Physically Motivated Generalized Parton Distributions
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1 hyscally otvated Geeralzed arto Dstrbutos J. Osvaldo Gozalez H. Fourth Year Sear
2 OUTLINE otvato: DVCS Observables ad GD s How to Buld a araetrzato? ossble applcatos Ogog ad Future rojects
3 DVCS Lght coe coordates e e y z large 3-oetu 3
4 Lght coe coordates DVCS 0 oetu Coservato relatve to roto Eergy Coservato covarat O-shell artos te ordered z y y 4
5 DVCS e e γ e e γ 5
6 DVCS q q = q+δ = - Δ γ * γ 6
7 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
8 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
9 DVCS 9
10 DVCS s s U U q q Tr e 0
11 DVCS s s U U q q Tr e 4 4 q q Tr d e z e z d z 0 4
12 DVCS 4 4 q q q q Tr e d e z z at z dz F F d g e z S e Bjore Lt s s U σ E H U F
13 DVCS 4 4 q q q q Tr e d e ~ ~ 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
14 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
15 DIS Observables ad GD s Optcal Theore q q = q+δ q q GD Δ 0 DF = - Δ 5
16 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
17 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
18 Observables ad GD s olyoalty: 0 0 ~ ~ E d g H d g A g g J A eve eve t B X E X dx t A X H X dx ~ ~ ~ ~ / / X X
19 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
20 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
21 Dquar odel What s ths verte?
22 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
23 Dquar odel What s ths verte? Sp Case: Soe of these choces produce cubersoe epressos. 3
24 Dquar odel 008 Gaberg Goldste Schlegel q q DF A epresso for a GD would ot be as sple.
25 Dquar odel * I J g f g f_scalar f Regge Behavor?? f_aal 5
26 How to Buld a araetrzato? 6
27 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
28 Covarat vs Te Ordered Covarat Lght Coe Foc Epaso + = s s U σ E H U F F d g e 8
29 Covarat vs Te Ordered Covarat g g Tr d... Calculate resdues Get result!!! g 9
30 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
31 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
32 Covarat vs Te Ordered Covarat Lght Coe Foc Epaso Relates O-shell codtos to TOT Keatc regos are easly terpreted partoc pcture 3
33 Covarat vs Te Ordered Covarat Lght Coe Foc Epaso D q q DGLA D q q ERBL atquar wth 33
34 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
35 Regge Behavor? Fro Regge Theory f s t p t Burardt 35
36 Regge Behavor? Have s paraers p 36
37 F araeters Tae to accout Altarell-ars equatos q q = q+δ = - Δ 37
38 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
39 Results DGLA d H D 6 3 d E D 6 3 3/ 3/ ] [ ] [ L L D L 39
40 Results ERBL Results d H E 6 3 d E E 6 3 ] ~ [ ] [ L L E ~ L 40
41 Results DGLA d H D 6 ~ 3 d E D 6 4 ~ 3 3/ 3/ ] [ ] [ L L D L 4
42 Results ERBL Results d H E 6 ~ 3 d E E 6 4 ~ 3 ] ~ [ ] [ L L E ~ L 4
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 DGLA 43
44 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
45 relary Nuercal Results DGLA Forward Lt for H H 00 45
46 relary Nuercal Results DGLA For δ = 0 H For δ = 0 E H E 46
47 relary Nuercal Results DGLA For δ = 0 ~ H H ~ 47
48 relary Nuercal Results DGLA For δ = 0 ~ H ~ E Dverges at δ = 0 ad at Δ = H ~ 48
49 relary Nuercal Results DGLA For δ = 0 ~ H For δ = δ a ~ E H ~ E ~ 49
50 ossble Aplcatos Data Aalyss for DVCS Jefferso Lab Neutro o-producto INERvA Ferlab 50
51 Ogog ad Future rojects ERBL Ipleetato of our paraetrzato Neutro oproducto data aalyss. Regge Behavor. 5
52 GRACIAS 5
53 GRACIAS 53
54 GRACIAS 54
55 GRACIAS 55
56 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
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