on deeply virtual compton scattering at next to leading...

ComptonScattering at

NLO

Introduction

Theoreticalframework

Comptonscattering

ExplicitExpressions

Evaluation ofComptonForm Factors

GPD Models

Comptonscattering

Impact onfutureexperiments

CLAS12

COMPASS

Conclusion

. . . . . .

On Deeply Virtual Compton Scattering atNext to Leading Order

...

H. Moutarde

Irfu/SPhN, CEA-Saclay

Baryons 2013

June 25th, 2013

. c⃝ animea, 2011.

In collaboration with : B. Pire, F. Sabatie,L. Szymanowski and J. Wagner.Phys. Rev. D87, 054029 (2013).

H. Moutarde (Irfu/SPhN, CEA-Saclay) Baryons 2013 - 25 / 06 / 2013 1 / 14


NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .

Motivation.Study the nucleon structure to shed new light on non-perturbative QCD.

.Perturbative

QCD..

......

.Asymptoticfreedom

..

......

.Non-perturbative

QCD..

.......Perturbative AND non-perturbative QCD at work..

......

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

Relate GPDs to measurements using factorization:Space- and timelike Compton Scattering (DVCS, TCS).

Get experimental knowledge of nucleon structure.H. Moutarde (Irfu/SPhN, CEA-Saclay) Baryons 2013 - 25 / 06 / 2013 2 / 14


NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .

Motivations.3D imaging of nucleon’s partonic content but also. . .

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

Insights on:

Spin structure,Energy-momentum structure.

Probabilistic interpretation of Fourier transform ofGPD(x , ξ = 0, t) in transverse plane.

.Obtain this 3d picture from exclusive measurements ?..

...... x ~ 0.3xx < 0.01 ~ 0.1

spintransverse

(c)

b

xP

longitud.

(a)

transverse

pioncloud quarks

valence

(b)

quarks, gluonssinglet

quarks movefaster

slowerWeiss, AIPConf. Proc.1149, 150(2009)



NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .

Timelike and spacelike Compton Scattering.Scattering amplitudes and their partonic interpretation.

..

e−

.

DVCS

.

e−

.

γ

.

Q2

.

p

.

γ

.

p

.t

.Compton Form Factors (CFF)..

......

Parametrize amplitudes.

Evaluation at LO.

Evaluation at NLO.

Other diagrams at NLO,including gluon GPDs.

..

e−

.

DVCS

.

e−

.

γ, Q2

.

p

.

p

.

γ

.

x + ξ

.

x − ξ

.

factorization µF



NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .


..

e−

.

DVCS

.

e−

.

γ

.

Q2

.

p

.

γ

.

p

.t


......


Evaluation at LO.

Evaluation at NLO.


..

e−

.

DVCS

.

e−

.

γ, Q2

.

p

.

p

.

γ

.

x + ξ

.

x − ξ

.

factorization µF

..

TCS

.

e−

.

e+

.

γ, Q2

.

p

.

p

.

x + ξ

.

x − ξ

.

γ

.

factorization µF

..

e−

.

DVCS

.

e−

.

γ, Q2

.

p

.

p

.

γ

.

x + ξ

.

x − ξ

.

factorization µF



NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .


..

e−

.

DVCS

.

e−

.

γ

.

Q2

.

p

.

γ

.

p

.t


......


Evaluation at LO.

Evaluation at NLO.


..

e−

.

DVCS

.

e−

.

γ, Q2

.

p

.

p

.

γ

.

x + ξ

.

x − ξ

.

factorization µF

..

e−

.

DVCS

.

e−

.

γ, Q2

.

p

.

p

.

γ

.

x + ξ

.

x − ξ

.

factorization µF

..

e−

.

DVCS

.

e−

.

γ, Q2

.

p

.

p

.

γ

.

x + ξ

.

x − ξ

.

factorization µF



NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .


..

e−

.

DVCS

.

e−

.

γ

.

Q2

.

p

.

γ

.

p

.t


......


Evaluation at LO.

Evaluation at NLO.


..

e−

.

DVCS

.

e−

.

γ, Q2

.

p

.

p

.

γ

.

x + ξ

.

x − ξ

.

factorization µF

..

e−

.

DVCS

.

e−

.

γ, Q2

.

p

.

p

.

γ

.

x + ξ

.

x − ξ

.

factorization µF



NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .

Explicit expressions of Compton Form Factors.Quark and gluon contributions to the CFF H at LO and NLO (at fixed t).

Convolution of singlet GPD H+q (x) ≡ Hq(x)− Hq(−x) :

Hq(ξ,Q2)

LO=

∫ +1

−1dx H+

q (x , ξ, µF )(Tq

(x , ξ, αS(µF ),

Q

µF

)+Cq

1 +1

2ln

|Q2|µ2F

Cqcoll

)+

∫ +1

−1dx Hg (x , ξ, µF )(Tg

(x , ξ, αS(µF ),

Q

µF

)+C g

1 +1

2ln

|Q2|µ2F

)Belistky and Muller, Phys. Lett. B417, 129 (1998)

Pire et al, Phys. Rev. D83, 034009 (2011)

Integration yields imaginary parts to H :

ImHq(ξ,Q2)

NLO= I(ξ)H+

q (ξ, ξ, µF )

+

∫ +1

−1dx T q(x)

(H+q (x , ξ, µF )− H+

q (ξ, ξ, µF ))

+ gluon contributions.



NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .


Convolution of singlet GPD H+q (x) ≡ Hq(x)− Hq(−x) :

Hq(ξ,Q2)

LO=

∫ +1

−1dx H+

q (x , ξ, µF )[Cq0 (x , ξ)+Cq

1 +1

2ln

|Q2|µ2F

CqColl

]+

∫ +1

−1dx Hg (x , ξ, µF )[0+C g

1

(Q

µF

)+

1

2ln

|Q2|µ2F

C gcoll

]Belistky and Muller, Phys. Lett. B417, 129 (1998)



ImHq(ξ,Q2)

LO= πH+

q (ξ, ξ, µF )

+

∫ +1

−1dx T q(x)

(H+q (x , ξ, µF )− H+

q (ξ, ξ, µF ))



ImHq(ξ,Q2)

NLO= I(ξ)H+

q (ξ, ξ, µF )

+

∫ +1

−1dx T q(x)

(H+q (x , ξ, µF )− H+

q (ξ, ξ, µF ))




NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .


Convolution of singlet GPD H+q (x) ≡ Hq(x)−Hq(−x) :

Hq(ξ,Q2)

NLO=

∫ +1

−1dx H+

q (x , ξ, µF )

[Cq0 + Cq

1 +1

2ln

|Q2|µ2F

CqColl

]+

∫ +1

−1dx Hg (x , ξ, µF )

(0 + C g

1 +1

2ln

|Q2|µ2F

C gColl

)Belistky and Muller, Phys. Lett. B417, 129 (1998)



ImHq(ξ,Q2)

NLO= I(ξ)H+

q (ξ, ξ, µF )

+

∫ +1

−1dx T q(x)

(H+q (x , ξ, µF )− H+

q (ξ, ξ, µF ))




NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .

Explicit expressions of Compton Form Factors.Compton Scattering: LO vs NLO.

.Imaginary part of Compton Form Factor Hq at NLO:..

......

ImHq(ξ,Q2)

NLO= I(ξ)H+

q (ξ, ξ, µF )

+

∫ +1

−1dx T q(x)

(H+q (x , ξ, µF )− H+

q (ξ, ξ, µF ))


.Due to O

(αS(µF )

)corrections:

..

......

ImHq is no more equal to πH+q (x = ξ, ξ) (LO):

Multiplicative factor I depends on ξ.Integral with off-diagonal terms.ImHq contains gluon contributions.

No more direct link to Hq even in valence region whereHq(−ξ, ξ) is expected to be small.

Question: What is the size of these O(αS(µF )

)corrections?



NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .



......

ImHq(ξ,Q2)

NLO= I(ξ)H+

q (ξ, ξ, µF )

+

∫ +1

−1dx T q(x)

(H+q (x , ξ, µF )− H+

q (ξ, ξ, µF ))


.Due to O

(αS(µF )

)corrections:

..

......


Multiplicative factor I depends on ξ.

Integral with off-diagonal terms.ImHq contains gluon contributions.



)corrections?



NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .



......

ImHq(ξ,Q2)

NLO= I(ξ)H+

q (ξ, ξ, µF )

+

∫ +1

−1dx T q(x)

(H+q (x , ξ, µF )− H+

q (ξ, ξ, µF ))


.Due to O

(αS(µF )

)corrections:

..

......


Multiplicative factor I depends on ξ.Integral with off-diagonal terms.

ImHq contains gluon contributions.



)corrections?



NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .



......

ImHq(ξ,Q2)

NLO= I(ξ)H+

q (ξ, ξ, µF )

+

∫ +1

−1dx T q(x)

(H+q (x , ξ, µF )− H+

q (ξ, ξ, µF ))


.Due to O

(αS(µF )

)corrections:

..

......


Multiplicative factor I depends on ξ.Integral with off-diagonal terms.ImHq contains gluon contributions.



)corrections?



NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .

Double Distribution models of the GPD H .Kroll - Goloskokov model.

Factorized Ansatz. For i = g , sea or val :

Hi (x , ξ, t) =

∫|α|+|β|≤1

dβdα δ(β + ξα− x)fi (β, α, t)

fi (β, α, t) = ebi t1

|β|α′thi (β)πni (β, α)

πni (β, α) =Γ(2ni + 2)

22ni+1Γ2(ni + 1)

(1− |β|)2 − α2]ni

(1− |β|)2ni+1

Expressions for hi and ni :

hg (β) = |β|g(|β|) ng = 2hqsea(β) = qsea(|β|)sign(β) nsea = 2hqval(β) = qval(β)Θ(β) nval = 1

Goloskokov and Kroll, Eur. Phys. J. C42, 281 (2005)

Comparison to existing DVCS measurements at LO.

Kroll et al. , Eur. Phys. J. C73, 2278 (2013)H. Moutarde (Irfu/SPhN, CEA-Saclay) Baryons 2013 - 25 / 06 / 2013 7 / 14


NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .

Double Distribution models of the GPD H .MSTW08 based model with classical Radyushkin’s factorized Ansatz.

Use MSTW08 Parton Distribution Functions.

Martin et al., Eur. Phys. J. C. 63 (2009) 189.

Assume factorized t-dependence:

H(x , ξ, t) =

∫|α|+|β|≤1

dβdα δ(β + ξα− x)π(β, α)f (β, t)

u and d quarks:

fu(β, α, t) =1

2F u1 (t)u(β)π(β, α)

fd(β, α, t) = F d1 (t)d(β)π(β, α)

with F u1 and F d

1 the u and d quark contributions to theproton form factor F1.s quark and gluons: dipole Ansatz.

Add D-term from Chiral Quark Soliton Model.

Goeke et al., Prog.Part.Nucl.Phys. 47 (2001) 401



NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .

Spacelike CFF H: large NLO contribution.Mostly due to gluons, maximum in HERMES / COMPASS kinematic region.

.ReH at LO and NLO (t = −0.1 GeV2, Q2 = µ2

F = 4. GeV2)..

...... Moutarde et al. , Phys. Rev. D87, 054029 (2013)

dotted: LO dashed: NLO quark corrections solid: full NLOLeft: KG model Right: MSTW08-based modelH. Moutarde (Irfu/SPhN, CEA-Saclay) Baryons 2013 - 25 / 06 / 2013 9 / 14


NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .

Spacelike CFF H: large NLO contribution.Mostly due to gluons, maximum in HERMES / COMPASS kinematic region.

.ImH at LO and NLO (t = −0.1 GeV2, Q2 = µ2

F = 4. GeV2)..




NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .

Timelike CFF H: large NLO contribution.Mostly due to gluons, maximum in HERMES / COMPASS kinematic region.

.ReH at LO and NLO (t = −0.1 GeV2, Q2 = µ2

F = 4. GeV2)..




NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .

Timelike CFF H: large NLO contribution.Mostly due to gluons, maximum in HERMES / COMPASS kinematic region.

.ImH at LO and NLO (t = −0.1 GeV2, Q2 = µ2

F = 4. GeV2)..




NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .

Projections: CLAS12 kinematics, DVCS channel.Sizeable NLO corrections and gluon contributions.

.Ee = 11 GeV, xB = 0.36,Q2 = µ2

F = 4. GeV2, t = −0.2 GeV2

..


dotted: LO dashed: NLO quark corrections solid: full NLOUpper line: KG model Lower line: MSTW08-based modelH. Moutarde (Irfu/SPhN, CEA-Saclay) Baryons 2013 - 25 / 06 / 2013 11 / 14


NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .

Projections: CLAS12 kinematics, TCS channel.Sizeable NLO corrections and gluon contributions.

.Eγ = 10 GeV (η ≃ 0.11),Q2 = µ2

F = 4. GeV2, t = −0.1 GeV2

..


dashed: pure BH dotted: BH solid: BH+ LO Interference + NLO Interference

KG model Cross section integrated over θ ∈(π4 ,

3π4

)H. Moutarde (Irfu/SPhN, CEA-Saclay) Baryons 2013 - 25 / 06 / 2013 12 / 14


NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .

Projections: COMPASS kinematics, DVCS channel.Sizeable NLO corrections and gluon contributions.

.Eµ = 160 GeV, xB = 0.1,Q2 = µ2

F = 4. GeV2, t = −0.2 GeV2

..


dotted: LO dashed: NLO quark corrections solid: full NLOUpper line: KG model Lower line: MSTW08-based modelH. Moutarde (Irfu/SPhN, CEA-Saclay) Baryons 2013 - 25 / 06 / 2013 13 / 14


NLO

Introduction


Comptonscattering

ExplicitExpressions


GPD Models

Comptonscattering


CLAS12

COMPASS

Conclusion

. . . . . .

Conclusion.Constraining gluon GPDs even from data in the valence region?

Large NLO ”corrections” to DVCS and TCS amplitudes.

Need resummed expressions!

Altinoluk et al., JHEP 1210 (049) 2012Altinoluk et al., arXiv:1206.3115 [hep-ph]

Enhanced effect in the TCS case.

Sensitivity to gluon GPDs even in the valence region.

Direct impact on extraction of CFFs from experimentaldata and their interpretation.

Need global GPD fits to separate quarks and gluoncontributions and allow an accurate interpretation ofextracted data.

DVCS experiments may provide constraints on gluonGPDs in the near future!


on deeply virtual compton scattering at next to leading...

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