Nuclear forces can be systematically derived using effective chiral Lagrangians consistent with the symmetries of QCD. I review the status of the calculations for two- and three-nucleon forces and their applications in few-nucleon systems. I also address issues like the quark mass dependence of the nuclear forces and resonance saturation for four-nucleon operators.

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Modern theory of nuclear forces

Charge symmetry, quarks and mesons

▪ Abstract Charge symmetry breaking (CSB) in the strong interaction occurs because of the difference between the masses of the up and down quarks. The use of effective field theories allows us to follow this influence of confined quarks in hadronic and nuclear systems. We review the progress in observing and understanding CSB, with particular attention to the recent successful observations of CSB in measurements involving the production of a single neutral pion, and to the related theoretical progress.

https://www.annualreviews.org/doi/pdf/10.1146/annurev.nucl.56.080805.140446

Charge Symmetry Breaking and QCD

The charge symmetry breaking amplitudes for the recently observed $dd\ensuremath{\rightarrow}\ensuremath{\alpha}{\ensuremath{\pi}}^{0}$ reaction are investigated. Chiral perturbation theory is used to classify and identify the leading-order terms. Specific forms of the related one- and two-body tree-level diagrams are derived. As a first step toward a full calculation, a few tree-level two-body diagrams are evaluated at each considered order, using a simplified set of $d$ and $\ensuremath{\alpha}$ wave functions and a plane-wave approximation for the initial $dd$ state. The leading-order pion-exchange term is shown to be suppressed in this model because of poor overlap of the initial and final states. The higher-order one-body and short-range (heavy-meson-exchange) amplitudes provide better matching between the initial and final states and therefore contribute significantly and coherently to the cross section. The consequences this might have for a full calculation, with realistic wave functions and a more complete set of amplitudes, are discussed.

Survey of charge symmetry breaking operators for d d → α π 0

A method is developed for treating the effect of the neutron-proton mass difference in isospin-violating nuclear forces. Previous treatments utilized an awkward subtraction scheme to generate these forces. A field redefinition is used to remove that mass difference from the free Lagrangian (and hence from asymptotic nucleon states) and replace its effect by effective interactions. Previous calculations of static class II charge-independence-breaking and class III charge-symmetry-breaking potentials are verified using the new scheme, which is also used to calculate class IV nuclear forces. Two-body forces of the latter type are found to be identical to previously obtained results. A three-body force is also found. Problems involving Galilean invariance with class IV one-pion-exchange forces are identified and resolved.

Nucleon-mass difference in chiral perturbation theory and nuclear forces

Charge symmetry breaking in the neutron-proton system

Charge-symmetry tests in neutron-proton elastic scattering

A sensitive test of the charge symmetry of nuclear forces is the angular symmetry about 90/sup 0/ of deuterons produced in the np ..-->.. d..pi../sup 0/ reaction. We predict a front-to-back asymmetry of about 0.8% in the ..delta.. (3,3) resonance region. The asymmetry arises primarily from ..pi../sup 0/-eta mixing.

C. Y. Cheung

Papers

Charge symmetry breaking in the neutron-proton system

Charge-symmetry tests in neutron-proton elastic scattering

Charge-symmetry test in the reaction np. -->. d. pi. /sup 0/