Download or read book Towards the Determination of the Spectrum of QCD Using a Space time Lattice written by Robert Edwards and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Progress by the Lattice Hadron Physics Collaboration in determining the baryon and meson resonance spectrum of QCD using Monte Carlo methods with space- time lattices is described. The extraction of excited-state energies necessitates the evaluation of correlation matrices of sets of operators, and the importance of extended three-quark operators to capture both the radial and orbital structures of baryons is emphasized. The use of both quark-field smearing and link-field smearing in the operators is essential for reducing the couplings of the operators to the high-frequency modes and for reducing statistical noise in the correlators. The extraction of nine energy levels in a given symmetry channel is demonstrated, and identifying the continuum spin quantum numbers of the levels is discussed.

Download or read book Exploring the Spectrum of QCD Using the Lattice written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The calculation of the spectrum of QCD is key to an understanding of the strong interactions, and vital if we are to capitalize on the experimental study of the spectrum. In this paper, we describe progress towards understanding the spectrum of resonances of both mesons and baryons from lattice QCD, focusing in particular on the resonances of the $I=1/2$ nucleon states, and of charmonium mesons composed of the heavy charmed quarks.

Download or read book Lattice Gauge Theory QCD from Quarks to Hadrons written by and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Lattice Gauge Theory enables an ab initio study of the low-energy properties of Quantum Chromodynamics, the theory of the strong interaction. The author begins these lectures by presenting the lattice formulation of QCD, and then outline the benchmark calculation of lattice QCD, the light-hadron spectrum. He then proceeds to explore the predictive power of lattice QCD, in particular as it pertains to hadronic physics. He discusses the spectrum of glueballs, exotics and excited states, before investigating the study of form factors and structure functions. He concludes by showing how lattice QCD can be used to study multi-hadron systems, and in particular provide insight into the nucleon-nucleon interaction.

Download or read book QCD Spectrum from the Lattice written by and published by . This book was released on 1989 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considerable progress has been made in the last year to derive the spectrum from QCD in the quenched approximation. I review the results for the proton to rho mass ratio and show that we are close to getting results to within 10%. I present new results for 0{sup ++} and 2{sup ++} glueballs. These results are qualitative since we do not address the question of mixing of glueballs with quark states. Finally, I give a status report on the full QCD calculations (2 flavors of dynamical Wilson fermions) being done on the Connection Machine 2. 12 refs., 3 figs.

Download or read book The Excited State Spectrum of QCD written by and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The determination of the highly excited state spectrum of baryons within QCD is a major theoretical and experimental challenge. I will present recent results from lattice QCD that give some indications on the structure of these highly excited states, and outline on-going and future work needed for a full determination of the spectrum, including strong decays.

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.

Download or read book Weak Transitions in Lattice QCD written by Guillermo Maturana and published by . This book was released on 1984 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Flavor Dependence of the Hadron Spectrum in Lattice QCD written by Dong Cheng and published by . This book was released on 1996 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Hadronic Resonances from Lattice QCD written by and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The determination of the pattern of hadronic resonances as predicted by Quantum Chromodynamics requires the use of non-perturbative techniques. Lattice QCD has emerged as the dominant tool for such calculations, and has produced many QCD predictions which can be directly compared to experiment. The concepts underlying lattice QCD are outlined, methods for calculating excited states are discussed, and results from an exploratory Nucleon and Delta baryon spectrum study are presented.

Download or read book An Analysis of the Hadronic Spectrum from Lattice QCD written by W. Armour and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Light Front Holographic QCD written by and published by . This book was released on 2012 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: The relation between the hadronic short-distance constituent quark and gluon particle limit and the long-range confining domain is yet one of the most challenging aspects of particle physics due to the strong coupling nature of Quantum Chromodynamics, the fundamental theory of the strong interactions. The central question is how one can compute hadronic properties from first principles; i.e., directly from the QCD Lagrangian. The most successful theoretical approach thus far has been to quantize QCD on discrete lattices in Euclidean space-time. Lattice numerical results follow from computation of frame-dependent moments of distributions in Euclidean space and dynamical observables in Minkowski spacetime, such as the time-like hadronic form factors, are not amenable to Euclidean lattice computations. The Dyson-Schwinger methods have led to many important insights, such as the infrared fixed point behavior of the strong coupling constant, but in practice, the analyses are limited to ladder approximation in Landau gauge. Baryon spectroscopy and the excitation dynamics of nucleon resonances encoded in the nucleon transition form factors can provide fundamental insight into the strong-coupling dynamics of QCD. New theoretical tools are thus of primary interest for the interpretation of the results expected at the new mass scale and kinematic regions accessible to the JLab 12 GeV Upgrade Project. The AdS/CFT correspondence between gravity or string theory on a higher-dimensional anti-de Sitter (AdS) space and conformal field theories in physical space-time has led to a semiclassical approximation for strongly-coupled QCD, which provides physical insights into its nonperturbative dynamics. The correspondence is holographic in the sense that it determines a duality between theories in different number of space-time dimensions. This geometric approach leads in fact to a simple analytical and phenomenologically compelling nonperturbative approximation to the full light-front QCD Hamiltonian 'Light-Front Holography'. Light-Front Holography is in fact one of the most remarkable features of the AdS/CFT correspondence. The Hamiltonian equation of motion in the light-front (LF) is frame independent and has a structure similar to eigenmode equations in AdS space. This makes a direct connection of QCD with AdS/CFT methods possible. Remarkably, the AdS equations correspond to the kinetic energy terms of the partons inside a hadron, whereas the interaction terms build confinement and correspond to the truncation of AdS space in an effective dual gravity approximation. One can also study the gauge/gravity duality starting from the bound-state structure of hadrons in QCD quantized in the light-front. The LF Lorentz-invariant Hamiltonian equation for the relativistic bound-state system is P{sub {mu}}P{sup {mu}}

Download or read book Lattice QCD Determination of States with Spin 5 written by and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Energies for excited isospin 1/2 states that include the nucleon are computed using quenched, anisotropic lattices. Baryon interpolating field operators that are used include nonlocal operators that provide G2 irreducible representations of the octahedral group. States with spin 5/2 or higher are identified as degenerate energies that occur in irreducible representations of the octahedral group corresponding to the subduction of the continuum spin.

Download or read book Lattice QCD at the Physical Point written by Thibaut Métivet and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The formalism of Quantum Chromodynamics on the lattice (or Lattice QCD) allows to perform ab-initio non-perturbative studies of strong-interaction driven processes, as it provides both a covariant regularisation of the theory of QCD and a natural framework for numerical computations. In this work, after a review of the main features of QCD and a step-by-step presentation of our discretization of QCD on a lattice, we undertake detailed studies of two problems of hadronic physics: the phenomenon of resonant scattering and the structure of the nucleon. The lattice calculations are performed with the Budapest-Marseille-Wuppertal Collaboration's 2+1-flavour gauge configurations, which give access to a wide range of lattice spacings, volumes and quarks masses, thereby allowing to study the sensibility of our results on these parameters, and to perform a complete continuum extrapolation. These configurations include dynamical quarks, and use a clover-improved Wilson QCD action. To investigate the scattering of particles on the lattice, we set up a Lüscher analysis for the emblematic case of pion-pion scattering in the channel of the rho meson resonance. We analyse our data with a variational generalized eigenvalue method, and give an in-depth calculation of the scattering phase-shifts and the corresponding resonance parameters, with a full control of the systematic errors. Our results provide an important step for lattice studies of scattering states, as they are the first to be performed at the physical pion mass, where one can see the actual decay of the rho into two pions. The obtained rho meson parameters are in good agreement with the experimental values, and consistent with a weak pion mass dependence of the coupling between the rho and two pions. As for our probe of the structure of the nucleon, we present a complete extraction of the electroweak isovector form factors, with a comprehensive study of the electric charge squared radius and of the axial charge. Our analysis also feature data at the physical pion mass, which turns out to be crucial in order to perform safe extrapolations to the physical point, as the chiral perturbation theory predicts violent variations of these quantities near the massless-quarks point. Our calculation includes source and sink projections onto the nucleon state, as well as a combined fit method between the two-point and three-point correlation functions to control the contamination of our data by excited states. Although one would need more data to perform a high-accuracy determination of the nucleon radius and axial charge at the physical point with a relevant estimation of the systematic errors, the results we obtain are in good agreement with the experiment and suggest that the excited-state effects are under control. Our analysis also highlights that gauge configurations ensembles near the physical pion mass and with large volumes must be used in order to extract accurate information about the nucleon structure from lattice calculations.

Download or read book Light Hadron Spectrum from Lattice QCD Simulations with 2 1 Flavours written by Robert John Tweedie and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Finite Size Effects on the QCD Spectrum Revisited written by and published by . This book was released on 1992 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: We have continued our study of finite size effects in the QCD spectrum on lattices ranging in size from 8[sup 3][times]24 to 16[sup 3][times]24. We have increased our statistics for quark mass am[sub q]=0.025 for the smallest lattice size. In addition, we have studied quark mass 0.01225 for lattice sizes 12[sup 3][times]24. These lattice sizes correspond to a box 1.8-3.6 fm on a side when the rho mass at zero quark mass is used to set the scale. We discuss the nucleon to rho mass ratio at a smaller value of m[pi]/m[rho] than previously studied with two dynamical flavors.

Download or read book Light Hadron Spectrum from Lattice QCD Simulations with 2 1 Flavours written by Robert John Tweedie and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: