Vacuum and Hadron Structure in Lattice QCD

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.

During this Erwin Schrödinger fellowship i realized the following projects at the New Mexico State University (NMSU) and 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 and hadron structure, in particular neutron physics. First a random center vortex model without the hypercubic lattice scaffolding used in the existing implementations. This was a proceeding of my main research focus on topological models in lattice QCD, mainly the center vortex model of confinement and its relevance for chiral symmetry breaking. Within this project, a new formulation of the random vortex model in three dimensions was developed. A Monte Carlo simulation of the model, disconnecting and fusing vortex lines was realized and confinement properties were measured. An extension of the model to four dimensions turned out to be inefficient and therefore a new smearing method was developed to make the rough lattice vortex configurations accessible to fermions in order to measure Dirac spectra and fermion topological charge and susceptibilities. Next, the electric dipole and spin polarizabilities of the neutron using the background field method in lattice QCD were investigated. 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. We were able to separate the individual effects using mathematical transformations allowing us to improve first lattice QCD results for the electric spin polarizability of the neutron. Besides refinement of the methods an important part was the inclusion of loop diagrams, which are numerically expensive but give a non-negligible contribution. Precise measurements of the polarizabilities are important for both testing QCD as the fundamental theory of quarks and gluons and making predictions and complementing experimental efforts. Therefore, throughout the project and mainly during the return phase, theoretical investigations of the radiative beta-decay of the neutron in direct relation to precision measurements of the neutron by Hartmut Abele et al., were performed in collaboration with Andrei Ivanov et al. linking the experimental and analytic competences using numerical methods.