QCD Analysis of $\Delta S=0$ Hadronic Parity Violation

Abstract

We present a QCD analysis of the effective weak Hamiltonian at hadronic energy scales for strangeness-nonchanging ($\Delta S=0$) hadronic processes. Performing a leading-order renormalization group analysis in QCD from the $W$ to the $\mathcal{O}(2\mathrm{GeV})$ energy scale, we derive the pertinent effective Hamiltonian for hadronic parity violation, including the effects of both neutral and charged weak currents. We compute the complete renormalization group evolution of all isosectors and the evolution through heavy-flavor thresholds for the first time. We show that the additional four-quark operators that enter below the $W$ mass scale from QCD operator mixing effects form a closed set, and they result in a $12\times 12$ anomalous dimension matrix. Computing the resulting effective Hamiltonian and comparing to earlier results, we affirm the importance of operator mixing effects and find, as an example, that the parity-violating pion-nucleon coupling constant, using the factorization Ansatz and an assessment of the pertinent quark charge of the nucleon in lattice QCD at the 2 GeV scale, is in better agreement with recent experiments.

13 pages, LaTeX, 2 figures; shortened to focus on error assessment in the effective Hamiltonian due, e.g., to scale and higher order in alpha_s uncertainties and in the parity-violating pion-nucleon coupling constant; references added; version to appear in PLB

References in corpus (5)

• Precision Nucleon Charges and Form Factors Using 2+1-flavor Lattice QCD
• The parity-violating nucleon-nucleon force in the 1/N_c expansion
• Parity violation in neutron capture on the proton: determining the weak pion-nucleon coupling
• First Precision Measurement of the Parity Violating Asymmetry in Cold Neutron Capture on ${}^3$He
• Large $N_c$ Expansion and the Parity Violating $\pi ,N,\Delta$ Couplings

Cited by in corpus (2)

• Towards a unified treatment of $\Delta S=0$ parity violation in low-energy nuclear processes
• $\Delta S=0$ Hadronic Parity Violation in Next-to-Leading Order QCD: Anomalous Dimension Matrices and Their Implications