526 research outputs found
Exact calculation of three-body contact interaction to second order
For a system of fermions with a three-body contact interaction the
second-order contributions to the energy per particle are
calculated exactly. The three-particle scattering amplitude in the medium is
derived in closed analytical form from the corresponding two-loop rescattering
diagram. We compare the (genuine) second-order three-body contribution to with the second-order term due to the density-dependent
effective two-body interaction, and find that the latter term dominates. The
results of the present study are of interest for nuclear many-body calculations
where chiral three-nucleon forces are treated beyond leading order via a
density-dependent effective two-body interaction.Comment: 9 pages, 6 figures, to be published in European Journal
Lattice calculations for A=3,4,6,12 nuclei using chiral effective field theory
We present lattice calculations for the ground state energies of tritium,
helium-3, helium-4, lithium-6, and carbon-12 nuclei. Our results were
previously summarized in a letter publication. This paper provides full details
of the calculations. We include isospin-breaking, Coulomb effects, and
interactions up to next-to-next-to-leading order in chiral effective field
theory.Comment: 38 pages, 11 figures, final publication versio
Lattice worldline representation of correlators in a background field
We use a discrete worldline representation in order to study the continuum
limit of the one-loop expectation value of dimension two and four local
operators in a background field. We illustrate this technique in the case of a
scalar field coupled to a non-Abelian background gauge field. The first two
coefficients of the expansion in powers of the lattice spacing can be expressed
as sums over random walks on a d-dimensional cubic lattice. Using combinatorial
identities for the distribution of the areas of closed random walks on a
lattice, these coefficients can be turned into simple integrals. Our results
are valid for an anisotropic lattice, with arbitrary lattice spacings in each
direction.Comment: 54 pages, 14 figure
Effective Field Theory and the Nuclear Many Body Problem
We review many body calculations of the equation of state of dilute neutron
matter in the context of effective field theories of the nucleon-nucleon
interaction.Comment: To appear in the proceedings of 4th International Conference On
Quarks And Nuclear Physics (QNP06), 5-10 June 2006, Madrid, Spain. European
Physical Journal A, in pres
More on the infrared renormalization group limit cycle in QCD
We present a detailed study of the recently conjectured infrared
renormalization group limit cycle in QCD using chiral effective field theory.
It was conjectured that small increases in the up and down quark masses can
move QCD to the critical trajectory for an infrared limit cycle in the
three-nucleon system. At the critical quark masses, the binding energies of the
deuteron and its spin-singlet partner are tuned to zero and the triton has
infinitely many excited states with an accumulation point at the three-nucleon
threshold. We exemplify three parameter sets where this effect occurs at
next-to-leading order in the chiral counting. For one of them, we study the
structure of the three-nucleon system in detail using both chiral and contact
effective field theories. Furthermore, we investigate the matching of the
chiral and contact theories in the critical region and calculate the influence
of the limit cycle on three-nucleon scattering observables.Comment: 17 pages, 7 figures, discussion improved, results unchanged, version
to appear in EPJ
Power counting and renormalization group invariance in the subtracted kernel method for the two-nucleon system
We apply the subtracted kernel method (SKM), a renormalization approach based
on recursive multiple subtractions performed in the kernel of the scattering
equation, to the chiral nucleon-nucleon (NN) interactions up to
next-to-next-to-leading-order (NNLO). We evaluate the phase-shifts in the 1S0
channel at each order in Weinberg's power counting scheme and in a modified
power counting scheme which yields a systematic power-law improvement. We also
explicitly demonstrate that the SKM procedure is renormalization group
invariant under the change of the subtraction scale through a non-relativistic
Callan-Symanzik flow equation for the evolution of the renormalized NN
interactions.Comment: Accepted for publication in Journal of Physics G: Nuclear and
Particle Physic
Consistency between renormalization group running of chiral operator and counting rule -- Case of chiral pion production operator --
In nuclear chiral perturbation theory (ChPT), an operator is defined in a
space with a cutoff which may be varied within a certain range. The operator
runs as a result of the variation of the cutoff [renormalization group (RG)
running]. In order for ChPT to be useful, the operator should run in a way
consistent with the counting rule; that is, the running of chiral counter terms
have to be of natural size. We vary the cutoff using the Wilsonian
renormalization group (WRG) equation, and examine this consistency. As an
example, we study the s-wave pion production operator for NN\to d pi, derived
in ChPT. We demonstrate that the WRG running does not generate any
chiral-symmetry-violating (CSV) interaction, provided that we start with an
operator which does not contain a CSV term. We analytically show how the
counter terms are generated in the WRG running in case of the infinitesimal
cutoff reduction. Based on the analytic result, we argue a range of the cutoff
variation for which the running of the counter terms is of natural size. Then,
we numerically confirm this.Comment: 28 pages, 5 figures, significantly changed, published versio
Ab initio alpha-alpha scattering
Processes involving alpha particles and alpha-like nuclei comprise a major
part of stellar nucleosynthesis and hypothesized mechanisms for thermonuclear
supernovae. In an effort towards understanding alpha processes from first
principles, we describe in this letter the first ab initio calculation of
alpha-alpha scattering. We use lattice effective field theory to describe the
low-energy interactions of nucleons and apply a technique called the adiabatic
projection method to reduce the eight-body system to an effective two-cluster
system. We find good agreement between lattice results and experimental phase
shifts for S-wave and D-wave scattering. The computational scaling with
particle number suggests that alpha processes involving heavier nuclei are also
within reach in the near future.Comment: 6 pages, 6 figure
Resonance saturation for four-nucleon operators
In the modern description of nuclear forces based on chiral effective field
theory, four-nucleon operators with unknown coupling constants appear. These
couplings can be fixed by a fit to the low partial waves of neutron-proton
scattering. We show that the so determined numerical values can be understood
on the basis of phenomenological one-boson-exchange models. We also extract
these values from various modern high accuracy nucleon-nucleon potentials and
demonstrate their consistency and remarkable agreement with the values in the
chiral effective field theory approach. This paves the way for estimating the
low-energy constants of operators with more nucleon fields and/or external
probes.Comment: 16 pp, REVTeX, 3 figure
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