Extracting Scattering Phase-Shifts in Higher Partial-Waves from Lattice QCD Calculations PDF Download

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 81

View

Book Description
Lüscher's method is routinely used to determine meson-meson, meson-baryon, and baryon-baryon s-wave scattering amplitudes below inelastic thresholds from lattice QCD calculations--presently at unphysical light-quark masses. In this work we review the formalism and develop the requisite expressions to extract phase shifts describing meson-meson scattering in partial waves with angular momentum l≤6 and l=9. The implications of the underlying cubic symmetry, and strategies for extracting the phase shifts from lattice QCD calculations, are presented, along with a discussion of the signal-to-noise problem that afflicts the higher partial waves.

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 8

View

Book Description
Here, we present a determination of nucleon-nucleon scattering phase shifts for L>0. The S, P, D and F phase shifts for both the spin-triplet and spin-singlet channels are computed for the first time with lattice Quantum ChromoDynamics. This required the design and implementation of novel lattice methods involving displaced sources and momentum-space cubic sinks. In order to demonstrate the utility of our approach, the calculations were performed in the SU(3)-flavor limit where the light quark masses have been tuned to the physical strange quark mass, corresponding to m[pi]=mKH"00~MeV. Two spatial volumes of V H"(3.5 fm)3 and V H"(4.6 fm)3 were used. Furthermore, the finite-volume spectrum is extracted from the exponential falloff of the correlation functions. Said spectrum is mapped onto the infinite volume phase shifts using the generalization of the Luscher formalism for two-nucleon systems.

Author: Timo A. Lähde
Publisher: Springer
ISBN: 3030141896
Category : Science
Languages : en
Pages : 396

View

Book Description
This primer begins with a brief introduction to the main ideas underlying Effective Field Theory (EFT) and describes how nuclear forces are obtained from first principles by introducing a Euclidean space-time lattice for chiral EFT. It subsequently develops the related technical aspects by addressing the two-nucleon problem on the lattice and clarifying how it fixes the numerical values of the low-energy constants of chiral EFT. In turn, the spherical wall method is introduced and used to show how improved lattice actions render higher-order corrections perturbative. The book also presents Monte Carlo algorithms used in actual calculations. In the last part of the book, the Euclidean time projection method is introduced and used to compute the ground-state properties of nuclei up to the mid-mass region. In this context, the construction of appropriate trial wave functions for the Euclidean time projection is discussed, as well as methods for determining the energies of the low-lying excitations and their spatial structure. In addition, the so-called adiabatic Hamiltonian, which allows nuclear reactions to be precisely calculated, is introduced using the example of alpha-alpha scattering. In closing, the book demonstrates how Nuclear Lattice EFT can be extended to studies of unphysical values of the fundamental parameters, using the triple-alpha process as a concrete example with implications for the anthropic view of the Universe. Nuclear Lattice Effective Field Theory offers a concise, self-contained, and introductory text suitable for self-study use by graduate students and newcomers to the field of modern computational techniques for atomic nuclei and nuclear reactions.

Author: Kristina D Launey
Publisher: #N/A
ISBN: 9813146060
Category : Science
Languages : en
Pages : 393

View

Book Description
This book is a unique collection of reviews that share a common topic, emergent phenomena in atomic nuclei, while revealing the multifaceted nature of the subject, from quarks to heavy nuclei. It tells an amazing story of a decades-long journey of trials and successes, up to present days, with the aim to understand the vast array of experimental data and the fundamentals of strongly interacting fermions. The emphasis is on discovering emergent orderly patterns amidst the overarching complexity of many-particle quantum-mechanical systems. Recent findings are discussed within an interesting framework: a combination of nuclear theory and experiment, of group theory and computational science, and of pivotal models of astonishing simplicity and state-of-the-art models empowered by supercomputers.A special theme resonates throughout the book: the important role of symmetries, exact and approximate, in exposing emergent features and guiding large-scale nuclear modeling. World-renowned experts offer their unique perspective on symmetries in the world of quarks and gluons, and that of protons and neutrons — from chiral symmetry, through spin-isospin and quasi-spin symmetries, to symplectic symmetry, — as well as on the emergent nature of nuclear collectivity, clustering, and pairing, viewed from spectroscopy, microscopic considerations, and first principles. The book provides an excellent foundation that allows researchers and graduate students in physics and applied mathematics to review the current status of the subject, and to further explore the research literature through exhaustive sets of references that also point to studies underpinned by similar techniques in condensed matter and atomic physics along with quantum information.

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 5

View

Book Description
Finite-volume lattice QCD calculations offer the possibility of extracting resonance parameters from the energy-dependent elastic phase-shift computed using the L\"uscher technique. In this letter, as a trial of the method, we report on the extraction of the non-resonant phase-shift for $S$ and $D$-wave $\pi\pi$ isospin-2 scattering from dynamical lattice QCD computations. We define a variational basis of operators resembling pairs of pions of definite relative momentum and extract a spectrum of excited states that maps to phase-shifts at a set of discrete scattering momenta. Computations are performed with pion masses between $400$ and $520$ MeV on multiple spatial volumes. We observe no significant quark mass dependence in the phase-shifts extracted which are in reasonable agreement with the available experimental data at low momentum.

Author: Thibaut Métivet
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

View

Book Description
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.

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

View

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: Huey-Wen Lin
Publisher: Springer
ISBN: 3319080229
Category : Science
Languages : en
Pages : 255

View

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:
Publisher:
ISBN:
Category :
Languages : en
Pages :

View

Book Description
We present a derivation of the finite-size formulae in a moving frame with total momentum P=(2pi/L)(e_1+e_2). These formulae allow us to calculate the S-wave and P-wave scattering phases at more energies with a fixed lattice size and thus help us to determine the resonance parameters precisely.

Author: Xu Feng
Publisher:
ISBN:
Category :
Languages : en
Pages : 7

View

Book Description