1 august 2003 m.sakuda neutrino － nucleus interactions 数 gev...

1 August 2003 M.Sakuda Neutrino － Nucleus Interactions

数 GeV 領域のニュートリノ原子核反応の測定と計算の進展

作田　誠 (KEK 、 IPNS)1 August 2003 @ 東工大

Outline1. ニュートリノ振動実験2. ニュートリノ原子核反応の測定データ3. 最近の計算の進展 (NuInt01/02)

Nucleon and Form Factors Spectral Function = Beyond Fermi Gas Deep Inelastic Scattering 　と　 Single Pion Prod

uction ４ . まとめ→問題提起


Workshop on Neutrino-Nucleus Interactions in the Few-GeV Region

NuInt01 (KEK, Dec.13-16,2001)

Nucl.Phys.B(Proc.Suppl.)112. published.

NuInt02

(UC Irvine ， Dec.12-15, 2002)


概要１． K2K 実験は、提案の 7 割のビームを消化し、順調にデータを収集

している。ニュートリノ振動を９９％まで再確認。２． K2K 実験や将来のニュートリノ実験ではニュートリノ原子核反応

の精度が数％で要求される。現在の精度は 10-30 ％。３． 1990 年になって JLAB 、 MAMI 等の偏極ビーム、偏極標的を使っ

た電子散乱実験で、 1960 年代に測定された核子構造が漸く 10 ％以下の精度で測られている。

GEp=D, GM

p=pD, GMn=nD, GE

n=nD, D=1/(1+Q2/MV

2)2, MV=0.843 (GeV/c2)pn=5.6, = Q2/4M2

　 Galster Paremetrization からのずれ。４．ニュートリノ実験もこれからは 10 ％以下を問題にしていかなけ

ればならない。ニュートリノ実験では、 V ー A の Axial Structure を探る。

５．電子原子核、ニュートリノ原子核反応は、対である。 V-A　解析実務では、束縛エネルギー、フェルミ運動量、パウリ禁止則、

形状因子、終状態相互作用、核内吸収等の原子核の古典的な問題との苦闘である。


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


RMC = .017 +/- 0.002

We account for the differenceof +/-10%

2) Proton Re-scattering


束縛エネルギーとフェルミ運動量（ホッフーリーツの教科書）Test of neutrino models using (e,e’) Data (•). The energy transfer (=Ee-Ee’) at the fixed scattering angle .

Oxygen

Carbon

Oxygen

Carbon

Oxygen

Oxygen

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


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


K2KSensitivity 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


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

K2K 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 measurementsThis has to be reevaluated with new vector FFs.

1.0

Singh@nuint01

MA (GeV/c2)


d/dQ2 ( production) from BNL Furuno@nuint02

μ －ｐ π ＋ ns

Q2(GeV)

Rein-Sehgal (MA=1. ０８ GeV/c2 )

Normalized by the entries

MA(1) (Rein-Sehgal model)

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


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

p Pq

e e

Electromagnetic current (Jaem) and weak hadronic charge

d current (JaCC=Va

1+i2–Aa1+i2) is written in terms of form

factors:

1

)()()(

1

)()()(

)()(2

1)(

4)()()(

)()()(

222

2

222

1

2

,

2

,

2(

,

2

22

2

2

1

2

2

2

2

1

2

QGQGQFand

QGQGQF

QGQGQG

M

QwithQFQFQG

QFQFQG

V

E

V

MVV

M

V

EV

n

ME

p

ME

V

ME

NNN

M

NNN

E

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

),()(2

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

),()(2

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

22

5

21

2

2

2

1

21

2

2

2

1

puQFqQFpupnApp

puQFqM

iQFpupnVpp

puQFqM

iQFpupNJpN

pA

i

VVi

NNem


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

　　 -m2/4M2 (| FV1 + FV

2 |2 + | FV1 +2Fp |2 –4(1+) |Fp|2]

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

Form Factors F1V,F2

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

]u)-)(sC(Qu)-)(sB(Q -)[A(QdQ

d 22222

2

2

22

8

cos

E

GM cF


How to Measure Nucleon Vector Form Factors

In the past, the nucleon electromagnetic form factors have been measured from unpolarized electron beam scattering experiments using the Rosenbluth separation technique.

The accuracy at high Q2 (>1 (GeV/c) 2) was limited with this method. Nucleaon form factors were studied using a simple dipole parametrizations. Since 1993, new accurate measurements of the nucleon form factors were made possible with a new method using polarized electron beams and polarized targets. Clear deviation from a simple dipole parametrization is seen for the form factors and the better parametrizations for vector form factors were proposed. Recoil polarization Px GE

N 　 , Px/Pz GEN/GM

N 　The effect of those new form factors on the neutrino quasi-elastic cross sections was shown to be a few %.

2/tan212/sin4

2/cos, 22

22

43

2'2

MME G

GG

E

EE

d

d


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. REDGMnGMp GEp

Curve – Bosted, PRC51,409,’95Curve=(1+a1Q+a2Q2+.+a5Q5)-1

E.J.Brash et al., , Phys.Rev.C65,051001(2002). Similar

Neutrino cross section shape will change if we use these data.

Q2

de Jager@PANIC02


GEp 　　 GM

n

Polarized electron beam experiments

Q2

All data Polarization

1 August 2003 M.Sakuda Neutrino － Nucleus Interactionsratio_JhaKJhaJ_D0DD.pict

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


Effect of finite GEn (with)/(without)


Effect of finite GEn Budd @nuint02

(without)/(with)


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)= ０ [PCAC] C3A (0)= 0. C4A (0)=-0.3, C5A (0)=1.2


N FF falls more rapidly than Nucleon FF (MV)

Size of is larger = Q2 distribution

small

New

1975


3.4) For better single pion production model

Rein-Sehgal model need nuclear correction. Much simpler model like Schreiner-von Hippel may work. Paschos,Singh,MS

Below for W<1.6 GeV/c2, model with Schreiner parameters and three resonances may be used.

Ci A,V = Ci A,V (0) G(W,Q2 ,kF) 1/2/ (1+Q2/MV,A2)2 /(1+Q2/3MN

2)

G(W,Q2 ,kF) Pauli effect. Non-resonant contribution,<20%, may be added.

For W>1.6, Bodek’s DIS may be used. Paschos-Pasquali-Yu, NPB588(‘00)263, already show that this scheme may work. Paschos,Yu, & Sakuda, DOTH0301, to be published.


d/dQ2 ( production) from BNL Furuno,Suzuki,Kitagaki,MS,etal, to be published.

μ －ｐ π ＋ ns

Q2(GeV)

Rein-Sehgal (MA=1. ０８ GeV/c2 )

Normalized by the entries

MA(1) (Rein-Sehgal model)

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


Flux independent ratio σ(single π)/σ(QE) : BNL reanalysis Furuno@nuint02

-pπ+

-nπ+

-pπ0

Eν （ GeV)

Eν （ GeV)

Eν （ GeV)


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 still poor, about 10-20% in cross section measurements and distributions.

We will combine both e-N data and -N data to understand -N interactions better. Re-analysis of old data (BNL,ANL) using current formalism is still valuable.

Old nucleon form factors are now being updated. It has +-5% effect on Q2 distribution and 2-3% on the cross section. N FF too. The calculation of resonance production is also being updated. Spectral function calculation which improves the old Fermi-gas model ca

lculation is extensively studied. Transition between DIS and resonance region is complex. Bodek’s calcu

lation is the first trial. K2K near detectors (1kton/SciFi) : producing new data. BooNE : soon. K2K upgraded detector (SciBar) will be complete this sum

mer. MINOS near detector and ICARUS will come in operation in 2006. All these studies will become a step toward the precision neutrino exper

iments.

5. Summary


Fig.1 Nuance quasi-elastic (hist) and (e,e’) Data (•). The energy transfer (=Ee-Ee’) at the fixed scattering angle .

Nuance uses Vb=-27MeV and kF=225 MeV/c. Ee’=Ee-

Carbon

Carbon

Oxygen

Oxygen

Oxygen

Oxygen


A Phased (Installation) High-resolution Detector: Basic Conceptual Design

2m x 2 cm x 2cm scintillator (CH) strips with fiber readout. (int = 80 cm, X0 = 44 cm)

Fiducial volume: (r = .8m L = 1.5 m): 3.1 tonsR = 1.5 m - p: =.45 GeV, = 51, K = .86, P = 1.2R = .75 m - p: =.29 GeV, = 32, K = .62, P = .93

Also 2 cm thick planes of C, Fe and Pb. 11 planes C = 1.0 ton (+Scintillator) 3 planes Fe = 1.0 ton (+MINOS) 2 planes Pb = 1.0 ton

Readout: Current concept is VLPC. (How about PMT or CCD + Image Intensifier?)

Use MINOS near detector as forward identifier / spectrometer.

Considering the use of side -ID detectors for low-energy identification.

2.0 m x 2.0 m x 2.0 m long

Scintillator Only

Scint. + Planes of C, Fe,W

Upstream Half

Downstream Half


Effect of Neutrino Interactions on Oscillation Analysis

K2K (Ahn et al., PRL90,041801,2003 and Itow@nuint02) shows that the oscillation analysis is not affected by the unc

ertainties in neutrino interactions at present. Analysis compares the spectrum at near and far detectors and the quasi-elastic and inelastic spectrum are similar in shape.

Precise knowledge of neutrino interactions will be important in the future precision experiments where the measurement of m2 at 1% level are proposed.

Itow@nuint01,Walter,Harris@nuint02


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


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

Jager ＠ PANIC02

1 august 2003 m.sakuda neutrino － nucleus interactions 数 gev...

Documents