Perturbative Pions and the Effective Range Expansion

For interactions involving two or more nucleons it is useful to divide pions into three classes: potential, radiation, and soft. The momentum threshold for the production of radiation pions is $Q_r = \sqrt{M_N m_\pi}$. We show that radiation pions can be included systematically with a power counting in $Q_r$. The leading order radiation pion graphs which contribute to NN scattering are evaluated in the PDS and OS renormalization schemes and are found to give a small contribut...

Using rigorous solutions, we compare the ERE parameters obtained in three different scenarios of EFT($\notpi$) in nonperturbative regime. A scenario with unconventional power counting (like KSW) is shown to be disfavored by the PSA data, while the one with elaborate prescription of renormalization but keeping conventional power counting intact seems more promising.

Nonperturbative effective field theory calculations for NN scattering seem to break down at rather low momenta. By examining several toy models, we clarify how effective field theory expansions can in general be used to properly separate long- and short-range effects. We find that one-pion exchange has a large effect on the scattering phase shift near poles in the amplitude, but otherwise can be treated perturbatively. Analysis of a toy model that reproduces 1S0 NN scattering...

In this talk we demonstrate the results of application of the perturbative effective theory formalism developed in recent papers to the calculation of $\pi N$ elastic scattering amplitude. Restrictions on the contributing resonance parameters are obtained and the low energy coefficients are calculated.

After a brief survey of effective field theories, the linear sigma model is discussed as a prototype of an effective field theory of the standard model below the chiral-symmetry-breaking scale. Although it can serve as a toy model for the pion-nucleon interaction, the linear sigma model is not a realistic alternative to chiral perturbation theory. The heavy-baryon approach to chiral perturbation theory allows for a systematic low-energy expansion of Green functions and amplit...

Low energy phenomena involving two nucleons can be successfully described using effective field theory. Because of the relatively large expansion parameter, it is only at next-to-next-to-leading order (NNLO) where one can expect to see agreement with experiment at the few percent level. The first part of this talk will focus on radiation pion effects, which first appear at NNLO. The power counting for radiation pions is simple for center of mass momentum p~\sqrt{M m_pi}=Q_r, ...

Both gravitons and pions are described by non-linear and non-renormalizable actions at low energies. These are most usefully treated by effective field theory, which is a full quantum field theoretic approach that relies only on the low energy degrees of freedom and their interactions. The gravitational case is particularly clean because of the masslessness of the graviton and the wide separation of scales. This essay provides an overview of this approach.

Two-nucleon effective field theory (EFT) beyond momenta of order the pion mass is studied for both cutoff regularization and dimensional regularization with power divergence subtraction (PDS). Models with two mass scales illustrate how effects of long-distance pion physics must be removed from the coefficients that encode short-distance physics. The modified effective range expansion shows that treating pions perturbatively, as in the PDS power counting, limits the radius of ...

We review the effective field theories (EFTs) developed for few-nucleon systems. These EFTs are controlled expansions in momenta, where certain (leading-order) interactions are summed to all orders. At low energies, an EFT with only contact interactions allows a detailed analysis of renormalization in a non-perturbative context and uncovers novel asymptotic behavior. Manifestly model-independent calculations can be carried out to high orders, leading to high precision. At hig...

The pionless effective field theory (EFT) is the appropriate low-energy EFT for short-range interactions that display a large scattering length. It has been successfully applied in atomic, nuclear and particle physics. We give an overview over recent calculations employing the pionless effective field theory and lay emphasis on applications in the three- and four-body sector where the most exciting developments have occurred.