A New Method of Calculating the Spin-Wave Velocity cc of Spin-1/2 Antiferromagnets With O(N)O(N) Symmetry in a Monte Carlo Simulation

Motivated by the so-called cubical regime in magnon chiral perturbation theory, we propose a new method to calculate the low-energy constant, namely the spin-wave velocity $c$ of spin-1/2 antiferromagnets with $O(N)$ symmetry in a Monte Carlo simulation. Specifically we suggest that $c$ can be determined by $c = L/\beta$ when the squares of the spatial and temporal winding numbers are tuned to be the same in the Monte Carlo calculations. Here $\beta$ and $L$ are the inverse temperature and the box size used in the simulations when this condition is met. We verify the validity of this idea by simulating the quantum spin-1/2 XY model. The $c$ obtained by using the squares of winding numbers is given by $c = 1.1348(5)Ja$ which is consistent with the known values of $c$ in the literature. Unlike other conventional approaches, our new idea provides a direct method to measure $c$. Further, by simultaneously fitting our Monte Carlo data of susceptibilities $\chi_{11}$ and spin susceptibilities $\chi$ to their theoretical predictions from magnon chiral perturbation theory, we find $c$ is given by $c = 1.1347(2)Ja$ which agrees with the one we obtain by the new method of using the squares of winding numbers. The low-energy constants magnetization density ${\cal M}$ and spin stiffenss $\rho$ of quantum spin-1/2 XY model are determined as well and are given by ${\cal M} = 0.43561(1)/a^2$ and $\rho = 0.26974(5)J$, respectively. Thanks to the prediction power of magnon chiral perturbation theory which puts a very restricted constraint among the low-energy constants for the model considered here, the accuracy of ${\cal M}$ we present in this study is much precise than previous Monte Carlo result.Comment: 5 pages, 7 figure

스태거드 페르미온을 이용한 격자 양자색역학에서 파이온 붕괴 상수와 초표준모형 B 파라미터의 계산

학위논문 (박사)-- 서울대학교 대학원 : 물리·천문학부(물리학전공), 2013. 2. 이원종.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 limitthe 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.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 BibliographyDocto

Light pseudoscalar decay constants, quark masses, and low energy constants from three-flavor lattice QCD

As part of our program of lattice simulations of three flavor QCD with improved staggered quarks, we have calculated pseudoscalar meson masses and decay constants for a range of valence quark masses and sea quark masses on lattices with lattice spacings of about 0.125 fm and 0.09 fm. We fit the lattice data to forms computed with staggered chiral perturbation theory. Our results provide a sensitive test of the lattice simulations, and especially of the chiral behavior, including the effects of chiral logarithms. We find: f_\pi=129.5(0.9)(3.5)MeV, f_K=156.6(1.0)(3.6)MeV, and f_K/f_\pi=1.210(4)(13), where the errors are statistical and systematic. Following a recent paper by Marciano, our value of f_K/f_\pi implies |V_{us}|=0.2219(26). Further, we obtain m_u/m_d= 0.43(0)(1)(8), where the errors are from statistics, simulation systematics, and electromagnetic effects, respectively. The data can also be used to determine several of the constants of the low energy effective Lagrangian: in particular we find 2L_8-L_5=-0.2(1)(2) 10^{-3} at chiral scale m_\eta. This provides an alternative (though not independent) way of estimating m_u; 2L_8-L_5 is far outside the range that would allow m_u=0. Results for m_s^\msbar, \hat m^\msbar, and m_s/\hat m can be obtained from the same lattice data and chiral fits, and have been presented previously in joint work with the HPQCD and UKQCD collaborations. Using the perturbative mass renormalization reported in that work, we obtain m_u^\msbar=1.7(0)(1)(2)(2)MeV and m_d^\msbar=3.9(0)(1)(4)(2)MeV at scale 2 GeV, with errors from statistics, simulation, perturbation theory, and electromagnetic effects, respectively.Comment: 86 pages, 22 figures. v3: Remarks about m_u=0 and the strong CP problem modified; reference added. Figs 5--8 modified for clarity. Version to be published in Phys. Rev. D. v2: Expanded discussion of finite volume effects, normalization in Table I fixed, typos and minor errors correcte

Full nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks

Dramatic progress has been made over the last decade in the numerical study of quantum chromodynamics (QCD) through the use of improved formulations of QCD on the lattice (improved actions), the development of new algorithms and the rapid increase in computing power available to lattice gauge theorists. In this article we describe simulations of full QCD using the improved staggered quark formalism, ``asqtad'' fermions. These simulations were carried out with two degenerate flavors of light quarks (up and down) and with one heavier flavor, the strange quark. Several light quark masses, down to about 3 times the physical light quark mass, and six lattice spacings have been used. These enable controlled continuum and chiral extrapolations of many low energy QCD observables. We review the improved staggered formalism, emphasizing both advantages and drawbacks. In particular, we review the procedure for removing unwanted staggered species in the continuum limit. We then describe the asqtad lattice ensembles created by the MILC Collaboration. All MILC lattice ensembles are publicly available, and they have been used extensively by a number of lattice gauge theory groups. We review physics results obtained with them, and discuss the impact of these results on phenomenology. Topics include the heavy quark potential, spectrum of light hadrons, quark masses, decay constant of light and heavy-light pseudoscalar mesons, semileptonic form factors, nucleon structure, scattering lengths and more. We conclude with a brief look at highly promising future prospects.Comment: 157 pages; prepared for Reviews of Modern Physics. v2: some rewriting throughout; references update

Nucleon-Nucleon Interaction: A Typical/Concise Review

Nearly a recent century of work is divided to Nucleon-Nucleon (NN) interaction issue. We review some overall perspectives of NN interaction with a brief discussion about deuteron, general structure and symmetries of NN Lagrangian as well as equations of motion and solutions. Meanwhile, the main NN interaction models, as frameworks to build NN potentials, are reviewed concisely. We try to include and study almost all well-known potentials in a similar way, discuss more on various commonly used plain forms for two-nucleon interaction with an emphasis on the phenomenological and meson-exchange potentials as well as the constituent-quark potentials and new ones based on chiral effective field theory and working in coordinate-space mostly. The potentials are constructed in a way that fit NN scattering data, phase shifts, and are also compared in this way usually. An extra goal of this study is to start comparing various potentials forms in a unified manner. So, we also comment on the advantages and disadvantages of the models and potentials partly with reference to some relevant works and probable future studies.Comment: 85 pages, 5 figures, than the previous v3 edition, minor changes, and typos fixe

Neutral B-meson mixing from three-flavor lattice QCD: Determination of the SU(3)-breaking ratio \xi

We study SU(3)-breaking effects in the neutral B_d-\bar B_d and B_s-\bar B_s systems with unquenched N_f=2+1 lattice QCD. We calculate the relevant matrix elements on the MILC collaboration's gauge configurations with asqtad-improved staggered sea quarks. For the valence light-quarks (u, d, and s) we use the asqtad action, while for b quarks we use the Fermilab action. We obtain \xi=f_{B_s}\sqrt{B_{B_s}}/f_{B_d}\sqrt{B_{B_d}}=1.268+-0.063. We also present results for the ratio of bag parameters B_{B_s}/B_{B_d} and the ratio of CKM matrix elements |V_{td}|/|V_{ts}|. Although we focus on the calculation of \xi, the strategy and techniques described here will be employed in future extended studies of the B mixing parameters \Delta M_{d,s} and \Delta\Gamma_{d,s} in the Standard Model and beyond.Comment: 36 pages, 7 figure