200mev-gev 領域での電子原子核反応実験sakemi/snws/slide/sakuda.pdf200mev-gev...

2 March, 2007 M.Sakuda RCNP Workshop

200MeV-GeV 領域での電子原子核反応実験

作田誠（岡大理）

2007年3月2日＠大阪大学核物理センター

Outline1. 電子原子核反応とニュートリノ原子核反応2. Quasi-elastic 3. Pion production 4. まとめ


Neutrino Cross Section (by Lipari ‘90)

For Eν< 2 GeV, Quasi-Elastic interaction and 1πproduction dominate the cross section.

QE

1π

Total

1. 2.(GeV)


Quasi-elastic and Resonanc cross sections (Fermi Gas Model) in the GeV region and the nuclear effect

Quasi-elastic

∆ production

W/o Pauli effect

W/ Pauli effect

Eν=1.3 GeV，kF=220 MeV/c

ν µ−

Pp

Pp

πqW∆

ν µ−

Pp

qnp

If P <kF , suppressed.

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

dσ/dQ2

dσ/dQ2 0.5 1.0


1. 電子原子核反応とニュートリノ原子核反応

µ

p

ν

p

e e q2q2

電子原子核反応ニュートリノ原子核反応

•e-N: Vector current, ν-N: V-A current•Ee 正確、Eν 不正確、電子散乱の方が精密に実験できる。•原子核効果（Pauli blocking, Final State Interaction）も、電子散乱でより正確に評価できる。•Axial current の情報は、ニュートリノ実験でのみ。


1.電子原子核反応とニュートリノ原子核反応

Electromagnetic current (Jaem) and weak hadronic

charged current (JaCC=Va

1+i2–Aa1+i2)

[ ] ),()()()'()(||)'(

),()(2

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

),()(2

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

225

21

22

21

21

22

21

puQFqQFpupnApp

puQFqMiQFpupnVpp

puQFqMiQFpupNJpN

pAi

VVi

NNem

ααα

βαβαα

βαβαα

γγ

σγ

σγ

+>=<

⎥⎦⎤

⎢⎣⎡ +>=<

⎥⎦⎤

⎢⎣⎡ +>=<

+

+

N Nq

e e

[ ]

τττ

τ

τ

+−

=++

=

−=

=+=

−=

1)()(

)(1

)()()(

)()(21)(

4)()()(

)()()(

222

2

222

1

2,

2,

2(,

2

22

22

12

22

21

2

QGQGQFand

QGQGQF

QGQGQG

MQ

withQFQFQG

QFQFQG

VE

VMV

VM

VEV

nME

pME

VME

NNNM

NNNE


The electron accelerator at JLAB

Ee=1-6 GeVAccelerated by two linacs in a racetrack design.

他にもMAINZA B C


e - N scattering formalism

( ) ( )[ ]2L

2T Qx, Qx,

dE'dd εσσσ

+Γ=Ω

σT (σL) is the Transverse (Longitudinal) virtual photon Cross Section

( )( )επ

α−

−=Γ

12'

2

22

EMQMWE

p

p

Transverse virtual photon flux

V. Tvaskis

NN

QQ22

e(E)e(E) ee’’(E(E’’))

θθ

1

22

2

2tan121

−

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛++=

θνεQ

/EE −=ν


2.Quasi-Elastic Interaction

Quasi-Elastic is understood to 10% for E=700MeV-2000MeV (and Q2>0.2 (GeV/c)2)

(Benhar et al., PRD72,053005,2005)Two key inputs:

Spectral Function S(p,E): validated by JLAB E97-006Final state interactions: validated by JLAB E97-006

Cf. D.Rohe et al.(JLAB E97-006),PRC72,054602,2005


Spectral Function for Various Nuclei-Tabulated by Benhar

Only 65% of the nucleons in nucleus is in Shell States. -D.Rohe @NuInt05 and (ＪＬＡＢ E97-006), PRC72,054602,2005

Fermi momemtum


Validation of FSI effect: Calculated transparency compared to data

D.Rohe, O.Benhar et al(E97-006), PRC72,054602,2005

Transparency= Probability that a nucleon can escape from the nucleus without being subject to any interaction.i.e. T=1.0 = Completely transparent=No interaction


Quasi-Elastic(QE) is Good with SP+FSIBenhar et al., PRD 72, 053005 (2005)

QE ΔDIP

Energy Transfer

QE (SP&FSI, red) is good to 10% level. Calculations with Fermi-Gas (dash) and SP only (blue) are also shown. But, Pion looked bad. Next.

Diff

eren

tial C

ross

Sec

tion


3. 1π production

Our approach to Pion ProductionHow well do we understand ep epπ: H(e,e’) ?

Calculations must agree on A=H (hydrogen).See the following Pages.

What are the new effects for A=C/O/Fe?The tail of QE is significant (SP+FSI).Meson exchange and Non-resonant pionproduction (MAID)2nd Resonance (Paschos-Lalakulich)


∆ production model Paschos,Yu,MS, PRD69(‘04)Sato-Lee, PRC67(‘03)

Pauli effect G(W,Q2 ,kF)Correct N-∆ form factor 3-4 resonancese-p data look good.


Paschos PRD69,D74=Sato-Lee, wrt ∆(1232)


Sato-Lee includes the non-resonant graphs.Paschos does not have it. MAID is doing something good.


∆ production and N ∆ transition form factors

)()(

)()''()()/()(

)'(

)(||)'(

)()()()(

)''()()/()(

)'(

)(||)'(

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

52

262

52

24

23

52

62

25

2

24

23

pqqM

QCgQCpqpqg

MQCqqg

MQC

p

pNAp

pqqQCpqpqgM

QCpqpqg

MQCqqg

MQC

p

pNVp

pNAppNVppNJp

AA

AA

VVVV

Ψ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡++−+−

Ψ=

>∆<

Ψ⎥⎦

⎤⎢⎣

⎡+−+−+−Ψ=

>∆<

>∆<−>∆>=<∆<

γγ

γγ

αµµααµµααµµα

µ

α

αµαµµααµµααµµαµ

α

ααα

・

・・


MAID2003

D. Drechsel, S.S. Kamalov, L. Tiator (Mainz U.), Nucl. Phys. A645 (1999) 145-174A Unitary Isobar Model for Pion Photo- and Electroproduction on the NucleonResonances: P33, and higher.Non-Resonant: Born terms, ρ /ω exchange.


1. QE (FG) + MAID (P33 only) , or Paschos P33 (FG) red2. QE(SP+FSI) , MAID (P33+non-res)SP: light blue3. Total: magenta

0

10

20

30

40

50

0 100 200 300 400 500 600

dσ/d

Ωdω

[10-7

fm2 /M

eV]

ω [MeV]

E = 880 MeV θ = 32 deg

O(e,e')FG QE+P33

SP QESP MAID

SP QE+MAID

QE Peak

Δ peakDIP

Anghinolfi et al., NPA602(’96),405.

Paschos FG (P33 only)


Hall-C 内部↓

Detector’s outline→High Momentum Spectrometer (HMS)

←Target

↑electron beam

Short OrbitSpectrometer (SOS)


QE and ∆ with target H,D,C(e,e’) at Ee=1.2 GeVOne data point consists of 600K events. Q2=0.05-0.6 (GeV/c)2.

E’ (GeV)

Q2 -1.15 -0.966 -0.811 -0.682 -0.573 -0.481 -0.404

10.8 0.0499 C C C C C C C

13 0.0715 H2,D2 H2,D2,C,Al H2,D2,C,Al H2,D2,C,Al H2,D2,C,Al H2,D2,C,Al H2,C

16 0.1063 H2,Al D2,C,Al D2,C,Al D2,C,Al D2,C,Al D2,C,Al

19 0.1467 D2 C C C C

22 0.1918 H2,D2,C,Al D2,C,Al H2,D2,C,Al H2,D2,C,Al H2,D2,C,Al

28 0.2932 H2,C,Al C C H2 C C

45 0.6136 H2,C,Al,Fe H2,D2,C,Al,Fe H2,C,Al,Fe H2,D2,C,Al,Fe H2,D2,C,Al,Fe H2,D2,C,Al,Fe

55 0.7946 H2,D2,C,Al,Fe H2,D2,C,Al,Fe H2,D2,C,Al,Fe H2,D2,C,Al,Fe H2,D2,Al,Fe

60 0.8782 D2

70 1.029 H2,D2,C,Al,Fe H2,D2,C,Al,Fe C ,Al ,Fe

Θ(d

eg)


Kinematic Coverage of E04-001

Low QLow Q2 2 data for data for ν ν modelingmodeling•• Targets: H,D, C, Al Targets: H,D, C, Al

•• Uncertainties in preliminary data Uncertainties in preliminary data

estimated at ~3 estimated at ~3 -- 8% 8%

(Much larger (Much larger RCsRCs and rates)and rates)

σσTT, , σσLL

•• Targets: D, C, Al, Fe , and Targets: D, C, Al, Fe , and some H some H

•• Uncertainties in preliminary data estimated Uncertainties in preliminary data estimated at 1.6 % ptat 1.6 % pt--pt in pt in εε (2% normalization).(2% normalization).

W2 (GeV)2

Q2 (

GeV

)2

W2 (GeV)2

Q2 (

GeV

)2

超前方＝原子核効果大


結果一例 (Semi-Online Analysis)

Target = H2e- energy (GeV) = 4.62

HMS deg = 10.6

Prelim

inary


0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4

θ = 20.00o

EBeam = 2.3 GeV, Target = D

W2 (GeV2)

dσ

/dΩ

/dE

/ /A (

µb/s

r/G

eV

)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 1 2 3 4

θ = 30.00o

W2 (GeV2)

dσ

/dΩ

/dE

/ /A (

µb/s

r/G

eV

)

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0 1 2 3 4

θ = 45.00o

W2 (GeV2)

dσ

/dΩ

/dE

/ /A (

µb/s

r/G

eV

)

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0 1 2 3 4

θ = 60.00o

W2 (GeV2)

dσ

/dΩ

/dE

/ /A (

µb/s

r/G

eV

)0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4

θ = 20.00o

EBeam = 2.3 GeV, Target = C

W2 (GeV2)

dσ

/dΩ

/dE

/ /A (

µb/s

r/G

eV

)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 1 2 3 4

θ = 30.00o

W2 (GeV2)

dσ

/dΩ

/dE

/ /A (

µb/s

r/G

eV

)

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0 1 2 3 4

θ = 45.00o

W2 (GeV2)

dσ

/dΩ

/dE

/ /A (

µb/s

r/G

eV

)

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0 1 2 3 4

θ = 60.00o

W2 (GeV2)

dσ

/dΩ

/dE

/ /A (

µb/s

r/G

eV

)

Preliminary Cross Section Results (JUPITER) Tvaskis/Bradford@NuInt05

Deuterium:Deuterium: Fits to previous Fits to previous JLabJLab & SLAC & SLAC resonance region data.resonance region data.

Heavy targets:Heavy targets: fits to DIS data (Ffits to DIS data (F22 & R) + & R) + yy--scaling QE model.scaling QE model.

----- Input models for RCs, etc.


CLAS: CEBAF Large Acceptance Spectrometer (Hall B)


CLAS Single Event Display

Charged particle angles 8o-144o

Neutral particle angles 8o-70o

Momentum resolution ~0.5% (charged)

Angular resolution ~0.5 mr (charged)

Identification of p, π+/π-, K+/K-, e+/e-, etc.


Exclusive measurements for the ν program at CLAS

Neutral and charged pions look different in ν detectors.

Eν is a critical quantity. Tune models that can be used in ν expts.

Oscillations

No oscillations

i.e., K2K result, Eν is important Paschos, Schienbein, Yu, hep-ph/0408148

ANP model calculationsK2K Collaboration, hep-ex/0212007.


まとめ

電子原子核実験は、高統計のものがたくさんあるので、原子核効果を含めたQuasi-elastic interaction やPion production を理解するには大変有効。

Spectral Function (E,P) やFSI も電子実験データのおかげで計算が正当化された。

JLAB data で、Q2<0.2 (GeV/c)2 の解析が進行中。

超前方（原子核効果）やDIP 領域も理解が進むと思われる。


Pauli effect G(W,Q2 ,kF)Correct vector form factor 3-4 resonancesConsistency with e-pdata

Improved ∆ production model - Paschos et.al PRD69(‘04),PRD71(‘05) and Sato-Lee, PRC67(‘03)


Resonance to 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-Yang

We will hear more details.Melnitchouk’s talk,

Phys.Rep.406,2005.

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

200mev-gev 領域での電子原子核反応実験sakemi/snws/slide/sakuda.pdf200mev-gev...

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