal (Nucl.Phys.B223:29,1983)
νπ• Cross-section is smaller than
the resonance-mediated mode.
• Direction of π has peak in forward( Experimentally observedin the higher energy neutrino experiments. )()ν + 12CÆ l± + 12C + π0
Recently, cross-section of charged current coherent pion production
was found to be very small in ~<GeV region.
M. Hasegawa et al.(K2K collaboration) ( hep-ex/0506008 )10. Coherent pion productions
Low energy charged current coherent pion production seems to be small.
( Results from the K2K and the SciBooNE experiments. )()ν + 12CÆ l± + 12C + π±
DashedRein & Sehgal( original )SolidRein & Sehgal( with lepton mass corr. )DottedKartavtsev et al.
Dot dashed Alvarez-Ruso

Blue : SciBooNE
Red : K2K

(

)

(

)

ν + X Æ ν + X + π012. Nuclear effects ( Final state interactions of hadrons )Large fraction of the π from single π production
are coming from the decay of Δ.
Cross-section of those π is large.
Interaction probability of π in nucleus
generated by the single π production is large.
Momentum of πfrom p → e+ π0
is ~460<MeV/c.

11. Nuclear effects ( Final state interactions of hadrons )re-scattering of pion, kaon, eta, omega and nucleon in nucleus

Different models are used in each simulation program.
Implementation in NEUT
Cascade model is used.
Each particle is tracked in the nucleus
until it escapes from the nucleus.
For low momentum pion ( < 500MeV/c , so-called Δ region )Mean free paths of absorption and inelastic-scattering
are calculated based on a model by L.Salcedo et al. .
(Nucl. Phys. A484(1998) 79)* These mean free paths are position and momentum dependent.
* The Fermi surface momentum also has radius dependence.

For the higher momentum pion ( > 500MeV/c),kaons, eta, omega and nucleons
Parameters are taken from various experiments.

11. Nuclear effects ( Final state interactions of hadrons )Low momentum pion ( < 500MeV/c , so-called Δ region )(L.L.Salcedo et al. Nucl. Phys. A484(1998) 79)

Calculate interaction probability using Δh modeland π & Δ self-energy.
Pion scattering

π+N→Δ→π+N( 2 body )Pion absorption
π + N + N → Δ + N → N + N ( 2 body )Δππ + N + N → Δ + N → N + Δ → N + N ( 3 body )( Note: There are several other diagrams. See reference. )( 3 body )11. Nuclear effects ( Final state interactions of hadrons )π+p → π+p Interaction probability2d k2⎛ f ⎞ 2
2 1 ~⎜⎟P(π p → π p) = 2 ∫n(k ) ⎜
q c.m. GΔ (q + k ) Γ(q + k )3⎟ω (2π )
2
3 ⎝ mπ ⎠
+

+

1

3

*

−1

Δ propagater
Corrected width of Δ

1 ⎞⎛GΔ = ⎜ S − M Δ + iΓ ⎟
2 ⎠
⎝
1~
1
1
Γ(q + k ) = Γ × ( μ 3 c.m. + μ c.m. + 2)
2
2
4

Use local density to determine kF
when considering Pauli blocking effect.

-1 ( if μ0 < -1 )μ0 ( if -1 ≤ μ0 ≤ 1 )
1 ( if μ0 > 1 )μ c.m=EΔ E N c .m. − E F W
μ =q + k q c .m.
0

EΔ = q 0 + k 0
Ec . m . = q 2 c . m . + M 2
2

EF = k F + M 2
W= s11. Nuclear effects ( Final state interactions of hadrons )Absorption probability2

2⎛ 1 ~
1 4⎛ f ⎞ 2 ~⎞⎜⎜⎟⎟ q c.m. GΔ (q + k ) ⎜ Γ − Im Σ Δ ⎟ ρP=ω 9 ⎝ mπ ⎠⎝2⎠*Im Σ Δ (ω ) = −[CQ ( ρ / ρ 0 )α + C A 2 ( ρ / ρ 0 ) β + C A3 ( ρ / ρ 0 )γ ]C (Tπ ) = ax 2 + bx + c

x = Tπ / μE.Oset et al. Nucl. Phys. A468 (1987) 631

CQ (MeV)CA2 (MeV)

CA3 (MeV)

α

β

a

-5.19

1.06

-13.46

0.382-0.038

b

15.35

-6.64

46.17 -1.322

0.204

c

2.06

22.66

-20.34

0.613

1.466

γ=2β

11. Nuclear effects ( Final state interactions of hadrons )Interaction probability ( mean free path ) depends onthe π momentum and location ( radius ~ density ).
Interaction probability( scattering )

ra
d

iu
s

(f
m

Interaction probability( absorption )

ra
d
)

pπ

/c
( M eV

)

iu
s

(f
m

)

eV
p (M

/c )

π

Fermi surface momentum depends on the local density.
Smaller q2 interaction is allowed at the peripheral region

11. Nuclear effects ( Final state interactions of hadrons )Kinematics of the scattered particles
Use the results of phase shift analysis of π-N scatteringAlso, the medium correction is applied to each phase shift.
( R.Seki et al., Phys. Rev. C27 (1983) 2817 )11. Nuclear effects ( Final state interactions of hadrons )Interaction Probability(arbitrary scale)

Higher momentum ( pπ ≥ 500MeV/c ),π - N interaction cross-section is used.
nπ+ Æ pπ0

π+ N

Nπ+ Æ Nπ+multi‐pi
Absorption

Mean multiplicity

pπ ( MeV / c )π+ p1.94 + 0.28 * log (s) + 0.130 * (log (s))2π- p0.59 + 0.81 * log (s) + 0.074 * (log (s))2

s : Total energy

Actual multiplicity is calculated from
J.Whitmore Phys. Rep. 27C (1976) 187.

11. Nuclear effects ( Final state interactions of hadrons )Interaction probabilities of π

generated in 16O

Checked with π+ 16O scatteringor photo - π production
experiments.
Monte-Carlo simulation reproduces
various distributions quite well.

Comparison with π+ 16O scattering experiment11. Nuclear effects ( Final state interactions of hadrons )Interaction probabilities of π
momentum of π0(atmospheric ν)@ SK(Simulation:
Vector level)

Blue
Red

: Before FSI: After FSI

π0 momentum (GeV/c)# of FC 2ring π0 events

Arbitrary unit

momentum of π0@ K2K-1KT

preliminary( MC is normalized
by area )11. Nuclear effects ( Final state interactions of hadrons )Interactions of η
η + N → N* → N + X

X : η, π, ππInteraction cross-section : Use Breit - Wigner formulaσ (k ) =

π
k

2

⋅

ΓηN ΓX(W − M N ) 2 + Γtot2 / 4
Γtot : Total width of N*
ΓηN : Partial decay width of N* → η + N
ΓηX : Partial decay width of N* → X

As the intermediate resonance (N*),
N(1535) and N(1650) are considered.

The direction of the scattered η is isotropic in the resonance rest frame.
ω is also simulated in the same manner as η.

11. Nuclear effects ( Final state interactions of hadrons )Nucleon re-scattering

Originally prepared by the members of IMB group. ( W. Gajewski for K2K )Nucleon re-scattering is also simulated by using the cascade model.
Elastic scattering, single π and two π productions are considered.
( Original ref. S.J.Lindenbaum and R.M.Sternheimer, Phys.Rev. 105 (1957),
Modifications in MECC7 and GCALOR have been taken into account. )N+N→N +N
N + N → N* + N
N + N → N* + N*

N* → N’ + πInteraction probabilities ( tables of each interaction mean free path )and direction of nucleons or intermediate resonances
are taken from MECC7 and GCALOR.
( Basic parameters are taken from various experiments. )Decay of the intermediate resonances
Isotropic in the resonance rest frame.

11. Nuclear effects ( Final state interactions of hadrons )Some distributions ( results of the simulation )Nucleon re-scattering

Target : 16O

Interaction probability (%)

Momentum dependenceof the interaction probabilities of proton

Blue
Black ( dashed )Red (dotted )Green ( dot dashed )Scattering angle of the outgoing nucleon( most energetic one )Incident momentum of proton
0.5 ~ 1.0 GeV / c ( uniform )No interaction
Elastic scattering
single π production
two π production

momentum of proton ( MeV / c )Scattering angle ( deg. )12. Remaining Issues
Nucleon emission after pion absorption
From the experience of SciBooNE,
we realized that the nucleon emission
after the pion absorption seems to be visible
with the full active detectors.

Need to incorporate various recent precise models.
From dipole form factors to more precise ones.
Use spectrum functions instead of the simplest Fermi gas mode.
More proper treatment of resonances in meduim.
Nuclear medium correctionin the meson production via resonance.
Another resonance production models.
Improved treatments of the higher momentum pion in nuclear medium.

Fin.

Sample program of NEUT
neut_ntpl [ CARD FILE ] [ output NTUPLE file ]The card file controls the energy distribution, direction, target etc..
In the following pages, there are some information how to control the program.

NEUT card file

C-------------------------------C Number of events ; EVCT-NEVT
EVCT-NEVT 1000
C-------------------------------C Particle Code ; EVCT-IDPT
EVCT-IDPT 14
C-------------------------------C fixed VERTEX ; EVCT-MPOS 1
C random VERTEX ; EVCT-MPOS 2C
C EVCT-MPOS 1C VECT-POS 100. 0. 0.
C
EVCT-MPOS 2
EVCT-RAD 100.
C-------------------------------C fixed DIRECTION ; EVCT-MDIR 1
C random DIRECTION ; EVCT-MDIR 2C
EVCT-MDIR 1
EVCT-DIR 0. 0. 1.
C-------------------------------C fixed MOMEMTUM ; EVCT-MPV 1
C random MOMEMTUM ; EVCT-MPV 2C
C EVCT-MPV 1
C EVCT-PV 1000.
EVCT-MPV 2
EVCT-PV 0. 10000.

C **** TARGET INFORMATION ****CC NUMBNDN : total number of neutronC(e.g. CH => 6, H2O => 8, Ar => 22, Fe => 30)
C
NEUT-NUMBNDN 8CC NUMBNDP : total number of bound protonC(e.g. CH => 6, H2O => 8, Ar => 18, Fe => 26)
C
NEUT-NUMBNDP 8C
C NUMFREP : total number of free protonC(e.g. CH => 1, H2O => 2, Ar => 0, Fe => 0)
C
NEUT-NUMFREP 2
C
C NUMATOM : atomic number of atom heavier than hydrogenC(e.g. CH => 12, H2O =>16, Ar => 40, Fe => 56)
C
NEUT-NUMATOM 16
C
NEUT-PFSURF 0.225
NEUT-PFMAX 0.225
CNEUT card file
C **** NEUTRINO INTERACTION ****CC FERM : Fermi motion 0 : on ( default ) 1 : offC
NEUT-FERM 0C
C PAUL : Pauli blocking 0 : on ( default ) 1 : offC
NEUT-PAUL 0
C
C NEFF : Nuclear effect in O16 0 : on ( default ) 1 : offC
NEUT-NEFF 0C
C IFORMLEN : Formation zone 1: on (default) 0: offC
NEUT-IFORMLEN 1C
C Nucleon rescatteringC
C NUCRES-RESCAT 1: on (default) 0: off
C
NUCRES-RESCAT 1C
C NUCRES-XNUCFACT
C cross-section factor to study uncertainty default = 1.
C
NUCRES-FACT 1.

CC PDF for DIS is set in this section
C (GRV94DI -> 7, GRV98_LO -> 12)
NEUT-PDF 12C PDF Correction is used?
C( original=0, modified=1)
NEUT-BODEK 1
C Select Coherent pion modelC
Rein & Sehgal=0(default)
C
Kartavtsev et al.
=1
NEUT-COHEPI 0C

C RAND : random seedC
0 : Read RANDOM number from FILE
C
1 : Generating RANDOM SEED from the timeC
NEUT-RAND 1

NEUT card file
C MODE : Interaction modeC
0 : normal ( default )C-1 : input cross section by NEUT-CRS / NEUT-CRSBCn : sellect one mode ( n > 0 )C
NEUT-MODE 0C
C CRS : Multiplied factor to cross section on each mode. ( neu )C CSRB : Multiplied factor to cross section on each mode. ( neu-bar )CC
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
NEUT-CRS 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
NEUT-CRSB 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
C
nu
nub
C 1
CC Q.E.
C 2-4:
CC 1piC 5:
CC DIS 1320
C 6-9:
NC 1pi
C 10:
NC DIS 1320
C 11-13 NC els
11-14:NC els
C 14,15: coherent
15,16:C 16:
CC eta17:
C 17,18: NC eta
18,19
C 19:
CC K
20:
C 20,21: NC K
21,22:
C 22:
dummy
C 23:
CC DISC 24:
NC DIS

Interaction modes used in NEUT######### NEUTRINO MODE #########***** CHARGED CURRENT *****-- ELASTIC -1 : NEU,N --> LEPTON-,P-- SINGLE PI FROM DELTA RESONANCE -11 : NEU,P --> LEPTON-,P,PI+
12 : NEU,N --> LEPTON-,P,PI0
13 : NEU,N --> LEPTON-,N,PI+
16 : NEU,O(16) --> LEPTON-,O(16),PI+-- SINGLE GAMMA FROM DELTA RESONANCE -17 : NEU,N --> LEPTON-,P,GAMMA-- MULTI PI (1.3 < W < 2.0 GeV) -21 : NEU,(N OR P) --> LEPTON-,(N OR P),MULTI PI-- SINGLE ETA FROM DELTA RESONANCE -(added 97/12/01 J.Kameda)
22 : NEU,N --> LEPTON-,P,ETA0-- SINGLE K FROM DELTA RESONANCE -(added 98/02/25 J.Kameda)
23 : NEU,N --> LEPTON-,LAMBDA,K+-- DEEP INELASTIC (2.0 GeV < W , JET set) -26 : NEU,(N OR P) --> LEPTON-,(N OR P),MESONS***** NEUTAL CURRENT *****-- SINGLE PI FROM DELTA RESONANCE -31 : NEU,N --> NEU,N,PI0
32 : NEU,P --> NEU,P,PI0
33 : NEU,N --> NEU,P,PI34 : NEU,P --> NEU,N,PI+
36 : NEU,O(16) --> NEU,O(16),PI0-- SINGLE GAMMA FROM DELTA RESONANCE -38 : NEU,N --> NEU,N,GAMMA
39 : NEU,P --> NEU,P,GAMMA-- MULTI PI (1.3 GeV < W < 2.0 GeV) -41 : NEU,(N OR P) --> NEU,(N OR P),MULTI PI-- SINGLE ETA FROM DELTA RESONANCE -(added 97/12/01 J.Kameda)
42 : NEU,N --> NEU,N,ETA0
43 : NEU,P --> NEU,P,ETA0
52 : NEU,N --> NEU,N-- SINGLE K FROM DELTA RESONANCE -(added 98/02/20 J.Kameda)
44 : NEU,N --> NEU,LAMBDA,K0
45 : NEU,P --> NEU,LAMBDA,K+-- DEEP INELASTIC (2.0 GeV < W , JET set) -46 : NEU,(N OR P) --> NEU,(N OR P),MESONS-- ELASTIC -51 : NEU,P --> NEU,P

Interaction modes used in NEUT######### ANTI NEUTRINO MODE #########***** CHARGED CURRENT *****-- ELASTIC --1 : NEUBAR,P --> LEPTON+,N-- SINGLE PI FROM DELTA RESONANCE --11 : NEUBAR,N --> LEPTON+,N,PI-12 : NEUBAR,P --> LEPTON+,N,PI0-13 : NEUBAR,P --> LEPTON+,P,PI-** NEUTAL CURRENT **-- SINGLE PI FROM DELTA RESONANCE --31 : NEUBAR,N --> NEUBAR,N,PI0-32 : NEUBAR,P --> NEUBAR,P,PI0-33 : NEUBAR,N --> NEUBAR,P,PI-34 : NEUBAR,P --> NEUBAR,N,PI+-36 : NEUBAR,O(16) --> NEUBAR,O(16),PI0-16 : NEUBAR,O(16) --> LEPTON+,O(16),PI--- SINGLE GAMMA FROM DELTA RESONANCE --38 : NEUBAR,N --> NEUBAR,N,GAMMA-39 : NEUBAR,P --> NEUBAR,P,GAMMA-- SINGLE GAMMA FROM DELTA RESONANCE --17 : NEUBAR,P --> LEPTON+,N,GAMMA-- MULTI PI (W > 1.4 GEV) --41 : NEUBAR,(N OR P) --> NEUBAR,(N OR P),MULTI PI-- MULTI PI (W > 1.4 GEV) --21 : NEUBAR,(N OR P) --> LEPTON+,(N OR P),MULTI PI-- SINGLE ETA FROM DELTA RESONANCE -(added 97/12/01 J.Kameda)-42 : NEUBAR,N --> NEUBAR,N,ETA0-43 : NEUBAR,P --> NEUBAR,P,ETA0-- SINGLE ETA FROM DELTA RESONANCE -(added 97/12/01 J.Kameda)-22 : NEUBAR,P --> LEPTON+,N,ETA0-- SINGLE K FROM DELTA RESONANCE -(added 98/02/25 J.Kameda)-23 : NEUBAR,P --> LEPTON+,LAMBDA,K0-- DEEP INELASTIC (2.0 GeV < W , JET set) --26 : NEUBAR,(N OR P) --> LEPTON+,(N OR P),MESONS-- SINGLE K FROM DELTA RESONANCE -(added 98/02/20 J.Kameda)-44 : NEUBAR,N --> NEUBAR,LAMBDA,K0-45 : NEUBAR,P --> NEUBAR,LAMBDA,K+-- DEEP INELASTIC (2.0 GeV < W , JET set) --46 : NEUBAR,(N OR P) --> NEUBAR,(N OR P),MESONS-- ELASTIC --51 : NEUBAR,P --> NEUBAR,P-52 : NEUBAR,N --> NEUBAR,NMeanings of the variables in ntuple
MODE
NUMNU
IPNU
ABSPNUPNU: Interaction mode
: Number of particles ( including initial neutrino and nucleon ): Particle Code: Absolute momentum of particle ( GeV / c ): Momentum of particle ( GeV / c )

NPAR
IPV
IORGV
ICRNV

: Number of particles ( after the final state interactions ): Particle code
: Parent particle: Tracking flag ( set to 0 if the particle was interacted,
absorbed or disappeared ): Interaction code ( If the particle already interacted with the oters,
this flag is set. )0:
Not interacted yet.
1:
Decayed to the other particles
2
:
N/A
3
:
Absorbed
4:
Charge exchanged5:
Stopped
6:
N/A
7:
Particle production
8:
Scattered: Absolute momentum of particle: Momentum of particle

IFLGV

ABSPV
PMOMV

Water Chernkov detector
High efficiency in detecting electrons
low momentum neutral pi0
Relatively low threshold in detecting muon and charged pion

Precise particle type identification
showering ( e-like ) electron, gamma
non-showering ( mu-like ) muon, charged pions, etc.

PID performance
Detection threshold is high for the massive particles like proton
Charge Identification is not possible

Konstantin S. Kuzmin et al. Eur.Phys.J.C54:517-538,2008

6. Deep Inelastic scatteringν + N Æ l + hadrons
Corrections proposed by Bodek and Yang
1. Bjorken scaling xÆ xw
Q2 + Bxw = x 2
Q + Ax( hep-ex/0203009, hep-ex/0308007 )A : target mass effecthigher twist effect
B : photoproduction limit(Q2=0)

2. Correction to the structure function F2
Q2
to fit both intermediate-x and low-x
F2 ( x) → 2
F2 ( xw )Q +C
3. d/u ratio
Correction to the conversion
dv Æ d’v(dv,uv)
from F2d to F2nuv Æ u’v(dv,uv)
4. Longitudinal R

1 + 4 Mx 2 Q 2
2 xF1 = F2
1+ R

Corrections for the spin of the target.

These correction parameters are obtainedby fitting various existing experimental results.

4. Single meson production via resonances(G.Mitsuka)
Simulation result -Integrated cross sectionBerger and Sehgal add the pion-pole term in the hadronic current.
This effect is the almost same as in the coherent-π production
hep-ph/0709.4378

Black : νe
Red : νμGren : ντ

Lepton mass / Original (%)

Lepton mass / Original (%)νμ p Æ μ- π+ p

An amount of reduction depends on lepton flavor and energy
These values are consistent with the description in references

4. Single meson production via resonances(G.Mitsuka)
Simulation result -Kinematics-

Pμ(GeV)cosθμ

Lepton momentum has no significant change
Lepton scattering angle has suppression in forward direction
Pion and nucleon kinematics are not changed