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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
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
.
b⊥
.
Impact
.
parameter b⊥
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
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
.
b⊥
.
Impact
.
parameter b⊥
.
xP+
.
Longitudinal
.momentum xP+
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
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
.
b⊥
.
Impact
.
parameter b⊥
.
xP+
.
Longitudinal
.momentum xP+
.
−1 < x < +1−1 < ξ < +1
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
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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.
H. Moutarde CLAS Coll. Meeting 2015 4 / 19
Needs assesment
. . . . . .
Needs assesment.
.
..
Higher
Twists?
.
New
Experiments?
.
Meson
Production?
.
Error
Propagation?
.
Compton
Scattering?
.
Theoretical
Constraints?
.Software
.
Model
Dependence?.
Next to
Leading
Order?
. . . . . .
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
H. Moutarde CLAS Coll. Meeting 2015 6 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
.
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
H. Moutarde CLAS Coll. Meeting 2015 6 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
.
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
H. Moutarde CLAS Coll. Meeting 2015 6 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
.
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
H. Moutarde CLAS Coll. Meeting 2015 6 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
.
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
H. Moutarde CLAS Coll. Meeting 2015 6 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
.
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
H. Moutarde CLAS Coll. Meeting 2015 6 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
H. Moutarde CLAS Coll. Meeting 2015 7 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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.
.
JLab12(UnitedStates)
.
COMPASS (CERN)
.
JLab6(United States)
.
HERMES
.
HERA
.Near-future and existing measurements
H. Moutarde CLAS Coll. Meeting 2015 7 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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.
.
JLab12(UnitedStates)
.
JLab6(United States)
.
HERMES
.
COMPASS
.
HERA
.
seaquarks
.
valencequarks
H. Moutarde CLAS Coll. Meeting 2015 7 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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.
.
JLab12(UnitedStates)
.
JLab6(United States)
.
HERMES
.
COMPASS
.
HERA
.
seaquarks
.
valencequarks
.
Need an EIC tomeasure gluon GPDs
.
ξ ≳ 10−4
H. Moutarde CLAS Coll. Meeting 2015 7 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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.
.
JLab12(UnitedStates)
.
JLab6(United States)
.
HERMES
.
COMPASS
.
HERA
.
Dominant andsub-dominantcontributionsto the DVCSamplitudein the large Q2
limit?
H. Moutarde CLAS Coll. Meeting 2015 7 / 19
PARTONS Project.
.
..
Higher
Twists?
.
New
Experiments?
.
Meson
Production?
.
Error
Propagation?
.
Compton
Scattering?
.
Theoretical
Constraints?
.Software
.
Model
Dependence?.
Next to
Leading
Order?
. . . . . .
PARTONS Project.
.
PARtonicTomographyOfNucleonSoftware
. . . . . .
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
H. Moutarde CLAS Coll. Meeting 2015 9 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
H. Moutarde CLAS Coll. Meeting 2015 9 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
.
GPD at µ ̸= µrefF
.
GPD at µrefF
.
DVCS
.
TCS
.
DVMP
.
DVCS
.
TCS
.
DVMP
.
Evolution
H. Moutarde CLAS Coll. Meeting 2015 9 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
.
GPD at µ ̸= µrefF
.
GPD at µrefF
.
DVCS
.
TCS
.
DVMP
.
DVCS
.
TCS
.
DVMP
.
Manyobservables.
Kinematic reach.
.
Evolution
H. Moutarde CLAS Coll. Meeting 2015 9 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
.
GPD at µ ̸= µrefF
.
GPD at µrefF
.
DVCS
.
TCS
.
DVMP
.
DVCS
.
TCS
.
DVMP
.
Manyobservables.
Kinematic reach.
.
Perturbativeapproximations.
Physical models.
Fits.
Numericalmethods.
Accuracy andspeed.
.
Evolution
.
Need formodularity
H. Moutarde CLAS Coll. Meeting 2015 9 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
.
GPD at µ ̸= µrefF
.
GPD at µrefF
.
DVCS
.
TCS
.
DVMP
.
DVCS
.
TCS
.
DVMP
.
Manyobservables.
Kinematic reach.
.
Perturbativeapproximations.
Physical models.
Fits.
Numericalmethods.
Accuracy andspeed.
.
Evolution
.
Need formodularity
H. Moutarde CLAS Coll. Meeting 2015 9 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
.
GPD at µ ̸= µrefF
.
GPD at µrefF
.
DVCS
.
TCS
.
DVMP
.
DVCS
.
TCS
.
DVMP
.
Manyobservables.
Kinematic reach.
.
Perturbativeapproximations.
Physical models.
Fits.
Numericalmethods.
Accuracy andspeed.
.
Evolution
.
Need formodularity
H. Moutarde CLAS Coll. Meeting 2015 9 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
.
GPD at µ ̸= µrefF
.
GPD at µrefF
.
DVCS
.
TCS
.
DVMP
.
DVCS
.
TCS
.
DVMP
.
Manyobservables.
Kinematic reach.
.
Perturbativeapproximations.
Physical models.
Fits.
Numericalmethods.
Accuracy andspeed.
.
Evolution
.
Need formodularity
H. Moutarde CLAS Coll. Meeting 2015 9 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
.
GPD at µ ̸= µrefF
.
GPD at µrefF
.
DVCS
.
TCS
.
DVMP
.
DVCS
.
TCS
.
DVMP
.
Manyobservables.
Kinematic reach.
.
Perturbativeapproximations.
Physical models.
Fits.
Numericalmethods.
Accuracy andspeed.
.
Evolution
.
Need formodularity
H. Moutarde CLAS Coll. Meeting 2015 9 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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!
H. Moutarde CLAS Coll. Meeting 2015 10 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
H. Moutarde CLAS Coll. Meeting 2015 12 / 19
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
. . . . . .
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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 −
H. Moutarde CLAS Coll. Meeting 2015 14 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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 −
H. Moutarde CLAS Coll. Meeting 2015 14 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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 −
H. Moutarde CLAS Coll. Meeting 2015 14 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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− .
)−1Invert both members of equation:
(. . )−1 =
(1− .
)× (. )−1
= (. )−1 − .H. Moutarde CLAS Coll. Meeting 2015 14 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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− .
)−1Invert both members of equation: Forgotten contributions!
(. . )−1 =
(1− .
)× (. )−1
= (. )−1 − .H. Moutarde CLAS Coll. Meeting 2015 14 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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− .
)−1Invert both members of equation: Forgotten contributions!
(. . )−1 =
(1− .
)× (. )−1
= (. )−1 − .
.Gluon propagator..
...... .
H. Moutarde CLAS Coll. Meeting 2015 14 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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− .
)−1Invert both members of equation: Forgotten contributions!
(. . )−1 =
(1− .
)× (. )−1
= (. )−1 − .
.Quark propagator..
...... .
H. Moutarde CLAS Coll. Meeting 2015 14 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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− .
)−1Invert both members of equation: Forgotten contributions!
(. . )−1 =
(1− .
)× (. )−1
= (. )−1 − .
.Vertex..
...... .
H. Moutarde CLAS Coll. Meeting 2015 14 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
H. Moutarde CLAS Coll. Meeting 2015 15 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
H. Moutarde CLAS Coll. Meeting 2015 15 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
H. Moutarde CLAS Coll. Meeting 2015 15 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
H. Moutarde CLAS Coll. Meeting 2015 15 / 19
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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
. . . . . .
Phenomenologyof Generalized
PartonDistributions
Introduction
Needsassesment
Experimentalaccess
Kinematic reachof DVCS
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.
H. Moutarde CLAS Coll. Meeting 2015 18 / 19
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. . . . . .
Needs assesmentExperimental accessKinematic reach of DVCS
PARTONS ProjectComputing chainExampleTeam
GPD modeling in the Dyson-Schwinger frameworkGap equationPion form factor