Novel Soft-Pion Theorem for Long-Range Nuclear Parity Violation

Area of Science:

• Nuclear Physics
• Particle Physics
• Quantum Chromodynamics (QCD)

Background:

• The parity-odd effect in weak neutral currents is not well understood.
• The pion-nucleon coupling constant (h_{π}^{1}) is crucial for this effect but lacks precise measurement.
• Decades of research have yet to fully determine the size of h_{π}^{1}.

Purpose of the Study:

• To derive a soft-pion theorem relating h_{π}^{1} to neutron-proton mass splitting.
• To simplify the calculation of h_{π}^{1} for more precise determination.
• To enable quantitative tests of the standard model's strangeness-conserving neutral current interaction.

Main Methods:

• Derivation of a soft-pion theorem.
• Analysis within chiral perturbation theory up to next-to-leading order.
• Reduction of a parity-odd matrix element to a spectroscopic quantity.

Main Results:

• A novel soft-pion theorem has been established.
• The theorem holds exactly at next-to-leading order in chiral perturbation theory.
• The calculation of h_{π}^{1} is significantly simplified, allowing for easier study with QCD models.

Conclusions:

• The derived theorem provides a pathway to more accurate calculations of h_{π}^{1}.
• This work facilitates a quantitative test of the standard model's weak neutral current.
• The simplified approach is expected to advance nuclear and particle physics research.