Physics Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/2800
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Item Lattice Quantum Chromodynamics (QCD) Calculations of Parton Physics with Leading Power Accuracy in Large Momentum Expansion(2023) Zhang, Rui; Ji, Xiangdong XJ; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Parton distributions describing how momenta of quarks and gluons are distributed inside a hadron moving at the speed of light, are important inputs to the Standard Model prediction of collider physics. Their non-perturbative nature makes traditional perturbative calculations from quantum field theory impossible. Besides a global fitting to experimental data, it is also possible to calculate parton physics from lattice QCD, a first-principle non-perturbative Monte Carlo simulation of the strong interaction on super computers. Among the different strategies to extract information for parton physics, the large momentum effective theory, based on a large momentum expansion of non-local Euclidean correlation functions, allows us to directly calculate the momentum-fraction or $x$-dependence. When matching the lattice-QCD calculations to the physical parton physics in the large momentum expansion, there are unavoidable power corrections in the expansion parameter $\Lambda_{\rm QCD}/P_z$, which is determined by the QCD characteristic non-perturbative scale $\Lambda_{\rm QCD}\approx300$~MeV and the hadron momentum $P_z$, and the leading term appears as $\mathcal{O}(\Lambda_{\rm QCD}/(2xP_z))$ due to the linear divergent self-energy of Wilson line in the Euclidean lattice correlators. For current lattice calculations of $P_z\sim 2-3$~GeV, this correction can be as large as $30\%$ at small $x$, dominating the uncertainties in the calculation. Achieving power accuracy in linear order of $\Lambda_{\rm QCD}/P_z$ is thus crucial for a high precision calculation of the parton physics from lattice QCD. In this dissertation, I summarize our work to eliminate this linear correction by consistently defining the renormalization for the linear divergence in lattice data and the resummation scheme of the factorially growing infrared-renormalon series in the perturbative matching. We show that the method significantly reduces the linear uncertainty by a factor of $\sim3-5$ and improves the convergence of the perturbation theory. We then apply the strategy to the calculation of pion distribution amplitude, which describes the pion light-cone wave function in a quark-antiquark pair. The method improves the short distance behavior of the renormalized lattice correlations, which is now consistent with the prediction of the short distance operator product expansion, showing a reasonable value for the moments of pion distribution amplitude. We also develop the first strategy to resum the large logarithms in the matching to physical pion distribution amplitude when the momentum of quark or antiquark in the pion are small, that could improve the accuracy of the prediction near the endpoint regions. After extracting the $x$-dependence from the large momentum expansion in mid-$x$ region, we complete the endpoint regions by fitting to the short distance correlations. Then a complete $x$-dependence is obtained for the pion distribution amplitude, which suggests a broader distribution compared to previous lattice QCD calculations or model predictions.Item Measurement of the Electric Form Factor of the Neutron at High Momentum Transfer(2009) Miller, Jonathan Andrew; Beise, Elizabeth J; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The electric form factor of the neutron, $G_{E}^{n}$, provides key understanding of the structure of one of the basic building blocks of visible matter in the universe. Recent interest in this quantity is the result of the improved quality of data provided by double polarization experiments, which have substantially improved in the last decade. This thesis presents precision measurements of $G_{E}^{n}$ by the E02-013 collaboration at $Q^{2}$ of 1.7, 2.5, and 3.5 GeV$^{2}$. This measurement used a double polarization technique, a highly polarized $^{3}$He target, a polarized electron beam, a large acceptance spectrometer to detect the scattered electrons, and a large neutron detector to detect the recoiling hadrons in the reaction $^{3}\vec{\mathrm{He}}(\vec{e},e'n)$. These measurements will be compared to a variety of models of the nucleon's internal structure, as well as used to extract individual contributions of the up and down quarks to the nucleon form factors.