Study Strong Interactions With Chiral Lattice Fermions

Renormalization in quantum field theory is aimed at eliminating the ultraviolet divergence in perturbative cacluations.In the first part of the thesis,we discuss our calculations of renormalization constants(RCs)of overlap quark bilinear operators,the configurations in which we use are 2+1 flavor dynamical domain wall configurations generated by RBC/UKQCD Collaboration.The lattice size is 483 x 96,and the in-verse of lattice spacing is a-1 = 1.730(4)GeV.We use two renormalization schemes-RI/MOM and RI/SMOM schemes to calculate the RCs,and compare results and systematic uncertainties from the two scheme numerically.The scale-independent axial vector current renormalization constantZA is obtained from Ward Identity via pion correlation functions.By usingZA,we derive others RCs for the quark field and other quark bilinear operators in RI/MOM and RI/SMOM schemes.All the RCs on lattice obtained by the two schemes are converted to MS scheme using conversion factors given by continuum perturbation calculaton and run to ?= 2 GeV from its initial scale p in MS scheme.We compare results from the two intermediate schemes and find that they are consistent with each other within uncertainty as expected.The quark chiral condensate<??>?-? is one of the two significant low energy constants at the lowest order for chiral perturbation theory(f?-??),and the accurate calculation for ? is truly important.There are many calculations for E using various methods in lattice QCD calculations.In the second part,we calculate the quark chiral condensate by using overlap fermions with exact lattice chiral symmetry on two lattices with different size and lattice spacings by using two different methods-the OPE of scalar and vector form factors from overlap quark propagators and pseudoscalar den-sity.In comparison to other lattice fermions,overlap fermion with excat lattice chiral symmetry has smaller systematic uncertianties in calculations related to chiral symme-try.Our results obtained via two methods are in agreement with that given by FLAG within a relatively large statistical uncertainty.For the first method,we use one lattice spacing and size only,and check the light sea quark mass dependence.By using the latter one,we use four ensambles with one lattice spacing but different lattice size,by which we can check the finite volume effects as well as the light sea quark dependence.In recent years,the XYZ particles and pentaquarks attract much attention,and physicists proposed of many models in order to understanding their inner structures.Diquark,composed of two quarks is one powerful or essential concept when constructing XYZ2amilies and pentaquarks.Studying the properties of diquarks on the lattice using non-perturbative methods,therefore,makes total sense.We,in the third part,calculate diquark masses with different quantum numbers and their mass differences on two ensambles of size 243 x 64 and one ensamble of size 323 × 64.Our results are consistent with those estimators from hadron spectroscopy analysis w:ithin a large uncertainty.Due to our small statistics,the statistical uncertainties are large and signal to noise ratios are bad at some valence quark masses.In this part,we examine the discretization effects and light sea quark mass dependence by using three ensambles with two lattice spacings and different light sea quark masses.