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On The Extraction Of Observables From Lattice Qcd And The First Lattice Calculation Of Nuclear Parity Violation
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Book Synopsis On the Extraction of Observables from Lattice QCD and the First Lattice Calculation of Nuclear Parity Violation by : Joseph Wasem
Download or read book On the Extraction of Observables from Lattice QCD and the First Lattice Calculation of Nuclear Parity Violation written by Joseph Wasem and published by . This book was released on 2010 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lattice QCD for Nuclear Physics by : Huey-Wen Lin
Download or read book Lattice QCD for Nuclear Physics written by Huey-Wen Lin and published by Springer. This book was released on 2014-11-21 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis On the Determination of Elastic and Inelastic Nuclear Observables from Lattice QCD by : Raúl A. Briceño
Download or read book On the Determination of Elastic and Inelastic Nuclear Observables from Lattice QCD written by Raúl A. Briceño and published by . This book was released on 2013 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Chiral Dynamics 2006 - Proceedings Of The 5th International Workshop On Chiral Dynamics, Theory And Experiment by : Mohammad W Ahmed
Download or read book Chiral Dynamics 2006 - Proceedings Of The 5th International Workshop On Chiral Dynamics, Theory And Experiment written by Mohammad W Ahmed and published by World Scientific. This book was released on 2007-10-18 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Advances In Nuclear Physics - Proceedings Of The International Symposium by : Dorin Poenaru
Download or read book Advances In Nuclear Physics - Proceedings Of The International Symposium written by Dorin Poenaru and published by World Scientific. This book was released on 2000-06-27 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Formal Developments for Lattice QCD with Applications to Hadronic Systems by : Zohreh Davoudi
Download or read book Formal Developments for Lattice QCD with Applications to Hadronic Systems written by Zohreh Davoudi and published by . This book was released on 2014 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Perturbative Renormalization of Proton Observables in Lattice QCD Using Domain Wall Fermions by : Bojan Bistrović
Download or read book Perturbative Renormalization of Proton Observables in Lattice QCD Using Domain Wall Fermions written by Bojan Bistrović and published by . This book was released on 2005 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Perturbative Renormalization of Proton Observables in Lattice QCD Using Domain Wall Fermions by :
Download or read book Perturbative Renormalization of Proton Observables in Lattice QCD Using Domain Wall Fermions written by and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Perspectives In Lattice Qcd - Proceedings Of The Workshop by : Yoshinobu Kuramashi
Download or read book Perspectives In Lattice Qcd - Proceedings Of The Workshop written by Yoshinobu Kuramashi and published by World Scientific. This book was released on 2007-12-13 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Disconnected Diagrams in Lattice QCD by : Arjun Singh Gambhir
Download or read book Disconnected Diagrams in Lattice QCD written by Arjun Singh Gambhir and published by . This book was released on 2017 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lattice QCD Studies of Observables Extracted from the Hadronic Vacuum Polarization by : Hanno Horch
Download or read book Lattice QCD Studies of Observables Extracted from the Hadronic Vacuum Polarization written by Hanno Horch and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Advances to Three-particle Quantization Conditions by : Tyler Davis Blanton
Download or read book Advances to Three-particle Quantization Conditions written by Tyler Davis Blanton and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The strong nuclear force is responsible for the vast majority of particles in nature; hundreds of hadrons with distinct masses and quantum numbers have been detected, and experimentalists are constantly searching for new hadron resonances and analyzing resonance decays to test the predictions of the Standard Model (e.g.~by measuring the value of a CP-violating phase).While the formalism of quantum chromodynamics (QCD) appears to accurately describe the strong interaction, using it to extract theoretical predictions of hadronic properties has proven exceedingly difficult due to the nonperturbative nature of low-energy QCD. Lattice QCD (LQCD) is the state-of-the-art approach for computing physical observables using first-principles QCD, utilizing stochastic techniques to estimate the path-integral expressions for correlation functions in a latticized Euclidean spacetime. With the computational and algorithmic advances over the past few decades, LQCD can now be used to calculate many observables (e.g.~hadron masses) to percent-level precision. However, LQCD simulations cannot directly calculate scattering amplitudes, due to both the necessary use of a finite volume and the need to analytically continue from Euclidean to Minkowski space, and thus a separate formalism is required. To bridge the gap between LQCD results and hadron spectroscopy, one needs some form of quantization condition (QC): a mathematical relation used to extract physical scattering amplitudes of light hadrons from finite-volume energy spectra calculated with LQCD. In this thesis, we present several theoretical and practical developments in the field of three-particle QCs (QC3s). We derive three significant advances to the theoretical formalism of QC3s within a generic relativistic effective field theory (RFT) framework. First, we perform an alternative derivation of the original QC3 for three identical scalars by using time-ordered perturbation theory (TOPT), which we find significantly simplifies the argument and thus renders the TOPT approach more amenable to generalization. We then demonstrate this point by using TOPT to derive a QC3 for the more complicated case of three nondegenerate scalars. Lastly, we use results from the TOPT approach to demonstrate the equivalence between the RFT QC3 for identical scalars and that of the finite-volume unitarity (FVU) approach. We also present three numerical applications of QC3s to systems of three identical scalars.We detail the first QC3 study to include levels in nontrivial irreducible representations (irreps) of the cubic group and with nonzero d-wave two-particle interactions. Next, we perform an exploratory investigation of bound states and resonances by solving two- and three-particle QCs in various scenarios. Finally, we present the first ever extraction of 3pi+ scattering information from LQCD data.
Book Synopsis Non-perturbative Methods and Lattice QCD by : Xiang-Qian Luo
Download or read book Non-perturbative Methods and Lattice QCD written by Xiang-Qian Luo and published by World Scientific. This book was released on 2001 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Calculation of the Axial Charge of a Heavy Nucleon in Lattice QCD by : Dimitra Anastasia Pefkou
Download or read book Calculation of the Axial Charge of a Heavy Nucleon in Lattice QCD written by Dimitra Anastasia Pefkou and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we aim to calculate the non-renormalized axial charge gA of a heavy nucleon made out of quarks at the physical mass of the strange quark. We present the framework of Lattice QCD which makes the calculation of such observables attainable from first principles. The data used for the estimation of gA were obtained on a 243 x64 hypercubic lattice with lattice spacing a ~ 0.12 fm and pion mass m[pi] = 0.450 GeV. Three different source-sink seperations were used, tsink = [12a, 14a, 16a]. For each timeslice seperation signal we perform a correlated x2 fit and obtain the following values for gA: 0.551, 0.564 and 0.556. The unrenormalized value value for gA is extracted taking the limit as tsink --> [infinity] and is shown to be gA = 0.558. We discuss how the accuracy of this result is compromised by the small number of tsink values, by excited state contamination and by the increase of statistical noise with time.
Book Synopsis Extraction of Parton Distributions from Lattice QCD. by :
Download or read book Extraction of Parton Distributions from Lattice QCD. written by and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We review the calculation of moments of both the polarized and unpolarized parton distribution functions of the nucleon in lattice QCD, and in particular their extrapolation to the physical region. We also discuss the reconstruction of the x dependence of the valence quark distributions in the nucleon from a finite number of lattice moments.
Book Synopsis Testing QCD Through Spin Observables in Nuclear Targets by : Don G. Crabb
Download or read book Testing QCD Through Spin Observables in Nuclear Targets written by Don G. Crabb and published by World Scientific. This book was released on 2003 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the invited talks and contributed papers presented at the workshop on ?Testing QCD Through Spin Observables in Nuclear Targets?, held at the University of Virginia in April 2002.The workshop was proposed in the context of the large number of experiments that have used polarized deuterons or polarized 3He to extract information about the spin parameters of the neutron. The motivation for this workshop was to study the effects of the nuclear medium on the spin properties of the bound nucleon and to explore issues in QCD that might be resolved through spin observables in nuclear targets: What is the effect of the nuclear medium on the measured asymmetries? How have the latest results on the spin structure of the nucleon and the nucleon form factors changed our thinking? What advances are anticipated in the development of polarized targets?
Book Synopsis Quark Mass Dependence of Nucleon Observables and Lattice QCD by : Massimiliano Procura
Download or read book Quark Mass Dependence of Nucleon Observables and Lattice QCD written by Massimiliano Procura and published by . This book was released on 2005 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt:
