On the Extraction of Observables from Lattice QCD and the First Lattice Calculation of Nuclear Parity Violation PDF Download
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Author: Joseph Wasem
Publisher:
ISBN:
Category : Quantum chromodynamics
Languages : en
Pages : 137
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Author: Joseph Wasem
Publisher:
ISBN:
Category : Quantum chromodynamics
Languages : en
Pages : 137
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Book Description
Author: Huey-Wen Lin
Publisher: Springer
ISBN: 3319080229
Category : Science
Languages : en
Pages : 255
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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: 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.
Author: Mohammad W Ahmed
Publisher: World Scientific
ISBN: 9814475882
Category : Science
Languages : en
Pages : 477
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Book Description
Chiral Dynamics 2006 is the 5th International Workshop which examines the implications and the development of an approximate low-energy solution to the QCD Lagrangian based upon Chiral Symmetry. Advances in theory and experiment are presented in 20 plenary session papers along with more than one-hundred papers, including summaries, from the three working groups.
Author: Dorin Poenaru
Publisher: World Scientific
ISBN: 9814542989
Category : Science
Languages : en
Pages : 450
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Book Description
The interest in understanding the physical world that we live in, the origin of its formation and evolution, is reflected in the world-wide activities in Europe, the USA and Japan to set up powerful research facilities providing beams of radioactive nuclei of various kinds, and beams of extremely large energies. At the same time, complex and large detector arrays with improved technical capabilities are built either around these facilities or independently (dedicated to cosmic rays). Recently, spectacular progress has been made in superheavy nuclei, cold binary and ternary fission, nuclear shell structure and nuclear astrophysics, to mention only a few directions. The energy spectrum of cosmic rays exceeds the upper limits provided by artificial accelerators. An international collaboration has committed itself to the installation of an extremely large area detector array, AUGER, in order to study the highest particle energies in the Universe.
Author: Bojan Bistrović
Publisher:
ISBN:
Category :
Languages : en
Pages : 546
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Book Description
Deep inelastic scattering unambiguously measures hadron observables characterizing the quark-gluon structure of hadrons. The only way to calculate these observables from first principles is lattice QCD. Experiments measure matrix elements of light cone operators ... where diagonal elements specify the quark density distribution q(x), quark helicity distribution [delta] q(x) and quark transversity distribution [delta] q(x). Off-diagonal elements determine form factors and general parton distributions. Due to the Minkowskian nature of these matrix elements, they cannot be evaluated on a Euclidean lattice so one uses the operator product expansion to calculate matrix elements ... which specify moments of these distributions. In this thesis, renormalization factors have been calculated for local bilinear operators of the form ... in a given irreducible representation of hypercubic group as well as mixing coefficients of those operators for low moments of physical interest. In the past, it was only possible to calculate with quark masses such that ... Now for the first time using Ginsparg-Wilson "Domain Wall" fermions with HYP smearing and full QCD configurations on large lattices make calculations possible in the physical chiral regime.
Author: Zohreh Davoudi
Publisher:
ISBN:
Category :
Languages : en
Pages : 245
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Book Description
In order to make reliable predictions with controlled uncertainties for a wide range of nuclear phenomena, a theoretical bottom-up approach, by which hadrons emerge from the underlying theory of strong interactions, quantum chromodynamics (QCD), is desired. The strongly interacting quarks and gluons at low energies are responsible for all the dynamics of nucleons and their clusters, the nuclei. The theoretical framework and the combination of analytical and numerical tools used to carry out a rigorous non-perturbative study of these systems from QCD is called lattice QCD. The result of a lattice QCD calculation corresponds to that of nature only in the limit when the volume of the spacetime is taken to infinity and the spacing between discretized points on the lattice is taken to zero. A better understanding of these discretization and volume effects, not only provides the connection to the infinite-volume continuum observables, but also leads to optimized calculations that can be performed with available computational resources. This thesis includes various formal developments in this direction, along with proposals for novel improvements, to be used in the upcoming LQCD studies of nuclear and hadronic systems. As the space(time) is discretized on a (hyper)cubic lattice in (most of) lattice QCD calculations, the lattice correlation functions are not fully rotationally invariant. This is known to lead to mixing between operators (those interpolating the states or inserting external currents) of higher dimensions with those of lower dimensions where the coefficients of latter diverge with powers of inverse lattice spacing, a, as the continuum limit is approached. This issue has long posed computational challenges in lattice spectroscopy of higher spin states, as well as in the lattice extractions of higher moments of hadron structure functions. We have shown, through analytical perturbative investigations of field theories, including QCD, on the lattice that a novel choice of operators, smeared over several lattice sites and deduced from a continuum angular momentum, has a smooth continuum limit. The scaling of the lower dimensional operators is proven to be no worse than a squared, explaining the success of recent numerical studies of excited state spectroscopy of hadrons with similar choices of operators. These results are presented in chapter 2 of this thesis. Due to Euclidean nature of lattice correlation function, the physical scattering parameters must be obtained via an analytical continuation to Minkowski spacetime. However, this continuation is practically impossible in the infinite-volume limit of lattice correlation function except at the kinematic thresholds. A formalism due to Luscher overcomes this issue by making the connection between the finite-volume spectrum of two interacting particles and their infinite-volume scattering phase shifts. We have extended the Luscher methodology, using an effective field theory approach, to the two-nucleon systems with arbitrary spin, parity and total momentum (in the limit of exact isospin symmetry) and have studied its application to the deuteron system, the lightest bound states of the nucleons, by careful analysis of the finite-volume symmetries. A proposal is presented that enables future precision lattice QCD extraction of the small D/S ratio of the deuteron that is known to be due to the action of non-central forces. By investigating another scenario, we show how significant volume improvement can be achieved in the masses of nucleons and in the binding energy of the deuteron with certain choices of boundary conditions in a lattice QCD calculation of these quantities. These results are discussed in chapters 3, 4 and 5. In order to account for electromagnetic effects in hadronic systems, lattice QCD calculations have started to include quantum electrodynamic (QED). These effects are particularly interesting in studies of mass splittings between charged and neutral members of isospin multiplets, e.g. neutral and charged pions. Due to the infinite range of QED interactions large volume effects plaque these studies. Using a non-relativistic effective theory for electromagnetic interactions of hadrons, we analytically calculate, and numerically estimate, the first few finite-volume corrections (up to 1 over L to the 4th power where L is the spatial extent of the volume) to the masses of hadrons and nuclei at leading order in the QED coupling constant, but to all orders in the short-distance strong interaction effects. These results are presented in chapter 6.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Deep inelastic scattering unambiguously measures hadron observables characterizing the quark-gluon structure of hadrons. The only way to calculate these observables from first principles is lattice QCD. Experiments measure matrix elements of light cone operators ... where diagonal elements specify the quark density distribution q(x), quark helicity distribution [delta] q(x) and quark transversity distribution [delta] q(x). Off-diagonal elements determine form factors and general parton distributions. Due to the Minkowskian nature of these matrix elements, they cannot be evaluated on a Euclidean lattice so one uses the operator product expansion to calculate matrix elements ... which specify moments of these distributions. In this thesis, renormalization factors have been calculated for local bilinear operators of the form ... in a given irreducible representation of hypercubic group as well as mixing coefficients of those operators for low moments of physical interest. In the past, it was only possible to calculate with quark masses such that ... Now for the first time using Ginsparg-Wilson "Domain Wall" fermions with HYP smearing and full QCD configurations on large lattices make calculations possible in the physical chiral regime.
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.
Author: Arjun Singh Gambhir
Publisher:
ISBN:
Category : Lattice field theory
Languages : en
Pages : 168
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Book Description
In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called "disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements of the nucleon at two different values of the lattice spacing. Finally, we employ these algorithms to do a high-precision study of strange sigma terms in light nuclei; to our knowledge this is the first calculation of its kind from Lattice QCD.
