Effective Interactions from Effective Field Theory U' van Kolck University of Arizona Supported in p

1
Effective Interactionsfrom Effective
Field TheoryU. van KolckUniversity of
ArizonaSupported in part by US DOE
Background by S. Hossenfelder
2
E is for effective
Effective Osnes
Spires

• An introductory guide to effective operators in
  nuclei,
• P.J. Ellis and E. Osnes,
• Rev. Mod. Phys. 49 (1977) 777.
• Realistic effective interactions for nuclear
  systems,
• M. Hjorth-Jensen, T.T.S. Ku, and E. Osnes,
• Phys. Rept. 261 (1995) 125.
• Effective interactions and the nuclear
  shell-model,
• D.J. Dean, T. Engeland, M. Hjorth-Jensen, M.
  Kartamyshev, and E. Osnes,
• Prog. Part. Nucl. Phys. 53 (2004) 419.
• 13 others

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Outline

• Effective Field Theories
• Pionful and Pionless
• Few Nucleons
• Few Atoms
• More Nucleons
• Conclusion

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Crucial issue
As A grows, given computational power
limits number of accessible one-nucleon states
HO basis
excluded space
A-body problem shell model
model space
What are the effective interactions in the
model space?
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Barrett, Vary Zhang 93
The traditional no-core shell model approach
start with god-given (can be non-local!)
potential, and run the RG in an HO basis
Free-particle basis Vlowk
Feshbach projection
convergence
arbitrary truncation (cluster approximation)
issues systematic truncation error, consistent
currents, etc. (plus, how much QCD does your god
know anyway?)
EFT addresses just these issues!
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SM
Forecast
QCD
lattice
large
necessary to extrapolate to
EFT
small
NCSM,
want model independence
?
lattice,
Few-nucleon systems
Many-nucleon systems
Nuclear matter
this talk
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Nuclear physics scales
His scales are His pride, Book of Job
(according to J. Friar)
1 GeV
100 MeV
30 MeV
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What is Effective?
Weinberg, Wilson, etc.
local underlying symmetries
renormalization-group invariance
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non-analytic, from loops
normalization
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
expansion in
perturbative QCD
unknown use brute force (lattice, )
1 GeV
hadronic theory
Chiral EFT
100 MeV
30 MeV
Contact EFT
no small coupling constants!
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Nuclear EFTs
pionful EFT

• degrees of freedom nucleons, pions deltas (
  roper, ?)
• symmetries Lorentz, P, T, chiral
• expansion in

non-relativistic
multipole
pion loop
Weinberg 79 Gasser Leutwyler 84
A 0, 1 chiral perturbation theory
A gt 2 resummed chiral perturbation theory
Weinberg 90, 92 Ordonez v.K. 92
see several talks at this conference
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bound-state pole at



However, RG invariance of iterated pion exchange
not trivial
Beane, Bedaque, Savage v.K. 02 Nogga,
Timmermans v.K. 05 Birse 06
corrected Weinbergs power counting
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Pion-mass dependence
unitarity limit
Fukugita et al. 95
Lattice QCD quenched
triplet scattering length
c.f. Beane, Bedaque, Orginos Savage 06
Beane, Bedaque, Savage v.K. 02
EFT (incomplete) NLO
Deuteron binding energy
Large deuteron size because
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Trapped fermions
Feshbach resonance
unitarity limit
MIT group webpage
optical trapping
standing waves
I. Bloch
low-tunneling regime
lasers
(band insulator)
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pionless EFT

• degrees of freedom nucleons
• symmetries Lorentz, P, T
• expansion in

non-relativistic
multipole
omitting spin, isospin
First orders apply also to atoms
e.g.,
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v.K. 97 99 Kaplan, Savage Wise 98 Gegelia
98



scattering length
unitarity
b.s. at



effective range

effective range expansion
Bethe Peierls 35 Bethe 49
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Chen, Rupak Savage 99
fitted
predicted
Nijmegen PSA
fitted
predicted
Nijmegen PSA
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3-body interaction
but only in
Wikipedia




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Bedaque v.K. 97 Bedaque, Hammer v.K. 98
Bedaque, Hammer v.K. 99 00 Hammer Mehen
01 Bedaque et al. 03
no 3-body force up to
3-body force already at
fitted
predicted
v.Oers Seagrave 67
Dilg et al. 71
v.Oers Seagrave 67
Kievsky et al. 96
fitted nothing
predicted
Dilg et al. 71
QED-like precision!
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Bedaque, Hammer v.K. 99 00 Hammer Mehen
01 Bedaque et al. 03
unless
dimensionful parameter
(dimensional transmutation)
Phillips line
potential models
exp
varying
RG limit cycle!
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four-body bound state can be addressed
similarly no four-body force at
Hammer, Meissner Platter 04
Tjon line
exp
potential models
varying
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larger nuclei?
No-Core Shell Model!
Stetcu, Barrett v.K., 06 Stetcu, Barrett, Vary
v.K., 07 Stetcu, Barrett v.K., in progress
start with EFT in restricted space fit
parameters in few-nucleon systems
for various and
and predict larger nuclei
IR
cutoffs
UV
strategies determine parameters from
light-nuclei binding energies
scattering phase shifts
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Trapped two-component fermions
LO
two-body force
pairs
no
reduced mass
three-body force
HO is physics
HO length
universal behavior
only low-energy scale is b
in general case?
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Stoeferle et al (ETH) 06
atoms
total angular momentum
magnetic quantum number
Busch, Englert, Rzazewski Wilkens 98
pseudopotential in trap
use, e.g. lowest level
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RG running
simple!
similar to free-particle basis
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Stetcu, Barrett, Vary v.K., 07
Find, within 10,
semi-analytical result
Werner Castin 06
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Stetcu, Barrett, Vary v.K., 07
repulsion
as in two-body system
attraction
confirmed Kestner Duan 07
inversion of parity!
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Stetcu, Barrett, Vary v.K., 07
larger errors
repulsion
attraction
cf. Chang Bertsch 07
GFMC
b.s.?
cf. Petrov, Salomon Shlyapnikov 05
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Untrapped nucleons
LO
pairs
triplets
EFT PC effectively justifies (modified) cluster
approximation
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• LO parameters

fitted to d, t, a ground-state binding energies
Stetcu, Barrett v.K., 06
limit cycle?
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LO
Stetcu, Barrett v.K., 06
fits
fits
works within 10 !
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Stetcu, Barrett v.K., 06
LO
fits
fits
works within 30
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works as expected!
next, to higher orders perturbation theory
cf. Alhassid, Bertsch Fang 07
smaller faster convergence, heavier systems
Stetcu, Barrett v.K., in progress
Trapped fermions
e.g.,
NLO
WernerCastin
LO
Preliminary

• with pionless EFT?
• with NCSM?

Issues how far can we go
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Conclusion

• is consistent with symmetries
• incorporates hadronic physics
• has controlled expansion

EFT the framework to describe nuclei within the SM

• A lt 4 low-E scatt, bss, probes
• A gt 4 bss

many successes so far

• grow to larger nuclei
• go to next orders
• extend to pionful EFT

but still much to do
by Eivinds 80th