role of axial-vector meson exchange interaction in the hypernuclear nonmesonic weak decays
DESCRIPTION
Role of axial-vector meson exchange interaction in the hypernuclear nonmesonic weak decays. K. Itonaga Univ. of Miyazaki T. Motoba Osaka E-C. Univ. T. Ueda Hiroshima Th. A. Rijken Radboud Univ. NP@JPARC Symposium Tokai, Jun. 1-2, 2007. §Basic problems: - PowerPoint PPT PresentationTRANSCRIPT
Role of axial-vector meson exchange interaction in the hypernuclear nonmesonic weak decays
NP@JPARC Symposium Tokai, Jun. 1-2, 2007
K. Itonaga Univ. of MiyazakiT. Motoba Osaka E-C. Univ. T. Ueda HiroshimaTh. A. Rijken Radboud Univ.
§Basic problems: □ To understand the nonmesonic decay
observables Γnm, Γn/Γp, α1
totally and consistently.
□ Meson theoretical model can explain the decay interaction or not?
□ If the meson exchange model works, which
specific role can each meson play?
□ To find a link between the meson theoreticalinteraction and the quark physics.
§Brief review
1. First step ; one-pion exchange int.natural, but naïvetensor force dominance →Γp : enhanced Γn/Γp : small
2. Second step;(a) meson-octet (psendo-scalar, vector)
exchange intheavy meson (ρ, ω, K , K* ) exch. int
←since Non-mesonic weak decay is high-mom. process
(b) 2π/σ-exch. : tensor-free int. 2π/ρ-exch. : tensor :
opposite-sign to that of 1π-exch.
Γnm : can be explainedΓn/Γp : ~ 0.3-0.4 (improved)
3. 3rd step : K-exch. int. is recognized to be important.Vπ+ V K : additive for (3S1 → 3P1)
destructive for (1,3S → 1,3S)and (3S1 → 3D1)
:Γn/Γp : enhanced “exp”
But, α1(αΛ) asymmetry parameter : cannot be explained in the meson-exchange model
4. Present stage : How to explain the asymmetry parameter?
α1(αΛ) : sign and magnitude?
(a) Effective field theory.
(b) Isoscalar int., σ-meson exchange + quark int.
(c) Axial-vector meson (meson-pair) exchange?a1-exchange is New.
[ note: a1-exchange is important in “strong” V(ΛN-ΛN) & V(NN-NN) int. in ESC04 mod
el ]
§Angular distribution of an emitted proton from the polarized hypernuclei
pure vector polarization PH
density matrix
nP=P
JP(1J
311J2
1)J
HH
HHHH
H
)・
Nonmesonic decay +p → n+p
k1 : neutron mom.k2 : proton mom. (kp=k2)
Angular distribution of the proton
parameterasymmetry:
)nk̂(cos
cos)T,J(P
M)J(Mtr2d
)k̂)J((d
0
11
p
HH1H0
Hk̂
pH
p
Asymmetry parameter (free space)
]fedc[3ba])dc2(f3/)d2c(baeRe[32
222222
***
p
α
§Why a1 meson exchange?
□ We need a potential which has properties:・ short range・ central force : negative
= opposite sigh to V 2 π/σ
・ tensor force : positive = opposite sign to V2π/ρ
□ In strong NN-force, a1-exch. pot
・ central : opposite to Vσ (NN)・ tensor : opposite sign to Vρ(NN)
⇒ a1 meson (ρπ-meson pair) exch. favorable in weak case ??
)()(])()()([)( )( NNVSrM4m3rm
4gNNV 2
a2112T2N
2
21c
2A
a 11
§ A1 exchange weak decay potential
N N
N
N
a1
w
N N
N
a1w
N N
N
N
a1
w
( A ) ( B )
a1 exch. σπ/a1 exch.
§ A1 exchange (/a1 exch.) weak decay potential a1 meson m=1230. MeV
J =1+
Chiral partner of (J =1-) meson
a1 → exp(a1 → ) = 250 - 600 MeV
/a1 exch. pot.
)pp()p()pp()p(M2
fi
gH
)(gH
,aN5NNNa
,aN5NNNaNNa
**aaa
1
1
111
111
N N
N
N
a1
ρπ/a1 ( B ) exch. weak decay potential
a1 meson
m=1230. MeV J = 1+
a1 →
exp(a1→) = 250 - 600 Me
V
)(M4
f
)(gH
)(gH
,,
,
*,
*aaa 111
N N
N
a1w
( B )
σπ/a1 exch. weak decay potential
a1 meson
m=1230. MeV J = 1+
a1 →
seen ( Part. Data Booklet )
)pp()p()pp()p(M2
fi
gH
)(gH
,aN5NNNa
,aN5NNNaNNa
,a**
aa
11
111
111
N N
N
N
a1
w
Coupling const. ga1
1. Width
p)mp(
311
m1
4g
)a( 22a
2a
11
1
P = 353 MeV/c Γ exp= 250 - 600 MeV
0.0f
5893.8g
MeV)600(400)a(ifMeV)5500(4490g
1
1
1
NNa
NNa
1a
due to Th.A. Rijken
2. Loop integral, parameters
1
11
a41
stronga
.approxstrong)A(a/
,i
n
2i
2
2i
3a
2
42
210
4
g,,
)NNNN(V)NNNN(V
:Assumed
parameters2,1nk
]ck[kFkFF)(
)(kd
diverge at large k2
regularization factor introduced
of ESC04 model
Λ
(N) N
Np2´
p2p1
kπ
ρ
p1´-p1+k
p1-k
p1´
a1
N
1ag.onstcCoupling
11
1
1
1
1
1
1
1
1
NNaAa
,a5A
a
22
3
222a
22a
2
3a
2
322a
1
C/MeV7.455P2a
32a
1
g2g2g
)(2
g2
currentvectorAxial.2
(?)159.9g.)cal(MeV4.278,45
2604)1969(177.PR,Weinberg.S
cos)mm(
)mm(m21
mF12)mm(
)a(
.cf
m2P
34
4g
)a(
Width.1
(A)IL
potentialtransitionV1a/
Force characteristics transitionchannel
Central negative, strong 1S0→1S0
opposite behavior 3S1→3S1
to V2
Tensor positive 3S1→3D1
opposite behaviorto V2
Vector 1S0→3P0
similar behavior 3S1→1P1
to V2
typer̂)(i 21
Characteristic features of V(ΛN – NN) potentials
Central Tensor Vector (pv.)ps π strong ( + ) e( + ), f( - )s 2π/σ strong ( + ) 0v 2π/ρ strong ( - ) e: strong ( + )v ω ( - )
ps K strong ( - ) f: strong ( - )av ρπ/a1 strong ( - ) strong ( + ) e: strong ( + )
av σπ/a1 ( - )
sum. ( - )strong weakb( - ), e( + ), f( - )
strong
0
.fm1r,VV.fm1r,VV Ta/
T/2
ca/
c/2 11
0.2 0.6 1 1.4 1.8 R (fm)
-200
-100
0
100
200
V(
N-N
N )
( G
eV )
Central
V2 /
V2 /
V
x10-10 (1S0)p-(1S0)npVK
V
SUM
No V/a1
0.2 0.6 1 1.4 1.8 R (fm)
-200
-100
0
100
200
V(
N-N
N )
( G
eV )
Central
V2 /
V2 /
V
x10-10 (1S0)p-(1S0)np
VK
V
SUMV a1
V a1
With V/a1+ V a1
0.2 0.6 1 1.4 1.8 R (fm)
-200
-100
0
100
200
V(
N-N
N )
( G
eV )
Vector
V2 / V2 /
V
x10-10 (1S0)p-(3P0)np
V
VK
SUM
No V/a1
0.2 0.6 1 1.4 1.8 R (fm)
-200
-100
0
100
200
V(
N-N
N )
( G
eV )
Vector
V2 /
V2 /
V
x10-10 (1S0)p-(3P0)np
V
VK
SUMV a1
V a1
With V/a1+ V a1
0.2 0.6 1 1.4 1.8 R (fm)
-400
-200
0
200
400
V(
N-N
N )
( G
eV )
Central
V2 /
V2 / V
x10-10 (3S1)p-(3S1)np
V
VK
SUM
No V/a1
0.2 0.6 1 1.4 1.8 R (fm)
-400
-200
0
200
400
V(
N-N
N )
( G
eV )
Central
V2 /
V2 /
V
x10-10 (3S1)p-(3S1)np
V
VK
SUMV a1
V a1
With V/a1+ V a1
0.2 0.6 1 1.4 1.8R (fm)
-400
-200
0
200
400
V(
N-N
N ) (
GeV
)
(3S1)p-(3D1)npTensor
V2
VK
V
V
x10-10
SUM
No V/a1
0.2 0.6 1 1.4 1.8R (fm)
-400
-200
0
200
400
V(
N-N
N ) (
GeV
)
(3S1)p-(3D1)npTensor
V2 VK
VV
x10-10SUM
V a1
V a1
With V/a1+ V a1
0.2 0.6 1.0 1.4 1.8 R (fm)
-100
0
100
200
300
V(
N-N
N )
( G
eV )
Vector
V2 /
V2 /
V
x10-10 (3S1)p-(1P1)np
V
VK
SUM
No V/a1
0.2 0.6 1.0 1.4 1.8 R (fm)
-100
0
100
200
300
V(
N-N
N )
( G
eV )
Vector
V2 /
V2 /
V
x10-10 (3S1)p-(1P1)np
V
VK
SUM
V a1
V a1
With V/a1+ V a1
0.2 0.6 1 1.4 1.8 R (fm)
-200
-100
0
100
200
V(
N-N
N )
( G
eV )
VectorV2 /
V2 /
V
x10-10 (3S1)p-(3P1)np
VK
SUM
No V/a1
0.2 0.6 1 1.4 1.8 R (fm)
-200
-100
0
100
200
V(
N-N
N )
( G
eV )
VectorV2 /
V2 /
V
x10-10 (3S1)p-(3P1)np
VK SUM
V a1
V a1
With V/a1+ V a1
Recoil:no Recoil:yes nm 0.279 0.278
n/p 0.107 0.109
0.367 0.417
nm 0.375 0.379
n/p 0.711 0.707
.001 0.833
a
+ a1
nm 0.359 0.358 ( 0.364)n/p 0.511 0.508 ( 0.503) 0.096 0.083 ( 0.100)
He5
nm[] , 1
Exp.nm=0.424±0.024[1] n /p=0.45±0.11±0.09[1] =0.07±0.08 [3] +0.080.00
Nonmesonic decay rates and asymmetry parameter
He5
aa
nmnp11
1
1
NNaa
a
NNa
g2gMeV 1650MeV 2000
MeV5020g
5893.8g
Asymmetry parameter
0d,0c0f,0b0e,0a
015.0010.0025.0)dc2(f3/)d2c(bae
083.0083.0/019.0)4(237.0)4(
011
1
0
He5
aa
nm+np 11
1
1
NNaa
a
NNa
g2gMeV 1600MeV 2000
MeV5500g
5893.8g
Asymmetry parameter
0d,0c0f,0b0e,0a
019.0010.0034.0)dc2(f3/)d2c(bae
100.0100.0/024.0)4(242.0)4(
011
1
0
Recoil:no Recoil:yes nm 0.621 0.620
n/p 0.100 0.101
0.330 0.340
nm 0.838 0.843
n/p 0.619 0.618
0.805 0.629
a
/a1
nm 0.757 0.754 ( 0.767)n/p 0.415 0.407 ( 0.404) 0.052 0.045 + 0.062 )
C12
nm []
1J1J
Exp.nm=0.940±0.035[1] n /p=0.56±0.12±0.04[1] =-0.16±0.28 [3]+0.180.00
Nonmesonic decay rates and asymmetry parameter
C12
aa
062.0045.0
404.0407.0/767.0754.0
MeV5500gMeV5020gJ
1J][
pn
nm
aa
1nm
11
11
1
1
NNaa
a
NNa
g2g
g
5893.8g
§Summary and outlook
1. The ρπ/a1 and σπ/a1 –exch. interactions have vital roles in modifying the short-range part of the ΛN→NN transition potential.
2. In our π+2π/σ+2π/ρ+ω+ K +ρπ/a1+σπ/a1 exch. model, the potential has following features:
central force : negatively strong at tensor force : positive at
weak at vector force : strong for (b), (e) & (f) channels.
.fm1r
.fm1r .fm1r
3. Nonmesonic decay rates Γnm, n/p ratio (Γ n /Γp) and asymmetry parameter α1 ( αΛ) are evaluated for .CandHe 125
)C(045.0),He(083.0:
)C(41.0),He(51.0:)/(
)C(75.0),He(36.0:
125cal
125calpn
125calnm
for the adopted coupling const. and parametersof ρπ/a1 and σπ/a1 – exch. int.
4. The decay observables (exp. data) are ratherwell explained in our model, though not enough,especially for Γnm.
5. The coupling constants and the parameters adopted in our model have some uncertainties which should be further studied.