R' Machleidt

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On the occasion of Eivind Osnes 70th birthday
Nucleon-Nucleon Interactions From Effective Field
Theories

• R. Machleidt
• University of Idaho

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Outline

• Introduction QCD and nuclear physics
• The effective field theory approach to nuclear
  forces Overview
• Current status of 2N forces
• Many-body forces and applications in light nuclei
• Summary and open issues

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How does nuclear physics emerge from QCD?
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QCD
Nuclear structure and reactions
R. Machleidt
NN and NNN Interactions Town Meet,
Chicago, 1-20-07
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QCD
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Ab initio calculations
Nuclear structure and reactions
R. Machleidt
NN and NNN Interactions Town Meet,
Chicago, 1-20-07
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QCD
Ab initio calculations
Nuclear structure and reactions
R. Machleidt
NN and NNN Interactions Town Meet,
Chicago, 1-20-07
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QCD

TetsuoHatsudas talk

Biras and my talk
Ab initio calculations
Nuclear structure and reactions
NN Interactions from EFT Oslo,
22-May-2008
R. Machleidt
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R. Machleidt
NN and NNN Interactions Town Meet,
Chicago, 1-20-07
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The EFT approach
Notice first Quarks and gluons are ineffective
degrees of freedom at low energy. Nuclear forces
are residual forces between colorless objects.

• Use the degrees of freedom which are
• relevant at nuclear physics energies
• nucleons (and pions).
• Observe the symmetries of low-energy QCD
• and the patterns of their breaking
• Symmetry generates and controls
• dynamics.

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The homework to be done

• Write down the most general Lagrangian including
  all terms consistent with the assumed symmetries,
  particularly, spontaneously broken chiral
  symmetry. (Note There will be infinitely many
  terms.)
• Calculate Feynman diagrams. (Note
  There will be infinitely many diagrams.)
• Find a scheme for assessing the importance of the
  various diagrams (because we cannot calculate
  infinitely many diagrams).

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The organizational scheme
Power Counting
Chiral Perturbation Theory (ChPT)
R. Machleidt
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3N forces
4N forces
2N forces
Leading Order
The Hierarchy of Nuclear Forces
Next-to Leading Order
Next-to-Next-to Leading Order
Next-to-Next-to-Next-to Leading Order
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2N forces
Leading Order
The Hierarchy of Nuclear Forces
The Hierarchy of Nuclear Forces
Next-to Leading Order
Next-to-Next-to Leading Order
Next-to-Next-to-Next-to Leading Order
R. Machleidt
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What order do we need for sufficient precision?
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Believe it or not, in answering this question,
the phenomenological high-precision
potentials of the 1990s can help us here.
R. Machleidt
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How many parameters do we need?
R. Machleidt
Recent Adv. in Th. of Nucl. Forces
EXOCT07, Catania, 14-June-07
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(No Transcript)
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Conclusion At least, N3LO is needed Entem
Machleidt, PLB 524, 93 (2002)
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R. Machleidt
Recent Adv. in Th. of Nucl. Forces
EXOCT07, Catania, 14-June-07
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red Idaho N3LO, green Juelich N3LO,
R. Machleidt
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3N Forces
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3N forces
3NF
2N forces
Leading Order
The Hierarchy of Nuclear Forces
The Hierarchy of Nuclear Forces
Next-to Leading Order
Next-to-Next-to Leading Order
3NF at NNLO
Next-to-Next-to-Next-to Leading Order
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Three-nucleon forces at N2LO
TPE-3NF
No new parameters!
OPE-3NF
One new parameter, D.
Contact-3NF
One new parameter, E.
Strategy Adjust D and E to two few-nucleon
observables, e.g., the triton and alpha-particle
binding energies. Then predict properties of
other light nuclei.
R. Machleidt
Nuclear Forces - Lecture 5 Visva Bharati
Workshop, Nov '06
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Calculating the properties of light nuclei
usingchiral 2N and 3N forces
No-Core Shell Model Calculations by P.
Navratil et al., LLNL
2N (N3LO) 3N (N2LO) forces
2N (N3LO) force only
R. Machleidt
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R. Machleidt
Nuclear Forces from ChEFT
INT-07-3 Sept. 25, 2007
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R. Machleidt
Review NN and Many-Body Int. SURA
Workshop, DC, 16-Oct-06
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Courtesy of M. Viviani latest data from TUNL.
R. Machleidt
Review NN and Many-Body Int. SURA
Workshop, DC, 16-Oct-06
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Ay puzzle at NLO and NNLO (2NF3NF)
NLO, ?²/dat100
The Ay puzzle is NOT solved by the 3NF at NNLO.
NNLO ?²/dat15
R. Machleidt
Recent Adv. in Th. of Nucl. Forces
EXOCT07, Catania, 14-June-07
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3N forces
2N forces
Leading Order
The Hierarchy of Nuclear Forces
The Hierarchy of Nuclear Forces
Next-to Leading Order
Next-to-Next-to Leading Order
3NF at N3LO
Next-to-Next-to-Next-to Leading Order
R. Machleidt
Nuclear Forces from ChEFT
INT-07-3 September 2007
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Why do we need the 3NF at N3LO?

• The 2NF is N3LO
• consistency requires that all contributions
  are at the same order.
• The are unresolved problems in 3N, 4N scattering
  and nuclear structure.

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The 3NF at N3LO
One-loop contributions
Juelich
R. Machleidt
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(No Transcript)
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(No Transcript)
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The 3NF at N3LO
One-loop contributions
Juelich
Idaho
R. Machleidt
NN Interactions from EFT Oslo,
22-May-2008
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R. Machleidt
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3N forces
2N forces
Leading Order
The Hierarchy of Nuclear Forces
The Hierarchy of Nuclear Forces
Next-to Leading Order
Next-to-Next-to Leading Order
Next-to-Next-to-Next-to Leading Order
R. Machleidt
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R. Machleidt
Nuclear Forces from ChEFT
INT-07-3 September 2007
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Nuclear Forces from ChEFT
INT-07-3 September 2007
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4NF at N3LO (leading order)
Do not expect much for 4N scattering!
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Summary

• Chiral EFT IS fundamental (QCD based) and
  quantitative.
• At N3LO, some accurate NN potentials have been
  developed (but, watch it, not all N3LO pots. are
  accurate!).
• Two- and many-forces are created on an equal
  footing.
• Current results in nuclear structure including
  the 3NF at N2LO are encouraging (however, the N-d
  A_y puzzle is not solved!).

R. Machleidt
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Open issues, problems

• The 3NF at N3LO very complicated
• Will it solve the N-d A_y puzzle, ,
• will it further improve the spectra of light
  nuclei, ?
• Do we need to go to N4LO, N5LO, ?
• - Not necessary for NN and if, then we have to
  go to N5LO - to get more contacts. Contacts at
  N5LO no problem, but the 2-pi, 3-pi, and 4-pi
  contributions will be a nightmare!

R. Machleidt
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R. Machleidt
Theory of Nuclear Forces FB18
Brazil 21-Aug-06
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Open issues, problems

• The 3NF at N3LO
• Will it solve the N-d A_y puzzle, ,
• will it further improve the spectra of light
  nuclei, ?
• Do we need to go to N4LO, N5LO, ?
• - Not necessary for NN and if, then we have to
  go to N5LO - to get more contacts. Contacts at
  N5LO no problem, but the 2-pi, 3-pi, and 4-pi
  contributions will be a nightmare!
• - Illinois 3NF contains N4LO and N5LO terms!

R. Machleidt
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Illinois 3NFs
N4LO and N5LO (in a theory w/o explicit Deltas)
R. Machleidt
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Open issues, problems

• The 3NF at N3LO very complicated
• Will it solve the N-d A_y puzzle, ,
• will it further improve the spectra of light
  nuclei, ?
• Do we need to go to N4LO, N5LO, ?
• - Not necessary for NN and if, then we have to
  go to N5LO - to get more contacts. Contacts at
  N5LO no problem, but the 2-pi, 3-pi, and 4-pi
  contributions will be a nightmare!
• - Illinois 3NF contains N4LO and N5LO terms!
• The renormalization of the chiral NN potemtial
  Whats the right power counting scheme? Weinberg
  counting has some problems!

R. Machleidt
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This
morning
QCD
Nuclear
Structure Talks
Ab initio calculations
Nuclear structure and reactions
NN Interactions from EFT Oslo,
22-May-2008
R. Machleidt
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R. Machleidt
NN and NNN Interactions Town Meet,
Chicago, 1-20-07
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