ΔI = 1 axial-vector mixing and charge symmetry breaking

Abstract

Phenomenological Lagrangians that exhibit (broken) chiral symmetry as well as isospin violation suggest short-range charge symmetry breaking (CSB) nucleon-nucleon potentials with a σ 1 ·σ 2 structure. This structure could be realized by the mixing of axial-vector (1 + ) mesons in a single-meson exchange picture. The Coleman-Glashow scheme for ∆I z = 1 charge symmetry breaking applied to meson and baryon SU (2) mass splittings suggests a universal scale. This scale can be extended to ∆I = 1 nonstrange CSB transitions a • 1 |H em |f 1 of size −0.005 GeV 2 . The resulting nucleon-nucleon axial-vector meson exchange CSB potential then predicts ∆I = 1 effects which are small.

Effective field theory of nuclear forces

“…We can use the values for the πNN coupling constants determined by the analysis to find that their isospin breaking is consistent with zero, with an uncertainty comparable to our expectation from dimensional analysis and from π − η − η ′ mixing [114]. Similarly, γ s might be viewed as originating in ρ − ω mixing, while pseudovector-meson exchange (in particular close-lying doublets such as a 1 − f 1 ) exchange contribute to the γ σ spin-spin force [114,115].…”

EFFECTIVE FIELD THEORY FOR FEW-NUCLEON SYSTEMS

“…We can use the values for the πNN coupling constants determined by the analysis to find that their isospin breaking (β 1 ) is consistent with zero, with an uncertainty comparable to our expectation from dimensional analysis and from π−η−η mixing (101). Similarly, the two contact interactions (γ s,t ) might be viewed as originating in ρ−ω mixing and pseudovector-meson exchange (in particular close-lying doublets such as a 1 -f 1 ) (101,102). The components of range ∼1/2m π come from two sources.…”

The time-reversal- and parity-violating nuclear potential in chiral effective theory

“…where U (r), W (r), X(r), and Y (r) are defined in Eqs. (75), (76), (77), and (78), respectively. In Eq.…”

“…which generate the dominant contributions to the short-range isospin-violating two-nucleon potential [64,51]. The isospin-violating coefficients γ i = O(εm 2 π /F 2 π M 2 QCD ) can be seen as low-energy remnants of ρ-ω mixing [51] and a 1 -f 1 mixing [77]. The TV parameters are related to them byγ i = ρ γ i = O(θm 2 π /F 2 π M 2 QCD ).…”