Physics Commons^™

Two Dimensional Lattice Gauge Theory With And Without Fermion Content, Dibakar Sigdel

FIU Electronic Theses and Dissertations

Quantum Chromo Dynamics (QCD) is a relativistic field theory of a non-abelian gauge field coupled to several flavors of fermions. Two dimensional (one space and one time) QCD serves as an interesting toy model that shares several features with the four dimensional physically relevant theory. The main aim of the research is to study two dimensional QCD using the lattice regularization.

Two dimensional QCD without any fermion content is solved analytically using lattice regularization. Explicit expressions for the expectation values of Wilson loops and the correlation of two Polyakov loops oriented in two different directions are obtained. Physics of the …

ΠN And Strangeness Sigma Terms At The Physical Point With Chiral Fermions, Yi-Bo Yang, Andrei Alexandru, Terrence Draper, Jian Liang, Keh-Fei Liu

Physics and Astronomy Faculty Publications

Lattice QCD calculations with chiral fermions of the πN sigma term σ_πN and strangeness sigma term σ_πN including chiral interpolation with continuum and volume corrections are provided in this work, with the excited-state contaminations subtracted properly. We calculate the scalar matrix element for the light/strange quark directly and find σ_πN = 45.9(7.4)(2.8)  MeV, with the disconnected insertion part contributing 20(12)(4)%, and σ_πN = 40.2(11.7)(3.5)  MeV, which is somewhat smaller than σ_πN. The ratio of the strange/light scalar matrix elements is y = 0.09(3)(1).

Diquark Mass Differences From Unquenched Lattice Qcd, Yujiang Bi, Hao Cai, Ying Chen, Ming Gong, Zhaofeng Liu, Hao-Xue Qiao, Yi-Bo Yang

Physics and Astronomy Faculty Publications

We calculate diquark correlation functions in the Landau gauge on the lattice using overlap valence quarks and 2+1-flavor domain wall fermion configurations. Quark masses are extracted from the scalar part of quark propagators in the Landau gauge. The scalar diquark quark mass difference and axial vector scalar diquark mass difference are obtained for diquarks composed of two light quarks and of a strange and a light quark. The light sea quark mass dependence of the results is examined. Two lattice spacings are used to check the discretization effects. The coarse and fine lattices are of sizes 24³ × 64 …

Orbital Angular Momentum And Generalized Transverse Momentum Distribution, Yong Zhao, Keh-Fei Liu, Yi-Bo Yang

Physics and Astronomy Faculty Publications

We show that, when boosted to the infinite momentum frame, the quark and gluon orbital angular momentum operators defined in the nucleon spin sum rule of Chen et al. are the same as those whose matrix elements correspond to the moments of generalized transverse momentum distributions. This completes the connection between the infinite momentum limit of each term in that sum rule and experimentally measurable observables. We also show that these orbital angular momentum operators can be defined locally and discuss the strategies of calculating them in lattice QCD.

Stochastic Model With Low Mode Substitution For Nucleon Isovector Matrix Elements, Yi-Bo Yang, Andrei Alexandru, Terrence Draper, Ming Gong, Keh-Fei Liu

Physics and Astronomy Faculty Publications

We introduce a stochastic method with low-mode substitution to evaluate the connected three-point functions. The isovector matrix elements of the nucleon for the axial-vector coupling g³_A, scalar couplings g³_S and the quark momentum fraction ⟨x⟩_u−d are calculated with overlap fermion on 2 + 1 flavor domain-wall configurations on a 24³ × 64 lattice at m_π = 330  MeV with lattice spacing a = 0.114  fm.

Hadron Resonaces From Qcd, Jozef J. Dudek

Physics Faculty Publications

I describe how hadron-hadron scattering amplitudes are related to the eigenstates of QCD in a finite cubic volume. The discrete spectrum of such eigenstates can be determined from correlation functions computed using lattice QCD, and the corresponding scattering amplitudes extracted. I review results from the Hadron Spectrum Collaboration who have used these finite volume methods to study ππ elastic scattering, including the ρ resonance, as well as coupled-channel πK, ηK scattering. The very recent extension to the case where an external current acts is also presented, considering the reaction πγ^* → ππ, from which the unstable ρ …

Connecting Physical Resonant Amplitudes And Lattice Qcd, Daniel R. Bolton, Raúl A. Briceño, David J. Wilson

Physics Faculty Publications

We present a determination of the isovector, P-wave π π scattering phase shift obtained by extrapolating recent lattice QCD results from the Hadron Spectrum Collaboration using m_{π =} 236 MeV. The finite volume spectra are described using extensions of Ltischer's method to determine the infinite volume Unitarized Chiral Perturbation Theory scattering amplitude. We exploit the pion mass dependence of this effective theory to obtain the scattering amplitude at m_π = 140 MeV. The scattering phase shift is found to agree with experiment up to center of mass energies of 1.2 GeV. The analytic continuation of the scattering amplitude …

Relativistic, Model-Independent, Multichannel 2 → 2 Transition Amplitudes In A Finite Volume, Raúl A. Briceño, Maxwell T. Hansen

Physics Faculty Publications

We derive formalism for determining 2+𝓙 → 2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or nonidentical and, in the latter case, can be either degenerate or nondegenerate. We further accommodate any number of strongly coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of the ρ-meson form factor, in which the unstable nature of …

𝜋𝜋 → 𝜋𝛾* Amplitude And The Resonant 𝜌 → 𝜋𝛾* Transition From Lattice Qcd, Raúl A. Briceño, Jozef J. Dudek, Robert G. Edwards, Christian J. Shultz, Christopher E. Thomas, David J. Wilson

Physics Faculty Publications

We present a determination of the P-wave 𝜋𝜋 → 𝜋𝛾⋆ transition amplitude from lattice quantum chromodynamics. Matrix elements of the vector current in a finite volume are extracted from three-point correlation functions, and from these we determine the infinite-volume amplitude using a generalization of the Lellouch-Lüscher formalism. We determine the amplitude for a range of discrete values of the 𝜋𝜋 energy and virtuality of the photon and observe the expected dynamical enhancement due to the ρ resonance. Describing the energy dependence of the amplitude, we are able to analytically continue into the complex energy plane and from the residue …