59 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
Asymmetric regularization of the ground and excited state of the helium-4 nucleus
We find the threshold structure of the two- and three-nucleon systems, with
the deuteron and 3H/3He as the only bound nuclei, sufficient to predict a pair
of four-nucleon states: a deeply bound state which is identified with the
helium-4 ground state, and a shallow, unstable state at an energy 0.38(25) MeV
above the triton-proton threshold which is consistent with data on the first
excited state of helium-4. The analysis employs the framework of Pionless EFT
at leading order with a generalized regulator prescription which probes
renormalization-group invariance of the two states with respect to higher-order
perturbations including asymmetrical disturbances of the short-distance
structure of the interaction. In addition to this invariance of the bound-state
spectrum and the diagonal triton-proton 1S0 phase shifts in the helium-4
channel with respect to the short-distance structure of the nuclear
interaction, our multi-channel calculations with a resonating-group method
demonstrate the increasing sensitivity of nuclei to the neutron-proton P-wave
interaction. We show that two-nucleon phase shifts, the triton channel, and
three-nucleon negative-parity channels are less sensitive with respect to
enhanced two-nucleon P-wave attraction than the four-nucleon triton-proton 1S0
phase shifts.Comment: 13 pages, 7 figures, 1 tabl
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
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
Effective Theory of 3H and 3He
We present a new perturbative expansion for pionless effective field theory
with Coulomb interactions in which at leading order the spin-singlet
nucleon-nucleon channels are taken in the unitarity limit. Presenting results
up to next-to-leading order for the Phillips line and the neutron-deuteron
doublet-channel phase shift, we find that a perturbative expansion in the
inverse 1S0 scattering lengths converges rapidly. Using a new systematic
treatment of the proton-proton sector that isolates the divergence due to
one-photon exchange, we renormalize the corresponding contribution to the
3H-3He binding energy splitting and demonstrate that the Coulomb force in
pionless EFT is a completely perturbative effect in the trinucleon bound-state
regime. In our new expansion, the leading order is exactly isospin-symmetric.
At next-to-leading order, we include isospin breaking via the Coulomb force and
two-body scattering lengths, and find for the energy splitting
(E_B(3He)-E_B(3H))^NLO = (-0.86 +/- 0.17) MeV.Comment: 37 pages, 14 figures, published versio
Strong and radiative decays of the and
Since their discovery in 2003, the open charm states and
provide a challenge to the conventional quark model. In recent
years, theoretical evidence has been accumulated for both states in favor of a
predominantly and molecular nature, respectively. However, a direct
experimental proof of this hypothesis still needs to be found. Since radiative
decays are generally believed to be sensitive to the inner structure of the
decaying particles, we study in this work the radiative and strong decays of
both the and , as well as of their counterparts
in the bottom sector. While the strong decays are indeed strongly enhanced for
molecular states, the radiative decays are of similar order of magnitude in
different pictures. Thus, the experimental observable that allows one to
conclusively quantify the molecular components of the and
is the hadronic width, and not the radiative one, in
contradistinction to common belief. We also find that radiative decays of the
sibling states in the bottom sector are significantly more frequent than the
hadronic ones. Based on this, we identify their most promising discovery
channels
Pion-less Effective Field Theory on Low-Energy Deuteron Electro-Disintegration
In view of its relation to Big-Bang Nucleo-Synthesis and a reported
discrepancy between nuclear models and data taken at S-DALINAC, electro-induced
deuteron break-up 2H(e,e' p)n is studied at momentum transfer q<100MeV and
close to threshold in the low-energy nuclear Effective Field Theory without
dynamical pions. The result at N2LO for electric dipole currents and at NLO for
magnetic ones converges order-by-order better than quantitatively predicted and
contains no free parameter. It is at this order determined by simple,
well-known observables. Decomposing the doubly differential cross-section into
the longitudinal-plus-transverse (L+T), transverse-transverse (TT) and
longitudinal-transverse interference (LT) terms, we find excellent agreement
with a potential-model calculation by Arenh"ovel et al using the Bonn
potential. Theory and data also agree well on \sigma_{L+T}. There is however no
space on the theory-side for the discrepancy of up to 30%, 3-\sigma between
theory and experiment in \sigma_{LT}. From universality, we conclude that no
theoretical approach with the correct deuteron asymptotic wave-function can
explain the data. Un-determined short-distance contributions that could affect
\sigma_{LT} enter only at high orders, i.e. at the few-percent level. We notice
some issues with the kinematics and normalisation of the data reported.Comment: 30 pages LaTeX2e, including 10 figures as 34 .eps files embedded with
includegraphicx. Increased figure sizes; contents identical to version
approved for publication in Phys Rev C -- spelling and grammatical
difference
A nucleon in a tiny box
We use Chiral Perturbation Theory to compute the nucleon mass-shift due to
finite volume and temperature effects. Our results are valid up to
next-to-leading order in the "\eps-regime" (mL ~ m\beta << 1) as well as in the
"p-regime" (mL ~ m\beta >> 1). Based on the two leading orders, we discuss the
convergence of the expansion as a function of the lattice size and quark
masses. This result can be used to extrapolate lattice results obtained from
lattice sizes smaller than the pion cloud, avoiding the numerical simulation of
physics under theoretical control. An extraction of the low-energy coefficient
c_3 of the chiral Lagrangean from lattice simulations at small volumes and a
``magic'' ratio \beta=1.22262 L might be possible.Comment: 7 figures, numerical examples and discussion changed. Minor misprints
corrected. Version accepted by Phys Rev
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