京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20901号 / 理博第4353号 / 新制||理||1625(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川合 光, 教授 青木 慎也, 准教授 菅沼 秀夫 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

La physique actuelle cherche, à côté des expériences, à vérifier et déduire les lois de la nature en simulant les modèles physiques sur d'énormes ordinateurs. Cette thèse explore comment accélérer ces simulations en améliorant les programmes qui les font tourner. L'application de référence est la chromodynamique quantique sur réseaux (LQCD pour "Lattice Quantum Chromodynamics"), une branche de la théorie quantique des champs, tournant sur le plus récent des supercalculateurs d'IBM, le Blue Gene/Q.Dans un premier temps, on améliore le code source de tmLQCD, un programme de LQCD, dont l'opération clef pour la performance est un stencil à 8 points en dimension 4. On étudie deux stratégies d'optimisation différentes: la première se donne comme priorité d'améliorer la localité spatiale et temporelle; la seconde utilise le préchargement matériel de flux de données. Sur le Blue Gene/Q, la première stratégie permet d'atteindre 20% de la performance crête théorique. La seconde, avec jusqu'à 54% de la performance crête est bien meilleure mais utilise 4 fois plus de mémoire car elle stocke les résultats dans l'ordre où les utilise le stencil suivant, ce qui requiert de dupliquer des données. Les autres techniques exploitées sont la programmation directe du système de communication (appelé MUSPI chez IBM), un mécanisme allégé de gestion des threads, le préchargement explicite de certaines données (à l'aide de l'instruction dcbt) et la vectorisation manuelle (en utilisant les instructions SIMD de largeur 4; appelé QPX par IBM). Le préchargement de liste et la mémoire transactionnelle - deux nouveaux mécanismes du Blue Gene/Q - n'améliorent pas les performances.Dans un second temps, on présente la réalisation d'une extension appelé Molly au compilateur LLVM, pour optimiser automatiquement le programme, et plus précisément la distribution des données et des calculs entre les nœuds d'un cluster tel que le Blue Gene/Q. Molly représente les tableaux par des polyèdres entiers et utilise l'extension existante Polly qui représente les boucles et les instructions par des polyèdres. Partant de la spécification de la distribution des données et de l'emplacement des calculs, Molly ajoute le code qui gère les flots de données entre les nœuds de calcul. Molly peut aussi permuter l'ordre des données en mémoire. La tâche principale de Molly est d'agréger les données dans des ensembles qui sont envoyés dans le même tampon au même destinataire, pour éviter l'overhead des transferts trop petits. Nous présentons un algorithme qui minimise le nombre de transferts pour des boucles non-paramétrées, basé sur les antichaînes du flot des données. De plus, nous implémentons une heuristique qui tient compte de la manière dont le programmeur a écrit son code. Les primitives de communication asynchrone sont insérées juste après que les données soient disponibles - respectivement juste avant qu'elles soient utilisées. Une bibliothèque runtime implémente ces primitives en utilisant MPI. Molly gère la distribution pour tout code représentable dans le modèle polyédrique, mais fonctionne mieux pour du code à stencil tel LQCD. Compilé avec Molly, le code LQCD atteint 2,5% de la performance crête. L'écart de performance est surtout dû au fait que les autres optimisations ne sont pas faites, par exemple la vectorisation. Les versions futures de Molly pourraient aussi gérer efficacement les codes non à stencil et exploiter les autres optimisations qui ont rendu le code LQCD optimisé à la main si rapide. / Motivated by modern day physics which in addition to experiments also tries to verify and deduce laws of nature by simulating the state-of-the-art physical models using oversized computers, this thesis explores means of accelerating such simulations by improving the simulation programs they run. The primary focus is Lattice Quantum Chromodynamics (QCD), a branch of quantum field theory, running on IBM newest supercomputer, the Blue Gene/Q.In a first approach, the source code of tmLQCD, a Lattice QCD program, is improved to run faster on the Blue Gene machine. Its most performance-relevant operation is a 8-point stencil in 4 dimensional space. Two different optimization strategies are perused: One with the priority of improving spatial and temporal locality, and a second making use of the hardware's data stream prefetcher. On Blue Gene/Q the first strategy reaches up to 20% of the peak theoretical floating point operation performance of that machine. The second strategy with up to 54% of peak is much faster at the cost of using 4 times more memory by storing the data in the order they will be used in the next stencil operation, duplicating data where necessary.Other techniques exploited are direct programming of the messaging hardware (called MUSPI by IBM), a low-overhead work distribution mechanism for threads, explicit data prefetching of data (using dcbt instruction) and manual vectorization (using QPX; width-4 SIMD instructions). Hardware-based list prefetching and transactional memory - both distinct and novel features of the Blue Gene/Q system -- did not improve the program's performance.The second approach is the newly-written LLVM compiler extension called Molly which optimizes the program itself, specifically the distribution of data and work between the nodes of a cluster machine such as Blue Gene/Q. Molly represents arrays using integer polyhedra and uses another already existing compiler extension Polly which represents statements and loops using polyhedra. When Molly knows how data is distributed among the nodes and where statements are executed, it adds code that manages the data flow between the nodes. Molly can also permute the order of data in memory. Molly's main task is to cluster data into sets that are sent to the same target into the same buffer because single transfers involve a massive overhead. We present an algorithm that minimizes the number of transfers for unparametrized loops using anti-chains of data flows. In addition, we implement a heuristic that takes into account how the programmer wrote the code. Asynchronous communication primitives are inserted right after the data is available respectively just before it is used. A runtime library implements these primitives using MPI.Molly manages to distribute any code that is representable by the polyhedral model, but does so best for stencils codes such as Lattice QCD. Compiled using Molly, the Lattice QCD stencil reaches 2.5% of the theoretical peak performance. The performance gap is mostly because all the other optimizations are missing, such as vectorization. Future versions of Molly may also effectively handle non-stencil codes and use make use of all the optimizations that make the manually optimized Lattice QCD stencil so fast.

QCD at non-zero baryon density is expected to have a critical point where the finite temperature crossover at zero density turns into a first order phase transition. To identify this point, we use the canonical ensemble approach to scan the temperaturedensity plane through lattice QCD simulations with Wilson-type fermions. In order to scan a wide range of the phase diagram, we develop an algorithm, the ”winding number expansion method” (WNEM) to fix the numerical instability problem due to the discrete Fourier transform for calculating the projected determinant. For a given temperature, we measure the chemical potential as a function of the baryon number and look for the signal of a first order phase transition. We carry out simulations using clover fermions with mπ ≈ 800MeV on 63 × 4 lattices. As a benchmark, we run simulations for the four degenerate flavor case where we observe a clear signal of the first order phase transition. In the two flavor case we do not see any signal for temperatures as low as 0.83 Tc. To gauge the discretization errors, we also run a set of simulations using Wilson fermions and compare the results to those from the clover fermion. The three flavor case is close to realistic QCD with two light u and d quarks and one heavier s quark. Any hint of the existence of the first order phase transition and, particularly, its critical end point will be valuable for the planned relativistic heavy-ion experiments to search for such a point. In the three flavor case we found a clear signal for the first order phase transition, the critical point is located at a temperature of 0.93(2) Tc and a baryon chemical potential of 3.25(7) Tc. Since the quark mass in our present simulation is relatively heavy, we would like to repeat it with lighter quark masses and larger volumes.

Precise predictions of hadronic matrix elements in heavy meson decays are important to constrain the fundamental parameters in the Standard Model of particle physics. The CKM matrix element Vub can be extracted from experimental data on the decay B → πℓν if the hadronic form factor is known. In addition, loop suppressed rare decays of B-mesons, such as B → K∗γ and B → K(∗)ℓℓ, provide valuable insight into new physics models. Hadronic form factors for exclusive meson decays can be calculated in the framework of lattice QCD. As the wavelength of heavy quarks is not resolved on currently available lattices I use an effective nonrelativistic theory to discretise the heavy degrees of freedom. In addition, the discretisation errors in the final state meson are reduced by working in a moving frame. I review the phenomenology of rare B decays and describe how lattice QCD can contribute to calculating the relevant form factors. As the short distance physics in the effective theory is different from that of QCD, the Lagrangian and decay currents need to be renormalised. I show how this can be achieved in the framework of lattice perturbation theory. I calculate the perturbative renormalisation constants of the leading order operators in the heavy quark Lagrangian. Motivated by nonperturbative studies I extend this approach to higher order kinetic terms which break rotational invariance. In combination with simulations in the weak coupling regime of the theory, results from diagrammatic lattice perturbation theory are used to calculate the heavy quark selfenergy corrections and predict the fundamental parameters of QCD. I calculate the one loop correction on a finite lattice with twisted boundary conditions which is used for the extraction of higher order perturbative corrections. I renormalise the heavy-light current to one loop order in lattice mNRQCD and present results from nonperturbative studies. Finally, I discuss how the results are used in the calculation of hadronic form factors.

In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG). We use the two dimensional nearest neighbor Ising model to introduce many conventional yet important concepts. We then generalize the model to Dyson's hierarchical model (HM), which has rich phase properties depending on the strength of the interaction. The partition function zeros (Fisher zeros) of the HM model in the complex temperature plane is calculated and their connection with the complex RG flows is discussed. The two lattice matching method is used to construct both the complex RG flows and calculate the discrete β functions. The motivation of calculating the discrete β functions for various HM models is to test the matching method and to show how physically relevant fixed points emerge from the complex domain. We notice that the critical exponents calculated from the HM depend on the blocking parameter b. This motivated us to analyze the connection between the discrete and continuous RG transformation. We demonstrate numerical calculations of the ERG equations. We discuss the relation between Litim and Wilson-Polchinski equation and the effect of the cut-off functions in the ERG calculation. We then apply methods developed in the spin models to more complicated and more physically relevant lattice gauge theories and lattice quantum chromodynamics (QCD) like theories. Finite size scaling (FSS) technique is used to analyze the Binder cumulant of the SU(2) lattice gauge model. We calculate the critical exponent nu and omega of the model and show that it is in the same universality class as the three dimensional Ising model. Motivated by the walking technicolor theory, we study the strongly coupled gauge theories with conformal or near conformal properties. We compare the distribution of Fisher zeros for lattice gauge models with four and twelve light fermion flavors. We also briefly discuss the scaling of the zeros and its connection with the infrared fixed point (IRFP) and the mass anomalous dimension. Conventional numerical simulations suffer from the critical slowing down at the critical region, which prevents one from simulating large system. In order to reach the continuum limit in the lattice gauge theories, one needs either large volume or clever extrapolations. TRG is a new computational method that may calculate exponentially large system and works well even at the critical region. We formulate the TRG blocking procedure for the two dimensional O(2) (or XY ) and O(3) spin models and discuss possible applications and generalizations of the method to other spin and lattice gauge models. We start the thesis with the introduction and historical background of the RG in general.

The Standard Model of particle physics is believed to be only the low energy limit of a more fundamental theory. In order to determine its range of validity, a major part of theoretical and experimental efforts in physics is dedicated to precision tests of the Standard Model. Lattice QCD is a non-perturbative, first-principles approach to Quantum Field Theory. It plays an important role in flavor physics by providing calculations of non-perturbative strong interaction contributions to weak processes involving quarks. Measurements of hadronic quantities can be used to constrain the Standard Model as well as theories Beyond the Standard Model. The first part of this thesis contains theoretical developments regarding non-perturbative renormalization. A new renormalization scheme, RI/mSMOM, for fermion bilinear operators in QCD at non-vanishing quark mass is presented. In order to investigate the properties of the mSMOM scheme, an explicit one-loop computation in perturbation theory using dimensional regularization is performed. Numerically, vertex functions are generated on the lattice, with an appropriate projector, based on the RI/SMOM scheme and the renormalization factors are extracted. Quantities measured include renormalization of the axial current ZA, required to renormalize the axial current entering the computation of the decay constant and the renormalization of the bag parameter. The second part of this report focuses on flavor physics phenomenology on the lattice. It presents results of the first run of the RBC/UKQCD charm project with (2+1)-flavor Domain Wall fermions. Observables and matrix elements are measured on lattices with Iwasaki gauge action. There are two ensembles at the physical point with inverse lattice spacings 1.73 and 2.36 GeV and a third finer ensemble at 2.76 GeV as well as four other auxiliary ensembles with smaller volumes and heavier pion masses which are used to perform the continuum extrapolations. The quantities measured in the region of the charm quark mass are meson masses, decay constants, the matrix element of the OV V +AA operator, the neutral D-meson mixing parameter B and the SU(3) breaking ratio ξ.

We present comprehensive analysis of the light and strange disconnected-sea quarks contribution to the nucleon electric and magnetic form factors. The lattice QCD estimates of strange quark magnetic moment GsM (0) = −0.064(14)(09) μN and the mean squared charge radius ⟨r2s⟩E = −0.0043(16)(14) fm2 are more precise than any existing experimental measurements and other lattice calculations. The lattice QCD calculation includes ensembles across several lattice volumes and lattice spacings with one of the ensembles at the physical pion mass. We have performed a simultaneous chiral, infinite volume, and continuum extrapolation in a global fit to calculate results in the continuum limit. We find that the combined light-sea and strange quarks contribution to the nucleon magnetic moment is−0.022(11)(09) μN and to the nucleon mean square charge radius is −0.019(05)(05) fm2. The most important outcome of this lattice QCD calculation is that while the combined light-sea and strange quarks contribution to the nucleon magnetic moment is small at about 1%, a negative 2.5(9)% contribution to the proton charge radius and a relatively larger positive 16.3(6.1)% contribution to the neutron charge radius come from the sea quarks in the nucleon. For the first time, by performing global fits, we also give predictions of the light-sea and strange quarks contributions to the nucleon electric and magnetic form factors at the physical point and in the continuum and infinite volume limits in the momentum transfer range of 0 ≤ Q2 ≤ 0.5 GeV2.

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 QCD vacuum is explained using these results. The Hamiltonian formalism of lattice QCD with fermion content serves as an approach to study quark excitations out of the vacuum. The formalism is first developed and techniques to numerically evaluate the spectrum of physical particles, namely, meson and baryons are described. The Hybrid Monte Carlo technique was used to numerically extract the lowest meson and baryon masses as a function of the quark masses. It is shown that neither the lowest meson mass nor the lowest baryon mass goes to zero as the quark mass is taken to zero. This numerically establishes the presence of a mass gap in two dimensional QCD.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21568号 / 理博第4475号 / 新制||理||1642(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 青木 慎也, 教授 田中 貴浩, 准教授 髙山 史宏 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23005号 / 理博第4682号 / 新制||理||1672(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 大西 明, 准教授 菅沼 秀夫, 教授 田中 貴浩 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM