Isospin dependence of the three nucleon force

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Evgeny Epelbaum
MENU2007, Jülich, 13.09.2007
Delta resonance contributions to the nuclear force
Evgeny Epelbaum
Research Center Jülich Bonn University, Germany
Outline
Motivation ?-contributions to the 2p-exchange 2N
potential ?-excitations and the 3N force Leading
isospin-breaking effects Summary and outlook
Work done in collaboration with Hermann Krebs and
Ulf-G. Meißner (Bonn Jülich)
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Motivation
Chiral expansion for the 2p-exchange potential
Q2
Q3
The subleading contribution is bigger than the
leading one!
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Why is the order-Q3 (i.e. subleading) 2pexchange
NN potential so strong?
including ? explicitly in EFT one may expect a
more natural size of certain LECs, better
convergence of the low-energy expansion
applicability at higher energies
a caveat calculations much more involved
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Implications for the 2p-exchange NN potential
Krebs, E.E., Meißner EPJA 32 (2007) 127
?- less EFT
?- full EFT additional graphs
NLO
Ordonez et al.96, Kaiser et al. 98
NNLO
Results in agreement with the decoupling theorem
(consistency check), i.e. the contributions due
to intermediate ?s expanded in powers of
can be exact-ly reproduced in EFT without
explicit ?s.
Both non-polynomial terms are reproduced in
?-less EFT via saturation of LECs . All
other contributions do not yield nonpolynomial
structures at order Q3.
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Determination of the LECs from pN threshold
coefficients
crossed graphs
Determinations of the LECs
Input
(SU(4), large Nc)
fit 1
fit 2
(Fettes Meißner 01)
Values of the S- and P-wave threshold param.
We found
improved description of P-wave threshold
parameters when ? is included strongly
reduced values for cis resulting cis
depend strongly on hA while the thresh. param.
do not
all values in units
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Chiral 2pexchange potential can be written in
coordinate space in the form
Chiral 2p-exchange up to NNLO with and without
explicit ?
with ?
without ?
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Chiral 2p-exchange up to NNLO with and without
explicit ?
without ?
with ?
much better convergence when ? is included
explicitly!
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3F3 partial wave up to NNLO with and without ?
NNLO-?
NNLO-?
NLO-?
NLO-?
LO (OPE)
(calculated in the first Born approximation)
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Delta excitations and the three-nucleon force
?- full EFT additional graphs
?- less EFT
NLO
van Kolck96
N2LO
N3LO
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Leading isospin-breaking 2pexchange due to
explicit ?s
Krebs, E.E., Meißner, in preparation
Leading contributions
Friar et al. 99,03,04 Niskanen 02 E.E.,
Meißner 05
Subleading CSB 2pexchange potential
Subleading contributions
E.E., Meißner 05
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Leading isospin-breaking 2pexchange due to
explicit ?s
Charge-symmetry-breaking 2pexchange potential
?-full EFT, LO
?-less EFT, NLO
full
Big contributions beyond the subleading
corrections in the ?-less EFT!
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Summary
The subleading contribution of the ? to the 2NF
have been worked out. The relevant LECs are
determined from the pN threshold coefficients.
Improved convergence for the chiral 2p-exchange
is demonstrated. We have looked at the 3NF up
to N2LO. We found no new effects beyond the
well-known Fujita-Miyazawa 3NF. We have studied
the effects of the ? in CSB 2p-exchange and found
impor-tant contributions beyond the subleading
level in ?-less EFT!
Outlook
Further explore effects of the ? in few-nucleon
observables ?-contributions at N3LO .