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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
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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 ?
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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
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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).
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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.
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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 ?
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• We are thus forced to look at the possibility to study
M=hfphen| OEFT | i
pheni• Can it work ?
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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.
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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.
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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.
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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
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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.
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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, … .
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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
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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
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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
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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
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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
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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
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Results(M2B/M1B) of the hep process
-4
-3
-2
-1
0
1
500 600 800
Lambda (MeV)
non-CTtotal
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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
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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
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Results(M2B/M1B) of the hen process
-4
-3
-2
-1
0500 600 800
Lambda (MeV)
2B non-CT2B total
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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)
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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)
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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)
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Invitation for dinnerThose who have not taken dinner last
night with Prof. Rho are invited for dinner tonight !