198 research outputs found
The Soft R\'egime and \beta Function of NRQCD
Progress towards a complete velocity power counting in non-relativistic
effective field theories, especially NRQCD, is motivated and summarised.Comment: 6 pages LaTeX2e, uses feynmp to generate 5 drawings in 1 figure and 1
table. Necessary metapost-files included. Talk presented at the
``Euroconference QCD '98'' in Montpellier, France, 2nd -- 8th July 1998 (to
appear in Nucl. Phys. B (Proc. Suppl.)), and at the conference ``Quark
Confinement and the Hadron Spectrum III'' at TJNL, Newport News, USA, 8th --
12th June 1998 (to be published in the proceedings
Nucleon Polarisabilities from Compton Scattering off the One- and Few-Nucleon System
These proceedings sketch how combining recent theoretical advances with data
from the new generation of high-precision Compton scattering experiments on
both the proton and few-nucleon systems offers fresh, detailed insight into the
Physics of the nucleon polarisabilities. A multipole-analysis is presented to
simplify their interpretation. Predictions from Chiral Effective Field Theory
with special emphasis on the spin-polarisabilities can serve as guideline for
doubly-polarised experiments below 300 MeV. The strong energy-dependence of the
scalar magnetic dipole-polarisability turns out to be crucial to
understand the proton and deuteron data. Finally, a high-accuracy determination
of the proton and neutron polarisabilities shows that they are identical within
error-bars. For details and a better list of references, consult the given
references.Comment: 10 pages LaTeX2e with 7 figures in 8 .eps files, using graphicx.
Invited seminar given at the 26th Course of the International School of
Nuclear Physics: Lepton Scattering and the Structure of Hadrons and Nuclei,
Erice (Italy), 16th - 24th September 2004. To be published in Prog. Nucl.
Part. Phys. 54, No. 2 as part of the proceeding
How To Classify 3-Body Forces -- And Why
For systems with only short-range forces and shallow 2-body bound states, the
typical strength of any 3-body force in all partial-waves, including external
currents, is systematically estimated by renormalisation-group arguments in the
Effective Field Theory of Point-Like Interactions. The underlying principle and
some consequences in particular in Nuclear Physics are discussed.Comment: 7 pages LaTeX2e using FBSart-class (provided); 2 figures in 3 .eps
files included using graphicx; to appear in Few-Body System
Compton scattering from the proton in an effective field theory with explicit Delta degrees of freedom
We analyse the proton Compton-scattering differential cross section for
photon energies up to 325 MeV using Chiral Effective Field Theory and extract
new values for the electric and magnetic polarisabilities of the proton. Our
EFT treatment builds in the key physics in two different regimes: photon
energies around the pion mass ("low energy") and the higher energies where the
Delta(1232) resonance plays a key role. The Compton amplitude is complete at
N4L0, O(e^2 delta^4), in the low-energy region, and at NLO, O(e^2 delta^0), in
the resonance region. Throughout, the Delta-pole graphs are dressed with pi-N
loops and gamma-N-Delta vertex corrections. A statistically consistent database
of proton Compton experiments is used to constrain the free parameters in our
amplitude: the M1 gamma-N-Delta transition strength b_1 (which is fixed in the
resonance region) and the polarisabilities alpha and beta (which are fixed from
data below 170 MeV). In order to obtain a reasonable fit we find it necessary
to add the spin polarisability gammaM1 as a free parameter, even though it is,
strictly speaking, predicted in chiral EFT at the order to which we work. We
show that the fit is consistent with the Baldin sum rule, and then use that sum
rule to constrain alpha+beta. In this way we obtain
alpha=[10.65+/-0.35(stat})+/-0.2(Baldin)+/-0.3(theory)]10^{-4} fm^3, and beta
=[3.15-/+0.35(stat)-/+0.2(Baldin)-/+0.3(theory)]10^{-4} fm^3, with chi^2 =
113.2 for 135 degrees of freedom. A detailed rationale for the theoretical
uncertainties assigned to this result is provided.Comment: 36 pages, 15 figures Version 2 is shortened for publication; version
1 is more self-contained. Results section unchange
On Parity-Violating Three-Nucleon Interactions and the Predictive Power of Few-Nucleon EFT at Very Low Energies
We address the typical strengths of hadronic parity-violating three-nucleon
interactions in "pion-less" Effective Field Theory in the nucleon-deuteron
(iso-doublet) system. By analysing the superficial degree of divergence of loop
diagrams, we conclude that no such interactions are needed at leading order.
The only two linearly independent parity-violating three-nucleon structures
with one derivative mix two-S and two-P-half waves with iso-spin transitions
Delta I = 0 or 1. Due to their structure, they cannot absorb any divergence
ostensibly appearing at next-to-leading order. This observation is based on the
approximate realisation of Wigner's combined SU(4) spin-isospin symmetry in the
two-nucleon system, even when effective-range corrections are included.
Parity-violating three-nucleon interactions thus only appear beyond
next-to-leading order. This guarantees renormalisability of the theory to that
order without introducing new, unknown coupling constants and allows the direct
extraction of parity-violating two-nucleon interactions from three-nucleon
experiments.Comment: 20 pages LaTeX2e, including 9 figures as .eps file embedded with
includegraphicx. Minor modifications and stylistic corrections. Version
accepted for publication in Eur. Phys. J.
Nuclear Physics Around the Unitarity Limit
We argue that many features of the structure of nuclei emerge from a strictly
perturbative expansion around the unitarity limit, where the two-nucleon S
waves have bound states at zero energy. In this limit, the gross features of
states in the nuclear chart are correlated to only one dimensionful parameter,
which is related to the breaking of scale invariance to a discrete scaling
symmetry and set by the triton binding energy. Observables are moved to their
physical values by small, perturbative corrections, much like in descriptions
of the fine structure of atomic spectra. We provide evidence in favor of the
conjecture that light, and possibly heavier, nuclei are bound weakly enough to
be insensitive to the details of the interactions but strongly enough to be
insensitive to the exact size of the two-nucleon system.Comment: 6 pages, 3 figures, published version, rewritten for clarit
Spin Polarizabilities of the Nucleon from Polarized Low Energy Compton Scattering
As guideline for forthcoming experiments, we present predictions from Chiral
Effective Field Theory for polarized cross sections in low energy Compton
scattering for photon energies below 170 MeV, both on the proton and on the
neutron. Special interest is put on the role of the nucleon spin
polarizabilities which can be examined especially well in polarized Compton
scattering. We present a model-independent way to extract their energy
dependence and static values from experiment, interpreting our findings also in
terms of the low energy effective degrees of freedom inside the nucleon: The
polarizabilities are dominated by chiral dynamics from the pion cloud, except
for resonant multipoles, where contributions of the Delta(1232) resonance turn
out to be crucial. We therefore include it as an explicit degree of freedom. We
also identify some experimental settings which are particularly sensitive to
the spin polarizabilities.Comment: 30 pages, 19 figure
Naive Dimensional Analysis for Three-Body Forces Without Pions
For systems of three identical particles in which short-range forces produce
shallow two-particle bound states, and in particular for the ``pion-less''
Effective Field Theory of Nuclear Physics, I extend and systematise the
power-counting of three-body forces to all partial-waves and orders, including
external currents. With low-energy observables independent of the details of
short-distance dynamics, the typical strength of a three-body force is
determined from the superficial degree of divergence of the three-body diagrams
which contain only two-body forces. This na\"ive dimensional analysis must be
amended as the asymptotic solution to the leading-order Faddeev equation
depends for large off-shell momenta crucially on the partial wave and
spin-combination of the system. It is shown by analytic construction to be
weaker in most channels with angular momentum smaller than 3 than expected.
This demotes many three-nucleon forces to high orders. Observables like the
quartet-S-scattering length are less sensitive to three-nucleon forces than
guessed. I also comment on the Efimov effect and limit-cycle for non-zero
angular momentum.Comment: 31 pages LaTeX2e, including 8 figures in 13 .eps files, embedded with
includegraphicx; linguistic corrections only, version to appear in Nucl Phys
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