Charged Multi-hadron Systems in Lattice QCD + QED PDF Download

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Languages : en
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Lattice QCD is currently entering the stage when it can usefully be applied to systems of multiple hadrons. I briefly review the status of recent calculations of scattering parameters in the two hadron sector and discuss recent calculations of systems composed of many mesons or baryons. In the mesonic case, the NPLQCD collaboration has continued its study of systems of up to twelve pions or kaons and have computed the effect of such a hadronic medium on the static quark potential. High statistics calculations on anisotropic lattices have allowed for precision extraction of the energies and scattering phase shifts of various two baryon systems and, for the first time, the energies of certain three baryon systems have been computed.

Author: Zohreh Davoudi
Publisher:
ISBN:
Category :
Languages : en
Pages : 245

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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: Ulf-G Meißner
Publisher: Cambridge University Press
ISBN: 1108476988
Category : Science
Languages : en
Pages : 625

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A detailed and comprehensive exploration of the foundations and fundamentals of effective field theories.

Author: Anthony M. Green
Publisher: World Scientific
ISBN: 9812701389
Category : Science
Languages : en
Pages : 385

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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.

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Languages : en
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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.

Author: Petrus Pennanen
Publisher:
ISBN: 9789514579653
Category :
Languages : en
Pages : 83

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Languages : en
Pages : 8

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Nuclear physics entails the study of the properties and interactions of hadrons, such as the proton and neutron, and atomic nuclei and it is central to our understanding of our world at the smallest scales. The underlying basis for nuclear physics is provided by the Standard Model of particle physics which describes how matter interacts through the strong, electromagnetic and weak (electroweak) forces. This theory was developed in the 1970s and provides an extremely successful description of our world at the most fundamental level to which it has been probed. The Standard Model has been, and continues to be, subject to stringent tests at particle accelerators around the world, so far passing without blemish. However, at the relatively low energies that are relevant for nuclear physics, calculations involving the strong interaction, governed by the equations of Quantum Chromodynamics (QCD), are enormously challenging, and to date, the only systematic way to perform them is numerically, using a framework known as lattice QCD (LQCD). In this approach, one discretizes space-time and numerically solves the equations of QCD on a space-time lattice; for realistic calculations, this requires highly optimized algorithms and cutting-edge high performance computing (HPC) resources. Progress over the project period is discussed in detail in the following subsections.

Author: Maxwell T. Hansen
Publisher:
ISBN:
Category :
Languages : en
Pages : 247

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We describe formal work that relates the finite-volume spectrum in a quantum field theory to scattering and decay amplitudes. This is of particular relevance to numerical calculations performed using Lattice Quantum Chromodynamics (LQCD). Correlators calculated using LQCD can only be determined on the Euclidean time axis. For this reason the standard method of determining scattering amplitudes via the Lehmann-Symanzik-Zimmermann reduction formula cannot be employed. By contrast, the finite-volume spectrum is directly accessible in LQCD calculations. Formalism for relating the spectrum to physical scattering observables is thus highly desirable. In this thesis we develop tools for extracting physical information from LQCD for four types of observables. First we analyze systems with multiple, strongly-coupled two-scalar channels. Here we accommodate both identical and nonidentical scalars, and in the latter case allow for degenerate as well as nondegenerate particle masses. Using relativistic field theory, and summing to all orders in perturbation theory, we derive a result relating the finite-volume spectrum to the two-to-two scattering amplitudes of the coupled-channel theory. This generalizes the formalism of Martin Luescher for the case of single-channel scattering. Second we consider the weak decay of a single particle into multiple, coupled two-scalar channels. We show how the finite-volume matrix element extracted in LQCD is related to matrix elements of asymptotic two-particle states, and thus to decay amplitudes. This generalizes work by Laurent Lellouch and Martin Luescher. Third we extend the method for extracting matrix elements by considering currents which insert energy, momentum and angular momentum. This allows one to extract transition matrix elements and form factors from LQCD. Finally we look beyond two-particle systems to those with three-particles in asymptotic states. Working again to all orders in relativistic field theory, we derive a relation between the spectrum and an infinite-volume three-to-three scattering quantity. This final analysis is the most complicated of the four, because the all-orders summation is more difficult for this system, and also because a number of new technical issues arise in analyzing the contributing diagrams.

Author: Hiroyasu Ejiri
Publisher: World Scientific
ISBN: 981454759X
Category :
Languages : en
Pages : 514

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The 14th RCNP OSAKA International Symposium on Nuclear Reaction Dynamics of Nucleon-Hadron Many Body System was held in Osaka from December 6 to 9, 1995. The symposium covered current topics from Nucleon Spins and Mesons in Nuclei to Quark Lepton Nuclear Physics. Thus it included the field of hadron/nuclear physics from sub-GeV to multi-GeV energy region, as well as recent activities and development at RCNP. It was also intended to be a kind of winter school for young researchers/graduate students.This proceedings consists of the invited talks and lectures presented by leading physicists in the field and short oral presentations.