QCD sum rules: Isospin symmetry breakings in pion-nucleon couplings

Abstract

We use the method of QCD sum rules in the presence of an external pion field to investigate isospin symmetry breakings in pionnucleon couplings. Possible manifestations of such isospin symmetry breaking are examined in the context of low-energy nucleonnucleon (NN) scattering. We discuss numerical results in relation to both the existing data and other theoretical predictions.

Nucleon-sigmacoupling constant in QCD sum rules

“…If we let χ G change in a wider range, say 6 GeV −1 ≤ −χ G ≤ 14 GeV −1 , this brings an additional 15% uncertainty to the value quoted in Eq. (32). The ratio in Eq.…”

“…These calculations were improved considering the coupling schemes at different Dirac structures and beyond the chiral limit contributions [28,29,30]. This coupling constant has also been calculated using the vacuum-to-vacuum method [31,32], and it was pointed out that the sum rule that is constructed for the coupling is independent and it is not reduced to the nucleon mass sum rule by a chiral rotation.…”

TheηNNcoupling constant

“…In [13] the pion is treated as the external field to analyze the possible isospin symmetry violations of the pion nucleon coupling constant. Later the light cone QSR (LCQSR) was employed to extract the πNN(1535) coupling constant, which was found to be strongly suppressed [14].…”

Isospin symmetry breakings as from QCD sum rules

“…The structure (which does not involve the trace of some product) seems quite different from the r°pp case, but it can be shown [8] that isospin symmetry is exact should we assume m~ =md and < flu >=< dd >.…”