July 22, 1998
We show how effectively effective quantum field theories work in nuclear physics. Using the physically transparent cut-off regularization, we study the simplest nuclear systems of two nucleons for both bound and scattering states at a momentum scale much less than the pion mass. We consider all the static properties of the deuteron, the two-nucleon scattering phase-shifts, the n + p --> d + \gamma process at thermal energy and the solar proton fusion process p + p --> d + e(+) + \nu(e), and we demonstrate that these are all described with great accuracy in the expansion to the next-to-leading order. We explore how a "new" degree of freedom enters in an effective theory by turning on and off the role of the pion in the Lagrangian.
Similar papers 1
November 25, 1997
We illustrate how effective field theories work in nuclear physics by using an effective Lagrangian in which all other degrees of freedom than the nucleonic one have been integrated out to calculate the low-energy properties of two-nucleon systems, viz, the deuteron properties, the np 1S0 scattering amplitude and the M1 transition amplitude entering into the radiative np capture process. Exploiting a finite cut-off regularization procedure, we find all the two-nucleon low-ene...
April 14, 2003
Motivated by recent advances in the application of effective field theory techniques to light nuclei we revisit the problem of electron-deuteron scattering in these approaches. By sidestepping problems with the description of electron-nucleon scattering data in effective field theories, we show that the effective theory expansion for deuteron physics converges well over a wide range of momentum transfers. The resultant description of the physics of the two-nucleon system is g...
March 22, 1998
The properties of low-energy neutron-proton systems are studied in an effective field theory where only nucleons figure as relevant degrees of freedom. With a finite momentum cut-off regularization scheme, we show that the large scattering lengths of the np systems do not spoil the convergence of the effective field theory, which turns out to be extremely successful in reproducing, with little cut-off dependence, the deuteron properties, the np 1S0 scattering amplitude and mo...
September 28, 2023
We use a combination of effective field theory and the renormalization group to determine the impact of radiative corrections on the nucleon-nucleon potential. In order to do so, we present a modified version of pionless effective field theory inspired by earlier work in nonrelativistic quantum electrodynamics. The renormalization group analysis of corrections in the deuteron indicate that radiative corrections generate $1-2\%$ of the binding energy. This work serves as an im...
March 15, 2002
In these lectures I first explain, in a rather basic fashion, the construction of effective field theories. I then discuss some recent developments in the application of such theories to two- and three-nucleon systems.
January 28, 2005
We use the framework of effective field theories to discuss the determination of the S-wave \pi N scattering lengths from the recent high-precision measurements of pionic deuterium observables. The theoretical analysis proceeds in several steps. Initially, the precise value of the pion-deuteron scattering length a_{\pi d} is extracted from the data. Next, a_{\pi d} is related to the S-wave \pi N scattering lengths a_+ and a_-. We discuss the use of this information for constr...
June 29, 1999
The central tenet of effective theory is that the details of short-distance physics will not have a significant impact on low-energy observables. Here we perform an analysis of electron-deuteron scattering at low momentum transfers which is based on effective field theory. We show that in our approach the deuteron electromagnetic form factors $F_C$ and $F_M$ indeed are largely insensitive to the short-range $NN$ potential at momenta $Q$ up to about 700 MeV. We also find that ...
September 21, 2000
Progress in the Effective Field Theory of two and three nucleon systems is sketched, concentrating on the low energy version in which pions are integrated out as explicit degrees of freedom. Examples given are calculations of deuteron Compton scattering, three body forces and the triton, and nd partial waves.
June 14, 1998
We discuss the effective field theory approach to nuclear phenomena with typical momentum below the pion mass. We particularly focus on the three body problem. In the $J=3/2$ channel,effective field theory is extremelly predictive and we are able to describe the nucleon-deuteron scattering amplitude at the percent level using only two parameters obtained from nucleon-nucleon scattering. We briefly comment onthe $J=1/2$ channel and the issues related to the non-perturbative re...
August 27, 2001
Progress in the Effective Field Theory of two and three nucleon systems is sketched, concentrating mainly on the low energy version in which pions are integrated out as explicit degrees of freedom. Examples given are: the extraction of nucleon polarisabilities from deuteron Compton scattering at very low energies; the energy dependence of the nucleon polarisabilities; three body forces and the triton; and $\mathrm{nd}$ partial waves at momenta below the pion cut.