We discuss effective field theory treatments of the problem of three particles interacting via short-range forces. One case of such a system is neutron-deuteron ͑nd͒ scattering at low energies. We demonstrate that in attractive channels the renormalization-group evolution of the 1 + 2 scattering amplitude may be complicated by the presence of eigenvalues greater than unity in the kernel. We also show that these eigenvalues can be removed from the kernel by one subtraction, resulting in an equation which is renormalization-group invariant. A unique solution for 1 + 2 scattering phase shifts is then obtained. We give an explicit demonstration of our procedure for both the case of three spinless bosons and the case of the doublet channel in nd scattering. After the contribution of the two-body effective range is included in the effective field theory, it gives a good description of the nd doublet phase shifts below deuteron breakup threshold.

A relativistic description of pion-nucleon scattering based on the fourdimensional Bethe-Salpeter equation is presented. The kernel of the equation consists of s-and u-channel nucleon and ∆(1232) pole diagrams, as well as ρ and σ exchange in the t-channel. The Bethe-Salpeter equation is solved by means of a Wick rotation, and good fits are obtained to the s-and p-wave πN phase shifts up to 360 MeV pion laboratory energy. The coupling constants determined by the fits are consistent with the commonly accepted values in the literature.

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The $\Lambda N - \Sigma N$ coupling in $\Lambda$--hypernuclei and $\Lambda \Lambda - \Xi N$ coupling in $\Lambda \Lambda$--hypernuclei produce novel physics not observed in the conventional, nonstrange sector. Effects of $\Lambda \leftrightarrow \Sigma$ conversion in $^3_{\Lambda}$H are reviewed. The role of $\Lambda N - \Sigma N$ coupling suppression in the $A=4,5$ $\Lambda$--hypernuclei due to Pauli blocking is highlighted, and the implications for the structure of $^{10}_{\;\, \Lambda}$B are explored. Suppression of $\Lambda \Lambda - \Xi N$ conversion in $^{\;\;\, 6}_{\Lambda \Lambda}$He is hypothesized as the reason that the $< V_{\Lambda \Lambda} >$ matrix element is small. Measurement of $^{\;\;\, 4}_{\Lambda \Lambda}$H is proposed to investigate the full $\Lambda \Lambda - \Xi N$ interaction. The implication for $\Lambda \Lambda$ analog states is discussed.Comment: 17 pages LATEX, 1 figure uuencoded postscrip

The Ward-Takahashi identities are central to the gauge invariance of the photoproduction amplitude. Here we demonstrate that unitarity and in particular the inclusion of both the πN and γπN thresholds on equal footing yields a photoproduction amplitude that satisfies both two-body unitarity and the generalized Ward-Takahashi identities. The final amplitude is a solution of a set of coupled channel integral equations for the reactions πN → πN and γN → πN .Typeset using REVT E X