BBBA05 - KEK理論センター・J
Download
Report
Transcript BBBA05 - KEK理論センター・J
Nucleon Form Factor
作田 誠(岡大理)@JPARC理論センター
Axial vector mass のまとめ
2.Quasi-elastic scattering の現状
3.Nucleon Form Factor の復習
4.まとめ=Axial vector form factor はこれから
1.
Nucleon Form Factors
i
N ( p' ) | J em | N ( p) u ( p' ) F1 N (Q 2 )
q F2N (Q 2 )u ( p),
2M
i
p( p' ) | V1i 2 | n( p) u ( p' ) F1V (Q 2 )
q F2V (Q 2 )u ( p),
2M
p( p' ) | A1i 2 | n( p) u ( p' ) 5 FA (Q 2 ) q Fp (Q 2 )u ( p),
G EN (Q 2 ) F1 N (Q 2 ) F2N (Q 2 )
G (Q ) F1 (Q ) F (Q )
N
M
2
N
2
N
2
2
Q2
with
4M 2
e
p
1
G
(Q ) G Ep, M (Q 2 ) G En , M (Q 2 )
2
G EV (Q 2 ) G MV (Q 2 )
G MV (Q 2 ) G EV (Q 2 )
V
2
V
2
F1 (Q )
and F2 (Q )
1
1
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions
V(
E,M
2
q
e
P
1. 前回の検討会での早戸氏のまとめ
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions
CC Quasi-elastic interaction
-Hayato
K2KのMA解析
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions
K2K Q2 distribution (QE=Shadow)
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions
MiniBooNE QE
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions
問題点
Q2<0.2 GeV2 で不定性。
断面積をどう補正するかで不定性残る。
形のみの解析。Dipole??で良いのか。
Energy scale がShape fit に効く。
バックグランドのない実験でT2K、SciBooNEで
きちんと出るか?
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions
2.Quasi-elastic の現状
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions
MiniBooNE QE Anomaly
(PRD81,092005,’09)
Is theory (IA calculation) underestimates quasi-elastic cross
section data C(n,m), while it agrees with C(e,e’) data??
MA:MA=1.0-1.2GeV 1.6GeV??
2p-2h/MEC large??
Benhar-Meloni, PRL105,132301,2010
C(e,e’)
C(n,m)
2p-2h/MEC or Contribution from the high
energy tail
Martini, Nieves, Donnelly …estimates 2p-2h/MEC contribution
(~20%) and proposes a solution to MiniBooNE QE anomaly.
Nieves et al., PRC83,045501,2011;Meucci et al.,
PRL107,172501,2011;Amaro et al.,PRD84,033004,2011
Benhar (hep-th/1110.1835) points out a big difference
between A(e,e’) and A(n,m), where En spead is large.
MiniBooNE anomaly quasi-elastic
10 Feb, 2012
Makoto Sakuda@JPARC
3.Form Factor の復習
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions
電子ー陽子散乱断面積の復習
Rutherford 散乱(古典電磁気学)
電子=Dirac粒子、
陽子は古典的点電荷
電子、陽子=Dirac粒子、反跳
陽子の電荷・磁気構造の考慮
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions
Rothenbluth の公式(電荷・磁気構造の考慮)
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions
核子構造の発見
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions
GE, GM の実験測定法
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions
Yennie, Levy,Ravenhall,Rev.Mod.Phys.29(1957)144
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions
Progress in Electron Scattering experiments
-Nucleon Vector Form FactorsIn the past, the nucleon electromagnetic form factors have been
measured from unpolarized electron beam scattering experiments using
the Rosenbluth separation technique.
d
2 E ' cos 2 / 2 GE2 GM2
2
2
E, 3 4
2
G
tan
/
2
M
d
4 E sin / 2 1
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 GEN , Px/Pz GEN/GMN
The effect of those new form factors on the neutrino quasi-elastic cross
sections was shown to be a few %.
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions
陽子・中性子の最新の電荷、磁気形状因子
核子の電気的、磁気的な広がりを表すもの G , G
E
M
一般的な電荷、磁気形状因子(Dipole型)
p
M
G
n
M
G
BBBA05とDipole型の比
形状因子による断面積の
(G/D)
陽子:電荷形状因子 違い
1
G D, D
m p mn
(1 Q2 4M 2 ) 2
p
E
1
G 0
n
E
0.4
電子原子核散乱で測定された最新 1
の形状因子(BBBA05)を用いる
)
1
k
a
k
k 0
2
G (Q
2
Dipole型
k
b
k 1 k
4
中性子:電荷分布
陽子:磁気分布
BBBA0
5
1
n n
0.
中性子:磁気分布
2
Q
4M 2
R.Bradford et al., Nucl. Phys. Proc.
Suppl.159:127-132 (2006).
1
エネルギー移行量Q2
0.
Kelly 2004
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions
GEp GMp
Polarized electron beam
experiments
All data
Polarization
Q2
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions
Gen : Riodan et al.,PRL105,262302,2010
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions
4. まとめ :Axial vector
Form Factor についての復習をした。
QE については、2p-2h (MEC)の解決とMA の
2つの独立の問題がある。
核子=Deutron (neutron)で精度の良いQE
実験がほしい。
(橋本氏の講演): Lattice QCD の形状因子
計算がこれほど進んでいるとは知らなかった
。今後の進展に大変興味ある。
21 September 2004
M.Sakuda Neutrino-Nucleus Interactions