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12th CNS International Summer School (CNSSS13) 28 August to 03 September 2013 -- CNS Wako Campus . Nuclear Forces - Lecture 4 -. Nuclear Forces from Chiral EFT. R. Machleidt University of Idaho. Nuclear Forces - Overview of all lectures -. Lecture 1: History, facts, and phenomenology

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slide1

12th CNS International Summer School (CNSSS13)

28 August to 03 September 2013 -- CNS Wako Campus

Nuclear Forces- Lecture 4 -

Nuclear Forces from Chiral EFT

R. Machleidt

University of Idaho

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide2

Nuclear Forces- Overview of all lectures -

  • Lecture 1: History, facts, and phenomenology
  • Lecture 2: The meson theory of nuclear forces
  • Lecture 3: QCD and nuclear forces; effective field theory (EFT) for low-energy QCD
  • Lecture 4: Nuclear forces from chiral EFT

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide3

Lecture 4: Nuclear Forces from EFT

  • Summary of basic arguments in favor of an EFT
  • The Hierarchy of nuclear forces
  • The new generation of chiral NN potentials
  • Beyond the two-nucleon force: 3NFs
  • Applications in nuclear structure
  • More on many-nucleon forces
  • Conclusions

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide4

From QCD to nuclear physics via chiral EFT

(in a nutshell)

  • QCD at low energy is strong.
  • Quarks and gluons are confined into colorless hadrons.
  • Nuclear forces are residual forces (similar to van der Waals forces)
  • Separation of scales

R. Machleidt

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide5

Calls for an EFT

  • soft scale: Q ≈ mπ ,hard scale: Λχ ≈ mρ ; pions and nucleon relevant d.o.f.
  • Low-energy expansion: (Q/Λχ)ν
  • with ν bounded from below.
  • Most general Lagrangian consistent with all symmetries of low-energy QCD, particularly, chiral symmetry which is spontaneously broken.
  • Weakly interacting Goldstone bosons = pions.
  • π-π and π-N perturbatively
  • NN has bound states:
  • (i) NN potential perturbatively
  • (ii) apply nonpert. in LS equation.
  • (Weinberg)

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide6

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

slide7

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

R. Machleidt

7

slide8

NN phase shifts up to 300 MeV

Red Line: N3LO Potential by Entem & Machleidt, PRC 68, 041001 (2003).

Green dash-dotted line: NNLO Potential, and

blue dashed line: NLO Potential

by Epelbaum et al., Eur. Phys. J. A19, 401 (2004).

LO

NLO

NNLO

N3LO

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

8

slide9

N3LO Potential by Entem & Machleidt, PRC 68, 041001 (2003).

NNLO and NLO Potentials by Epelbaum et al., Eur. Phys. J. A19, 401 (2004).

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide10

Summary: χ²/datum

  • NLO: ≈ 100
  • NNLO: ≈ 10
  • N3LO: ≈ 1
  • Great rate of convergence of ChPT!

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

parameters
Parameters
  • pi-pi Lagrangian:
  • pi-N Lagrangians:
  • N-N Lagrangian (“Contacts”): 2+7+15=24 essentially free parameters.

The free parameters are used to adjust the potential to the empirical NN phase shifts and data.

No free parameters.

no free parameters.

In principal fixed by pi-N data; but cf. Table on next slide.

4 parameters.

4 parameters.

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

parameters cont d pi n lagrangian parameters
Parameters, cont’dpi-N Lagrangian parameters

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

parameters cont d of contact parameters compared to phenomenological fits
Parameters, cont’d.# of contact parameters compared to phenomenological fits

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide14

How does the chiral EFT approach

compare to

conventional meson theory?

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide15

Main differences

  • Chiral perturbation theory (ChPT) is an expansion in terms of small momenta.
  • Meson theory is an expansion in terms of ranges (masses).

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide16

The nuclear force in the meson picture

Short

Inter-

mediate

Long range

Taketani, Nakamura, Sasaki (1951): 3 ranges

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide17

2N forces

Leading Order

Next-to Leading Order

Next-to-Next-to Leading Order

Next-to-Next-to-Next-to Leading Order

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide18

ChPT Conventional meson theory

OPE

TPE

Short range

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide19

Question: When everything is so equivalent to conventional meson theory, why not continue to use conventional meson theory?

  • Chiral EFT claims to be a theory, while “meson theory” is a model.
  • Chiral EFT has a clear connection to QCD, while the QCD-connection of the meson model is more hand-woven.
  • In ChPT, there is an organizational scheme (“power counting”) that allows to estimate the size of the various contributions and the uncertainty at a given order (i.e., the size of the contributions we left out).
  • Two- and many-body force contributions are generated on an equal footing in ChPT.

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide20

Three-nucleon forces (3NF)

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide21

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

The 3NF

at NNLO;

used so far.

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide22

Now, showing only

3NF diagrams.

The 3NF

at NNLO;

used so far.

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

three nucleon forces at nnlo
Three-nucleon forces at NNLO

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.

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide24

Calculating the properties of light nuclei usingchiral 2N and 3N forces

“No-Core Shell Model “ Calculations by P. Navratil et al., LLNL

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide25

Calculating the properties of light nuclei usingchiral 2N and 3N forces

“No-Core Shell Model “ Calculations by P. Navratil et al., LLNL

2N (N3LO) force only

R. Machleidt

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide26

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

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide27

Oxygen

Calcium

R. Machleidt

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

27

slide28

p-d

Analyzing

Power

Ay

2NF+3NF

Calculations by

the Pisa Group

2NF only

The Ay puzzle is NOT solved

by the 3NF at NNLO.

p-3He

2NF+3NF

2NF only

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

28

slide29

And so,

we need 3NFs beyond NNLO,

because …

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

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide30

The 3NF

at NNLO;

used so far.

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide31

The 3NF

at NNLO;

used so far.

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide32

Apps of N3LO 3NF:

Triton: Skibinski et al.,

PRC 84, 054005 (2011).

Not conclusive.

Neutron matter:

Hebeler, Schwenk

and co-workers,

PRL 110, 032504 (2013).

Not small!(?)

N-d scattering (Ay):

Witala et al.

Small!

The 3NF

at NNLO;

used so far.

Small?

slide33

N-d Ay calculations by Witala et al.

R. Machleidt

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

Chiral EFT of Nucl. Forces INPC 2013, Florence, 06/05/2013

33

slide34

The 3NF

at NNLO;

used so far.

Small?

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide35

The 3NF

at NNLO;

used so far.

Small?

1-loop graphs: 5 topologies

2PE 2PE-1PE Ring Contact-1PE Contact-2PE

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide36

The 3NF

at NNLO;

used so far.

Small?

1-loop graphs: 5 topologies

2PE 2PE-1PE Ring Contact-1PE Contact-2PE

R. Machleidt

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

36

slide37

The 3NF

at NNLO;

used so far.

Small?

Large?!

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide38

The 3NF

at NNLO;

used so far.

Small?

Large?!

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide39

3NF contacts

at N4LO

Girlanda, Kievsky, Viviani, PRC 84, 014001 (2011)

The 3NF

at NNLO;

used so far.

Small?

Large?!

Spin-Orbit

Force!

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide40

The 3NF

at NNLO;

used so far.

Small?

Large?!

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide41

A realistic,

investigational

approach:

  • use Δ-less

The 3NF

at NNLO;

used so far.

  • include NNLO 3NF
  • skip N3LO 3NF

Small?

  • at N4LO start with
  • contact 3NF, use
  • one term at a time,
  • e.g. spin-orbit
  • that may already
  • solve some of your
  • problems.

Large?!

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

current problems with chiral 3nfs
Current problems with chiral 3NFs
  • “Explosion” of 3NFs at higher orders.
  • For the time being, deal with it selectively. Do not try “complete” calculations.
  • Many open questions
  • Will the chiral 3NF converge with increasing order?
  • (This is quite in contrast to the chiral 2NF, where things are under control.)

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide43

Four-nucleon forces (4NF)

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide44

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

4N forces

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide45

4NF at N3LO (leading order)

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

conclusions
Conclusions
  • After 80 years of struggle, we have now a proper theory for nuclear forces that is based upon the fundamental theory of strong interactions, QCD. It is chiral effective field theory for low-energy QCD, in which the pion plays a fundamental role (Goldstone boson). Thus, the original Yukawa idea that there is ONE MESON that makes the nuclear force is re-instated. But as compared to the early attempts, a crucial constraint has been added: chiral symmetry generates and controls pion-exchanges.
  • Based upon chiral perturbation theory (ChPT), quantitative NN potentials have been successfully developed (at N3LO) and are applied in nuclear structure calculations.
  • In ChPT, two- and many-body forces are generated on an equal footing. Concerning the 3NF, there are still some open issues including its order-by-order convergence.
  • A new and exciting era has started for microscopic nuclear structure!

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)

slide47

The End

Thank you all for listening patiently,

And thank you to the organizers!

Review article:

R. Machleidt and D.R. Entem,

Chiral Effective Field Theory and Nuclear Forces,

Physics Reports 503, 1 (2011).

Nuclear Forces - Lecture 4 NF from EFT (CNSSS13)