Tae-Sun Park Korea Institute for Advanced Study (KIAS) in collaboration with Y.-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/ Y.-H. Song and TSP, nucl-th/ K. Kubodera and TSP, Ann. Rev. Nucl. Part. Sci. vol.54 (2004) KIAS-Hanyang

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/ ) hep: 3 He + p ! 4 He + e + + e Q: Can EFT be a breakthrough ?

hep history (S-factor in 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) 4  25 D-state & MEC ’89 (Wolfs) 15.3  4.7 analogy to 3 He+n ’91 (Wervelman) 57 3 He+n with shell-model Modern wave functions ’91 (Carlson et al.) 1.3 VMC with Av14 ’92 (Schiavilla et al.) VMC with Av28 (N+  )  S 0 = 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 : | 4 He  ' |  = |S 4 :most symmetric  | 3 He + p  ' |  = | S 31 :next-to-most symmetric   S 4 | g A  i  i  i | S 31  =0. : (Gamow-Teller)  h 1B-LO i is difficult to evaluate :  We need realistic (not schematic) wave functions.  h 1B-LO i is small : h 1B-LO i » h MEC (N 3 LO) i  Meson-exchange current (MEC) plays an essential role. 2. MEC is highly model-dependent, h soft 1  -exchange i =0 ( Ã a generic feature of GT operator). 

MEC in EFT (Heavy-baryon ChPT) MEC= N 2 LO+N 3 LO +  (N 2 LO=0 for GT), N 3 LO= (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=h  f EFT | O EFT |  i EFT i |  EFT i 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=h  f phen | O EFT |  i phen i Can it work ?

How we do with  ? Model-dependence  cut-off dependence: M(  )= h  f | O (  ) |  i i = M non-CT (  ) +  (  ) h  f |   (r) |  i i. – Model-dependence resides in short-range, which we explore in terms of . Consider another known process which depends on  : M 0 exp  M 0 non-CT (  ) +  (  ) h  0 f |   (r) |  0 i i. 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(  )=   h  f | O (  ) |  i i = 0 ? O (  ’ ) = O (  ) + c 0   (r) + c 2 r 2   (r) + , thus equivalent (up to N 3 LO) to replace  (  ) !  (  ’) =  (  ) + c 0, which has no effect in matrix elements. We will check the RG-inv. numerically.

Model-invariance ?  M (a) = h  f(a) | O |  i(a) i : a-independent ?  (a: model-index) V low-k : if we limit our model space to k <  then all the accurate phenomenological potentials are equivalent. H low-k = U (a) y H (a) U (a) is a-independent, |  (a) i = U (a) |  low-k i M (a) = h  low-k | U y (a) O U ( a) |  low-k i = h  low-k | O (a) |  low-k i We also expect O (a) = O low-k (  ) + d 0   (r) + d 2 r 2   (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 N 3 LO Results: –isoscalar M1 (M1S) in n+p ! d+  –pp (p+p ! d + e + + e ) –hep ( 3 He + p ! 4 He + e + + e ) –hen ( 3 He + n ! 4 He +  ) 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 ,   : m N and/or  f  3. Weinberg’s power counting rule for irreducible diagrams.

CT contributions to the currents at N 3 LO g 4S : isoscalar M1 –  d, spin observables(np ! d+ ,  ( 3 He)+  ( 3 H), hen,... g 4V : isovector M1 –  ( np ! d+  ),  ( 3 He)-  ( 3 H), 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=N 2 LO=0. At N 3 LO, there appear CT (g 4S ) and 1  -exchange. The value of g 4S is determined from the exp. value of  d. Aspects of the actual calculation: –Argonne v 18 wave functions. –Hardcore regularization,    (r) !  (r-r C )/(4  r 2 ), r C » 1/ . –Up to N 3 LO and up to N 4 LO. 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( M 2B /M 1B ) of M1S, up to N 3 LO cf) J.-W. Chen, G. Rupak & M. Savage, PLB464(’99)1

Results( M 2B /M 1B ) of M1S, up to N 4 LO

pp process 1B-LO is not suppressed, NLO=N 2 LO=0. LO À N 3 LO. Most solar neutrinos are due to pp process. At N 3 LO, 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 v 18 + Urbana X. –Gaussian regularization, exp(-q 2 /  2 ) No experimerimetal data yet: Coulomb repulsion makes it difficult at low-energy. TSP, L. Marcucci,..., PRC 67 :055206,2003, nucl-th/

Results( M 2B /M 1B ) of the pp process

hep process 1B-LO is strongly suppressed, NLO=N 2 LO=0. LO » N 3 LO. Highest-E solar neutrinos are due to hep process. At N 3 LO, 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 v 18 + Urbana X. –Gaussian regularization, exp(-q 2 /  2 ) No experimerimetal data yet: Coulomb repulsion makes it difficult at low-energy. Required accuracy: order of magnitude. TSP, L. Marcucci,..., PRC 67 (’03)055206, nucl-th/ K. Kubodera & TSP, Ann. Rev. N&P Sci. vol.54, ’04

Results( M 2B /M 1B ) of the hep process

hep S-factor in MeV-barn: S hep (theory)=(8.6  1.3) hep neutrino flux in 10 3 cm -2 s -1 :  hep (theory) = (8.4  1.3)  hep (experiment) < 40  Super-Kamiokande data, hep-ex/

The hen ( 3 He + n  4 He +  ) 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 3 He + N ! 4 He. Q: Can we test our hep prediction by applying the same method to the hen process ? Y.-H. Song & TSP, nucl-th/

Results( M 2B /M 1B ) of the hen process

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 as More-effective effective field theory (MEEFT)

Invitation for dinner Those who have not taken dinner last night with Prof. Rho are invited for dinner tonight !