1. Chiral Nuclear Effective Field Theory
U. van Kolck
University of Arizona
Supported in part by US DOE and Sloan Foundation
Background by S. Hossenfelder

2. In Memoriam Vijay Pandharipande See talks by Carlson, Sick 1/1/2019
v. Kolck, Pion Renormalization

3. v. Kolck, Pion Renormalization
Outline
Effective Field Theories
Pionful (Nuclear) EFT
Non-Perturbative Renormalization
and Power Counting
Role of the Delta Isobar
Outlook
See parallel session R2
1/1/2019
v. Kolck, Pion Renormalization

4. Wanted f Dead sor s Alive
QCD EXPLANATION OF NUCLEAR PHYSICS
Reward
understanding of gross features:
Why is ?
How large are few-nucleon forces?
Why is isospin a good symmetry? …
Beware
coupling constants not small
1/1/2019
v. Kolck, Pion Renormalization

5. Nuclear physics scales
“His scales are His pride”, Book of Job
perturbative QCD
~1 GeV
no small coupling
need a more general
way to treat
multi-scale problems
~100 MeV
~30 MeV
Effective Field Theory (EFT)
(expansion in )
1/1/2019
v. Kolck, Pion Renormalization

6. v. Kolck, Pion Renormalization
What is Effective?
local
underlying symmetries
renormalization-group invariance
1/1/2019
v. Kolck, Pion Renormalization

7. For Q ~ m, truncate consistently with RG invariance
normalization
non-analytic, from loops
“power counting”
e.g. # loops L
For Q ~ m, truncate consistently with RG invariance
so as to allow systematic improvement (perturbation theory):
1/1/2019
v. Kolck, Pion Renormalization

8. Nuclear physics scales
perturbative QCD
~1 GeV
sum ?
hadronic th
with chiral symm
this talk
~100 MeV
sum
~30 MeV
sum
halo nuclei
See talks by Hammer, Braaten
1/1/2019
v. Kolck, Pion Renormalization

9. Nuclear EFT pionful EFT
degrees of freedom: nucleons, pions, deltas (+ roper?, …)
symmetries: Lorentz, P, T, chiral
expansion in:
non-relativistic
multipole
pion loop
calculated from QCD: lattice, …
chiral symmetry
fitted to data
1/1/2019
v. Kolck, Pion Renormalization

10. Form of pion interactions determined by chiral symmetry… … … … … …
Form of pion interactions
determined by
chiral symmetry
1/1/2019
v. Kolck, Pion Renormalization

11. v. Kolck, Pion Renormalization
Role of the RG LO
absorbed
absorbed
NLO
Naturalness:
absorbed in
higher-order
coefficients
1/1/2019
v. Kolck, Pion Renormalization

12. A= 0, 1: chiral perturbation theory
Weinberg ’79
Gasser + Leutwyler ’84 …
Gasser, Sainio + Svarc ’87
Jenkins + Manohar ’91
A= 0, 1: chiral perturbation theory
nucleon
dense but
short-ranged
long-ranged
but sparse
# loops
# vertices
of type i
1/1/2019
v. Kolck, Pion Renormalization

13. v. Kolck, Pion Renormalization1 2 1 2 LO
But…
other counterterms?
RESUM
absorbed
Naturalness:
absorbed in
higher-order
coefficients
for
1/1/2019
v. Kolck, Pion Renormalization

14. A > 2: resummed chiral perturbation theory
Weinberg ’90, ‘91
Ordonez + v.K. ’92 …
A > 2: resummed chiral perturbation theory
infrared
enhancement! = +
+ … = +
A-nucleon irreducible
A-nucleon reducible
Schematically,
bound state at
1/1/2019
v. Kolck, Pion Renormalization

15. v. Kolck, Pion Renormalization
Ordonez + v.K. ’92
v.K. ’94 … = + +
+ … + +
+ …
For parity violation + +
+ …
See talk by Maekawa = +
+ … +
+ … +
+ …
higher powers of
etc.
more nucleons
1/1/2019
v. Kolck, Pion Renormalization

16. Issue: power counting (relative sizes)
Etc.
1/1/2019
v. Kolck, Pion Renormalization

17. similar to phenomenological potential models: at N2LO,
Weinberg ’90, ’91, ‘92
Ordonez + v.K. ’92
v.K. ’94
Ordonez, Ray + v.K. ‘96
...
Naïve
Dimensional
Analysis
(NDA)
LO: S-wave contacts + OPE
(non-perturbative pions)
NLO: P-wave contacts + TPE + 3N forces via delta …
+ (PUNT) subLOs also iterated in Lippman-Schwinger eq.
similar to phenomenological potential models: at N2LO,
1/1/2019
v. Kolck, Pion Renormalization

18. e.g., = + + + + + + … TM’ pot See talk by Robilotta
v.K. ’94
Friar, Hueber + v.K. ‘99
Coon + Han ’99
...
e.g.,
Fujita-Miyazawa pot = + +
one unknown
parameter
two unknown
parameters + + +
+ …
Tucson-Melbourne pot with
TM’ pot
cf. Brazil pot
See talk by Robilotta
1/1/2019
v. Kolck, Pion Renormalization

19. models with s, w, … might be misleading…
Note: NOT your usual potential!
Ordonez + v.K. ’92
(cf. Stony Brook TPE)
e.g., + +
+ …
Rentmeester et al. ’01, ‘03
chiral v.d. Waals force
Nijmegen PSA of 1951 pp data
Kaiser, Brockmann + Weise ’97
at least
as good!
parameters found
consistent with pN data!
models with s, w, …
might be misleading…
1/1/2019
v. Kolck, Pion Renormalization

20. Many successes of Weinberg’s counting, e.g.,
See talks by
Machleidt, Meissner
Many successes of Weinberg’s counting, e.g.,
At N3LO, fit to NN phase shifts comparable to those of
“realistic” phenomenological potentials
With N3LO NN and N2LO 3N potentials, good description of
3N observables and 4N binding energy
levels of p-shell nuclei
Entem + Machleidt ’03
Epelbaum, Gloeckle + Meissner ’04
Epelbaum et al. ’02
Gueorguiev, Navratil,
Ormand + Vary ’05
Binding Energy (MeV)
Exp: (3)
Thy: *
*Convergence study not completed
1/1/2019
v. Kolck, Pion Renormalization
No-Core Shell Model

21. No! Is Weinberg’s power counting consistent?
BUT
Is Weinberg’s power counting consistent?
No!
attractive in
some channels
singular
potential
not enough contact interactions for RG invariance even at LO!
1/1/2019
v. Kolck, Pion Renormalization

22. v. Kolck, Pion Renormalization
1/1/2019
v. Kolck, Pion Renormalization

23. Renormalization of the potential
OPE:
s wave
matching
so that
1/1/2019
v. Kolck, Pion Renormalization

24. approaches fixed point
Beane, Bedaque, Savage + v.K. ’02
integer
determined by low-energy data
exact solution,
fit to scatt length
analytical form,
fit to scatt length
neglecting
term
approaches fixed point
1/1/2019
v. Kolck, Pion Renormalization

25. expand around the chiral limit (perturbative pions) or promote
including
fitted to eff range
Nijmegen
PSA
expand around the chiral limit (perturbative pions) or
promote
to leading order (due to infrared enhancement)
First breach of W pc
1/1/2019
v. Kolck, Pion Renormalization

26. exact vs perturbation th
Beane, Bedaque, Childress, Kryjevski, McGuire + v.K. ’02
determined by
low-energy data
3rd 4
exact
1st
2nd
exact vs perturbation th
1/1/2019
v. Kolck, Pion Renormalization
limit-cycle-like behavior

27. analogous, but for coupled channels…
Frederico, Timoteo + Tomio ’99
Beane, Bedaque, Savage + v.K. ’02
Ruiz-Arriola + Valderrama ‘05
analogous, but for coupled channels…
Nijmegen
PSA
in MeV
EFT – Nijm PSA
slope ~2
sufficient in leading order !?
1/1/2019
v. Kolck, Pion Renormalization

28. Pion-mass dependence Triplet scattering length Deuteron binding energy
Lattice QCD:
quenched
Fukugita et al. ‘95
Deuteron
binding energy
EFT:
(incomplete) NLO
Beane, Bedaque, Savage + v.K. ’02
Beane + Savage ’03
Epelbaum, Gloeckle + Meissner ‘03
1/1/2019
v. Kolck, Pion Renormalization

29. Problems! But what about higher partial waves?
Nogga, Timmermans + v.K. ’05
But what about higher partial waves?
Attractive-tensor channels:
Problems!
cutoff dependence
incorrect
renormalization…
1/1/2019
v. Kolck, Pion Renormalization

30. one undetermined phase in each channel
promote
counterterms
limit-cycle-like
behavior
cutoff
independence
e.g.,
LO EFT
Nijmegen PSA
1/1/2019
v. Kolck, Pion Renormalization

31. v. Kolck, Pion Renormalization
LO EFT
W pc
Nijmegen PSA
Promising…
1/1/2019
v. Kolck, Pion Renormalization

32. triton short-range interactions stronger than in
Nogga, Timmermans + v.K. ’05
short-range interactions stronger than in
Weinberg’s pc for attractive tensor channels
where
centrifugal barrier
c.f. Birse ’05
+ subLOs in perturbation theory
Second breach of W pc
on the other hand:
triton
correct
renormalization…
LO EFT
indeed
1/1/2019
v. Kolck, Pion Renormalization
… but leading-order value not so great because of kinetic-potential energy cancellation!?

33. No! Can one integrate out the delta with small error? + …
Pandharipande, Phillips + v.K. ’05
EFT folklore:
in nuclei,
can integrate out delta
with small error
+ …
But
30% error
1/1/2019
v. Kolck, Pion Renormalization

34. relatively large error from the pN scattering fit leaks into 3N force +
+ …
at threshold
while
relatively large error
from the pN scattering fit
leaks into 3N force
extrapolation
involved
best strategy is not
to integrate out delta
(cf Ordonez, Ray + v.K. ’96
Gerstendoerfer, Kaiser + Weise ’98)
1/1/2019
v. Kolck, Pion Renormalization

35. Conclusions and Outlook
EFT allows a systematic, model-independent, unified description of
strong interactions at low energies
Power counting complicated by nonperturbative nature of nuclei
Weinberg’s power counting not entirely correct due to failure of NDA
in attractive-tensor channels where pions have to be iterated
New power counting has been formulated:
more counterterms at each order relative to Weinberg’s;
expect even better description of observables
Consistency and convergence of new power counting yet to be checked:
two-nucleon
NLO calculation of
systems
other few-nucleon
Finally a consistent and efficient power counting
in the pionful EFT?!
1/1/2019
v. Kolck, Pion Renormalization