Tae-Sun Park Korea Institute for Advanced Study (KIAS)

in collaboration withY.-H. Song, K. Kubodera, D.-P. Min, M. Rho

L.E. Marcucci, R. Schiavilla, M. Viviani, A. Kievsky, S. Rosati

More-effective EFT: Electroweak response functions of A=2,3,4

TSP et al., PRC67(’03)055206, nucl-th/0208055Y.-H. Song and TSP, nucl-th/0311055K. Kubodera and TSP, Ann. Rev. Nucl. Part. Sci. vol.54 (2004)

KIAS-Hanyang 2004@KIAS

J. Bahcall’s challenge:

“... do not see any way at present to determine from experiment or

first principle theoretical calculations a relevant, robust upper limit to

the hep production cross section.” (hep-ex/0002018)

hep: 3He + p ! 4He + e+ + e

Q: Can EFT be a breakthrough ?

hep history (S-factor in 10-23 MeV-b unit):

Schemetic wave functions ’52 (Salpeter) 630 Single particle model ’67 (Werntz) 3.7 Symmetry group consideration ’73 (Werntz) 8.1 Better wave functions (P-wave) ’83 (Tegner) 425 D-state & MEC ’89 (Wolfs) 15.34.7 analogy to 3He+n ’91 (Wervelman) 57 3He+n with shell-model

Modern wave functions ’91 (Carlson et al.) 1.3 VMC with Av14 ’92 (Schiavilla et al.) 1.4-3.1 VMC with Av28 (N+) S0 = 2.3 (“standard value”) ’01 (MSVKRB) 9.64 CHH with Av18 (N+) + p-wave PRL84(’00)5959, PRC63(’00)015801

What’s wrong with the hep ?

1. Pseudo-orthogonality :

|4He' | = |S4:most symmetric |3He + p ' | = | S31:next-to-most symmetric

S4 | gA i i i | S31=0. : (Gamow-Teller)

h1B-LOi is difficult to evaluate : We need realistic (not schematic) wave functions.

h1B-LOi is small : h1B-LOi » hMEC (N3LO)i Meson-exchange current (MEC) plays an essential role.

2. MEC is highly model-dependent, hsoft 1-exchangei =0 (Ã a generic feature of GT operator).

MEC in EFT (Heavy-baryon ChPT)

• MEC= N2LO+N3LO + (N2LO=0 for GT),• N3LO= (hard 1-exchange) + (r) ( ij

– Long-range part (hard 1-exchange) is well-known.– The value of is not fixed by symmetry, and should be

determined either by QCD or by other experiments.– Once the value of is fixed, no other uncertainty left.

Nuclear matrix element in EFT

M=hfEFT| OEFT |i

EFTi

• |EFTi is yet to come !– Schematic wave functions are not good.– A few accurate phenomenological wave functions

available.• How we can go further ?

• We are thus forced to look at the possibility to study

M=hfphen| OEFT | i

pheni• Can it work ?

How we do with ?

• Model-dependence cut-off dependence: M()=hf | O() | ii= Mnon-CT () + () hf | (r) | ii .

– Model-dependence resides in short-range, which we explore in terms of .

• Consider another known process which depends on :M0exp M0

non-CT () + () h0f | (r) | 0ii .

This step determines the value of for a given and .– have strong dependence on , but independent of the

details (quantum numbers, A, Z, ...) of the process.

RG-invariance

M()= hf | O() | ii = 0 ?

• O(’) = O() + c0 (r) + c2 r2 (r) + ,

thus equivalent (up to N3LO) to replace ()! (’) = () + c0, which has no effect in matrix

elements.

We will check the RG-inv. numerically.

Model-invariance ?

M(a)= hf(a) | O | i(a)i : a-independent ? (a: model-index)

• Vlow-k: if we limit our model space to k < then all the accurate phenomenological potentials are equivalent. Hlow-k = U(a)

y H(a) U(a) is a-independent, |(a)i = U(a) |low-ki

M(a)= hlow-k | Uy(a) O U(a)| low-ki = hlow-k | O(a) | low-ki

We also expect O(a) = Olow-k() + d0 (r) + d2 r2 (r) + , since the finite range-part is dictated by the chiral symmetry.

Contents

• Brief review on heavy-baryon chiral perturbation theory

• CT contributions to the currents at N3LO• Results:

– isoscalar M1 (M1S) in n+p! d+– pp (p+p ! d + e+ + e)– hep (3He + p ! 4He + e+ + e)– hen (3He + n ! 4He + )

• Discussions

Heavy-baryon Chiral Perturbation Theory

1. Pertinent degrees of freedom: pions and nucleons. Others are integrated out. Their effects appear as higher order operators of ’s and N’s.

2. Expansion parameter = Q/

Q : typical momentum scale and/or m,

: mN and/or f

3. Weinberg’s power counting rule for irreducible diagrams.

CT contributions to the currents at N3LO

• g4S : isoscalar M1

– d, spin observables(np! d+, (3He)+(3H), hen,...

• g4V : isovector M1– (np! d+), (3He)-(3H), hen,...

•

– pp, hep, tritium- decay (TBD), -d capture, d scattering, … .

Isoscalar M1 (M1S) in n+p! d+

• Due to pseudo-orthogonality, 1B-LO is highly suppressed, NLO=N2LO=0.

• At N3LO, there appear CT (g4S ) and 1-exchange.

• The value of g4S is determined from the exp. value of d. • Aspects of the actual calculation:

– Argonne v18 wave functions.

– Hardcore regularization, (r) ! (r-rC)/(4 r2), rC» 1/ .– Up to N3LO and up to N4LO.

• No experimerimetal data yet: it can be in principle measured via the spin observables, but requires ultra-high polarizations.

TSP, K. Kubodera, D.-P. Min & M. Rho, PLB472(’00)232

Results(M2B/M1B) of M1S, up to N3LO

0

0.20.4

0.60.8

11.2

0.01 0.4 0.8r_c (fm)

w/o CTtotal

cf) J.-W. Chen, G. Rupak & M. Savage, PLB464(’99)1

Results(M2B/M1B) of M1S, up to N4LO

-0.8-0.6-0.4-0.2

00.20.40.60.8

0.01 0.4 0.8

r_c (fm)

total up toN3LON4LO

total up toN4LO

pp process• 1B-LO is not suppressed, NLO=N2LO=0. LO À N3LO.• Most solar neutrinos are due to pp process.• At N3LO, there appear CT ( ) and 1-exchange.• The value of is determined from exp. value of TBD rate.

– Bridging different A sector, A=2 $ A=3.• Aspects of the actual calculation:

– CHH method with Argonne v18 + Urbana X.– Gaussian regularization, exp(-q2/2)

• No experimerimetal data yet: Coulomb repulsion makes it difficult at low-energy.

Rd̂Rd̂

TSP, L. Marcucci,..., PRC67:055206,2003, nucl-th/0106025

Results(M2B/M1B) of the pp process

00.020.040.060.080.1

0.120.14

500 600 800Lambda (MeV)

2B (w/o CT)2B

hep process• 1B-LO is strongly suppressed, NLO=N2LO=0. LO » N3LO.• Highest-E solar neutrinos are due to hep process.• At N3LO, there appear CT ( ) and 1-exchange.• The value of is determined from exp. value of TBD rate.

– Bridging different A sector, A=3 $ A=4.• Aspects of the actual calculation:

– CHH method with Argonne v18 + Urbana X.– Gaussian regularization, exp(-q2/2)

• No experimerimetal data yet: Coulomb repulsion makes it difficult at low-energy.

• Required accuracy: order of magnitude.

Rd̂Rd̂

TSP, L. Marcucci,..., PRC67(’03)055206, nucl-th/0107012 K. Kubodera & TSP, Ann. Rev. N&P Sci. vol.54, ’04

Results(M2B/M1B) of the hep process

-4

-3

-2

-1

0

1

500 600 800

Lambda (MeV)

non-CTtotal

hep S-factor in 10-23 MeV-barn:

Shep(theory)=(8.6 1.3)

hep neutrino flux in 103 cm-2 s-1 :

hep(theory) = (8.4 1.3)

hep(experiment) < 40 Super-Kamiokande data, hep-ex/0103033

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

• Accurate experimental data are available for the hen • 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

3He + N ! 4He.

Q: Can we test our hep prediction by applying the same method to the hen process ?

Y.-H. Song & TSP, nucl-th/0311055

Results(M2B/M1B) of the hen process

-4

-3

-2

-1

0500 600 800

Lambda (MeV)

2B non-CT2B total

hen history

(exp)= (55 ±3) b, (54 ± 6) b

2-14 b : (1981) Towner & Kanna 50 b : (1991) Wervelman (112, 140) b : (1990) Carlson et al ( 86, 112) b : (1992) Schiavilla et al

(our work)= ?? (See Young-Ho Song’s talk)

Discussions• Developed an EFT method which enables us to do a

systematic and consistent EFT calculation on top of accurate but phenomenological wave functions.

• Confirmed the RG-invariance numerically to a very satisfactory degree.

• Also demonstrated the convergence of chiral expansion in the isoscalar M1 channel of the np! d, check for other proceeses are future works.

• For all the cases we have studied, our method works quite well– extremely high accuracy in 2-body processes,– the first accurate & reliable theory prediction for the hep

and hen,– -d (S. Ando etal., PLB555(’03)49), -d (S.Nakamura etal,

NPA707 (’02)561,NPA721(’03)549)

Compared to Hybrid model approaches: (Chemtob-Rho type of current-algebra based phenomenological current

operators + phen. wave functions) systematic & consistent expansion scheme full control on the short-range physics ,,,

Compared to Pure EFT approaches: more flexible and more powerful ...

!so, we are calling our method asMore-effective effective field theory (MEEFT)

Invitation for dinnerThose who have not taken dinner last

night with Prof. Rho are invited for dinner tonight !