Download or read book Transverse Momentum dependent Parton Distribution Functions in Lattice QCD written by and published by . This book was released on 2013 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fundamental structural property of the nucleon is the distribution of quark momenta, both parallel as well as perpendicular to its propagation. Experimentally, this information is accessible via selected processes such as semi-inclusive deep inelastic scattering (SIDIS) and the Drell-Yan process (DY), which can be parametrized in terms of transversemomentum-dependent parton distributions (TMDs). On the other hand, these distribution functions can be extracted from nucleon matrix elements of a certain class of bilocal quark operators in which the quarks are connected by a staple-shaped Wilson line serving to incorporate initial state (DY) or final state (SIDIS) interactions. A scheme for evaluating such matrix elements within lattice QCD is developed. This requires casting the calculation in a particular Lorentz frame, which is facilitated by a parametrization of the matrix elements in terms of invariant amplitudes. Exploratory results are presented for the time-reversal odd Sivers and Boer-Mulders transverse momentum shifts.
Download or read book Process dependent Transverse Momentum Distributions from Lattice QCD written by and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Certain single-spin asymmetries in semi-inclusive DIS (SIDIS) and the Drell-Yan process (DY) can be explained by transverse momentum dependent parton distribution functions (TMDs) that are predicted to differ in sign for SIDIS and DY. On the lattice, we can use non-local operators with U-shaped Wilson lines to study these TMDs, in particular the Sivers- and the Boer-Mulders function. We discuss the method, its limitations and preliminary results from an exploratory calculation using lattices generated by the MILC and LHP collaborations.
Download or read book Transverse Momentum Dependent Quark Densities from Lattice QCD written by and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We study transverse momentum dependent parton distribution functions (TMDs) with non-local operators in lattice QCD, using MILC/LHPC lattices. Results obtained with a simpli?ed operator geometry show visible dipole de- formations of spin-dependent quark momentum densities. We discuss the basic concepts of the method, including renormalization of the gauge link, and an ex- tension to a more elaborate operator geometry that would allow us to analyze process-dependent TMDs such as the Sivers-function.
Download or read book Transverse Momentum Distributions Inside the Nucleon from Lattice QCD written by and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We study transverse momentum dependent parton distribution functions (TMDs) with non-local operators in lattice QCD, using MILC/LHPC lattices. Results obtained with a simplified operator geometry show visible dipole deformations of spin-dependent quark momentum densities. We discuss the basic concepts of the method, including renormalization of the gauge link, and an extension to a more elaborate operator geometry that would allow us to analyze process-dependent TMDs such as the Sivers-function.
Download or read book Exploring Quark Transverse Momentum Distributions with Lattice QCD written by and published by . This book was released on 2011 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: We discuss in detail a method to study transverse momentum dependent parton distribution functions (TMDs) using lattice QCD. To develop the formalism and to obtain first numerical results, we directly implement a bi-local quark-quark operator connected by a straight Wilson line, allowing us to study T-even, "process-independent" TMDs. Beyond results for x-integrated TMDs and quark densities, we present a study of correlations in x and transverse momentum. Our calculations are based on domain wall valence quark propagators by the LHP collaboration calculated on top of gauge configurations provided by MILC with 2+1 flavors of asqtad-improved staggered sea quarks.
Download or read book Transverse Momentum Dependent Parton Distribution Functions with Domain Wall Valence Fermions written by and published by . This book was released on 2011 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transverse Momentum Dependent Parton Distribution Functions (TMDs) reveal the intrinsic motion of quarks inside the nucleon. They are essential ingredients needed to understand angular asymmetries studied in SIDIS experiments, including current and planned experiments at JLab. Within a class B proposal, we ask for time on the Jefferson Lab computer cluster to extract amplitudes for TMDs from existing lattice QCD gauge configurations and propagators calculated by the USQCD/MILC/LHP collaborations [Aubin 2004, Bratt 2010]. The proposal encompasses more comprehensive studies with a simplified operator [Haegler 2010] along with more realistic and more demanding calculations that promise to give access to time reversal odd TMDs such as the Sivers function. We ask for cluster computer time equivalent to 1.26 million J/Psi core hours, plus disk and tape storage worth 159000 J/Psi core hours.
Download or read book Studying the Sivers and Boer Mulders Function with Lattice QCD written by and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Transverse momentum dependent parton distribution functions (TMDs) characterize the intrinsic momentum distribution of quarks inside the nucleon. However, they also encode final or initial state interactions of the processes in which they are measured, such as semi-inclusive deep inelastic scattering (SIDIS) or the Drell-Yan process (DY). Consequently certain TMDs are process-dependent and predicted to be equal but opposite in sign for SIDIS and DY. Extending our method on the lattice to non-local operators with U-shaped Wilson lines, we can study these naively time-reversal odd TMDs, in particular the Sivers- and the Boer-Mulders function. We express our results in terms of Fourier-transformed TMDs that appear naturally in the Fourier transformed cross section of, e.g., SIDIS, and in Bessel-weighted asymmetries. We discuss the method, its limitations and preliminary results from an exploratory calculation using lattices generated by the MILC and LHP collaborations.
Download or read book Transverse Momentum Distributions Inside the Nucleon from Lattice QCD written by Bernhard Ulrich Musch and published by . This book was released on 2009 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Parton Densities in Quantum Chromodynamics written by Igor Olegovich Cherednikov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-11-21 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give a systematic pedagogical exposition of the quantitative analysis of Wilson lines and gauge-invariant correlation functions in quantum chromodynamics. Using techniques from the previous volume (Wilson Lines in Quantum Field Theory, 2014), an ab initio methodology is developed and practical tools for its implementation are presented. Emphasis is put on the implications of gauge invariance and path-dependence properties of transverse-momentum dependent parton density functions. The latter are associated with the QCD factorization approach to semi-inclusive hadronic processes, studied at currently operating and planned experimental facilities. Contents: Introduction Particle Number Operators in Quantum Mechanics and in Quantum Field Theory Geometry of Quantum Field Theories Basics of Wilson Lines in QCD Gauge-Invariant Parton Densities Simplifying Wilson Line Calculations Brief Literature Guide Conventions and Reference Formulae Integrations Bibliography Index
Download or read book Foundations of Perturbative QCD written by John Collins and published by Cambridge University Press. This book was released on 2011-04-28 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: Giving an accurate account of the concepts, theorems and their justification, this book is a systematic treatment of perturbative QCD. It relates the concepts to experimental data, giving strong motivations for the methods. Ideal for graduate students starting their work in high-energy physics, it will also interest experienced researchers.
Download or read book Exclusive Reactions at High Momentum Transfer IV written by Anatoly Radyushkin and published by World Scientific. This book was released on 2011 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings include talks given at the 4th Workshop on Exclusive Reactions at High Momentum Transfer at Jefferson Lab, Newport News, VA USA, the world's leading facility performing research on nuclear, hadronic and quark-gluon structure of matter. Exclusive reactions are becoming one of the major sources of information about the deep structure of the nucleons and other hadrons. The workshop focused on the application of a variety of exclusive reactions at high momentum transfer, utilizing unpolarized and polarized beams and targets, to obtain information about nucleon ground state and excited state structure at short distances. This is a subject which is central to the programs of current accelerators and especially planned future facilities. The topics include: generalized parton distributions, deeply virtual Compton scattering, deeply virtual meson production (DVMP), transverse structure of hadrons (TMD), hadron form factors ? elastic and transition, quantum chromodynamics (perturbative, non-perturbative, lattice calculations), and physics to study at an Electron Ion Collider.
Download or read book A COMPREHENSIVE STUDY OF THE PROTON STRUCTURE written by Shohini Bhattacharya and published by . This book was released on 2021 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been known since the 1930's that protons and neutrons, collectively called as nucleons, are not "point-like" elementary particles, but rather have a substructure. Today, we know from Quantum Chromodynamics (QCD) that nucleons are made from quarks and gluons, with gluons being the elementary force carriers for strong interactions. Quarks and gluons are collectively called as partons. The substructure of the nucleons can be described in terms of parton correlation functions such as Form Factors, (1D) Parton Distribution Functions (PDFs) and their 3D generalizations in terms of Transverse Momentum-dependent parton Distributions (TMDs) and Generalized Parton Distributions (GPDs). All these functions can be derived from the even more general Generalized Transverse Momentum-dependent Distributions (GTMDs). This dissertation promises to provide an insight into all these functions from the point of view of their accessibility in experiments, from model calculations, and from their direct calculation within lattice formulations of QCD. In the first part of this dissertation, we identify physical processes to access GTMDs. By considering the exclusive double Drell-Yan process, we demonstrate, for the very first time, that quark GTMDs can be measured. We also show that exclusive double-quarkonium production in nucleon-nucleon collisions is a direct probe of gluon GTMDs. In the second part of this dissertation, we shift our focus to the "parton quasi-distributions". Over the last few decades, lattice QCD extraction of the full x-dependence of the parton distributions has always been prohibited by the explicit time-dependence of the correlation functions. In 2013, there was a path-breaking proposal by X. Ji to calculate instead parton quasi-distributions (quasi-PDFs). The procedure of "matching" is a crucial ingredient in the lattice QCD extraction of parton distributions from the quasi-PDF approach. We address the matching for the twist-3 PDFs gT (x), e(x), and hL(x) for the very first time. We pay special attention to the challenges involved in the calculations due to the presence of singular zero-mode contributions. We also present the first-ever lattice QCD results for gT (x) and hL(x) and we discuss the impact of these results on the phenomenology. Next, we explore the general features of quasi-GPDs and quasi-PDFs in diquark spectator models. Furthermore, we address the Burkhardt-Cottingham-type sum rules for the relevant light-cone PDFs and quasi-PDFs in a model-independent manner and also check them explicitly in perturbative model calculations. The last part of this dissertation focuses on the extraction g1T (x,~k2⊥) TMD for the very first time from experimental data using Monte Carlo techniques. This dissertation therefore unravels different aspects of the distribution functions from varied perspectives.
Download or read book Evolution of the Helicity and Transversity Transverse Momentum Dependent Parton Distributions written by and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We examine the QCD evolution of the helicity and transversity parton distribution functions when including also their dependence on transverse momentum. Using an appropriate definition of these polarized transverse momentum distributions (TMDs), we describe their dependence on the factorization scale and rapidity cutoff, which is essential for phenomenological applications.
Download or read book Are There Approximate Relations Among Transverse Momentum Dependent Distribution Functions written by and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Certain {\sl exact} relations among transverse momentum dependent parton distribution functions due to QCD equations of motion turn into {\sl approximate} ones upon the neglect of pure twist-3 terms. On the basis of available data from HERMES we test the practical usefulness of one such ''Wandzura-Wilczek-type approximation'', namely of that connecting $h_{1L}^{\perp(1)a}(x)$ to $h_L^a(x)$, and discuss how it can be further tested by future CLAS and COMPASS data.
Download or read book Photon hadron Interactions written by Richard P. Feynman and published by Addison-Wesley Longman. This book was released on 1989-01-21 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analyzes the theoretical questions related to electron and photon interactions at high energies.
Download or read book Pion Parton Distribution Functions from Lattice QCD written by and published by . This book was released on 2003 with total page 3 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bessel Weighted Asymmetries in Semi Inclusive Deep Inelastic Scattering written by and published by . This book was released on 2011 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of weighted asymmetries is revisited for semi-inclusive deep inelastic scattering. We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. Advantages of employing these Bessel weights are that they suppress (divergent) contributions from high transverse momentum and that soft factors cancel in (Bessel- ) weighted asymmetries. Also, the resulting compact expressions immediately connect to previous work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions and to quantities accessible in lattice QCD. Bessel weighted asymmetries are thus model independent observables that augment the description and our understanding of correlations of spin and momentum in nucleon structure.
