Hen process in Effective field theory

Young-Ho Song(SNU)Tae-Sun Park(KIAS)Dong-Pil Min (SNU)

Manque Rho (Saclay)Kuniharu Kubodera(USC)

(Preparing to submit to PLB)KIAS-HanYang Joint Workshop(OCT,2004)

What is the Hen?• (Hen) radiative neutron capture on 3He

• Related topics:

(hep)

scattering, capture

magnetic moments of D, T, 3He

isoscalar and isovector M1 in n + p D +

3 4He n He

3 4eHe p He e

d d

Closly related to the hen

hen history

(exp)= (55 ±3) b, (54 ± 6) b

14-125 b : (’81) Towner & Kanna 29-65 b : (’91) Wervelman (112, 140) b : (’90: VMC) Carlson et al ( 86, 112) b : (’92: VMC) Schiavilla et al

a(3He - n)= (3.50, 3.25) fm

• Accurate recent exp: a(3He - n)= 3.278(53) fm

Why is it so difficult to calculate the hen ( hep ) ?

1. Leading order 1B is highly suppressed.

1B-LO is small and difficult to evaluate We need realistic (not schematic) wave functions. Meson-exchange current (MEC) plays an important role.

Pseudo-orthogonality between |4He and |3He + n :

|4He | : most symmetric +

|3He + n = | : next-to-most symmetric +

Hen matrix elements by Schiavilla et al(’92: VMC)

2. There is a substantial cancellation between 1B and MEC. Errors are amplified.

3. Getting realistic/reliable 4-body wave functions is quite non-trivial. Furthermore we need w.f.s for both scattering states as well as bound states.

The hen process is one of examples that SNPA have sizable discrepancies from the experimental data for light nuclei reactions.

100 M.E. (fm3/2)

IA -0.165

MI 0.756

EFT Operator

EFT W.F.

EFT W.F.

Hybrid MethodPrinciple Problems of Nuclear Physics

Obtain the matrix elements f | O | i

SNPA W.F.

SNPA W.F.

Short-range physicsthe short-range physics can be well described by

the local operators in EFT,– For most cases, it is sufficient to consider only

C0 (non-derivative contact term)

2short 0( ) ( )n

nn

c r c r

hybrid method + renormalization procedure for the short ranged contributions

By using the hybrid mehod, obtain the wave function and the matrix elements. And then, fix the value of C0 at given cutoff so as to reproduce other known experimental data.

The value of C0 is model-dependent, which cancels out the model-dependence of f ri so as to have model-independent

f | Oshort | i

, which is the renormalization c

ondition.Once we fix the value of C0 , we can predict other processes

which depends on the C0.

MEEFT strategy for M= f i

Successful applications of the MEEFT method

isoscalar and isovector M1 in n + p D + T.-S.Park et al, Phys.Rev.Lett. 74,4153(1995) Nucl.Phys. A596, 515(1996) Phys.Lett. B472,232 (2000) -d capture rate, S.Ando et al, Phys.Lett. B533, 25 (2002)-d scattering S.Nakamura et al, Nucl.Phys. A707, 561(2002) Nucl.Phys.A721,549 (2003) S.Ando et al, Phys. Lett. B555, 49 (2003) hep T.-S.Park et al. Phys.Rev. C 67, 055206 (2003)

The hen (3He + n 4He + ) process

• The hen process has much in common with hep :

– The leading order 1B contribution is strongly suppressed due to pseudo-orthogonality.

– A cancellation mechanism between 1B and 2B occurs.

– Trivial point: both are 4-body processes that involve 3

He + N and 4He.

– Differences: Coulomb interaction, M1 and GT …

• hep process have not been confirmed by experiments

• Accurate experimental data are available for the hen

The hen process is governed by isoscalar and isovector M1 operators.

there is soft-OPE contribution to the isovector M1, which is NLO compared to 1B.

The N3LO of Isovector M1 corresponds to 1-loop.

At N3LO, there appear two 4F contact counter-terms, g4S

and g4V, which we can fix by imposing the condition t

o reproduce the magnetic moments of 3H and 3He

Up to N3LO, three-body and four-body current operators do not appear.

Remarks on the hen process

MEEFT Strategy for M(Hen)= f i

VMC wave functions with Av14 + Urbana VIII Up to N3LO in heavy-baryon chiral-perturbation theory (HBChPT)Weinberg’s power counting rule for irreducible diagrams.

AV14 potential+U8

VMC wave function (Wiringa 91)

3H 4He

E(VMC: av14+U8)

-8.20 -27.2

E(exp) -8.48 -28.3

3He+n Scattering W.F.

In our work, we have fit the Woods-Saxon potential parameters

to reproduce the scattering length of 3He+n

an=3.278 fm and the low-E 3He-n phase shifts

3He-n phase shift [deg] wrt Ecm [MeV]solid line = Woods-Saxon potential

dots= R-matrix analysis by Fofmann & Hale, NPA613(’97)

M1 channel (hen process)

• the two-body currents in momentum space are valid only up to a certain cutoff This implies that when we go to coordinate space, the currents should be appropriately regulated. This is the key point in our approach.

• Cutoff defines the energy momentum scale of EFT that divides low energy degrees of freedom and high energy d.o.f.

To control the short-range physics consistently,we apply the same (Gaussian) regulator

for all the A=2,3 and 4 systems, witheV

Results(hen)

• 4F contact terms have a role of removig the -dependence

g4s g4v

500 0.485 1.300

600 0.379 0.242

800 0.186 -1.024

Summary

(theory)= (51 ±2 ±1) b , which is in good agreement with the exp., (55 ±3) b, (54 ± 6) b.

However, there are caveats

1. Potential model(AV14+U8 is enough?) More exact potential model is preferred. AV18 + U9 potential?

2. Scattering state W.F.The matrix elements is not sensitive on the scattering of the 3He+n Different from the reported calculations Different parameters of the W-S potential? Variational W.F. for the scattering state?