Physically Motivated Generalized Parton Distributions

Similar documents
Coherent Potential Approximation

Solutions to problem set ); (, ) (

Some Different Perspectives on Linear Least Squares

Introduction. Free Electron Fermi Gas. Energy Levels in One Dimension

Some results and conjectures about recurrence relations for certain sequences of binomial sums.

7.0 Equality Contraints: Lagrange Multipliers

KURODA S METHOD FOR CONSTRUCTING CONSISTENT INPUT-OUTPUT DATA SETS. Peter J. Wilcoxen. Impact Research Centre, University of Melbourne.

Department of Mechanical Engineering ME 322 Mechanical Engineering Thermodynamics. Ideal Gas Mixtures. Lecture 31

3.1 Introduction to Multinomial Logit and Probit

PRACTICAL CONSIDERATIONS IN HUMAN-INDUCED VIBRATION

A New Method for Solving Fuzzy Linear. Programming by Solving Linear Programming

Non-degenerate Perturbation Theory

A Penalty Function Algorithm with Objective Parameters and Constraint Penalty Parameter for Multi-Objective Programming

CHAPTER VI Statistical Analysis of Experimental Data

1 Lyapunov Stability Theory

Stationary states of atoms and molecules

Economic drivers. Input and output prices Adjustment under ITQs

Chapter 2 - Free Vibration of Multi-Degree-of-Freedom Systems - II

A Conventional Approach for the Solution of the Fifth Order Boundary Value Problems Using Sixth Degree Spline Functions

Debabrata Dey and Atanu Lahiri

for each of its columns. A quick calculation will verify that: thus m < dim(v). Then a basis of V with respect to which T has the form: A

Standard Deviation for PDG Mass Data

A Bivariate Distribution with Conditional Gamma and its Multivariate Form

Review Exam I Complex Analysis. Cauchy s Integral Formula (#0). Let G be a region in C, let Bar (, ) G and let γ be the circle C(a,r), oriented.

2/20/2013. Topics. Power Flow Part 1 Text: Power Transmission. Power Transmission. Power Transmission. Power Transmission

Ellipsometry Overview

DKA method for single variable holomorphic functions

Lecture 12 APPROXIMATION OF FIRST ORDER DERIVATIVES

Long blade vibration model for turbine-generator shafts torsional vibration analysis

ELECTRON HEATING IN THE CONDUCTION BAND OF INSULATORS UNDER FEMTOSECOND LASER PULSE IRRADIATION

The Geometric Least Squares Fitting Of Ellipses

The theoretical background of

ECE 595, Section 10 Numerical Simulations Lecture 19: FEM for Electronic Transport. Prof. Peter Bermel February 22, 2013

DIFFERENTIAL GEOMETRIC APPROACH TO HAMILTONIAN MECHANICS

Chapter 4: Linear Momentum and Collisions

Basic Concepts in Numerical Analysis November 6, 2017

On Convergence a Variation of the Converse of Fabry Gap Theorem

A Family of Non-Self Maps Satisfying i -Contractive Condition and Having Unique Common Fixed Point in Metrically Convex Spaces *

Chapter 14 Logistic Regression Models

The Mathematical Appendix

Simple Linear Regression

Relations to Other Statistical Methods Statistical Data Analysis with Positive Definite Kernels

Kantowski-Sachs Cosmological Model in f(r,t) Theory of Gravity

Queueing Networks. γ 3

5. Data Compression. Review of Last Lecture. Outline of the Lecture. Course Overview. Basics of Information Theory: Markku Juntti

The Application of hybrid BEM/FEM methods to solve Electrical Impedance Tomography s forward problem for the human head

Objectives of Multiple Regression

The Modified Bi-quintic B-spline Base Functions: An Application to Diffusion Equation

ECON 5360 Class Notes GMM

Lecture 8. A little bit of fun math Read: Chapter 7 (and 8) Finite Algebraic Structures

. The set of these sums. be a partition of [ ab, ]. Consider the sum f( x) f( x 1)

Performance of a Queuing System with Exceptional Service

ECE606: Solid State Devices Lecture 13 Solutions of the Continuity Eqs. Analytical & Numerical

Initial-Value Problems for ODEs. numerical errors (round-off and truncation errors) Consider a perturbed system: dz dt

( t) ( t) ( t) ρ ψ ψ. (9.1)

Summary of the lecture in Biostatistics

Camera calibration & radiometry

FREQUENCY ANALYSIS OF A DOUBLE-WALLED NANOTUBES SYSTEM

THE COMPLETE ENUMERATION OF FINITE GROUPS OF THE FORM R 2 i ={R i R j ) k -i=i

Mechanics of Materials CIVL 3322 / MECH 3322

X-ray vortices from nonlinear inverse Thomson scattering

Solving Constrained Flow-Shop Scheduling. Problems with Three Machines

Algorithms behind the Correlation Setting Window

A Variable Structure Model Reference Adaptive Control For MIMO Systems

III-16 G. Brief Review of Grand Orthogonality Theorem and impact on Representations (Γ i ) l i = h n = number of irreducible representations.

Block-Based Compact Thermal Modeling of Semiconductor Integrated Circuits

Lecture 14. P-N Junction Diodes: Part 3 Quantitative Analysis (Math, math and more math) Reading: Pierret 6.1

A Proof of Factorization Theorem of Drell Yan Process at Operator Level

TRANSIENT PLANE WAVES IN MULTILAYERED HALF-SPACE

Functions of Random Variables

b) Choose one o f the graphs in part a that did b) is the atomic number o f

Decomposition of Hadamard Matrices

C-1: Aerodynamics of Airfoils 1 C-2: Aerodynamics of Airfoils 2 C-3: Panel Methods C-4: Thin Airfoil Theory

On Hilbert Kunz Functions of Some Hypersurfaces

Department of Mathematics UNIVERSITY OF OSLO. FORMULAS FOR STK4040 (version 1, September 12th, 2011) A - Vectors and matrices

Power Flow S + Buses with either or both Generator Load S G1 S G2 S G3 S D3 S D1 S D4 S D5. S Dk. Injection S G1

BERNSTEIN COLLOCATION METHOD FOR SOLVING NONLINEAR DIFFERENTIAL EQUATIONS. Aysegul Akyuz Dascioglu and Nese Isler

Fourth Order Four-Stage Diagonally Implicit Runge-Kutta Method for Linear Ordinary Differential Equations ABSTRACT INTRODUCTION

Theory study about quarter-wave-stack dielectric mirrors

Order Nonlinear Vector Differential Equations

Cubic Nonpolynomial Spline Approach to the Solution of a Second Order Two-Point Boundary Value Problem

MOLECULAR VIBRATIONS

MATRIX ANALYSIS OF ANCHORED STRUCTURES

AN EULER-MC LAURIN FORMULA FOR INFINITE DIMENSIONAL SPACES

Estimation of Stress- Strength Reliability model using finite mixture of exponential distributions

DYNAMIC ANALYSIS OF CONCRETE RECTANGULAR LIQUID STORAGE TANKS

X ε ) = 0, or equivalently, lim

arxiv:hep-ph/ v1 18 Nov 2002

CS5620 Intro to Computer Graphics

VIII Dynamics of Systems of Particles

CS 2750 Machine Learning. Lecture 7. Linear regression. CS 2750 Machine Learning. Linear regression. is a linear combination of input components x

SUPER GRACEFUL LABELING FOR SOME SPECIAL GRAPHS

Beam Warming Second-Order Upwind Method

= lim. (x 1 x 2... x n ) 1 n. = log. x i. = M, n

Training Sample Model: Given n observations, [[( Yi, x i the sample model can be expressed as (1) where, zero and variance σ

Chapter 8 Heteroskedasticity

Evolution Operators and Boundary Conditions for Propagation and Reflection Methods

Linear Regression with One Regressor

STATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS. x, where. = y - ˆ " 1

3D Reconstruction from Image Pairs. Reconstruction from Multiple Views. Computing Scene Point from Two Matching Image Points

Transcription:

hyscally otvated Geeralzed arto Dstrbutos J. Osvaldo Gozalez H. Fourth Year Sear

OUTLINE otvato: DVCS Observables ad GD s How to Buld a araetrzato? ossble applcatos Ogog ad Future rojects

DVCS Lght coe coordates 00 000 00 000 3 0 e e 3 00 0 y z large 3-oetu 3

Lght coe coordates DVCS 0 oetu Coservato relatve to roto Eergy Coservato covarat O-shell artos te ordered z y y 4

DVCS e e γ e e γ 5

DVCS q q = q+δ = - Δ γ * γ 6

q q+δ = - Δ DVCS Jμ s the teractg curret. μν ε I* ε J μν s a Loretz varat. e d e T[ J J 0] 4 Apltude depeds o three Loretz varats Q * I J q I J Q p q where 7

DVCS q + q q = q+δ = - Δ Asyptotc freedo QCD observable Bjore lt. = - Δ Q q Q q B fte e d 4 e T[ j j 0] ; j Ψ γ Ψ Relevat varats : t 8

DVCS 9

DVCS s s U U q q Tr e 0

DVCS s s U U q q Tr e 4 4 q q Tr d e z e z d z 0 4

DVCS 4 4 q q q q Tr e d e 0. 0 0 z z at z dz F F d g e z S e Bjore Lt s s U σ E H U F

DVCS 4 4 q q q q Tr e d e 0. 0 0 ~ ~ 5 z z at z dz F F d g e z A e Bjore Lt s s U E H U F ~ ~ ~ 5 5 3

Observables ad GD s Helcty o-flp Helcty flp Upolarzed rotos olarzed rotos H ~ H E ~ E Real fuctos Loretz Ivarat Reduce to ordary DF s forward lt 4

DIS Observables ad GD s Optcal Theore q q = q+δ q q GD Δ 0 DF = - Δ 5

Observables ad GD s olyoalty: od od 0 0 t C t B X E X d t C t A X H X d eve eve 6 / / X X

Observables ad GD s olyoalty: 0 0 E d F H d F σ F F J 7 od od 0 0 t C t B X E X d t C t A X H X d eve eve / / X X

Observables ad GD s olyoalty: 0 0 ~ ~ E d g H d g A 5 5 5 g g J A eve eve t B X E X dx t A X H X dx ~ ~ ~ ~ 0 0 8 / / X X

It s ot possble to calculate GD s by eleetary eas operturbatve ature of QCD Soe odels have bee bult:. Burardt 00.Dehl T.Felda Jaob Kroll 005. Gudal olyaov RadyushyVaderhaege005 Ca we corporate soe hyscs to a paraetrzato? 9

Dquar odel roto s thought as beg coposed by a quar a dquar of ass ust cosder: Loretz Ivarace arty Sp propertes Dquar S= 0 Dquar S= ust be a aal vector Costras Drac Structure 0

Dquar odel What s ths verte?

Dquar odel Verte fucto ca be wrtte as: z Aal couplg Scalar couplg y g asc guaratees sall perpedcular copoets of oetu araetrzato wored out usg scalar couplg. Slar to eyerulders

Dquar odel What s ths verte? Sp Case: Soe of these choces produce cubersoe epressos. 3

Dquar odel 008 Gaberg Goldste Schlegel q q DF A epresso for a GD would ot be as sple.

Dquar odel * I J g f g f_scalar f Regge Behavor?? f_aal 5

How to Buld a araetrzato? 6

The recpe Tae Scalar dquar odel. Calculate GD s : Covarat calculato. Lght Coe Foc Epaso. Reggezato. F araeters: Altarell-ars equatos. = 0 case: GD s DF s. ζ = 0 case: Ft to For Factors. 7

Covarat vs Te Ordered Covarat Lght Coe Foc Epaso + = s s U σ E H U F F d g e 8

Covarat vs Te Ordered Covarat g g Tr d... Calculate resdues Get result!!! g 9

Covarat vs Te Ordered Lght Coe Foc Epaso Start fro atr eleet: e F dz z 0 z at z 0 z 0. LC Wave Fuctos Calculate LCWF Get result!!! 30

Covarat vs Te Ordered Covarat Lght Coe Foc Epaso Not Clear how to treat verte: g Verte fucto sees to chage pole structure What s o-shell? 3

Covarat vs Te Ordered Covarat Lght Coe Foc Epaso Relates O-shell codtos to TOT Keatc regos are easly terpreted partoc pcture 3

Covarat vs Te Ordered Covarat Lght Coe Foc Epaso D q q DGLA D q q ERBL atquar wth 33

Covarat vs Te Ordered Covarat Lght Coe Foc Epaso Use to detere for of verte TOT Use Foc epaso to calculate atr eleet F. s s U σ E H U F F d g e Chec pole structure 34

Regge Behavor? Fro Regge Theory f s t p t Burardt 35

Regge Behavor? Have s paraers p 36

F araeters Tae to accout Altarell-ars equatos q q = q+δ = - Δ 37

F araeters = 0 case: GD s DF s. H 00 f ~ H 00 g F Λ α δ = 0 case: Ft to For Factors. F d H F d E g A 0 0 ~ ~ g d E 0 d H 0 F βp 38

Results DGLA d H D 6 3 d E D 6 3 3/ 3/ ] [ ] [ L L D L 39

Results ERBL Results d H E 6 3 d E E 6 3 ] ~ [ ] [ L L E ~ L 40

Results DGLA d H D 6 ~ 3 d E D 6 4 ~ 3 3/ 3/ ] [ ] [ L L D L 4

Results ERBL Results d H E 6 ~ 3 d E E 6 4 ~ 3 ] ~ [ ] [ L L E ~ L 4

Results Soe propertes: Cotuty of DGLA ad ERBL Helcty structure. S 3/ ] [ ] [ L D E at ~ * * F F p s p s p s p s 5 A DGLA 43

Results Soe propertes: Cotuty of DGLA ad ERBL Helcty structure. S 3/ ] [ ] [ L D E at ~ * * F F p s p s p s p s 5 A ERBL 44

relary Nuercal Results DGLA Forward Lt for H H 00 45

relary Nuercal Results DGLA For δ = 0 H For δ = 0 E H E 46

relary Nuercal Results DGLA For δ = 0 ~ H H ~ 47

relary Nuercal Results DGLA For δ = 0 ~ H ~ E Dverges at δ = 0 ad at Δ = 0 4 0 H ~ 48

relary Nuercal Results DGLA For δ = 0 ~ H For δ = δ a ~ E H ~ E ~ 49

ossble Aplcatos Data Aalyss for DVCS Jefferso Lab Neutro o-producto INERvA Ferlab 50

Ogog ad Future rojects ERBL Ipleetato of our paraetrzato Neutro oproducto data aalyss. Regge Behavor. 5

GRACIAS 5

GRACIAS 53

GRACIAS 54

GRACIAS 55

ore dagras Radatve Correctos Fal State Iteractos q q = q+δ q q = q+δ = - Δ = - Δ q q = q+δ q q = q+δ = - Δ = - Δ 56