Mesonexchange nucleonnucleon interaction

On the hadronic level, strong NN interaction results from the exchange of mesons between the nucleons. The origin of this description goes back to 1935, when Yukawa (1935) proposed that nucleons interact via exchange of virtual massive particles of the Compton wavelength ~ 10-13 cm. In the language of the field theory, strong interactions result from the coupling of the nucleon fields to the meson fields.

Of course, the fundamental theory of strong interactions between hadrons is the QCD, where the fundamental fields are those of quarks and gluons. From the today's perspective, the Meson Exchange Model (MEM) of strong interactions is an effective theory, where quarks and gluons do not appear explicitly, and the building blocks are mesons, nucleons, and their resonances (like A isobars). The MEM is successful in describing NN scattering data (at laboratory energies <350 MeV), the 2H properties, and properties of "dilute" nucleon systems. The MEM operates with the nucleon and meson fields, ^ and p. It is sufficient to include only mesons of rest mass below 1 GeV/c2. Therefore, the MEM does not describe very short-range NN interactions at distances < 0.2 fm. Meson-nucleon couplings are described by corresponding Lagrangian densities, depending on the symmetry behavior of a meson field under rotations and reflections. As far as the symmetry is concerned, the selected mesons are:

pseudoscalar (field ^>(ps), mass mps), scalar (field ^>(s), mass ms), and vector (field p^, i = 0,..., 3, mass mv).14

In a short-hand notation, in which the isospin structure is not indicated, we have the following meson-nucleon coupling Lagrangian densities:

mps scalar (s) mesons a, ê (JP = 0+) : Ls = gs ; (5.12)

fv T

4m where dpF = dF/dx= ]/2, m is the nucleon mass, while JP

denotes the meson spin J and parity P.15 The experimentally measured meson masses are: mnc2 = 138 MeV, mnc2 = 548 MeV, mpc2 = 769 MeV, mw c2 = 783 MeV, and ms c2 = 983 MeV. The scalar a meson plays a special role: it represents a scalar state of an exchanged pion pair, and its mass is found from fitting the MEM to NN scattering data (in this way, one gets mac2 = 550 MeV, see below). For the sake of simplicity, we neglect charge splitting of meson masses. Apart from experimental meson masses, the MEM contains coupling constants f and g determined by fitting experimental data. Finally, in order to account for finite sizes of interacting hadrons, one has to introduce form-factors at every meson-nucleon vertex. These form-factors, parameterized in terms of momentum transfer in a meson exchange, are determined by fitting experimental NN data. The form-factors describe the effect of shortest-range strong interactions, which depend on the quark structure of baryons and are not calculable within the MEM.

One-meson exchange processes can be visualized as lowest order (second order in the meson-nucleon coupling constant) Feynman diagrams, e.g., diagram (a) in Fig. 5.3. One-n and one-w exchange contributions explain two basic features of the NN interaction. The longest range (h/mn c & 1.4 fm) one-n exchange yields a long-range tensor force, while one-w exchange produces a

14Our notations follow Berestetskil et al. (1982). We use Greek indices p = 0,1, 2, 3 to label timespace components, and Latin indices k = 1, 2, 3 to label spatial components. The 2 X 2 Pauli matrices are denoted by ak, and the 2 X 2 unit matrix is denoted by I. The spacetime metric tensor is =

irac matrices are: 7" = I

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