1. Electro-weak Reactions on Light Nuclei: From QCD to Astrophysics
Doron Gazit
Institute for Nuclear Theory
University of Washington

2. Introduction Precision era in few-body nuclear physics:
Available methods for solving exactly the Schroedinger equation for few body systems, from nucleonic dof.
High precision nuclear interaction, phenomenological or cPT based.
Allows parameter free calculations of nuclear wave functions and reaction rates, with sub-percentage accuracy.
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3. Outline Solving the mathematical problem...
Nuclear potentials and electro-weak scattering operators.
Applications:
QCD: correlations in 3H, predictions of 4He.
The weak structure of the nucleon from m capture on 3He.
Inelastic n scattering on light nuclei in supernovae.
Is there a gA1 suppression in heavy nuclei? Hints from 6He b decay.
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4. Calculating a reaction
Wave functions:
Scattering Operator
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5. Interaction of weak probes and a nucleus
lepton current
Nuclear current
Scattering operator
Currents in the nucleus
PhD. Progress report

6. Weak currents in the nucleus
The standard model dictates only the structure of the currets:
Charged current
Neutral current:
The current of polar (axial) vector symmetry is the Noether current of the QCD Lagrangian, with respect to SU(2)V [SU(2)A] symmetry.
Includes:
single nucleon current (leading order)
Meson exchange currents.
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7. Single Nucleon Currents
Weinberg PR, 112, 1375 (1958)
Single Nucleon Currents p' q'
Vector
Magnetic
Second class currents p
Axial
Induced
Pseudo-Scalar
MEC? Not so easy.
’ – based on meson models, without relation to underlyig thoery.
To be continued.

8. Calculating a reaction
Wave functions:
Weak currents in the nucleus ? ✔
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9. ab initio methods to solve the Schroediger equation
Expanding the wave functions in a known basis to get an exact solution to the equation.
Using effective interaction approach to accelerate the convergence (mainly for A>3).
Hyperspherical Harmonics (EIHH)
No Core Shell Model (NCSM)
Correct long range behavior.
Difficult to antisymmetrize.
Large basis.
Incorrect long range behavior.
Antisymmetrization – easier.
Easier calculations of non- local force.
Amax~15, spectra
Amax~7, reactions,
Barnea, Leidemann, Orlandini, Phys. Rev. C, (2001).
Navratil, Vary, Barrett, Phys. Rev. Lett., (2000).
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10. Benchmark calculation of a four body bound state with a realistic NN potential AV8’
Method
Eb [MeV]
Matter radius [fm] FY
25.94(5)
1.485(3)
CRCGV
25.90
1.482
SVM
25.92
1.486 HH
25.90(1)
1.483
GFMC
25.93(3)
1.490(5)
NCSM
25.80(20)
1.485
EIHH
25.944(10)
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Kamada et al, Phys. Rev. C 64, (2001)
TRIUMF, October 2008

11. Calculation of 4He bound state with state of the art NN+NNN potentials AV18+UIX
Eexp= MeV
Eb [MeV]
Matter radius [fm]
EIHH [DG et. al]
28.418
1.432
FY [Nogga et. al]
28.50
HH [Viviani et. al]
28.46
1.428
GFMC [Wiringa et. al]
28.34
1.43
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12. Calculating a reaction
Wave functions:
Weak currents in the nucleus ? ✔ ? ✔ ? ✔
However,
As weakly bound systems, light nuclei have almost no excited bound states.
Theoretical description of continuum states is hard, out of reach for A>3.

13. Calculating an inelastic reaction
Response function
Wave functions
Weak currents in the nucleus ? ✔ ? ✔ ? ✔
However,
As weakly bound systems, light nuclei have almost no excited bound states.
Theoretical description of continuum states is hard, out of reach for A>3.
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14. Lorentz Integral Transform (LIT)
We define the LIT of R(w) as
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15. substituting:
using closure:
where:
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16. HOW DO WE SOLVE FOR WFs? Same way as explained before.
Therefore we have to solve the Schroedinger like equations:
Few Remarks:
There is no solution to the homogeneous equation.
The boundary conditions are of a bound state.
Assures full final state interaction.
HOW DO WE SOLVE FOR WFs? Same way as explained before.
Efros, Leidemann & Orlandini, Phys. Lett. B 408, 1 (1994)
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17. Photoabsorption on 4He At low-energy:
Scattering constrained by current conservation (Siegert theorem).
Governed by the dipole operator.
DG, Bacca, Branea, Leidemann, Orlandini, Phys. Rev. Lett. 96, (2007)
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18. Calculating a reaction
Response function
Wave functions:
Weak currents in the nucleus ✔ ? ? ✔ ✔

19. The Nuclear Hamiltonian
NN forces:
Reproduces NN phase shifts to great accuracy.
However, underbind 3H, 3He, 4He, p-shell nuclei…
Need three-nucleon-forces (3NF).
In the 1990’, phenomenological force models were developed: Argonne potentials, CD Bonn (NN), Urbana, Tucson, Illinois (3NF) …
However, they have no microscopic origin – thus do not give any insight to scattering operators.
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20. Calculation of a four body bound state with a realistic NN+NNN potentials AV18+UIX
Eexp= MeV
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DG, Bacca, Branea, Leidemann, Orlandini, Phys. Rev. Lett. 96, (2007)

21. Phenomenological Nuclear Forces
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Taken from ANL web-page.

22. Effective field theory (EFT) for nuclear physics: Chiral perturbation theory (cPT)
Symmetries are important NOT degrees of freedom:
In QCD – an approximate chiral symmetry:
Pions – Goldstone bosons of the broken symmetry.
Identify Q – the energy scale of the process. (around 100 MeV)
In view of Q -Identify the relevant degrees of freedom. (pions and nucleons).
Choose L – the theory cutoff. ( MeV)
Write all the possible operators which agree with the symmetries of the underlying theory (INFINITE)
Calculate Feynman diagrams (INFINTE)
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23. A perturbative expansion
The “big deal” in cPT
Weinberg proved that each Feynman diagram can be characterized by a power :
A perturbative expansion
+ an error estimate
nucleons
order of interaction
Derivatives
or pion masses
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24. Modern approach to calculating weak reactions
Chiral Lagrangian
Weak currents
Wave functions
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25. Nuclear forces in cPT Epelbaum et al, Nucl. Phys. A671, 295 (2000).
Machleidt, Entem, Phys. Rev. C 68, (2003)
Figure taken from Machleidt, arXiv:nucl-th/
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26. Calibrating them from binding energy of triton and:
Nuclear 3NF in cPT
2 pion exchange
To fourth order: only two contact parameters that include more than 1 nucleon.
Calibrating them from binding energy of triton and:
Scattering length of three nucleons
Binding energy of 3He
Binding energy of 4He
Contact terms cD cE
All correlated!
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27. Parameters which reproduce 3H, 3He binding energies:
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Navratil et al, Phys. Rev. Lett. 99, (2007).
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28. Nuclear currents in cPT
Single nucleon operators: same as in standard nuclear physics.
To fourth order: only ONE contact parameter that includes more than 1 nucleon.
Same parameter as in 3NF
Calibrating it from triton half life?
1 pion exchange
Contact term cD
T.-S. Park et al, Phys. Rev. C 67, (2003).
DG, PhD. thesis, arXiv: (2007).
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29. 3NF from triton binding energy and half life
Deviation from experimental
GT strength
Experimental
error bar
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DG, S. Quaglioni, P. Navratil, in preperation.
TRIUMF, October 2008

30. What can the 3NF and MEC teach us?
Without MEC and 3NF the decay rate is underpredicted by 2%.
MEC are essential for this observable.
Contact term in MEC is essential.
3NF are not essential!
How do we understand this?
In Gamow Teller operator, the short range weak correlations and the short range correlations in the nucleus (3NF) are not correlated !!!
3 Nucleon
Forces
Meson Exchange
Currents
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31. A current road block in fully consistent calculations – and a solution
The force models were developed only recently.
Up to now – only N2LO 3NF were developed.
HOWEVER:
There are phenomenological quantitive force models.
They (usually) have a correct long pion tail.
We already saw some disentanglement in short range correlations in the nucleus.
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32. EFT* - Practical approach to calculating weak reactions
Phenomenological force
Chiral Lagrangian
Triton half-life – completely constraints MEC.
Keeping the L dependence
Keeping the microscopic connection
Wave functions
Weak current
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T.-S. Park et al, Phys. Rev. C 67, (2003), M. Rho arXiv: nucl-th/

33. m- capture on 3He: 3He(m-,nm) 3H
D. Gazit, Phys. Lett. B 666, 472 (2008).
A muonic atom has a radius smaller by mm/me~207. probability of a capture
Competes with free m- decay:
3He 3H m e
The decay rates become comparable for Z~10.
As a result:
Less than one percent in hydrogen is due to capture.
Hard to measure for protons or light nuclei, where the theory is clean.
3He
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34. Muon Capture by a proton
MuCap Collaboration (PSI) on going measurement:
2.4%, expected to reach 1%.
For the (exclusive) process an incredible measurement (0.3%):
MuCap coll., Phys. Rev. Lett. 99, (2007).
Ackerbauer et al, Phys. Lett. B417, 224 (1998).

35. The Nuclear Wave functions
Previous calculations have shown no significant sensitivity to the nuclear model  ideal for EFT*
The resulting kinematics:

36. Single Nucleon Currents
Vector
Magnetic
Second class currents
Axial
Induced
Pseudo-Scalar
Weinberg Phys. Rev., 112, 1375 (1958)

37. Second class terms - G parity breaking
G parity is the symmetry to a combined charge conjugation and rotation in isospin space:
Due to the fact that isospin is an approximate symmetry:
Using QCD sum rules:
Shiomi, J. Kor. Phys. Soc., 29, S378 (1996)

38. Conserved Vector Current Hypothesis
The weak vector current is an isospin rotation of the electromagnetic current, and in particular conserved.
Thus, relations between multipoles.
So, if CVC holds then:

39. Results

40. Previous results
Ab-initio calculations, based on phenomenological MEC or :
Congleton and Truhlik [PRC, 53, 956 (1996)]: 150232 Hz.
Marcucci et. al. [PRC, 66, (2002)]: 14844 Hz.

41. Radiative corrections to the process
Beta decay has prominent radiative corrections. Why not for muon capture?
Czarnecki, Marciano, Sirlin PRL 99, (2007), showed that radiative corrections increase the cross section by 3.00.4%.
This ruins the good agreement of the old calculations.
But…

42. Final result:

43. Conclusions(i) Induced Pseudo-scalar:
From PT [Bernard, Kaiser, Meissner, PRD 50, 6899 (1994); Kaiser PRC 67, (2003)]:
From muon capture on proton [Czarnecki, Marciano, Sirlin, PRL 99, (2007); V. A. Andreev et. al., PRL 99, (2007)]:
This work:

44. Conclusions(ii) Induced Tensor: From QCD sum rules:
Experimentally [Wilkinson, Nucl. Instr. Phys. Res. A 455, 656 (2000)]:
This work:

45. Conclusions(iii) Induced Scalar: (limit on CVC)
“Experimentally” [Severijns et. al., RMP 78, 991 (2006)]:
This work:

46. Conclusions(iv)
The current formalism correctly describes the weak process
A great success to the theory – correct structure of currents  can be used for other stuff…
The calculation is done without free parameters, thus - a prediction.

47. Type II supernovae
Core collapse supernovae are giant explosions of massive stars.
99% of the energy released is carried away by neutrinos, thus the phenomena inside are sensitive to neutrino interactions with matter.
SNe are the probable site for r-process nucleosynthesis.
Supernova 1987A
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48. The death of a massive star “the nuclear physicist paradigm”
After millions of years of evolving…
Iron peak nuclei don’t burn to heavier nuclei  no support to the core mass.
The core becomes gravitationally unstable collapses.
Nuclear forces halt the collapse, and drive an outgoing shock.
The shock loses energy due to dissociation, neutrino radiation.
The shock stalls…
~1 sec
~100 msec
PhD. Progress report

49. Density profile
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50. Microscopic input to SNe modeling
EOS – determines the equilibrium composition:
Lately it was shown that due to the higher density at the neutrinosphere, this area is dominated by: free nucleons, deutron, 3H, 3He, and 4He.
Cross-sections for neutrino scattering, especially inelastic scattering:
Deposits energy – changes composition and temperature.
Changes composition – n nucleosynthesis.
O’Connor, DG, Horowitz, Schwenk, Barnea, Phys. Rev. C 75, (2007).
Arcones, Martinez-Pinedo, O’Connor, Schwenk, Janka, Horowitz, Langanke.
arXiv: (2008).
Neutrino cross-sections are usually unavailable experimentally as they are small, and demand neutrino factories.
Until then – one resorts to theoretical evaluations.
Haxton, Phys. Rev. Lett 69, 1999 (1988).
Woosley et al., Astrophys. J. 356, 272 (1990).
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51. Composition near neutrinosphere
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52. Neutrino cross-sections
First ab-initio calculations:
Within EFT*:
AV18+UIX NN+NNN interactions.
MEC from HBcPT
Accuracy of about 2%
DG, Barnea Phys. Rev. C 70, (2004); Phys. Rev. Lett. 75, (2007); Nucl. Phys. A 790, 356 (2007); Few Body Syst. (2008).
O’Connor, DG, Horowitz, Schwenk, Barnea, Phys. Rev. C 75, (2007).
DG, PhD. thesis, arXiv: (2007).
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53. Energy deposition near neutrinosphere
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54. Conclusions
A=3 nuclei can have a substantial influence on phenomena near the neutrinosphere.
Recent results [Arcones et. al] show a change in the electron antineutrino spectrum due to the A=3 nuclei.
Effects of inelastic n-4He reactions on the:
explosion mechanism.
n-spectra.
n-nucleosynthesis
should be checked in detailed simulations.
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55. And an outlook to heavier nuclei…
Using beta decay one sees that the beta-decay rate of nuclei is under-predicted by theory.
This is resolved by a quenching: gA1 as A grows, saturated for A>40, for which gA=1.
This fits the mystery of restoration of axial symmetry in meson spectra.
The problem starts already for 6He:
VMC calculations with phenomenological NN+NNN and phenomenological MEC showed a 6% discrepancy, which was worsened by the inclusion of MEC.
Schiavilla, Wiringa, Phys.Rev. C65 (2002)
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56. 6He b-decay rate in EFT*– the way to a solution?
To date, we use a phenomenological non-local nucleon-nucleon potential JISP16.
Calibrating the cPT MEC using triton b-decay rate.
Single nucleon Gamow-Teller with this potential, recovers that of state of the art potentials.
The MEC effect improves the comparison to experiment – a qualitative difference to the phenomenological MEC.
The discrepancy is reduced from 6% to less than 2% - within the calculation uncertainty.
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Vaintraub, DG, Barnea, in preparation.

57. Final Remarks gA1 problem:
The precision era in nuclear physics allows a deep look into the structure and dynamics of nuclei, and its underlying theory QCD.
Muon capture on 3He:
Experimental constraints on the weak form factors of the nucleon.
SNe:
A=3 nuclei can have a substantial influence on phenomena near the neutrinosphere.
Effects of inelastic n-4He reactions on the explosion mechanism, n- spectra, n-nucleosynthesis should be checked in detailed simulations.
gA1 problem:
Seems like the discrepancy in 6He decay rate vanishes when including HBcPT currents.
Still a lot of work to be done until a real conclusion can be drawn.
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58. Collaborators Hebrew University: N. Barnea, S. Vaintraub.
TRIUMF: S. Bacca, A. Schwenk, E. O’Connor.
Trento: G. Orlandini, W. Leidemann.
LLNL: S. Quaglioni, P. Navratil.
ICTP: Ho-Ung Yee.
U. Indiana: C. Horowitz.
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