Inhalt

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   Abstract
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   Zusammenfassung
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   Contents
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   1 Introduction
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    Theory
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   2 QCD on the lattice
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   2.1 Gauge action
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   2.1.1 On-shell improvement
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   2.1.2 Lüscher-Weisz gauge action
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   2.2 Fermion action
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   2.2.1 Wilson fermions
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   2.2.2 Improved Wilson fermions
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  3 The Schrödinger functional
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  3.1 Continuum formulation
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   3.1.1 Gluon action
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   3.1.2 Quarks in the Schrödinger functional
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   3.2 Lattice formulation
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  3.3 Schrödinger functional correlation functions
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   3.3.1 Boundary sources
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   3.3.2 Expectation values
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   3.3.3 Correlation functions
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   3.3.4 Flavor off-diagonal bilinears
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  3.4 Addendum: Open Boundary Conditions
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   3.4.1 Motivation
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   3.4.2 Setup
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   3.4.3 Boundary improvement
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  4 Operator improvement and renormalization
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  4.1 Improvement of the action: Revisited
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   4.1.1 Mass renormalization
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   4.1.2 Improvement of the coupling
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   4.2 Operator improvement
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   4.2.1 Renormalization of improved operators
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   4.2.2 Improvement of local currents
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  4.3 Improved quark masses
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   4.3.1 Renormalization of the bare subtracted quark mass
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   4.3.2 The PCAC relation
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   4.3.3 Current quark masses
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   4.3.4 Relations between renormalized quark masses
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   4.3.5 The ratio-difference method
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  5 Algorithmic techniques
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   5.1 Simulation algorithms
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   5.1.1 Hybrid Monte Carlo
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   5.1.2 Integration schemes
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   5.1.3 HMC with dynamical quarks
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   5.1.4 Rational Hybrid Monte Carlo
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   5.1.5 Reweighting
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  5.2 Frequency splitting
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   5.2.1 Hasenbusch splitting
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   5.2.2 Splitting the rational determinant
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   5.2.3 Twisted mass reweighting
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   5.3 Solver
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   5.3.1 Conjugate Gradient solver
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   5.3.2 Multi-shift Conjugate Gradient solver
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   5.3.3 Even-odd preconditioning
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   5.3.4 Block preconditioning
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   5.3.5 Deflation acceleration
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   5.3.6 Distance preconditioning
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  5.4 Errors in Monte Carlo data
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   5.4.1 Correlations
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   5.4.2 Slow modes
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  6 Extraction of physical observables
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  6.1 Meson masses
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   6.1.1 The spectral decomposition of correlation functions
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   6.1.2 Correlation functions and open boundary conditions
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   6.2 The generalized eigenvalue problem
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   6.3 Fitting
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   6.3.1 Fitting correlated data
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   6.4 Gradient flow observables
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   6.4.1 The Wilson flow
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   6.4.2 The Zeuthen flow
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   6.4.3 Setting a scale from the flow
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   6.4.4 The gradient flow coupling in the Schrödinger functional
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   6.4.5 The topological charge from the gradient flow
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  6.5 Smearing
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   6.5.1 APE smearing
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   6.5.2 HYP smearing
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   6.5.3 Gaussian smearing
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   6.5.4 Smearing from three-dimensional fermions
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   6.5.5 Smearing from three-dimensional bosons
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  7 Heavy Quark Effective Theory
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   7.1 Continuum HQET
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   7.1.1 Derivation of the HQET Lagrangian
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   7.1.2 Heavy Quark Symmetry
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  7.2 HQET on the lattice
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   7.2.1 Lattice action
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   7.2.2 Expectation values at next-to-leading order
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  7.3 Non-perturbative matching with QCD
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   7.3.1 Matching in finite volume
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   7.3.2 Determination of the matching parameters
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   7.3.3 Quark mass dependence
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  7.4 HQET observables
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   7.4.1 The axial current in HQET
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   7.4.2 The B meson mass
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   7.4.3 The GEVP in HQET
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    The line of constant physics for a non-perturbative matching of HQET and QCD
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  8 Simulations along a line of constant physics
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   8.1 The line of constant physics: QCD
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   8.1.1 The running of the coupling
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   8.1.2 Interpolation of the coupling at fixed L/a
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   8.1.3 Target precision
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   8.1.4 Tuning towards the critical hopping parameter
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   8.1.5 Step scaling to the matching volume
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   8.1.6 The matching volume
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   8.2 The line of constant physics: HQET
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   8.2.1 Tuning in the matching volume
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   8.2.2 Step scaling towards large volume simulations
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   8.2.3 Contact to the large-volume simulations
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  8.3 The running of the mass
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   8.3.1 The step scaling function of the mass
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   8.3.2 Determination of RGI quark masses
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   8.3.3 Determination of the step scaling function
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   8.4 Conclusions
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  9 Algorithmic experiences
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   9.1 Solvers
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   9.1.1 Quark mass dependence
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   9.1.2 Tuning of the deflated solver
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   9.2 RHMC
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  9.3 Scaling of autocorrelation times
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   9.3.1 The topological charge in finite volume
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    Renormalization and Improvement from finite-volume simulations
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  10 Strategy
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   10.1 Estimators from time slice averages
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  10.2 Quark mass parametrization
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   10.2.1 Redefinition of the estimators
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   10.2.2 Polynomial interpolations
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   10.3 The line of constant physics
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  11 Quark mass improvement in the strongly coupled regime of QCD
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   11.1 Gauge ensembles
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   11.1.1 Topological charge
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  11.2 Results
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   11.2.1 Mass parametrizations and determination of the estimators
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   11.2.2 Chiral interpolations
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   11.2.3 Interpolation in the coupling
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   11.2.4 Errors and correlations
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   11.3 Ambiguity checks
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   11.4 Estimators from time slice averages
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   11.5 Conclusions
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   12 Quark mass renormalization for the matching of QCD and HQET
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   12.1 PCAC masses
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   12.2 Estimators
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   12.3 Ambiguities
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  12.4 Renormalization of the pseudoscalar density and the axial current
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   12.4.1 Renormalization of the pseudoscalar density
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   12.4.2 Renormalization of the axial current
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   12.5 Hopping parameters for constant renormalized quark masses
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   12.6 Verification of improvement
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   12.7 Conclusions
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    The mass of the charm quark
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   13 CLS ensembles
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   13.1 The chiral trajectory
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   13.2 Quark mass shifts
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  14 Determination of the charm quark mass
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   14.1 Calibration of the measurements
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   14.2 The renormalized charm quark mass from current quark masses
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  15 Lattice computation
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   15.1 Correlation functions
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   15.2 Meson masses
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   15.2.1 Fit ranges
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   15.2.2 Extraction of the effective mass
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   15.3 Current quark masses
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   15.3.1 Fit ranges
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   15.4 Distance preconditioning
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   15.4.1 Tuning procedure
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   15.4.2 Impact on physical observables
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   15.5 Stochastic sources
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   15.6 Chiral-continuum extrapolation
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   15.7 Preliminary result and discussion
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    HQET in large volume
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  16 Heavy Quark Effective Theory with open boundary conditions
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   16.1 Setup of the measurements
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   16.2 Optimization of the variational basis
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   16.2.1 Definition of a suitable basis
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   16.2.2 Reduction of the number of smearing procedures
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   16.2.3 Variational basis from smearing method
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   16.3 Boundary effects
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   16.3.1 Boundary states
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   16.3.2 Asymmetry in the correlation matrix
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   17 Computation of the B*Bpi coupling
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   17.1 Heavy Meson Chiral Perturbation Theroy
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   17.2 Lattice computation
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   17.3 Setup
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  17.4 Results
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   17.4.1 Plateaus
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   17.4.2 Chiral-continuum extrapolation
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   17.5 Discussion
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   17.6 The matrix element of the first radial excitations
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    Conclusions
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   18 Conclusions
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  A Conventions
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   A.1 The special unitary group
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   A.2 Dirac matrices
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   A.3 Lattice derivatives
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  B Tables
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   B.1 The line of constant physics for a non-perturbative matching of HQET and QCD
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   B.2 Renormalization and improvement from finite-volume simulations
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   B.3 The mass of the charm quark
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   B.4 HQET in large volume
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    Bibliography