isospin mixing in the 4 he ground state and the nucleon strange form factor
DESCRIPTION
Dedicated to Adelchi. Isospin mixing in the 4 He ground state and the nucleon strange form factor. XI Convegno di Cortona M.Viviani INFN - Pisa (Italy). In collaboration with A. Kievsky, L.E. Marcucci, S. Rosati , L. Girlanda R. Schiavilla (Jlab). 2. g. g. Z 0. - PowerPoint PPT PresentationTRANSCRIPT
1
Isospin mixing in the 4He ground state and the nucleon strange form factor
XI Convegno di Cortona
M.Viviani INFN - Pisa (Italy)
In collaboration withA. Kievsky, L.E. Marcucci,
S. Rosati, L. Girlanda
R. Schiavilla (Jlab)
Dedicated to Adelchi
Corto
na O
ttob
re 2
00
6
Electron-nucleus scattering
The parity violating left-right asymmetry ALR
Parity violating scattering e-4He
Z0
2~LR
LRLRA
Corto
na O
ttob
re 2
00
6
EM & neutral-weak currents
Strange quark contribution
Z0
EMEM JQ
M
24
NCV
NCA
NCPV JgJg
GM 5
5
22
ssTJTJ
ssdduuJ
EMW
EMW
WWNC
)1()sin42()0(sin4
)sin3
41()sin
3
81(
22
22
)1()0(3
1
3
2 TJTJssdduuJ EMEMEM
Corto
na O
ttob
re 2
00
6
Nucleon Strange Form Factors
Dirac-Pauli
Sachs
)(2
)()()'()(||)'(
2)(22)(
1 pUqM
QiFQFpUpNsspN
N
ss
)()()( )(4
)()( 2)(2
2)(1
2)(2)(22
22)(
12)( QFQFQGQF
M
QQFQG sss
Ms
N
ssE
Corto
na O
ttob
re 2
00
6
The experiments
Experiments on nucleon:Jefferson Lab (USA): HAPPEX & G0 MIT-Bates (USA): SAMPLEMainz: A4
Sensitive to an admixture of GE(s) and GM
(s) HAPPEX 2005; G0 2005; SAMPLE 2004; A4 2004
Experiments on 4He:HAPPEX-He @ Jlab
In the case of a target (J,T)=(0+,0), at low Q2:
2/)()(
)(sin4
24 2)(2)(
2)(2
2
QGQG
QGQGA n
Ep
E
sE
WLR
Musolf et al, 1994
Corto
na O
ttob
re 2
00
6
World Data at Q2 ~ 0.1 GeV2
HAPPEX-He @ Jlab (2006-preliminary, K.Aniol QNP06) ALR = +6.43 0.23 (stat) 0.22 (syst) ppm
Extrapolated from G0 Q2=[0.12,0.16] GeV2
2005 world data
Corto
na O
ttob
re 2
00
6
4He LR asymmetry (1)
Currents
Three contributions
Left-right asymmetry
ssTJTJJ EMW
EMW
NC )1()sin42()0(sin4 22
)(),1(),0()( )(|)(|)()( 40
42)(0 sTTXHeXJHeQF EMX
C
)1()0( TJTJJ EMEMEM
)(sJss EM
)(
)()1sin2(2
)(
)(sin4
24 2)0(0
2)1(02
2)0(0
2)(02
2
QF
QF
QF
QFQGA T
C
TC
WTC
sC
WLR
Corto
na O
ttob
re 2
00
6
4He LR asymmetry (2)
Charge density operators
irqi
A
I
nE
pEEM e
QGQGTJ
1
2)(2)(
0 2
)()()0(
irqi
A
I
sE
EM eQGsJ1
2)(0 )()(
irqi
A
Iz
nE
pEEM ei
QGQGTJ
1
2)(2)(
0 )(2
)()()1(
Corto
na O
ttob
re 2
00
6
4He LR asymmetry (3)
At low Q2: MEC and spin-orbit contribution in J=0
are small and then
One needs to know:
2/)()(
)(
)(
)(2)(2)(
2)(
2)0(0
2)(0
QGQG
QG
QF
QFR n
Ep
E
sE
TC
sC
s
)(
)(2)0(
0
2)0(0
1 QF
QFR T
C
TC
T
08.1)1sin2(2 2 W
122
08.1sin424
TsWLR RRQG
A
Corto
na O
ttob
re 2
00
6
NN interaction
Realistic (phenomenological) potentialsArgonne V18 [Wiringa et al, 1995]CD Bonn [Machleidt, 2001]Nijmegen [Stoks et al, 1994]Doleshall [Doleshall et al, 2000]
Effective field theory based on chiral symmetry[Weinberg 1991, van Kolck 1994]
N3LO potential [review: Epelbaum, 2005] “Julich” [Epelbaum et al, 2005]“N3LO” [Emtem & Machleidt, 2003 ]
“Effective” potentials Vlow-k [Bogner, Kuo & Schwenk, 2003, Coraggio et al, 2005]JISP [Shirokov et al, 2005]UCOM [Roth et al, 2004]
Corto
na O
ttob
re 2
00
6
NN potentials in p-space
very long tail
CD BONN
VN3LO(k,k’)0 for k,k’>5 fm-1
Vlow-k
AV18
N3LO
Vlow-k(k,k’)=0 for k,k’>2.1 fm-1
Corto
na O
ttob
re 2
00
6
CSB NN interaction
Isospin symmetry breakingnp singlet scattering length –23.74±0.02 fmpp singlet scattering length –17.3±0.4 fm (Coulomb corrected)nn singlet scattering length –18.5±0.4 fm
They come ultimately from u-d different charge & mass
In the “modern” Hamiltonians:CoulombNuclear effects (mass difference between +, - and 0,…)Other e.m. interactions (magnetic moments,…)n-p mass difference
Important forStrange FF of 4HeReaction d+d 4He+ 0
[Gardestig & Phillips, 2005]
CSB from PT: [Epelbaum & Meissner, 2005]
[Miller et al, nucl-ex/0602021]
Corto
na O
ttob
re 2
00
6
3N force
“Old models” Brazil & Tucson Melbourne [Friar et al, 1999] Urbana [Pudliner et al, 1997]
New proposed modelsIllinois (3 exchanges) [Pieper et al, 2001]
Chiral symmetry [Friar et al, 1999] [Epelbaum et al, 2002] N3LO: work in progress
CSB: and exchange (effects unknown)[Kaiser, 2006]
4NF from PT: [Epelbaum, 2006, Rozpedzik et al., 2006]
Corto
na O
ttob
re 2
00
6
HH method (1)
Hyperspherical coordinates
HH functions
)()(3
)(2
)(1 ,,, pppp
)(cos)(cos
)ˆ()ˆ()ˆ()()(
3)(
2
)(3
)(2
)(1
)(][
32
332211
pn
pn
pml
pml
pml
pK
PP
YYYHH
ij
k
m
ijp r
)(
3
)(2
p )(
1p
2)(3
2)(2
2)(1 )()()( ppp
)(2
)(2
)(2
)(3
cos
cosppp
ijp r
2)(2
2)(1
)(2 )()( ppp
)(2 32321 nnlllK Grand angular q.n.
Fabre de la Ripelle, 1983
Corto
na O
ttob
re 2
00
6
HH method (2)
Expansion of the wave function
Rainal-Revai coefficients
Matrix elements of the interaction
)()( )1(]'[]'[],[
)(][ KKK
nspermutatio
pK HHAHH
)()(,, )(][
],[],[1
p
nspermutatioKm
mKmKA HHfarr
22222
22
212
'',2]'[],[2)1(]'[12
)1(][
)'()( )()(
)',(),',( '
rRr
rrVrrGddrdrHHVHH jSLLSKKKK
12
3
4
rr
123
2 1
Fabre de la Ripelle, 1983
Corto
na O
ttob
re 2
00
6
HH method (3)
Fourier transform
Usual choice: Lagrange polynomials
)()()(1 ,,, pp
Np
)()(,, )(][
],[],[1
p
nspermutatioKm
mKmKA HHfarr
)()(~
,, )(][
],[],[1
pQ
nspermutatioKm
mKmKA HHQfapp
)()()(
)()(~
2/)23(
012/3
13
mNKN
NK
m fQJQ
diQf
eLf Nmm )()( )13(
m
k
NKNkkm
Km
QPbiQf
02
2/312/3
)/2(1
1)()(
~
31AN
Corto
na O
ttob
re 2
00
6
HH method (4)
Bound state
Rayleigh-Ritz variational principle Boundary conditions:
Scattering states
Kohn variational principle Boundary conditions:
)()( ][][
][ KK
K HHu
)sin()()(,
][][
][ rqHHu ABBABA
KK
K
r
A
B
)( 4][
iQ
K
eu
0)(][Ku
Corto
na O
ttob
re 2
00
6
Convergence
Corto
na O
ttob
re 2
00
6
3H binding energy
Binding energy (MeV)
BE (MeV) PD (%) PT=3/2 (%)
Method
HH F NCSM HH F HH F
AV18 7.618 7.6218.511
8.510
.002 .002
CD-Bonn
7.998 7.997 7.99 7.02 7.02 .005 .005
N3LO 7.854 7.8547.85(1)
6.31 6.32 .001 .001
F: Nogga et al, PRC65, 054003 (2002); Deltuva et al, PRC68, 024005 (2003)NCSM: Navratil & Barret, PRC59, 014311 (2004)
Corto
na O
ttob
re 2
00
6
4He binding energy
BE (MeV) PD (%) R (fm)
Method HH FYNCSM
HH FY HH FY
AV18 24.22 24.25 13.74 13.78 1.512 1.516
CD-Bonn 26.13 26.16 10.74 10.77 1.454
N3LO 25.38 25.37 25.36 9.29 9.29 1.516
FY: Nogga et al, PRC 65, 054003 (2002)
NCSM: Navratil & Barret, PRC 59, 014311 (2004)
Corto
na O
ttob
re 2
00
6
T>0 components (1)
Previous estimates of PT=1:[Ramavataram et al, 1994] – based on an approx 4He w.f.PT=10.0007% : RT=1 was estimated to be negligible
Current estimates of PT=1 3 to 5 times largerPot. PT=1 (%) PT=2 (%)
AV18 0.0028 0.0052
NIJ-II 0.0016 0.0074
CD Bonn 0.0029 0.0108
N3LO 0.0035 0.0024
Corto
na O
ttob
re 2
00
6
T>0 components (2)
Origin of the T>0 components
Hamilt.103xPT=1
(%)103xPT=2
(%)
H0 0 0
+Coulomb 1.5 0.1
+CSB 3.0 4.9
+e.m. +m
2.8 5.2
Corto
na O
ttob
re 2
00
6
4He FF (1)
Q2=0.0772 GeV2 q1.4 fm-
1
PRELIMINARY
22222 1/12 qMqMQ
)(
)(2)0(
0
2)0(0
1 QF
QFR T
C
TC
T
Corto
na O
ttob
re 2
00
6
4He FF (2)
122
08.1sin424
TsWLR RRQG
A
Preliminary HAPPEX estimate @ Q2=0.0772 GeV2 (q1.4fm-1):
ALR = +6.43 0.23 (stat) 0.22 (syst) ppm
Rs-1.08 RT=1= 0.009 0.03
Hamiltonian RT=1(q1.4fm-1) GEs
- 0 0.0040.02
AV18UIX -0.0017 0.0030.02
CDBonn+3N -0.0017 0.0030.02
N3LO+3N -0.0023 0.0030.02
K. Aniol, QNP06 Madrid June 2006
PRELIMINARY
In agreement with recent lattice calculations GEs= 0.001 0.004
[Leinweber et al, hep-lat/0601025]
Corto
na O
ttob
re 2
00
6
Summary
Current models predict a non-negligible contribution of the T>0 components to the LR asymmetry
GEs is currently predicted (at low Q2) to be very
small
The next generation of the HAPPEX-He experiment could measure … RT=1
CSB in NN interaction is of maior interestd+d 4He+0 at IUCF
Corto
na O
ttob
re 2
00
6
We’d like to invite everybody to the
EUROPEAN FEW BODY CONFERENCE XX
PISA (Italy) preregistration: http://www.pi.infn.it/efb20
10-15 September 2007
Corto
na O
ttob
re 2
00
6
NN potentials in p-space
AV18
Corto
na O
ttob
re 2
00
6
NN potentials in p-space
CD BONN
AV18
very long tail
Corto
na O
ttob
re 2
00
6
NN potentials in p-space
CD BONN
AV18
N3LO VN3LO(k,k’)0 for k,k’>5 fm-1
very long tail
AV18
CD BONN
Corto
na O
ttob
re 2
00
6
NN potentials in p-space
very long tail
CD BONN
VN3LO(k,k’)0 for k,k’>5 fm-1
Vlow-k
AV18
N3LO
Vlow-k(k,k’)=0 for k,k’>2.1 fm-1
Corto
na O
ttob
re 2
00
6
Deuton wave function
In r-space:
3S1 wave
0 2.5 5.0 7.5 10.0 12.5 15.0 r (fm)
Corto
na O
ttob
re 2
00
6
Deuton wave function
In p-space:3S1 wave
Corto
na O
ttob
re 2
00
6
NN potentials in r-space
Corto
na O
ttob
re 2
00
6
NN potentials in r-space: N3LO
V(r,r’)=<3S1|V(r,r’)| 3S1 >
Corto
na O
ttob
re 2
00
6
NN potentials in r-space: Vlow-k
V(r,r’)=<3S1|V(r,r’)| 3S1 >
Corto
na O
ttob
re 2
00
6
A=4 scattering
p-3He, p-3H, d-d,…3N force effect?
Fusion
Theoretical methods still under developmentFaddeev-Yakubovsky [Lazauskas & Carbonell, 2004] [Fonseca, 1999, Deltuva & Fonseca, work in progress]
Variational – HH [MV et al, 2006]
Resonating Group Model [Pfitzinger, Hofmann & Hale, 2001]
Corto
na O
ttob
re 2
00
6
A=4 scattering with the N3LO potential
n-t scattering lenghts [fm]Experimental situation
Theoretical calculations
Experiment as (singlet) at (triplet)
Rauch et al, 1985 (I)
4.980.12 3.130.11
Hale et al, 1990 4.450.10 3.320.02
FY: Lazauskas & Carbonell, 2004
HH FY
Pot. Singlet Triplet Singlet Triplet
AV18 4.30 3.80 4.28 3.80
AV18UIX 4.05 3.58 4.04 3.60
N3LO 4.21 3.70PRELIMINARY
Corto
na O
ttob
re 2
00
6
n-t scattering lengths (expt)
=1.700.03 b
[Phillips et al, 1980]
Coherent scattering length
ac=3.590.02 fm
[Rauch et al, 1985]
ac=3.6070.017 fm
[Hale et al, 1990]
Corto
na O
ttob
re 2
00
6
n-t scattering lengths (expt)
=1.700.03 b
[Phillips et al, 1980]
Coherent scattering length
ac=3.590.02 fm
[Rauch et al, 1985]
ac=3.6070.017 fm
[Hale et al, 1990]
AV18UIX
Corto
na O
ttob
re 2
00
6
n-t scattering lengths
as
at
Rauch et al, 1985 (I)
Hale et al, 1990PRELIMINARY
Corto
na O
ttob
re 2
00
6
n-t scattering lengths
as
at
Rauch et al, 1985 (I)
Hale et al, 1990PRELIMINARY
Corto
na O
ttob
re 2
00
6
p-t scattering at low energies (1)
Isospin state T=1/2,Tz=-1/2
)sin()()( 3
,
rqHHu ABpH
BA
r
p
3H
Isospin state T=1/2,Tz=+1/2
The “internal” part contains T=0 and
T=1 isospin channels
Corto
na O
ttob
re 2
00
6
p-t scattering at low energies (2)
Triplet phase shift [deg]Ecm=0.1 MeV
Pot.
3S1
HH FY
AV14 -3.56 -3.536
N3LO -3.40
FY: Lazauskas & Carbonell, 2004K
[deg]
2 -3.54
6 -3.51
10 -3.44
14 -3.41
18 -3.40
N3LO
PRELIMINARYPRELIMINARY