Uncertainty Quantification in Lattice QCD Calculations for Nuclear Physics PDF Download
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Author:
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Languages : en
Pages :
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Book Description
The numerical technique of Lattice QCD holds the promise of connecting the nuclear forces, nuclei, the spectrum and structure of hadrons, and the properties of matter under extreme conditions with the underlying theory of the strong interactions, quantum chromodynamics. A distinguishing, and thus far unique, feature of this formulation is that all of the associated uncertainties, both statistical and systematic can, in principle, be systematically reduced to any desired precision with sufficient computational and human resources. As a result, we review the sources of uncertainty inherent in Lattice QCD calculations for nuclear physics, and discuss how each is quantified in current efforts.
Author:
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Languages : en
Pages :
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Book Description
The numerical technique of Lattice QCD holds the promise of connecting the nuclear forces, nuclei, the spectrum and structure of hadrons, and the properties of matter under extreme conditions with the underlying theory of the strong interactions, quantum chromodynamics. A distinguishing, and thus far unique, feature of this formulation is that all of the associated uncertainties, both statistical and systematic can, in principle, be systematically reduced to any desired precision with sufficient computational and human resources. As a result, we review the sources of uncertainty inherent in Lattice QCD calculations for nuclear physics, and discuss how each is quantified in current efforts.
Author: Maria Piarulli
Publisher: Frontiers Media SA
ISBN: 2832532098
Category : Science
Languages : en
Pages : 233
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Book Description
Author: Huey-Wen Lin
Publisher: Springer
ISBN: 9783319080239
Category : Science
Languages : en
Pages : 244
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Book Description
With ever increasing computational resources and improvements in algorithms, new opportunities are emerging for lattice gauge theory to address key questions in strongly interacting systems, such as nuclear matter. Calculations today use dynamical gauge-field ensembles with degenerate light up/down quarks and the strange quark and it is possible now to consider including charm-quark degrees of freedom in the QCD vacuum. Pion masses and other sources of systematic error, such as finite-volume and discretization effects, are beginning to be quantified systematically. Altogether, an era of precision calculation has begun and many new observables will be calculated at the new computational facilities. The aim of this set of lectures is to provide graduate students with a grounding in the application of lattice gauge theory methods to strongly interacting systems and in particular to nuclear physics. A wide variety of topics are covered, including continuum field theory, lattice discretizations, hadron spectroscopy and structure, many-body systems, together with more topical lectures in nuclear physics aimed a providing a broad phenomenological background. Exercises to encourage hands-on experience with parallel computing and data analysis are included.
Author: Anthony M Green
Publisher: World Scientific
ISBN: 9814481920
Category : Science
Languages : en
Pages : 385
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Book Description
Particle and nuclear physicists frequently take results from Lattice QCD at their face value without probing into their reliability or sophistication. This attitude usually stems from a lack of knowledge of the field. The aim of the present volume is to rectify this by introducing in an elementary way several topics, which we believe are appropriate for, and of possible interest to, both particle and nuclear physicists who are non-experts in the field.
Author: Xiang-Qian Luo
Publisher: World Scientific
ISBN: 9812811370
Category : Science
Languages : en
Pages : 320
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Book Description
Lattice field theory is the most reliable tool for investigating non-perturbative phenomena in particle physics. It has also become a cross-discipline, overlapping with other physical sciences and computer science. This book covers new developments in the area of algorithms, statistical physics, parallel computers and quantum computation, as well as recent advances concerning the standard model and beyond, the QCD vacuum, the glueball, hadron and quark masses, finite temperature and density, chiral fermions, SUSY, and heavy quark effective theory.
Author: Laurent Lellouch
Publisher: OUP Oxford
ISBN: 0191621269
Category : Science
Languages : en
Pages : 760
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Book Description
The book is based on the lectures delivered at the XCIII Session of the École de Physique des Houches, held in August, 2009. The aim of the event was to familiarize the new generation of PhD students and postdoctoral fellows with the principles and methods of modern lattice field theory, which aims to resolve fundamental, non-perturbative questions about QCD without uncontrolled approximations. The emphasis of the book is on the theoretical developments that have shaped the field in the last two decades and that have turned lattice gauge theory into a robust approach to the determination of low energy hadronic quantities and of fundamental parameters of the Standard Model. By way of introduction, the lectures begin by covering lattice theory basics, lattice renormalization and improvement, and the many faces of chirality. A later course introduces QCD at finite temperature and density. A broad view of lattice computation from the basics to recent developments was offered in a corresponding course. Extrapolations to physical quark masses and a framework for the parameterization of the low-energy physics by means of effective coupling constants is covered in a lecture on chiral perturbation theory. Heavy-quark effective theories, an essential tool for performing the relevant lattice calculations, is covered from its basics to recent advances. A number of shorter courses round out the book and broaden its purview. These included recent applications to the nucleon—nucleon interation and a course on physics beyond the Standard Model.
Author: Yoshinobu Kuramashi
Publisher: World Scientific
ISBN: 9814477206
Category : Science
Languages : en
Pages : 323
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Book Description
This book consists of a series of lectures to cover every facet of the modern version of lattice QCD. All the lectures are self-contained starting with the necessary background material and ending up with the latest development. Most of the lectures are given by pioneers in the field.This book may be useful as an advanced textbook for graduate students in particle physics and its modern and fascinating contents will inspire the interest of the non-experts.
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Languages : en
Pages :
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Book Description
Lattice gauge theory provides our only means of performing \textit{ab initio} calculations in the non-perturbative regime. It has thus become an increasing important component of the Jefferson Laboratory physics program. In this paper, we describe the contributions of lattice QCD to our understanding of hadronic and nuclear physics, focusing on the structure of hadrons, the calculation of the spectrum and properties of resonances, and finally on deriving an understanding of the QCD origin of nuclear forces.
Author: Yoshinobu Kuramashi
Publisher: World Scientific
ISBN: 9812790926
Category : Science
Languages : en
Pages : 323
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Book Description
This novel book introduces cellular automata from a rigorous nonlinear dynamics perspective. It supplies the missing link between nonlinear differential and difference equations to discrete symbolic analysis. The book provides a scientifically sound and original analysis, and classifications of the empirical results presented in Wolfram's monumental "New Kind of Science."
Author: Raúl A. Briceño
Publisher:
ISBN:
Category : Lattice field theory
Languages : en
Pages : 169
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Book Description
One of the overarching goals of nuclear physics is to rigorously compute properties of hadronic systems directly from the fundamental theory of the strong interaction, Quantum Chromodynamics (QCD). In particular, the hope is to perform reliable calculations of nuclear processes which would impact our understanding of environments ranging from big bang nucleosynthesis, stars and supernovae, to nuclear reactors and high-energy density facilities. Such calculations, being truly ab-initio, would include all two-nucleon and three-nucleon (and higher) interactions in a consistent manner. Currently, lattice QCD (LQCD) provides the only reliable option for performing calculations of low-energy hadronic observables. LQCD calculations are necessarily performed in a finite Euclidean spacetime. As a result, it is necessary to construct formalism that maps the finite-volume observables determined via LQCD to the infinite-volume quantities of interest. For 2 --> 2 bosonic elastic scattering processes, Martin Luscher first showed that one can obtain the physical scattering phase shifts from the finite volume (FV) two-particle spectrum (for lattices with spatial extents that are much larger than the range of interactions). This thesis discusses the extension of this formalism for three important classes of systems. Chapter 1 discusses key aspects of the standard model, paying close attention to QCD at low-energies and the necessity of effective field theories (EFTs) and LQCD. Chapter 2 reviews the result by Luscher for two bosons with arbitrary momentum. After a detailed derivation of the quantization condition for two bosons below the inelastic threshold, it is straightforward to determine the spectrum of a system with arbitrary number of channels composed of two hadrons with nonzero total momentum. In Section 2.3, Luscher's result is re-derived using the auxilary field formalism, also known as the "dimer formalism". Chapter 3 briefly reviews the complexity of the nuclear sector, as compared to the scalar sector, and it shown that this rich structure can be recovered by the generalization of the auxilary field formalism for the two nucleon system. Using this formalism, the quantization condition for two non-relativistic nucleons1 in a finite volume is derived. The result presented hold for a two nucleon system with arbitrary partial-waves, spin and parity. Provided are the explicit relations among scattering parameters and their corresponding point group symmetry class eigenenergies with orbital angular momentum l [less than or equal to] 4. Finally, Chapter 4 presents the quantization condition for the spectrum of three identical bosons in a finite volume. Unlike the two-body analogue, the quantization condition of the three-body sector is not algebraic and in general requires numerically solving an integral equation. However, for systems with an attractive two-body force that supports a twobody bound-state, a diboson, and for energies below the diboson breakup, the quantization condition reduces to the well-known Luscher formula with exponential corrections in volume that scale with the diboson binding momentum. To accurately determine infinite volume phase shifts, it is necessary to extrapolate the phase shifts obtained from the Luscher formula for the boson-diboson system to the infinite volume limit. For energies above the breakup threshold, or for systems with no two-body bound-state (with only scattering states and resonances) the Luscher formula gets power-law volume corrections and consequently fails to describe the three-particle system. These corrections are nonperturbatively included in the quantization condition presented.
