Chiral Nuclear Effective Field Theory

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Chiral Nuclear Effective Field Theory
U. van Kolck
University of Arizona
Supported in part by US DOE and Sloan Foundation
Background by S. Hossenfelder
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In Memoriam Vijay Pandharipande
See talks by Carlson, Sick
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Outline

• Effective Field Theories
• Pionful (Nuclear) EFT
• Non-Perturbative Renormalization
• and Power Counting
• Role of the Delta Isobar
  
• Outlook

See parallel session R2
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• Wanted fDead 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

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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 )
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What is Effective?
local underlying symmetries
renormalization-group invariance
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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)
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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
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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
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Role of Chiral Symmetry
Chiral Limit
chiral symmetry
Chiral circle
two isospin axis not shown
pion decay constant

on chiral circle
piece invariant under
function of
explicitly
piece in
direction
function of
isospin breaking
CHIRAL SYMMETRY
WEAK PION INTERACTIONS
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Form of pion interactions determined by chiral
symmetry
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Role of the RG
LO
absorbed
absorbed
NLO
Naturalness
absorbed in higher-order coefficients
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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
vertices of type i
loops
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1
2
1
2
LO
But other counterterms?
RESUM
absorbed
Naturalness
absorbed in higher-order coefficients
for
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Weinberg 90, 91 Ordonez v.K. 92
A gt 2 resummed chiral perturbation theory
infrared enhancement!





A-nucleon reducible
A-nucleon irreducible
Schematically,
bound state at
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Ordonez v.K. 92 v.K. 94







For parity violation



See talk by Maekawa







higher powers of
etc.
more nucleons
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Issue power counting (relative sizes)
Etc.
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Weinberg 90, 91, 92 Ordonez v.K. 92 v.K.
94 Ordonez, Ray v.K. 96 ...
Naïve Dimensional Analysis (NDA)
(non-perturbative pions)
LO S-wave contacts OPE
NLO P-wave contacts TPE 3N forces via delta

(PUNT) subLOs also iterated in
Lippman-Schwinger eq.
similar to phenomenological potential models at
N2LO,
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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
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Ordonez v.K. 92 (cf. Stony Brook TPE)
Note NOT your usual potential!
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
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See talks by Machleidt, Meissner
Many successes of Weinbergs 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 -64.7507(3) Thy
-64.03 Convergence study not completed
No-Core Shell Model
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BUT
Is Weinbergs power counting consistent?
No!
attractive in some channels
singular potential
not enough contact interactions for RG invariance
even at LO!
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Kaplan, Savage Wise 98
require higher-order counterterms !?
Solved if counterterms are larger than NDA
perturbative pions
NNLO
but then series does NOT converge for
LO
Nijm
Fleming, Mehen Stewart 01
NLO
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need to understand non-perturbative
renormalization of pion exchange
BUT, STILL
can be quite different from renormalization of
perturbative series
e.g.
3-body system with short-range forces
Bedaque, Hammer v.K. 99 00 01
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(No Transcript)
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Renormalization of the
potential
OPE
s wave
matching
so that
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Beane, Bedaque, Savage v.K. 02
determined by low-energy data
integer
exact solution, fit to scatt length
analytical form, fit to scatt length
term
neglecting
approaches fixed point
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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
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Nogga, Timmermans v.K. 05 (cf. Birse
McGovern 04)
LO EFT
Nijmegen PSA
Other singlet channels
no counterterms need to be promoted
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Beane, Bedaque, Childress, Kryjevski, McGuire
v.K. 02
determined by low-energy data
3rd
4
exact
1st
2nd
exact vs perturbation th
limit-cycle-like behavior
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fits to scatt length for various cutoffs
various pairs of cutoffs
slope 2
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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 !?
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Pion-mass dependence
Triplet scattering length
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
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Nogga, Timmermans v.K. 05
But what about higher partial waves?
Attractive-tensor channels
Problems!
cutoff dependence
incorrect renormalization
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one undetermined phase in each channel
promote counterterms
limit-cycle-like behavior
cutoff independence
e.g.,
LO EFT
Nijmegen PSA
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Add counterterms
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Add counterterm
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Bound-state spectrum
Without extra counterterms
Shallow spurious bound states!
With extra counterterms
spurious bound states deep and nearly cutoff
independent
deuteron
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LO EFT
W pc
Nijmegen PSA
Promising
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LO EFT
Nijmegen PSA
Promising
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Power Counting
In attractive-tensor waves, if 1PE is iterated,
running of parameters is driven by pion
exchange, NOT short-range physics as implicit in
NDA
suppressed by powers of , NOT
(that is, enhanced by over
NDA)
Infinite number of parameters to remove cutoff
dependence of all attractive-tensor channels?!
No! There is an extra suppression due to the
centrifugal barrier
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after renormalization, LO potential is no
longer singular
Goldberger Watson 64
For a regular, central potential of finite range
d if then (barring fine-tuning)
(classically, no scattering for impact parameter
)
For
ratio between counterterms in subsequent waves
But large factors from
suppression offset in lower waves
Iterate 1PE, together with necessary
counterterms, in S, P, D waves
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TPE suppressed by
compared to OPE
Other counterterms should still be driven by
short-range physics, that is, are suppressed by
powers of
Treat 1PE in other waves, 2PE, etc., together
with necessary counterterms, in perturbation
theory

• 2PE (including delta isobar) in S, P, D waves
• S, P, D contact interactions

e.g., NLO
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Birse 05
Indeed, a subsequent analysis of the
coordinate-space solutions of 1PE gives
breakdown of 1PE perturbative expansion
within EFT regime solve 1PE exactly
outside EFT regime treat 1PE in Born expansion
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Nogga, Timmermans v.K. 05
short-range interactions stronger than
in Weinbergs pc for attractive tensor
channels where
centrifugal barrier
c.f. Birse 05
subLOs in perturbation theory
Second breach of W pc
triton
on the other hand
LO EFT
correct renormalization
indeed
but leading-order value not so great because of
kinetic-potential energy cancellation!?
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Can one integrate out the delta with small error?
No!
Pandharipande, Phillips v.K. 05
EFT folklore
in nuclei,
can integrate out delta with small error

But
30 error
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pN scattering


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)
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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
Weinbergs 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
Weinbergs 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?!