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Taste Non-Goldstone Pion Decay Constants and Beyond the Standard Model B-parameters in Lattice QCD with Staggered Fermions : 스태거드 페르미온을 이용한 격자 양자색역학에서 파이온 붕괴 상수와 초표준모형 B 파라미터의 계산
DC Field | Value | Language |
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dc.contributor.advisor | 이원종 | - |
dc.contributor.author | 윤보람 | - |
dc.date.accessioned | 2017-07-14T00:56:31Z | - |
dc.date.available | 2017-07-14T00:56:31Z | - |
dc.date.issued | 2013-02 | - |
dc.identifier.other | 000000009668 | - |
dc.identifier.uri | https://hdl.handle.net/10371/121498 | - |
dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 물리·천문학부(물리학전공), 2013. 2. 이원종. | - |
dc.description.abstract | In part I, we calculate the next-to-leading order corrections to pion decay constants for the taste non-Goldstone pions using staggered chiral perturbation theory. This is a generalization of the calculation for the taste Goldstone case. New low-energy couplings are limited to analytic corrections that vanish in the continuum limit | - |
dc.description.abstract | the chiral logarithms contain no new couplings. We report results for quenched, fully dynamical, and partially quenched cases of interest in the chiral SU(3) and SU(2) theories. The results can be used to refine existing determinations of decay constants and low energy constants.
In part II, we calculate the beyond the standard model B-parameters using HYP-smeared improved staggered fermions on the MILC asqtad lattices with Nf = 2 + 1 flavors. We use three different lattice spacings (a ? 0.045, 0.06 and 0.09 fm) to obtain the continuum results. Operator matching is done using one-loop perturbative matching, and results are run to 2 and 3 GeV in the MS scheme. For the chiral and continuum extrapolations, we use SU(2) staggered chiral perturbation theory. We present preliminary results with only statistical errors. In part III, we give a detailed introduction to the data anlysis including basic probability theory, error anlalysis techniques and least chi-square fitting method. We also explain how to analyse highly correlated data by applying a number of prescriptions such as diagonal approximation, singular value decomposition (SVD) method and Bayesian method. We propose a brand new method, the eigenmode shift method which allows a full covariance fitting without modifying the covariance matrix. | - |
dc.description.tableofcontents | 1. Introduction
1.1. Quantum chromodynamics 1.2. Lattice QCD 1.3. Recent progress of the lattice calculation 1.4. Summary of this thesis 1.4.1. Decay constants in staggered chiral perturbation theory 1.4.2. Kaon mixing matrix elements from BSM operators 1.4.3. Art of data analysis 2. QCD on the Lattice 2.1. Gluons on the lattice 2.2. Fermions on the lattice 2.2.1. Fermion doubling 2.2.2. Wilson fermions 2.2.3. Staggered fermions 3. Chiral Perturbation Theory 3.1. Introduction to chiral perturbation theory 3.1.1. Chiral Effective Lagrangian 3.2. Staggered chiral perturbation theory 3.2.1. Chiral Lagrangian for staggered quarks 3.2.2. Propagators 4. Decay Constants in Staggered Chiral Perturbation Theory 4.1. Chiral Lagrangian that contribute to the decay constants at NLO 4.2. Decay constants of flavor-charged pseudo-goldstone bosons 4.2.1. Wavefunction renormalization correction 4.2.2. Current correction 4.2.3. Next-to-leading order analytic contributions 4.3. Results 4.3.1. SU(3) chiral perturbation theory 4.3.1.1. Fully dynamical case 4.3.1.2. Partially quenched case 4.3.1.3. Quenched case 4.3.2. SU(2) chiral perturbation theory 4.3.2.1. Fully dynamical case 4.3.2.2. Partially quenched case 4.4. Conclusion 5. Introduction to the Kaon Mixing Matrix Elements from BSM Operators 5.1. Kaon mixing matrix elements from the Standard Model 5.2. Kaon mixing matrix elements from beyond the Standard Model 6. Numerical Study of Kaon Mixing Matrix Elements from BSM Operators 6.1. Computation of BSM B-parameters 6.2. SU(2) fitting 6.3. RG evolution 6.4. Continuum extrapolation 6.5. Conclusion 7. Basic Probability Theory 7.1. Mean and variance 7.1.1. Probability and probability distribution 7.1.2. Mean and variance 7.1.3. Sample mean and sample variance 7.1.4. Fundamental theorems of probability 7.2. Special distributions 7.2.1. Normal distribution 7.2.2. chi-square-distribution and noncentral chi-square-distribution 8. Error Analysis 8.1. Propagation of error 8.2. Resampling methods 8.2.1. Bootstrap method 8.2.2. Jackknife method 8.3. Calculating error of error 8.4. Dealing with Jackknife samples 8.4.1. From jackknife samples to original samples 8.4.2. From jackknife results to bootstrap results 9. Least chi-square Fitting 9.1. Theory of least chi-square fitting 9.1.1. Uncorrelated chi-square 9.1.2. Correlated chi-square 9.1.3. Quality of the fit 9.1.4. Uncertainty of fitting parameters 9.2. Constrained fitting 9.3. Finding fitting parameters 9.3.1. Fitting data to linear functions 9.3.2. Fitting data to nonlinear functions 10.Covariance Fitting of Highly Correlated Data 10.1. Trouble with correlated data fitting 10.2. Prescriptions 10.2.1. Diagonal approximation 10.2.2. Cutoff method 10.2.3. Eigenmode shift method 10.2.3.1. Equivalence of cutoff method and unconstrained ES method 10.2.4. Bayesian method 10.2.5. Probability distribution of minimized chi-square 10.2.5.1. Distribution of chi-square for the full covariance fitting 10.2.5.2. Distribution of chi-square for the cutoff method 10.2.5.3. Distribution of chi-square for the ES method 10.2.6. An example of fitting with random data 11.Multidimensional Function Minimizer 11.1. Amoeba method 11.2. Conjugate gradient algorithm 11.2.1. Calculation of α(i) 11.2.2. Calculation of β(i+1) 11.2.3. Convergence 11.2.4. Practical implementation 11.2.5. Variants 11.3. Function minimization using CG 11.3.1. Minimization of quadratic functions 11.3.2. Outline of minimization for general functions 11.3.3. Calculation of β(i+1) 11.3.4. Calculation of α(i) 11.3.5. Limits 11.3.6. Practical implementation 11.4. Function minimization using Newton method 11.4.1. Outline of Newton method A. Noether current B. Gamma function C. A Derivation of the Probability Distribution Function of chi-square distribution C.1. chi-square distribution with one degrees of freedom C.2. chi-square distribution with two degrees of freedom C.3. chi-square distribution with k degrees of freedom D. Error of Jackknife Estimation for Variance of Mean Bibliography | - |
dc.format | application/pdf | - |
dc.format.extent | 2343126 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | quantum chromodynamics | - |
dc.subject | lattice QCD | - |
dc.subject | chiral perturbation theory | - |
dc.subject | pion decay constant | - |
dc.subject | beyond the standard model bag parameters | - |
dc.subject.ddc | 523 | - |
dc.title | Taste Non-Goldstone Pion Decay Constants and Beyond the Standard Model B-parameters in Lattice QCD with Staggered Fermions | - |
dc.title.alternative | 스태거드 페르미온을 이용한 격자 양자색역학에서 파이온 붕괴 상수와 초표준모형 B 파라미터의 계산 | - |
dc.type | Thesis | - |
dc.contributor.AlternativeAuthor | Boram Yoon | - |
dc.description.degree | Doctor | - |
dc.citation.pages | 179 | - |
dc.contributor.affiliation | 자연과학대학 물리·천문학부(물리학전공) | - |
dc.date.awarded | 2013-02 | - |
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