Lattice QCD Calculation of the Momentum Fraction Carried by Quarks in the Nucleon, and the Roper Puzzle

This thesis is concerned with the lattice QCD calculation of the momentum fraction carried by quarks in the nucleon. Particularly, the strange quark contribution, (x)s, is calculated, as well as the ratio of the strange (x) to that of u/d in the disconnected insertion which will be useful in constraining the global fit of parton distribution functions at small x. The disconnected insertion is known to be hard to calculate on the lattice. We adopt the overlap fermion action on several 2 + 1 flavor domain-wall fermion ensembles with a light sea quark mass which corresponds to pion mass of 330 MeV and 139 MeV. Smeared grid sources with Z3 noise are deployed to calculate the nucleon propagator with low-mode substitution. Even-odd grid sources and the time-dilution technique with stochastic noises are used to calculate the high mode contribution to the quark loop. Low mode averaging (LMA) for the quark loop is applied to reduce the statistical error of the disconnected insertion calculation. We also address the puzzle on the mass of the Roper resonance. Using overlap fermion on top of domain-wall fermion configurations, as well as using the clover fermion action, we explore various smeared sources, and use the variational approach to isolate the Roper. We explain why chiral symmetry is important in resolving the discrepancies between lattice calculations and experiment