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CP-Violating Yukawa Couplings in the Skyrme Model and the Neutron Electric Dipole Moment
High Energy Physics - Phenomenology · Submitted 16 Dec 1992
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim These results show that the leading contribution to the neutron electric dipole moment in large-$\Nc$ Skyrme model is the direct one ($\Dn \sim \Nc m^2_\pi$), rather than the pion loop contribution.
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The abstract, sentence by sentence
We argue that the large-$\Nc$ behaviour of the Yukawa couplings in the Skyrme model involves issues more subtle than the vanishing of linear fluctuations needed for classical stability of the skyrmion. The chiral fluctuations about the skyrmion must be quantized in order to reach a conclusion. An improved quantization procedure allows us to confront this question directly. The pion-nucleon coupling constants $\gcup$ (CP conserving) and $\bgcup$ (CP violating) are calculated in the large-$\Nc$, three-flavour Skyrme model by direct evaluation of the leading matrix elements appearing in the LSZ reduction formula. We find that $\gcup \sim \Nc^{{3 \over 2}}$, but that, at most, $\bgcup \sim m^2_\pi \Nc^{-\shalf}$. These results show that the leading contribution to the neutron electric dipole moment in large-$\Nc$ Skyrme model is the direct one ($\Dn \sim \Nc m^2_\pi$), rather than the pion loop contribution.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We argue that the large-$\Nc$ behaviour of the Yukawa couplings in the Skyrme model involves issues more subtle than the vanishing of linear fluctuations needed for classical stability of the skyrmion. | background 0.50 | 0.36 | 0.06 | asserted 0.56 |
| s1 | The chiral fluctuations about the skyrmion must be quantized in order to reach a conclusion. | background 0.39 | 0.12 | 0.02 | asserted 0.99 |
| s2 | An improved quantization procedure allows us to confront this question directly. | method 0.89 | 0.72 | 0.03 | asserted 0.98 |
| s3 | The pion-nucleon coupling constants $\gcup$ (CP conserving) and $\bgcup$ (CP violating) are calculated in the large-$\Nc$, three-flavour Skyrme model by direct evaluation of the leading matrix elements appearing in the LSZ reduction formula. | method 0.84 | 0.94 | 0.07 | asserted 1.00 |
| s4 | We find that $\gcup \sim \Nc^{{3 \over 2}}$, but that, at most, $\bgcup \sim m^2_\pi \Nc^{-\shalf}$. | result 1.00 | 0.97 | 0.35 | asserted 0.92 |
| s5 | These results show that the leading contribution to the neutron electric dipole moment in large-$\Nc$ Skyrme model is the direct one ($\Dn \sim \Nc m^2_\pi$), rather than the pion loop contribution. | interpretation 0.70 | 0.92 | 0.82 | asserted 1.00 |
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Original abstract
We argue that the large-$\Nc$ behaviour of the Yukawa couplings in the Skyrme model involves issues more subtle than the vanishing of linear fluctuations needed for classical stability of the skyrmion. The chiral fluctuations about the skyrmion must be quantized in order to reach a conclusion. An improved quantization procedure allows us to confront this question directly. The pion-nucleon coupling constants $\gcup$ (CP conserving) and $\bgcup$ (CP violating) are calculated in the large-$\Nc$, three-flavour Skyrme model by direct evaluation of the leading matrix elements appearing in the LSZ reduction formula. We find that $\gcup \sim \Nc^{{3 \over 2}}$, but that, at most, $\bgcup \sim m^2_\pi \Nc^{-\shalf}$. These results show that the leading contribution to the neutron electric dipole moment in large-$\Nc$ Skyrme model is the direct one ($\Dn \sim \Nc m^2_\pi$), rather than the pion loop contribution.
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