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.