QCD ANALYSIS OF FLAVOR-NONCHANGING HADRONIC WEAK PROCESSES THROUGH NEXT-TO-LEADING ORDER

Studies in quantum chromodynamics (QCD), the fundamental theory of the strong interactions, of low-energy hadronic weak processes utilize an effective Hamiltonian framework. Below the weak-mass scale, an effective Hamiltonian contains a series of Wilson coefficients and four-quark operators that come from the operator product expansion in the Standard Model. The effective hadronic Hamiltonian pertinent to a weak process is then obtained via a renormalization group analysis in QCD from the weak-mass scale to the low-energy scale of O(2 GeV). In this thesis, the construction and phenomenological implications of such an effective Hamiltonian for flavor-conserving, parity-violating quark processes in the Standard Model will be presented. Extensive studies of QCD corrections in flavor-changing meson decays have been conducted starting already in the 1990s. But the status in the flavor-conserving sector is completely different, and such rigorous studies have been lacking. In this work, we establish a robust connection between flavor-conserving and flavor-changing physics and utilize it to find the relevant anomalous dimension matrices for flavor-nonchanging processes through next-to-leading order in QCD. The anomalous dimension matrices represent the renormalization and mixing profile of the operators in the presence of QCD corrections and are an essential ingredient in the renormalization group flow between energy scales. Following the computation of the complete effective low-energy Hamiltonian at GeV scales, we are able to apply it to the study of hadronic parity-violating processes and compute its quantifying parameters, the parity-breaking meson nucleon couplings. The thus computed couplings are shown to be in good agreement with their extracted values from phenomenological analyses of recent, precise measurements of the parity-violating asymmetry in neutron-spin reversal in few-body low-energy nuclear reactions. This has been accomplished for the first time. Finally, we are also able to discuss how this effective Hamiltonian can be applied to studies of weak effects in the hadronic decays of flavor-neutral mesons, such as, η, η′, resulting in P and CP violation. We note how future experiments and lattice QCD studies could sharpen our findings and that our study serves as an essential guide for these future endeavors in arriving at a robust description of hadronic parity violations

Towards a unified treatment of ΔS=0\Delta S=0 parity violation in low-energy nuclear processes

We revisit the unified treatment of low-energy hadronic parity violation espoused by Desplanques, Donoghue, and Holstein to the end of an ab initio treatment of parity violation in low-energy nuclear processes within the Standard Model. We use our improved effective Hamiltonian and precise non-perturbative assessments of the quark charges of the nucleon within lattice QCD to make new assessments of the parity-violating meson-nucleon coupling constants. Comparing with recent, precise measurements of hadronic parity violation in few-body nuclear reactions, we find improved agreement with these experimental results, though some tensions remain. We thus note the broader problem of comparing low-energy constants from nuclear and few-nucleon systems, considering, too, unresolved theoretical issues in connecting an ab initio, effective Hamiltonian approach to chiral effective theories. We note how future experiments could sharpen the emerging picture, promoting the study of hadronic parity violation as a laboratory for testing ``end-to-end'' theoretical descriptions of weak processes in hadrons and nuclei at low energies.Comment: 13 pages, REVTeX, 1 figure; note partial overlap in content with arXiv:2203.00033v1 (not v2

Universal RCFT correlators from the holomorphic bootstrap

We elaborate and extend the method of Wronskian differential equations for conformal blocks to compute four-point correlation functions on the plane for classes of primary fields in rational (and possibly more general) conformal field theories. This approach leads to universal differential equations for families of CFT's and provides a very simple re-derivation of the BPZ results for the degenerate fields phi(1,2) and phi(2,1) in the c < 1 minimal models. We apply this technique to compute correlators for the WZW models corresponding to the Deligne-Cvitanovic exceptional series of Lie algebras. The application turns out to be subtle in certain cases where there are multiple decoupled primaries. The power of this approach is demonstrated by applying it to compute four-point functions for the Baby Monster CFT, which does not belong to any minimal series

ΔS=0\Delta S=0 Hadronic Parity Violation in Next-to-Leading Order QCD: Anomalous Dimension Matrices and Their Implications

We construct the effective Hamiltonian for hadronic parity violation in strangeness-nonchanging ($\Delta S=0$) processes in next-to-leading order (NLO) in QCD, for all isosectors, and at a renormalization scale of 2 GeV, thus extending our earlier leading-order (LO) analysis. Hadronic parity violation, studied in the context of the low-energy interactions of nucleons and nuclei, exposes the complex interplay of weak and strong interactions in these systems, and thus supports our extension to NLO. Here we exploit the flavor-blind nature of QCD interactions to construct the needed anomalous dimension matrices from those computed in flavor physics, which we then use to refine our effective Hamiltonian and finally our predicted parity-violating meson-nucleon coupling constants, to find improved agreement with few-body experiments