Feynman--Hellmann approach to transition matrix elements and quasi-degenerate energy states

Abstract

The Feynman--Hellmann approach to computing matrix elements in lattice QCD by first adding a perturbing operator to the action is described using the transition matrix and the Dyson expansion formalism. This perturbs the energies in the two-point baryon correlation function, from which the matrix element can be obtained. In particular at leading order in the perturbation we need to diagonalise a matrix of near-degenerate energies. While the method is general for all hadrons, we apply it here to a study of a Sigma to Nucleon baryon transition vector matrix element.

arXiv comment50 pages. Minor typos fixed. Published version

References in corpus (35)

• The Chroma Software System for Lattice QCD
• FLAG Review 2021
• On the generalized eigenvalue method for energies and matrix elements in lattice field theory
• Tests of the standard electroweak model in beta decay
• Twisted Boundary Conditions in Lattice Simulations
• Aharonov-Bohm effect and nucleon-nucleon phase shifts on the lattice
• New physics searches in nuclear and neutron $\beta$ decay
• Nucleon structure functions from lattice operator product expansion
• A guide to light-cone PDFs from Lattice QCD: an overview of approaches, techniques and results
• Pion and Rho Structure Functions from Lattice QCD
• Flavour blindness and patterns of flavour symmetry breaking in lattice simulations of up, down and strange quarks
• Nucleon electromagnetic form factors on the lattice and in chiral effective field theory
• Twisted valence quarks and hadron interactions on the lattice
• The pion's electromagnetic form factor at small momentum transfer in full lattice QCD
• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• On the Feynman-Hellmann Theorem in Quantum Field Theory and the Calculation of Matrix Elements
• Non-perturbative improvement of stout-smeared three flavour clover fermions
• Electromagnetic form factors at large momenta from lattice QCD
• A Lattice Study of the Glue in the Nucleon
• Hadronic form factors in Lattice QCD at small and vanishing momentum transfer
• Variational Approach to the Calculation of gA
• Controlling Excited-State Contamination in Nucleon Matrix Elements
• Disconnected contributions to the spin of the nucleon
• A Feynman-Hellmann approach to the spin structure of hadrons
• Lattice QCD evaluation of the Compton amplitude employing the Feynman-Hellmann theorem
• New explicit expressions for Dirac bilinears
• First Lattice QCD Study of the Sigma -> n Axial and Vector Form Factors with SU(3) Breaking Corrections
• Update on $|V_{us}|$ and $|V_{us}/V_{ud}|$ from semileptonic kaon and pion decays
• Nucleon matrix elements using the variational method in lattice QCD
• An update on the BQCD Hybrid Monte Carlo program
• Lattice QCD Inputs for Nuclear Double Beta Decay
• Lattice QCD study of the elastic and transition form factors of charmed baryons
• SU(3) breaking in hyperon transition vector form factors
• Continuum limit of hyperon vector coupling $f_1(0)$ from 2+1 flavor domain wall QCD
• Patterns of flavour symmetry breaking in hadron matrix elements involving u, d and s quarks

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