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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
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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%
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
Single Pion Production Cross Section
Prediction = Rein-Sehgal MA=1.2 GeV/c2
1x10-381.0(cm2)
0.0
MS@nuint01
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
Strange particle production and CC/NC Coherent Pion Production
nK+Comparison with NUANCE / Neugen
(Zeller@nuint02)
10-38
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
Total Charged-Current Cross Section
Total cross section increases with energy, = E.
1.0x10-38
(cm2)
/ E
/ E
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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.
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
MA measurements
1.0
Singh@nuint01
MA (GeV/c2)
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
3. Recent Progress in Calculation (NuInt01/02)
Elastic Form Factors Spectral Function = Beyond Fermi Gas Deep Inelastic Scattering Single Pion Production
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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
12 February 2003 M.Sakuda Neutrino - Nucleus Interactionsratio_JhaKJhaJ_D0DD.pict
Effect of New Vector Form Factors GMn,GMp,GEp ,GEn
12 February 2003 M.Sakuda Neutrino - Nucleus Interactionsratio_JhaKJhaJ_D0DD.pict
Effect of finite GEn (with)/(without)
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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
・
・・
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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.
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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
12 February 2003 M.Sakuda Neutrino - Nucleus Interactions
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