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

Abstract

The parity-odd effect in the Standard Model weak neutral current reveals itself in the long-range parity-violating nuclear potential generated by the pion exchanges in the $\Delta I=1$ channel with the parity-odd pion-nucleon coupling constant $h_{\pi }^1$. Despite decades of experimental and theoretical efforts, the size of this coupling constant is still not well-understood. In this Letter we derive a soft-pion theorem relating $h_{\pi }^1$ and the neutron-proton mass-splitting induced by an artificial parity-even counterpart of the $\Delta I=1$ weak Lagrangian, and demonstrate that the theorem still holds exact at the next-to-leading order in chiral perturbation theory. A considerable amount of simplification is expected in the study of $h_{\pi }^1$ by using either lattice or other QCD models following its reduction from a parity-odd proton-neutron-pion matrix element to a simpler spectroscopic quantity. The theorem paves the way to much more precise calculations of $h_{\pi }^1$, and thus a quantitative test of the strangeness-conserving neutral current interaction of the Standard Model is foreseen.

6 pages, 1 figure

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Cited by in corpus (5)

• First Observation of $P$-odd $\gamma$ Asymmetry in Polarized Neutron Capture on Hydrogen
• Effective Field Theory in The Study of Long Range Nuclear Parity Violation on Lattice
• Experimental Upper Bound and Theoretical Expectations for Parity-Violating Neutron Spin Rotation in 4He
• Towards a unified treatment of $\Delta S=0$ parity violation in low-energy nuclear processes
• Fundamental Neutron Physics: a White Paper on Progress and Prospects in the US