12 February 2003 M.Sakuda Neutrino － Nucleus Interactions Low Energy Neutrino-Nucleus Interactions Makoto Sakuda (KEK) in collaboration with C.Walter,

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions

Low Energy Neutrino-Nucleus Interactions

Makoto Sakuda (KEK) in collaboration with C.Walter, K.McConnel, E. Paschos et al.

10 June 2003 @ NuFact03 Outline1. Neutrino-Nucleus Interactions 2. Data of low-energy neutrino-nucleus scattering3. Recent Progress in Calculation (NuInt01/02)

Elastic Form Factors Spectral Function = Beyond Fermi Gas Deep Inelastic Scattering Single Pion Production

4. Summary


1. Neutrino-Nucleus Interactions in the Few-GeV Region

1. Oscillation analysis need cross section and spectrum.　　 Y(E)=(Neutrino flux) · （ E) · (Number of target nucleons) .

Accurate measurements of CC neutrino cross sections exist for E>20 GeV ， with accuracy ±3%. Naples@ nuint02

Measurements of neutrino-nucleus cross sections at E=0.5-20 GeV are still poor. Accuracy is about ±20% and spectrum even worse.

Nuclear effects become significant. Neutrino oscillation experiments (K2K ， MiniBooNE, MINOS ， OPER

A, ICARUS, JHF-Kamioka) have to work in this complex energy region. We want to measure →e oscillations at sin2213~0.01, especially

after KamLAND result. Cross section and spectrum at a few % level are needed in the future.

2. Weak nucleon form factor itself is very interesting. We need to update both vector and axial-vector form factors if we wan

t to predict the spectrum better than 10%. Horowitz@nuint02,Singh@nuint01, Budd@nuint02


Ishida(K2K)@nuint02Sensitivity to MA

(MA)stat. ~ .06GeV/c2.(MA)sys. ~ .15GeV/c2.

d/dQ2 (quasi-elastic scattering)

BNL Deuterium BCCalculation by Ch.L.Smith et al.MA= 1.07±0.05


2. Data of low-energy neutrino-nucleus scattering

Overall flux error is about ±10-20% at low energy.Experiments below 20 GeV were performed with wide-band beams.

Many processes contribute equally, with ±20% errors.Quasi-elastic scatteringSingle pion productionMulti-pion production/DISCoherent-pion productionNC

Nuclear effects can be different for different target.Fermi-motion and Binding energyPauli exclusion effectsNuclear rescattering Pion absorption


Pauli exclusion effect

Quasi-elastic

production

W/o Pauli effect

W/ Pauli effect

10-15% suppression At low Q2Total 3% reduction

E=1.3 GeV ， kF=220 MeV/c

Pp

Pp

q

W

np

Pp

q

If P <kF , suppressed.

Total 8%

Nuclear effects are large in the low Q2 region, where the cross section is large.

d/dQ2

d/dQ2 0.5 1.0


Charged-Current Quasi-elastic Scattering

This is the simplest and the most important reaction. Calculation by Ch.L.Smith et al. with MA=1.0.

np)pn)

1x10-381.0(cm2)

0.0.1 1.0 10. 10.50. 1.0.1

1.0

Pauli effect ~8%


Single Pion Production Cross Section

Prediction = Rein-Sehgal MA=1.2 GeV/c2

1x10-381.0(cm2)

0.0

MS@nuint01


Strange particle production and CC/NC Coherent Pion Production

nK+Comparison with NUANCE ／ Neugen

(Zeller@nuint02)

10-38


Total Charged-Current Cross Section

Total cross section increases with energy, = E.

1.0x10-38

(cm2)

/ E

/ E


Neutral Current Interactions

1kton Neutral-Current 0

production (P0)

(Mauger @nuint01, Preliminary)

P0

0. 1.0 1.00. (GeV/c)

Very few data are available at low energy.

E734reports MA=1.06+-0.05 for p→ p.


MA measurements

1.0

Singh@nuint01

MA (GeV/c2)


d/dQ2 ( production) from BNL Furuno@nuint02

μ －ｐ π ＋ ns

Q2(GeV)

Rein-Sehgal (MA=1.2 GeV/c2 )

Normalized by the entries

MA(1) (Rein-Sehgal model)

SKAT89 MA=1.01+/-0.09+/-0.15CF3Br

BEBC89 MA=1.01+/-0.10D2


3. Recent Progress in Calculation (NuInt01/02)

Elastic Form Factors Spectral Function = Beyond Fermi Gas Deep Inelastic Scattering Single Pion Production


3.1) Nucleon Form Factors 　　　 de Jager @PANIC02

1

)()()(

1

)()()(

)()(2

1)(

)()(2

1)(

4)()()(

)()()(

)()(2

)()'()(||)'(

222

2

222

1

2

2,1

2

2,1

2

2,1

2

,

2

,

2)(

,

2

22

2

2

1

2

2

2

2

1

2

2

2

2

1

QGQGQFand

QGQGQF

orQFQFQF

QGQGQG

M

QwithQFQFQG

QFQFQG

puQFqM

iQFpupNpN

CurrentneticElectromag

V

E

V

MVV

M

V

EV

npV

n

ME

p

ME

SV

ME

NNN

M

NNN

E

NN

emJp P

qe e


22

22

222

2

22

5

21

2

2

2

1

21

2121

212121

)(2)(

0035.02617.1)0(,)/1(

)0()(

)()()()'()(||)'(

)()(2

)()'()(||)'(

)(||)'()(||)'(

arg

Qm

QMFQF

FwithMQ

FQF

puQFqQFpupnApp

puQFqM

iQFpupnVpp

pnAVpppnJpp

AVJ

CurrentedCh

AP

A

A

AA

pA

i

VVi

iiCC

iii


3.1) Quasi-elastic interaction 　 np

A = Q2/4M2 [(4 + Q2/M2)|FA|2 - (4 - Q2/M2)|FV1|2

+ Q2/M2(1-Q2/4M2)|FV2|2+ 4Q2/M2ReFV*

1FV2 ]

B = -Q2/M2ReF*A(FV

１ + FV２ ),

C = 1/4(|FA|2 + |FV1|2 + Q2/4M2|FV

2|2).

Vector Form factors 　 GE

p=D, GMp=pD, GM

n=nD, GEn=nD,

D=1/(1+Q2/MV2)2, MV=0.843 (GeV/c2)

pn=5.6, = Q2/4M2

Axial-vector form factor FA

FA(Q2)=-1.2617/(1+Q2/MA2)2

ddQ2

[A(Q2)-B(Q2)(s-u)+C(Q2)(s-u)2]M2G2cos2c

(8E2)

=

Form Factors F1V,F2

V,and FA and (s-u)=4ME-Q2-M2


Nucleon Vector Form Factors

A simple dipole form D=(1+Q2/MV

2) -2, MV=0.843is good to 10-20% level forVector Form Factors.

Fig -- Bosted, PRC51,409,’95Red=DipoleCurve=(1+a1Q+a2Q2+.+a5Q5)-1

GMnGMp,GEpCross section shape will change if we use these data.

GMp/pD

GEp/D

GM ｎ / ｎ D

(GE ｎ /D )2

Q2

12 February 2003 M.Sakuda Neutrino － Nucleus Interactionsratio_JhaKJhaJ_D0DD.pict

Effect of New Vector Form Factors GMn,GMp,GEp ,GEn


Effect of New Vector Form Factors GMn,GMp,GEp ,GEn


Effect of finite GEn (with)/(without)


3.1) Model beyond the Fermi-gas modelSpectral Function Calculation or Local Density Approximation (Pandharipande@nuint01,Benhar,Nakamura,Gallagher@nuint02)

Spectral Functions P(p,E) for various nuclei, eg.16O, are estimated by Benhar et al. using e-N data.

P(p,E) : Probability of removing a nucleon of momentum p from ground state leaving the residual nucleus with excitation energy E.

0. 100. 200. P (MeV/c)

20.

40.

E(MeV)

Fermi momemtum

Fermi Gas model

p


Lepton energy in quasi-elastic -N interaction -Comparison of Fermi Gas model and Spectral Function Calculation-

Large E and Large p tail exist in data.

Shift at a level of 10 MeV may exist. <B>=25 MeV (Fermi-Gas)

<E>LDA=40 MeV

Benhar,Gallagher,Nakamura@nuint02


Test of neutrino models using (e,e’) Data (•). The energy transfer (=Ee-Ee’) at the fixed scattering angle .

Oxygen

Carbon

Oxygen

Carbon

Oxygen

Oxygen

Spectral function calculation agrees with data.

Thus, the lepton energy kinematics can be checked within a few MeV.

For example, accuracy of <10 MeV is needed in E reconstruction in the future while the present accuracy is about 20-40 MeV due to the energy calibration and nuclear effects.

MS @nuint01,Walter ， Wood@nuint02

)(

)(~2

kmL

GeVEm

q

eEe’

n p


3.3) N transition form factors

)()(

)()''()(

)/()(

)'(

)(||)'(

)()()()(

)''()(

)/()(

)'(

)(||)'(

)(||)'()(||)'()(||)'(

52

2

62

52

2

4

2

3

5

2

62

2

5

2

2

4

2

3

pqq

M

QCgQCpqpqg

M

QCqqg

M

QCp

pNAp

pqqQCpqpqgM

QCpqpqg

M

QCqqg

M

QCp

pNVp

pNAppNVppNJp

VV

VV

VVVV

・

・・


Schreiner-von Hippel(’73)/Adler (‘68) model

Form factors CiV,A (i=1,6) for N

Vector form factors C3V (Q2) = 2.05/ (1+Q2/Mv 2)2 , 　 Mv 2 =0.54 　（ GeV) 2

C4V (Q2)=-M/M C3V (Q2),

C5V (Q2)=0. C6V (Q2)=0. (CVC) Axial form factors Ci A (Q2) = Ci A (0) /(1+ Q2/MA

2)2, (i=3,4,5)

C6A (Q2)= C5A (Q2) M2/(m2+Q2) [PCAC] C3A (0)= 0. C4A (0)=-0.3, C5A (0)=1.2


SLAC/Jlab resonance data (not used in the fit)

3.3) DIS (Bodek-Yang at NuInt01/02)

).735.1/()624.0(

)(188.0

)(

)()()(

22

22

2

2

22

xQQxxwhere

xFQ

QxF

xqxxxqexF

w

w

iiii

Dashed: GRV94 Red:Bodek-YangThis correction is significant at low Q2 region.NB. Three resonances are evident.


Nuclear PDF and its effect on the DIS cross section

0.7

0.8

0.9

1

1.1

1.2

0.001 0.01 0.1 1

EMC NMC E139 E665

0.7

0.8

0.9

1

1.1

1.2

0.001 0.01 0.1 1

x

BCDMS E87 E139 E140

Q2= 5 GeV2


The accuracy of Neutrino-Nucleus (-N) interactions at E=0.1-10 GeV is about +-10% or more. We will combine both e-N data and -N data to understand -N interactions better. It is very important for the running and the future neutrino oscillation experiments.

A strong community of nuclear and high-energy physicists has been formed at NuInt01/02 Workshop. Some JLAB people not only collaborate on the analysis of form factors and nuclear effects, but also ask proposals for measurements at JLAB usuful for neutrino physics.

K2K near detectors (1kton/SciFi) : producing new data. BooNE : soon. K2K upgraded detector (SciBar) will be complete this summ

er. MINOS near detector and ICARUS will come in 2006. Joint nuclear/high-energy physics proposals at NuMI for dedicated measur

ement of neutrino-nucleus interactions are being discussed. Measurement of strange spin by NC/CC is proposed.

Re-analysis of old data (BNL,ANL) using current formalism is still valuable. Open Neutrino Generators are available: Nuance and Fluka.

5. Summary

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions Low Energy Neutrino-Nucleus Interactions Makoto Sakuda (KEK) in collaboration with C.Walter,

Documents

nucleus cross sections

data of low

low q2total

15cf3brbebc89 ma

nuint02 nsq2gevreinsehgal

complex energy region

e734 reports ma

different target