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20031110_07

VIEWS: 4 PAGES: 26

  • pg 1
									            Announcements
   Please let us have copies of your
    power-point files (ppt) or OHP films for
    all the invited talks.
   Please sign on the sheet for the
    Wednesday’s excursion by today, if you
    are willing to participate.



                         Korea Institute for Advanced Study
        The solar hep process
               confronts
      the terrestrial hen process
                     Tae-Sun Park (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

TSP et al., PRC67(’03)055206, nucl-th/0208055
Y.-H. Song and TSP, nucl-th/0311xxx
K. Kubodera and TSP, to appear in Ann. Rev. Nucl. Part. Sci

KIAS-APCTP 2003 Symposium in Astro-hadron physics on
Compact Stars @ KIAS, Nov. 10 – 14, 2003
                            Korea Institute for Advanced Study
Among the solar burning processes (4 p  4He + 2 e+ + 2 e + ’s),
   (pp) p + p  d + e+ + e              E = 0  0.4 MeV
   (pep) p + e + p  d + e             E = 1.4 MeV

   (8B)   8B    8Be + e+ + e           E <     18 MeV
   (hep) 3He + p  4He + e+ + e         E <      20 MeV

           pppep  (8B  hep

pp produces the dominant solar neutrinos.
hep produces the highest-energy solar neutrinos. There can be a
significant distortion of the high-end of the 8B neutrino spectrum.




                                            Korea Institute for Advanced Study
Korea Institute for Advanced Study
 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)             425         D-state & MEC
’89 (Wolfs)            15.34.7       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 until recently”)
’01 (MSVKRB)                 9.64      CHH with Av18 (N+) + p-wave
                                     PRL84(’00)5959, PRC63(’00)015801

                                         Korea Institute for Advanced Study
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)

Q: Can effective field theory (EFT) be a breakthrough ?
A: The more-effective EFT (MEEFT) can be.




                              Korea Institute for Advanced Study
What’s wrong with the hep ?

1. LO(1B) is highly suppressed.

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

    S4 | gA i i i | S31=0.   :     (Gamow-Teller)

   1B-LO is small and difficult to evaluate
   We need realistic (not schematic) wave functions.



                                      Korea Institute for Advanced Study
2. Meson-exchange current (MEC) is not dominated by the
one-pion-exchange: short-ranged operators with unknown
coefficients plays an important role.

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

4. 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.



                                 Korea Institute for Advanced Study
          Q: What’s wrong with the traditional or
          standard nuclear physics approach (SNPA) ?
   SNPA:
      Chemtob-Rho type current operators ( , , , , ...)
                                            prw
      Phenomenological but very accurate potentials:    2 1
      State-of-the-art technique for many-body wave functions

      Extensively tested for many processes with impressive successes

Answer:
        Not systematic
        Uncertainties in the short-range physics




                                        Korea Institute for Advanced Study
   Effective field theory (EFT) a la Weinberg
      Consistent and systematic expansion for the current

       operators (and the potential)
             =   = 0  1   2    
                  

       Wave functions need infinite summation for a given V,
        which can be done by solving Schroedinger equation
                         0
        | Y  = |  + G V | Y
                      0       0    0
              = (1+G V + G V G V + ...) |  
       Recently great progresses are being made
       Difficulties in getting many-body wave functions



                                   Korea Institute for Advanced Study
 Hybrid model
|Y : Standard Nuclear Physics Approach SNPA)
  : Heavy-baryon chiral-perturbation theory (HBChPT)

       More convenient and more powerful: we can concentrate
        only on the current operators
       Better accuracy (inherited from SNPA) for the 1B and
        the long-ranged contributions
       Problems (limitations)
           model dependence

           mismatch/inconsistency




                                  Korea Institute for Advanced Study
   More-effective EFT (Marriage of SNPA & EFT)
    = hybrid model + renormalization procedure
       The whole problem (of SNPA and hybrid-model) lies in
        the short-range physics, which can be well described by
        the local operators in EFT,

              short =  cn  2 n (r ) = c0 (r )    
                        n
       We can impose the renormalization conditions for Cn to
        reproduce other known experimental data, which absorb
        the mismatch/model-dependence/inconsistency.
          
            The values of Cn : model-dependent
           Yf | O | Yi  : model-independent
           For most cases, it is sufficient to consider only C
                                                               0



                                    Korea Institute for Advanced Study
   MEEFT Strategy for M= Yf |  | Yi 

|Y : Standard Nuclear Physics Approach SNPA)

 Variational Monte-Carlo(VMC) or
 Correlated-hyperspherical-harmonics (CHH) with
  Argonne Av14/18 potential
+ Urbana-IX three-nucleon interactions

 : Heavy-baryon chiral-perturbation theory (HBChPT)

to take full advantage of the extremely high accuracy of the
wave functions achieved in SNPA while securing a good
control of the transition operators via systematic chiral
expansion.
                                  Korea Institute for Advanced Study
    Effective Field Theory (HBChPT)

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

2. Expansion parameter = Q/L
   Q : typical momentum scale and/or mp,
   L : mN and/or 4p fp

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




                                  Korea Institute for Advanced Study
        Gamow-Teller channel (pp and hep)
                      pi i  pi   i pi 
                                          2
A1B = g A   i  i             2          = LO  N LO
                                                      2

          i     
                             2m N          
                                            
               
            OPE  4 F
A2 B =  Aij  Aij = N 3 LO
        i j




                    p



                   OPE              4F


There is no soft-OPE (which is NLO) contributions
                                     Korea Institute for Advanced Study
 OPE      gA           1       i                           
Aij =                            ( i  j ) p ( i   j )  q
        2mN fp2 mp  q 2  2
                      2
                               
                          
      4c3 qq  ( i i   j j )
        ˆ
            1                             
      cˆ4  ( i  j )q  [( i   j )  q ]
            4                                  



The values of c’s are determined from the p-N data
          c3 = 3.66  0.08, c4 = 2.11  0.08
          ˆ                  ˆ




                                         Korea Institute for Advanced Study
 4F
Aij = 
         gA
        mN fp2
                    
               2d1 i i     j
                                ˆ
                ˆ (     )  d (   )(   )
                               j   2 i   j
                                             
                                             i   j                  
Thanks to Pauli principle and the fact that the contact terms are
effective only for L=0 states, only one combination is relevant:

      dˆ R  d  2d  1 c  2 c  1
             ˆ    ˆ     ˆ3     ˆ4
              1     2
                      3     3     6
The same combination enters into
 pp, hep, tritium-b decay (TBD),
 m-d capture, d scattering, … .
We use the experimental value of TBD to fix            ˆ R,
                                                       d
then all the others can be predicted !
                                       Korea Institute for Advanced Study
To control the short-range physics consistently,
we apply the same (Gaussian) regulator

                 
             exp  q 2 L2   
for all the A=2,3 and 4 systems, with

            L = 500, 600, 800 MeV
ˆ
d R is a function of L, and determined for each value
of L to reproduce experimental value of TBD rate


                                Korea Institute for Advanced Study
                      Results(pp)
L (MeV)      d R 1B
             ˆ                     2B
 500       1.00 4.85 0.076  0.035 ˆ R = 0.041
                                   d
 600       1.78 4.85 0.097  0.031 ˆ R = 0.042
                                   d
 800                               ˆ
           3.90 4.85 0.129  0.022 d R = 0.042

with   ˆ
       d R-term, L-dependence has gone !!!
the astro S-factor (at threshold)
 Spp= 3.94 (1  0.15 %  0.10 %) 10-25 MeV-barn

                                 Korea Institute for Advanced Study
                    Results(hep)
L (MeV) 1B                2B                   1B2B
 500        0.81                 ˆ
                      1.35  0.85 d R = 0.49        0.32
 600        0.81                 ˆ
                      1.76  1.22 d R = 0.52        0.29
 800        0.81                 ˆ
                      2.38  1.78 d R = 0.59        0.22
ˆ R -term removes the major L-dependence. The small
d
L-dependence in 2B is however amplified due to the
cancellation between 1B & 2B.

Sizable but still reasonable L-dependence in net amplitude.

                                 Korea Institute for Advanced Study
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

Q: Is the hep prediction confirmed by experiment ?
A: No !
                                      Korea Institute for Advanced Study
     The hen (3He + n  4He + ) process
    Both pp and hep process have not been confirmed by
     experiments
    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

Q: Can we test our hep MEEFT calculation by
   applying the same method to the hen process ?
                                Korea Institute for Advanced Study
            Remarks on the hen process
The hen process is governed by isoscalar and isovector
   M1 operators
Contrary to GT, there is soft-OPE contribution to the
   isovector M1, which is NLO compared to 1B
At N3LO, there appear two 4F contact counter-terms, g4S
   and g4V, which we can fix by imposing the
   renormalization condition to reproduce the magnetic
   moments of 3H and 3He




                                Korea Institute for Advanced Study
                          hen history

                 (exp)= (55 ±3) mb, (54 ± 6) mb

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



    a(3He - n)= (3.50, 3.25) fm
•    Accurate recent exp: a(3He - n)= 3.278(53) fm
                                   Korea Institute for Advanced Study
              Preliminary Results(hen)
L (MeV) 1B                      2B                 1B2B
  500          1.76      5.24  1.80 = 7.04            5.29
  600          1.76      6.79  0.35 = 7.14            5.39
  800          1.76      8.31  0.99 = 7.32            5.57
Contact terms remove the major L-dependence.
(theory)= (60 ±3 ±1) mb , which is in reasonable
agreement with the exp., (55 ±3) mb, (54 ± 6) mb.

A caveat: we have not included the so-called fixed-term contribution,
which is expected-to-be small but hard-to-evaluate.
                                        Korea Institute for Advanced Study
                      Discussion
Numerically, the results of MEEFT and the latest SNPA
    agree each other for the Gamow-Teller channel (pp and
    hep). But in the M1 channel, MEEFT can explain the hen
    cross section, while SNPA could not.
MEEFT allows us to reduce theoretical uncertainties
    drastically.
Other successful applications of MEEFT:
    isoscalar and isovector M1 in n + p  D + ,
    m-d capture rate, -d scattering, … .
Accurate experimental data of the pp and hep cross section at
    low energy would be extremely important for both solar
    neutrino physics and EFTs.


                                 Korea Institute for Advanced Study

								
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