Recent Developments in the Phenomenology of Generalized ...clas2015.roma2.infn.it/talks/18_moutarde.pdfof DVCS PARTONS Project Computing chain Example Team GPD modeling Gap equation

Recent Developmentsin the Phenomenology ofGeneralized Parton Distributions

CLAS Coll. Meeting 2015 | Hervé MOUTARDE

Feb. 18th, 2015. . . . . .

Phenomenologyof Generalized

PartonDistributions

Introduction

Needsassesment

Experimentalaccess

Kinematic reachof DVCS

PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..

Motivation.Study nucleon structure to shed new light on nonperturbative QCD.

.Perturbative

QCD..

......

.Asymptoticfreedom

..

......

.Nonperturbative

QCD..

.......Perturbative AND nonperturbative QCD at work..

......

Define universal objects describing 3D nucleon structure:Generalized Parton Distributions (GPD).

Relate GPDs to measurements using factorization:Virtual Compton Scattering (DVCS, TCS),Deeply Virtual Meson production (DVMP).

Get experimental knowledge of nucleon structure.H. Moutarde CLAS Coll. Meeting 2015 2 / 19


PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..

Anatomy of the nucleon.GPDs, 3D nucleon imaging, and beyond.

Correlation of the longitudinal momentum and thetransverse position of a parton in the nucleon.

DVCS recognized as the cleanest channel to access GPDs..Deeply Virtual Compton Scattering (DVCS)..

........

e−

.

DVCS

.

e−

.

γ∗, Q2

.p

.p

.

γ

.

x + ξ

.

x − ξ

.

factorization µF

. t ..

R⊥

.

Transverse center

.

of momentum R⊥

.

R⊥ =∑

i xi r⊥i

24 GPDs F i (x , ξ, t, µF ) for each parton typei = g , u, d , . . . for leading and sub-leading twist.

H. Moutarde CLAS Coll. Meeting 2015 3 / 19


PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..




........

e−

.

DVCS

.

e−

.

γ∗, Q2

.p

.p

.

γ

.

x + ξ

.

x − ξ

.

factorization µF

. t ..

R⊥

.

Transverse center

.

of momentum R⊥

.

R⊥ =∑

i xi r⊥i

.

b⊥

.

Impact

.

parameter b⊥




PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..




........

e−

.

DVCS

.

e−

.

γ∗, Q2

.p

.p

.

γ

.

x+ ξ

.

x− ξ

.

factorization µF

. t ..

R⊥

.

Transverse center

.

of momentum R⊥

.

R⊥ =∑

i xi r⊥i

.

b⊥

.

Impact

.

parameter b⊥

.

xP+

.

Longitudinal

.momentum xP+




PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..




........

e−

.

DVCS

.

e−

.

γ∗, Q2

.p

.p

.

γ

.

x + ξ

.

x − ξ

.

factorization µF

. t ..

R⊥

.

Transverse center

.

of momentum R⊥

.

R⊥ =∑

i xi r⊥i

.

b⊥

.

Impact

.

parameter b⊥

.

xP+

.

Longitudinal

.momentum xP+

.

−1 < x < +1−1 < ξ < +1




PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..

Anatomy of the nucleon.Different questions and different tools to answer them.

1 Study of exclusive processes.

2 Metrology of Generalized Parton Distributions.

3 Understanding of QCD mechanisms and modeling ofGeneralized Parton Distributions.


Needs assesment

. . . . . .

Needs assesment.

.

..

Higher

Twists?

.

New

Experiments?

.

Meson

Production?

.

Error

Propagation?

.

Compton

Scattering?

.

Theoretical

Constraints?

.Software

.

Model

Dependence?.

Next to

Leading

Order?

. . . . . .


PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..

Exclusive processes of current interest.Factorization and universality.

..

e−

.

DVCS

.

e−

.

γ∗

.

Q2

.p

.p

. t.

x + ξ

.

x − ξ

.

γ

.

factorization

.

.

.

nucleon

.

GeneralizedParton

Distributions

.

γ∗

.

Q2

.

by

. bx

..

e−

.

DVMP

.

e−

.

γ∗

.

Q2

.p

.p

. t.

x + ξ

.

x − ξ

.

factorization

.

π, ρ, . . .

..

TCS

.

e−

.

e+

.

γ∗

.

Q2

.p

.p

. t.

x + ξ

.

x − ξ

.

γ

.

factorization



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..


..

e−

.

DVCS

.

e−

.

γ∗

.

Q2

.p

.p

. t.

x + ξ

.

x − ξ

.

γ

.

factorization

.

Perturbative

.

Nonperturbative

.

.

.

nucleon

.

GeneralizedParton

Distributions

.

γ∗

.

Q2

.

by

. bx

..

e−

.

DVMP

.

e−

.

γ∗

.

Q2

.p

.p

. t.

x + ξ

.

x − ξ

.

factorization

.

π, ρ, . . .

..

TCS

.

e−

.

e+

.

γ∗

.

Q2

.p

.p

. t.

x + ξ

.

x − ξ

.

γ

.

factorization



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..


..

e−

.

DVCS

.

e−

.

γ∗

.

Q2

.p

.p

. t.

x + ξ

.

x − ξ

.

γ

.

factorization

.

Perturbative

.

Nonperturbative

.

.

.

nucleon

.

GeneralizedParton

Distributions

.

γ∗

.

Q2

.

by

. bx

..

e−

.

DVMP

.

e−

.

γ∗

.

Q2

.p

.p

. t.

x + ξ

.

x − ξ

.

factorization

.

π, ρ, . . .

.

Perturbative

.

Nonperturbative

..

TCS

.

e−

.

e+

.

γ∗

.

Q2

.p

.p

. t.

x + ξ

.

x − ξ

.

γ

.

factorization



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..


..

e−

.

DVCS

.

e−

.

γ∗

.

Q2

.p

.p

. t.

x + ξ

.

x − ξ

.

γ

.

factorization

.

Perturbative

.

Nonperturbative

.

.

.

nucleon

.

GeneralizedParton

Distributions

.

γ∗

.

Q2

.

by

. bx

..

e−

.

DVMP

.

e−

.

γ∗

.

Q2

.p

.p

. t.

x + ξ

.

x − ξ

.

factorization

.

π, ρ, . . .

.

Perturbative

.

Nonperturbative

..

TCS

.

e−

.

e+

.

γ∗

.

Q2

.p

.p

. t.

x + ξ

.

x − ξ

.

γ

.

factorization

.

Perturbative

.

Nonperturbative



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..


..

e−

.

DVCS

.

e−

.

γ∗

.

Q2

.p

.p

. t.

x + ξ

.

x − ξ

.

γ

.

factorization

.

Nonperturbative

.

Perturbative

.

.

.

nucleon

.

GeneralizedParton

Distributions

.

γ∗

.

Q2

.

by

. bx

..

e−

.

DVMP

.

e−

.

γ∗

.

Q2

.p

.p

. t.

x + ξ

.

x − ξ

.

factorization

.

π, ρ, . . .

.

Nonperturbative

.

Perturbative

..

TCS

.

e−

.

e+

.

γ∗

.

Q2

.p

.p

. t.

x + ξ

.

x − ξ

.

γ

.

factorization

.

Nonperturbative

.

Perturbative



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..


..

e−

.

DVCS

.

e−

.

γ∗

.

Q2

.p

.p

. t.

x + ξ

.

x − ξ

.

γ

.

factorization

.

Perturbative

.

Nonperturbative

.

.

.

nucleon

.

GeneralizedParton

Distributions

.

γ∗

.

Q2

.

by

. bx

..

e−

.

DVMP

.

e−

.

γ∗

.

Q2

.p

.p

. t.

x + ξ

.

x − ξ

.

factorization

.

π, ρ, . . .

.

Perturbative

.

Nonperturbative

..

TCS

.

e−

.

e+

.

γ∗

.

Q2

.p

.p

. t.

x + ξ

.

x − ξ

.

γ

.

factorization

.

Perturbative

.

Nonperturbative



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..

Need for global fits of world data.Different facilities will probe different kinematic domains.

.Kinematic reach of existing or near-future DVCS measurements..

......

..ξ

.0..

0.2

.

0.4

.

0.6

.

Q2[GeV

2]

.0. .

2.

.

4.

.

6.

.

8.

.

10.

.

12.

.

14.

.

JLab6(United States)

.

HERMES (Germany)

.

HERA (Germany)

.Near-future and existing measurements



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..



......

..ξ

.0..

0.2

.

0.4

.

0.6

.

Q2[GeV

2]

.0. .

2.

.

4.

.

6.

.

8.

.

10.

.

12.

.

14.

.

JLab12(UnitedStates)

.

COMPASS (CERN)

.


.

HERMES

.

HERA

.Near-future and existing measurements



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..



......

..ξ

.0..

0.2

.

0.4

.

0.6

.

Q2[GeV

2]

.0. .

2.

.

4.

.

6.

.

8.

.

10.

.

12.

.

14.

.


.


.

HERMES

.

COMPASS

.

HERA

.

seaquarks

.

valencequarks



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..



......

..ξ

.0..

0.2

.

0.4

.

0.6

.

Q2[GeV

2]

.0. .

2.

.

4.

.

6.

.

8.

.

10.

.

12.

.

14.

.


.


.

HERMES

.

COMPASS

.

HERA

.

seaquarks

.

valencequarks

.

Need an EIC tomeasure gluon GPDs

.

ξ ≳ 10−4



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..



......

..ξ

.0..

0.2

.

0.4

.

0.6

.

Q2[GeV

2]

.0. .

2.

.

4.

.

6.

.

8.

.

10.

.

12.

.

14.

.


.


.

HERMES

.

COMPASS

.

HERA

.

Dominant andsub-dominantcontributionsto the DVCSamplitudein the large Q2

limit?


PARTONS Project.

.

..

Higher

Twists?

.

New

Experiments?

.

Meson

Production?

.

Error

Propagation?

.

Compton

Scattering?

.

Theoretical

Constraints?

.Software

.

Model

Dependence?.

Next to

Leading

Order?

. . . . . .

PARTONS Project.

.

PARtonicTomographyOfNucleonSoftware

. . . . . .


PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..

Computing chain design.Differential studies: physical models and numerical methods.

..

Firstprinciples andfundamentalparameters.

Computationof amplitudes

.

Experimentaldata andphenomenology

.

Large distancecontributions

.

Small distancecontributions

.

Full processes



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..


..



.


.

GPD at µ ̸= µrefF

.

GPD at µrefF

.

DVCS

.

TCS

.

DVMP

.

DVCS

.

TCS

.

DVMP

.

Evolution



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..


..



.


.


.

GPD at µrefF

.

DVCS

.

TCS

.

DVMP

.

DVCS

.

TCS

.

DVMP

.

Manyobservables.

Kinematic reach.

.

Evolution



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..


..



.


.


.

GPD at µrefF

.

DVCS

.

TCS

.

DVMP

.

DVCS

.

TCS

.

DVMP

.

Manyobservables.

Kinematic reach.

.

Perturbativeapproximations.

Physical models.

Fits.

Numericalmethods.

Accuracy andspeed.

.

Evolution

.

Need formodularity



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..

Status.Currently: integration, tests, validation.

3 stages:

1 Design.

2 Integration and validation.

3 Production.

Flexible software architecture.

1 new physical development = 1 new module.

What can be automated will be automated.

Get ready for 12 GeV!



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..

GPD computing made simple.Each line of code corresponds to a physical hypothesis.

gpdEvolutionExample()1 // Load QCD evolution module2 EvolQCDModule∗ pEvolQCDModule = pModuleObjectFactory−>3 getEvolQCDModule( VinnikovEvolQCDModel::moduleID ) ;4

5 // Configure QCD evolution module6 pEvolQCDModule−>setQcdOrderType( QCDOrderType::LO ) ;7

8 // Load GPD module9 GPDModule∗ pGK11Module =

10 pModuleObjectFactory−>getGPDModule( GK11Model::moduleID ) ;11

12 // Create kinematic configuration ( x, xi , t , MuF, MuR )13 GPDKinematic gpdKinematic( 0.25, 0.29, −0.28, 1.82, 1.82 ) ;14

15 // Compute GPD and store results16 GPDOutputData results = pGPDService−>17 computeGPDModelWithEvolution( gpdKinematic, pGK11Module,18 pEvolQCDModule, GPDComputeType::H ) ;19

20 // Print results21 std :: cout


PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..

Members and areas of expertise.Collaborations at the national and international levels.

...

Argonne

National

Laboratory

.

Thomas

Jefferson

National

Laboratory

.

University

of Huelva

.

CERN

.

Johannes Gutenberg

Universität

.

NationalCenterfor

Nuclear

Research

.

Development team

B. Berthou M. Boer C. Mezrag H. Moutarde F. Sabatié J. Wagner

.

IPN and LPT (Orsay), Irfu (Saclay) and CPhT (Polytechnique)Experimental data analysis Perturbative QCDWorld data fits GPD modeling


GPD modeling in the Dyson-Schwinger framework.

.

..

Higher

Twists?

.

New

Experiments?

.

Meson

Production?

.

Error

Propagation?

.

Compton

Scattering?

.

Theoretical

Constraints?

.Software

.

Model

Dependence?.

Next to

Leading

Order?

. . . . . .

GPD modeling in the Dyson-Schwinger framework.

.

Emergence ofeffective degrees offreedom andinteraction

. . . . . .


PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..

The gap equation.Description of quark dressing.

Resuming gluon contributions to the quark propagator:

. . = . + . + . + . . .

=. . ×

1 + . +( . )2 + . . .

= . ×

(1− .

)−1

Invert both members of equation:

(. . )−1 =

(1− .

)× (. )−1

= (. )−1 −



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..



. . = . + . + . + . . .

=. . ×

1 + . +( . )2 + . . .

= . ×

(1− .

)−1Invert both members of equation:

(. . )−1 =

(1− .

)× (. )−1

= (. )−1 − .H. Moutarde CLAS Coll. Meeting 2015 14 / 19


PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..



. . = . + . + . + . . .

=. . ×

1 + . +( . )2 + . . .

= . ×

(1− .

)−1Invert both members of equation: Forgotten contributions!

(. . )−1 =

(1− .

)× (. )−1

= (. )−1 − .H. Moutarde CLAS Coll. Meeting 2015 14 / 19


PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..



. . = . + . + . + . . .

=. . ×

1 + . +( . )2 + . . .

= . ×

(1− .


(. . )−1 =

(1− .

)× (. )−1

= (. )−1 − .

.Gluon propagator..

...... .



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..



. . = . + . + . + . . .

=. . ×

1 + . +( . )2 + . . .

= . ×

(1− .


(. . )−1 =

(1− .

)× (. )−1

= (. )−1 − .

.Quark propagator..

...... .



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..



. . = . + . + . + . . .

=. . ×

1 + . +( . )2 + . . .

= . ×

(1− .


(. . )−1 =

(1− .

)× (. )−1

= (. )−1 − .

.Vertex..

...... .



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..

The gap equation.Building effective degrees of freedom from quarks and gluons.

.Dyson - Schwinger gap equation..

....... ..

−1. =.

−1. − . .

.

Fundamentaldegrees offreedom

..

Model interaction:

Gluon propagator

Quark-gluon vertex

.

Consistently getdressed quarkpropagator.

Effectivedegrees offreedom



PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..

Dyson - Schwinger and Bethe - Salpeter.First step towards the modeling of nucleon GPDs.

0.0

0.5

1.0

Ξ

-1.0-0.50.00.51.0

x

0.0

0.5

1.0

1.5

Training ground: pion.

Modeling of GPD, PDFand form factor.

Goal: nucleon.

0 0.5 1 1.5 2 2.5 3

-t [GeV2]

0

0.5

1

Fπ(t

)

Model (M=0.35 GeV)

Amendolia et al (1986)

Huber et al. (2008)

Model (M=0.25 GeV)

Model (M=0.45 GeV)

0 0.1 0.2 0.3 0.4

-t [GeV2]

0.5

1

Fπ(t

)

Model (M=0.35 GeV)

Amendolia et al (1986)

Huber et al. (2008)

Model (M=0.25 GeV)

Model (M=0.45 GeV)

Mezrag et al., arXiv:1406.7425Chang et al., Phys. Lett. B737, 23 (2014)

Mezrag et al., Phys. Lett. B741, 190 (2015)H. Moutarde CLAS Coll. Meeting 2015 16 / 19

Conclusions

. . . . . .


PartonDistributions

Introduction

Needsassesment

Experimentalaccess


PARTONSProject

Computingchain

Example

Team

GPD modeling

Gap equation

Pion form factor

Conclusions

. . . . . .

..

Conclusions.Versatile tools for hadron structure studies.

Two major developments:

Software project: PARTONS.

GPD modeling: Schwinger-Dyson.

Aims ( by the end of 2015):

DVCS computing chain validated and automated.

Beginning of Dyson-Schwinger modeling of nucleon GPDs.


Commissariat à l’énergie atomique et aux énergies alternatives DSMCentre de Saclay | 91191 Gif-sur-Yvette Cedex IrfuT. +33(0)1 69 08 73 88 | F. +33(0)1 69 08 75 84 SPhNEtablissement public à caractère industriel et commercial | R.C.S. Paris B 775 685 019

. . . . . .

Needs assesmentExperimental accessKinematic reach of DVCS

PARTONS ProjectComputing chainExampleTeam

GPD modeling in the Dyson-Schwinger frameworkGap equationPion form factor

Recent Developments in the Phenomenology of Generalized ...clas2015.roma2.infn.it/talks/18_moutarde.pdfof DVCS PARTONS Project Computing chain Example Team GPD modeling Gap equation

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