I am applying for an Erwin Schrödinger fellowship in order to realize the following project together with
Ass.-Prof. Dr. Michael Engelhardt (M.E.) at the New Mexico State University (NMSU), including a return
phase to the Institute of Atomic and Subatomic Physics at the Vienna University of Technology. The
proposal addresses important questions in lattice QCD, the main tool for probing the quantum
chromodynamics of quarks and gluons (QCD) in the non-perturbative regime, with an emphasis on vacuum
structure and hadron or especially neutron physics.
First we plan to investigate ways of generating random center vortex ensembles without the hypercubic
lattice scaffolding used in the existing implementation of the vortex model. This is somewhat a proceeding of
the applicants experience of topological models in lattice QCD with focus on the center vortex model of
confinement and its relevance for chiral symmetry breaking. M.E. has analyzed Dirac spectra and the chiral
condensate in the random vortex surface model and together with the PhD student Derar Altarawneh made
significant progress in formulating the random vortex model in three dimensions. Within this project the
model shall be extended to four dimensions, requiring the triangulation of vortex surfaces. Further, Monte
Carlo updates of the model shall be introduced, disconnecting and fusing vortex lines and finally new
smearing methods have to be developed to make the rough vortex configurations accessible to fermions for
further tests of the model in order to even extract some hadron phenomenology.
Then we plan to investigate the electric spin polarizability of the neutron in lattice QCD. Polarizabilities
represent fundamental properties of hadrons, encoding their linear response to externally applied fields.
Experimentally, they manifest themselves, e.g., in the non-Born part of the low-energy Compton scattering
amplitude. While the leading low-energy response is controlled by the static polarizabilities found in the
presence of constant external fields, at subsequent orders of a derivative expansion, the effective hadron
Hamiltonian becomes sensitive to temporal and spatial structures in the applied fields. Present investigations by M.E. provides first lattice QCD results for the electric spin polarizability of the neutron. Besides refinement of the methods an important part of this proposal is the interpretation of the neutron polarizability data with simple models. Further, the efficiency enhancement of loop diagram calculations, which are not only necessary for polarizability but in many hadron structure investigations, is planned. M.E. is also contributing in such nucleon structure calculations on the lattice within the framework of the existing LHPC collaboration. These are important for both testing QCD as the fundamental theory of quarks and gluons and making predictions and complementing experimental efforts that aim to measure the full three-dimensional picture of the proton and nucleon, and to explore the origin of the nucleon spin. A main purpose is the calculation of standard low-energy observables like (axial) vector couplings, which are of special interest for analytic calculations, worth mentioning a future investigation of the radiative beta-decay of the neutron performed by Mario Pitschmann et al. in close relation to precision measurements of the neutron by Hartmut Abele et al., who directly measure these observables in experiments. Both groups are working at the Institute of Atomic and Subatomic Physics strongly support the applicants idea to link the experimental and analytic competences with the numerical approach of lattice QCD. The proposed project would be an excellent opportunity to get in direct contact with leading experts working together at the LHPC collaboration.