No abstract

Using a recently developed effective field theory for the interactions of nucleons at non-relativistic energies, we calculate non-perturbatively Coulomb corrections to proton-proton scattering. Including the dimension-eight derivative interaction in the PDS regularization scheme, we recover a modified form of the Blatt-Jackson relation between the scattering lengths. The effective range receives no corrections from the Coulomb interactions to this order. Also the case of scattering in channels where the Coulomb force is attractive, is considered. This is of importance for hadronic atoms.

Klein's paradox is resolved in simple diagrammatic terms arising from considerations of its analogue in classical relativistic mechanics. The same results are also obtained directly from standard operator methods of quantum field theory.

We show how the presence of a very light scalar with a cubic self-interaction in six dimensions can stabilize the extra dimensions at radii which are naturally exponentially large, r ∼ ℓ exp [(4π) 3 /g 2 ], where ℓ is a microscopic physics scale and g is the (dimensionless) cubic coupling constant. The resulting radion mode of the metric becomes a very light degree of freedom whose mass, m ∼ 1/(Mpr 2 ) is stable under radiative corrections. For 1/r ∼ 10 −3 eV the radion is extremely light, m ∼ 10 −33 eV. Its couplings cause important deviations from General Relativity in the very early universe, but naturally evolve to phenomenologically acceptable values at present.

Using a recently developed effective field theory for the interactions of nucleons at non-relativistic energies, we calculate the Coulomb corrections to proton-proton scattering. Including the dimension-eight derivative interaction in PDS regularization scheme, we obtain a modified Jackson-Blatt relation for the scattering lengths which is found to be phenomenologically satisfactory. The effective range is not modified by Coulomb effects to this order in the calculation. PACS: 03.65.Nk; 13.75.Cs; 25.40.C During the last year Kaplan, Savage and Wise have proposed an effective field theory for the interactions of nucleons at low energies [1]. These are characterized by scattering lengths which are much larger than the natural hadronic scale which in these systems is set by the pion mass. This made it initially difficult to construct consistent power counting rules which are necessary in any effective theory calculation to ensure that all contributions to a given order are included. By the introduction of a new regularization scheme called Power Divergence Subtraction (PDS) which is an extension of the more common MS scheme, these problems were solved. A very similar scheme was proposed at the same time by Gegelia[2]. Very recently, Mehen and Stewart [3] have made this off-shell scheme (OS) more well-defined and shown that it is in fact equivalent to the PDS scheme.Within this framework several applications to problems involving the deuteron have now been made[4] [5]. The first attempts to describe three-nucleon systems with two neutrons have also been initiated [6]. In this way the properties of the triton nucleus can be investigated. But also systems like 3 He with two protons are of obvious interest to consider in this new approach. For this to succeed, one must know how to include the repulsive Coulomb force between the two protons. As a first step in this direction we will here consider proton-proton scattering at very low energies.The effective Lagrangian for non-relativistic protons with mass M in the spin-singlet channel iswhen we only include the lowest order contact interaction parameterized by the coupling constant C 0 . It corresponds to the singular potential C 0 δ(r) which will affect interactions