from data to interpretation - Easycyprusconferences.org/einn2013/uploads/prsentations/Day... ·...
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Franck Sabatié CEA Saclay – Irfu/SPhN
in collaboration with P. Kroll, C. Mezrag, H. Moutarde,
B. Pire, L. Szymanowski, J. Wagner
Generalized Parton Distributions : from data to interpretation
> Theoretical framework
> Deeply Virtual Compton Scattering
> A test of Universality
> Beyond leading-order, RDDA, leading twist > Strategies for fitting GPDs
> Conclusion and outlook
Oct. 27th 2013
GPDs : matrix elements of bi-local twist-2 operators
… and equivalent expressions for gluons
In full analogy with the PDF definition :
+ another set for chiral-odd GPDs (with parton helicity flip)
Müller, Ji, Radyushkin
GPD properties
> Forward limit > Sum rules including Ji’s > Polynomiality > Impact parameter interpretation > Universality …
(see recent review by Leader, Lorcé)
Generalized Parton Distributions are Universal !
DVCS DVMP
TCS
The partonic interpretation of all these hard exclusive processes
relies on collinear factorization theorems valid in the Bjorken limit
of large Q2 and W, fixed xB ≈ 2ξ / (1+ξ)
The GPD’s then depend on an arbitrary factorization scale µF
which is the separation scale between soft and hard parts
The soft part, i.e. GPD’s, should be the same for DVCS, DVMP, TCS, … :
Not only is Universality an essential property
But we need it to Explore the whole GPD landscape
(indeed, all those processes have different dependences wrt
the GPD’s and quark flavors/gluons)
Factorization and Universality
Different Hard Processes : different advantages Deeply Virtual Compton Scattering q Theory is under control : up to , twist-3, target mass corrections, etc
q Sensitive to the quark combination :
q At JLab/HERMES energies, mostly sensitive to valence and sea quarks
q Sensitive to gluon GPDs through scale dependence at NLO or beyond
Direct access to the Re and Im part of Compton Form Factors
through interference with known Bethe-Heitler process
Hard Meson Electroproduction
q Many channels available for flavor separation (ρ0, ρ+, π0, π+, ϕ, …)
q J/Ψ and φ are especially interesting to access gluon GPDs (H and even E)
q Theory less under control : convolution with (unknown) meson WF,
very slow scaling, large power and NLO corrections
Müller et al, Braun et al
Diehl, Gousset, Pire, Ralston, …
4
9u+
1
9d+
1
9s+
4
9c
↵2S
The GK parametrization of GPDs
Double Distribution ansatz (Radyushkin, ’96 and later) :
Fi(x, ⇠, t) =
Z +1
�1d�
Z 1�|�|
�1+|�|d↵�(� � ↵⇠ � x)fi(↵,�, t) +Di⇥(⇠2 � x
2)
fi(↵,�, t) = zero-skewness GPD x weight fct. (generates dependence) ⇠
(Regge-like t-dependence)
D-term largely unknown, neglected in GK parametrization Advantages of DD’s: - polynomiality of GPD moments automatically satisfied
- parametrization in terms of PDF is easy Drawbacks of DD’s: been shown to lack flexibility, skewness-ratio problem
D-term
Goloskokov & Kroll, 2005-2011
F (⌅, ⇤ = 0, t) = f(⌅) exp⇥(bf + �0
f ln(1/⌅))t)⇤
f = q,�q, ⇥q for H, eH,HT or c⌅��f (0)(1� ⌅)⇥f
Goloskokov & Kroll, 2005-2011
Example of fits to ρ and φ cross-section HERA data
Excellent fit over a large kinematical range
Subprocess amplitude via Modified Perturbative Approach
Sterman et al, 92
ZEUS
H1
ZEUS
H1
ZEUS
Integration Kernel has been worked out up to NLO
GPD’s
Compton Form Factor (CFF) CFF are complex functions !
GPD’s enter DVCS through Compton Form Factors
Müller et al and many others
F(⇠, t, Q2) =
Z +1
�1dx C
✓x, ⇠,↵S(µR),
Q
µF
◆F (x, ⇠, t, µF )
Factorization scale dependence through evolution equations
⇠ ' xB
2� xB
Definition of DVCS observables
In the one-photon exchange approximation of QED, the BH, DVCS and interference parts of the cross section read :
DVCS Bethe-Heitler
Diehl et al
|MBH|2 � 1
|t|1
P (cos�)
3X
n=0
⇥cBHn cos(n�) + sBH
n sin(n�)⇤
|MDVCS|2 �3X
n=0
⇥cDVCSn cos(n�) + sDVCS
n sin(n�)⇤
MI � 1
|t|1
P (cos�)
3X
n=0
⇥cIn cos(n�) + sIn sin(n�)
⇤
The lp → lpγ cross section on an unpolarized target for a given beam charge el and beam helicity hl /2 can be written as :
If one has access to both different beam charges and helicities, one can extract :
If one only has access to different beam helicities, one can extract :
(equivalent expressions for polarized target case)
Definition of DVCS observables
d�hl,el(⇥) = d�UU(⇥) [1 + hlALU,DVCS(⇥) + elhlALU,I(⇥) + elAC(⇥)]
AC(⇥) =1
4d�UU(⇥)
(d�
+! + d�+ )� (d�
�! + d�� )
�
ALU,I(⇥) =1
4d�UU(⇥)
(d�
+! � d�+ )� (d�
�! � d�� )
�
ALU,DVCS(⇥) =1
4d�UU(⇥)
(d�
+! � d�+ ) + (d�
�! � d�� )
�
AelLU(⇥) =
d�el! � d�
el
d�el! + d�
el =
elALU,I(⇥) +ALU,DVCS(⇥)
1 + elAC(⇥)
Definition of DVCS observables
Finally, experiments sometimes prefer to publish Fourier Harmonics of the asymmetries which are linked to the CFF’s. Taking the charge asymmetry for instance, it is evaluated this way : In the BMK approximation, a few different harmonics read :
Acos(n⇥)C = N
Z2�
0
d�AC(�) cos(n�)
N is 1/2� in the case n = 0 and 1/� for n � 1
Acos�C ⇥ Re
hF1
H+ �(F1
+ F2
)H̃� t
4m2
F2
Ei
Asin�LU,I ⇥ Im
hF1
H+ �(F1
+ F2
)H̃� t
4m2
F2
Ei
Asin�UL,I ⇥ Im
h�(F
1
+ F2
)(H+�
1 + �E) + F
1
eH� �(�
1 + �F1
+t
4M2
F2
)eEi
Acos�LL,I ⇥ Re
h�(F
1
+ F2
)(H+�
1 + �E) + F
1
eH� �(�
1 + �F1
+t
4M2
F2
)eEi
DVCS data set worldwide
Various asymmetries with beam helicity, charge and target L and T polarizations
Various asymmetries with beam helicity and target L polarization
Helicity-dependent cross sections
DVCS cross sections and charge asymmetry
Experiment Observable Normalized CFF dependence
Acos 0�C
ReH+ 0.06ReE + 0.24Re eH
Acos�C
ReH+ 0.05ReE + 0.15Re eH
Asin�LU,I ImH+ 0.05ImE + 0.12Im eH
A+,sin�UL
Im eH+ 0.10ImH+ 0.01ImE
HERMES A+,sin 2�UL
Im eH� 0.97ImH+ 0.49ImE � 0.03ImeE
A+,cos 0�LL
1 + 0.05Re eH+ 0.01ReH
A+,cos�LL
1 + 0.79Re eH+ 0.11ImH
Asin(���S)
UT,DVCS
ImHReE � ImEReH
Asin(���S) cos�UT,I ImH� 0.56ImE � 0.12Im eH
A�,sin�LU
ImH+ 0.06ImE + 0.21Im eH
CLAS A�,sin�UL
Im eH+ 0.12ImH+ 0.04ImE
A�,sin 2�UL
Im eH� 0.79ImH+ 0.30ImE � 0.05ImeE
��sin� ImH+ 0.07ImE + 0.47Im eH
HALL A �cos 0� 1 + 0.05ReH+ 0.007HH⇤
�cos� 1 + 0.12ReH+ 0.05Re eH
HERA �DVCS
HH⇤ + 0.09EE⇤ + eH eH⇤
DVCS data kinematics
q DVCS data cover complementary kinematical regions
DVCS data kinematics
q DVCS data cover complementary kinematical regions
q Warning : |t|/Q2 is not always small
DVCS data and their sensitivity to CFF’s Experiment Observable Normalized CFF dependence
Acos 0�C
ReH+ 0.06ReE + 0.24Re eH
Acos�C
ReH+ 0.05ReE + 0.15Re eH
Asin�LU,I ImH+ 0.05ImE + 0.12Im eH
A+,sin�UL
Im eH+ 0.10ImH+ 0.01ImE
HERMES A+,sin 2�UL
Im eH� 0.97ImH+ 0.49ImE � 0.03ImeE
A+,cos 0�LL
1 + 0.05Re eH+ 0.01ReH
A+,cos�LL
1 + 0.79Re eH+ 0.11ImH
Asin(���S)
UT,DVCS
ImHReE � ImEReH
Asin(���S) cos�UT,I ImH� 0.56ImE � 0.12Im eH
A�,sin�LU
ImH+ 0.06ImE + 0.21Im eH
CLAS A�,sin�UL
Im eH+ 0.12ImH+ 0.04ImE
A�,sin 2�UL
Im eH� 0.79ImH+ 0.30ImE � 0.05ImeE
��sin� ImH+ 0.07ImE + 0.47Im eH
HALL A �cos 0� 1 + 0.05ReH+ 0.007HH⇤
�cos� 1 + 0.12ReH+ 0.05Re eH
HERA �DVCS
HH⇤ + 0.09EE⇤ + eH eH⇤
Our framework
GPD’s we used are from Goloskokov-Kroll model (fitted to DVMP, PDF, FF data)
GPD’s H and H evolutions are therefore done through PDF’s at µF=Q
GPD’s were not adjusted using DVCS data
Kernel is calculated at Leading-Order of αS
Leading-Twist (in the hadronic tensor OPE)
No D-term
No finite-t or target-mass corrections (Braun et al. recent work)
Exact calculation of all leptonic parts (no 1/Q expansion as in BMK, DS)
Error bands are evaluated using polarized and unpolarized PDF errors Article published in Eur. Phys. J. C (2013) 73:2278 [arXiv:1210.6975]
~
Low-xB DVCS cross sections (H1 and ZEUS)
q q Dominated by ImH of sea quarks q Important evolution effects (Q2 from 3 to 25 GeV2) q Reasonable agreement over the whole data range
71 GeV W 104 GeV
DVCS Charge Asymmetry (HERMES) arXiv:1203.6287
q Dominated by ReH q In perfect agreement over the whole t-range
hxBi ' 0.1⌦Q
2↵
' 2.5 GeV2
DVCS Beam Spin Asymmetries (HERMES, CLAS) q Dominated by ImH q In perfect agreement for HERMES recoil data q Something missing at higher xB (CLAS)
HERMES arXiv:1203.6287
Recoil data from arXiv:1206.5683
Non-recoil data from arXiv:1203.6287
CLAS arXiv:0711.4805
hxBi ' 0.1⌦Q
2↵
' 2.5 GeV2
h�ti ' 0.3 GeV2
DVCS helicity-dependent cross sections (Hall A)
q Δσ dominated by ImH, in perfect agreement q Total cross section more challenging q … and more data to come, e.g. see M. Defurne’s poster
nucl-ex/0607029
hxBi ' 0.36⌦Q
2↵
' 2.3 GeV2
New Hall A DVCS data Please see M. Defurne’s poster !
DVCS L-Target Spin Asymmetries (HERMES, CLAS)
q Dominated by ImH
q sinφ harmonic in good agreement q HERMES sin2φ unexpectedly large q Expect large
improvement with recent EG1-DVCS data
~
CLAS hep-ex/0605012
HERMES arXiv:1004.0177
hxBi ' 0.28⌦Q
2↵
' 1.82 GeV2
hxBi ' 0.1⌦Q
2↵
' 2.5 GeV2
DVCS T-Target Spin Asymmetries (HERMES)
hxBi ' 0.09⌦Q
2↵
' 2.5 GeV2
Asin(���S)UT,DVCS � Im[E⇤H]
Asin(���S)UT,DVCS ⇥= 0 =� E ⇥= 0
cancellation between Esand Eg
does not occur as for �0 asymmetry,
DVCS observables are very sensitive to Esea
Esea < 0 is favored by DVCS data
Conclusion on this universality check q Using GPD’s fit to low-to-mid-xB DVMP data (+PDF, FF) we evaluated DVCS observables at LO and Leading-Twist q Agreement with data is good for HERA and HERMES, fair for JLab Possible improvements, recent work:
q NLO kernel + NLO GPD evolution : next part of this talk (Moutarde, Pire, F.S., Szymanowski, Wagner, PRD87 (2013) 054029, arXiv:1301.3819) q Resummation of soft-collinear contributions in DVCS (Altinoluk, Pire, Szymanowski, Wallon, JHEP 1210 (2012) 049, arXiv:1207.4609) q Modification of the profile function and/or add D-term (Mezrag, Moutarde, F.S., PRD88 (2013) 014001, arXiv:1304.7645) q Finite-t and target mass corrections (work in progress based on Braun et al., non-trivial) q And … of course, of upmost importance, add more data :
CLAS 6 & 12, Hall A 6 & 12, COMPASS-II and … EIC
From Leading-Order to Next-to-Leading-Order
Generic expression of Compton Form Factor :
From Leading-Order to Next-to-Leading-Order
From Leading-Order to Next-to-Leading-Order
Main differences : - gluon GPDs contribute to DVCS at NLO - factorization scale dependence of the kernel at NLO
- extra logs in the kernel, integrals are trickier to evaluate
Belitsky, Müller, Pire et al, etc
An important consequence, no direct access to H(ξ,ξ) anymore at NLO !
From Leading-Order to Next-to-Leading-Order
Next-to-leading order studies : ReH
LO
Full NLO
NLO, no gluons
RDDA using MSTW08 Goloskokov-Kroll
Significant corrections for quarks Very large/huge (model-dependent) corrections from gluons
NLO correction peaks in the COMPASS-II kinematical range
LO
Full NLO
NLO, no gluons
Significant corrections for quarks Large corrections from gluons, less model dependence than for the Re part
The good : large sensitivity to gluon GPDs even at moderate/large xB
The bad : a quantitative extraction of GPDs at LO is not legitimate
Next-to-leading order studies : ImH
Effect on observables at Ebeam= 6 GeV
φ [deg] φ [deg] φ [deg] φ [deg]
CLAS 6 GeV data LO NLO quarks only Full NLO
GK model with LO/NLO kernel
LO
Full NLO
NLO, no gluons
Effect on observables at Ebeam= 11 GeV
LO
Full NLO
NLO, no gluons
BH
GK model
MSTW08 RDDA model
HERMES data versus Double-Distribution models
Guidal, Moutarde, Vanderhaeghen Rept. Prog. Phys. 76, 066202 (2013)
Usual Double-Distribution based models lack flexibility to describe worldwide data
Extending Double Distribution-based models C. Mezrag, H. Moutarde, F.S.
PRD88 (2013) 014001, arXiv:1304.7645 Please check out Cédric’s poster this evening !
Higher-twist & Power corrections
Dynamical/geometrical/genuine/… twist: - a work in progress, very few phenomenology results about this,
- will be needed for quantitative GPD extraction A recent example (Braun et al., 2012): Finite-t and target mass corrections are potentially sizeable (recent phenomenological evaluation seems to indicate small effect on DVCS observables)
GPD fitting strategies, so far
Local fits : treat each kinematic bin independantly, fit CFF Global fits : Take all kinematic bins at once (either low-xB or high-xB),
Use a parametrization of GPDs (or CFFs). Hybrid fits : Start from local fits and … connect the dots Neural Network fits : same technique as for PDF, better for error estimate
of extrapolated areas Four methods, one thing in common : A LOT OF WORK IS NEEDED > Either many d.o.f. or too few. Very rough hypothesis. For now, gives at best a qualitative estimate of some CFFs in specific kinematic regimes (see M. Guidal’s talk/slides)
BMK, Hall A, Guidal, Moutarde, Mueller, Murray (detailed in M. Guidal’s talk on monday)
Kumericki, Mueller
Moutarde
Kumericki, Mueller, Schäfer
Conclusion : what did we learn ? > Dominance of twist-2, validity of a GPD analysis of DVCS data > Within hypothesis, ImH well known, ReH poorly constrained for now > Some of those hypothesis are « rough » : Leading Order, Leading-twist,
H-dominance > In order to get better than 20-30% accuracy, a lot of work is needed For now, GPD/CFF extraction accuracy is actually completely dominated by limitations stemming from theory and phenomenology, not by data accuracy.
(for JLab data especially)
Backup Slides
What did we learn about GPD’s from DVMP
Slide from P. Kroll, QCD-N’12 Bilbao
Typical kinematics of experimental data sets
What data to be expected in the future?
Short-term (2012-2013) : JLab CLAS: Finalized analysis of DVCS cross sections (1st run) JLab CLAS: Updated results with 2nd half of DVCS run JLab CLAS: Finalized analysis of NH3 and ND3 data on DVCS JLab Hall A: Rosenbluth separation of DVCS cross section (+ π0) Mid-term (2014-2020+) : JLab CLAS12: Approved DVCS program (LH2, LD2, NH3) + more to come JLab Hall A: Approved DVCS program with up to 11 GeV beam JLab Hall C: Approved DVCS program with up to 11 GeV beam COMPASS-II: Short DVCS run in 2012, then 2016+ (also DVMP) Long-term (2025+) EIC : DVCS and DVMP
Analysis of Deep Virtual Meson Production
Subprocess amplitude via Modified Perturbative Approach Sterman et al, 92
LO pQCD + quark + Sudakov suppression (large transverse separation)
On the proton side, partons are emitted/absorbed colinearly Meson wave function are gaussians : Fit to all meson data from H1, ZEUS, E665, HERMES, COMPASS Large range of xB (10-4-0.1), Q2 (3-100 GeV2) and W (5-180 GeV) Why not CLAS data (on ρ0 for instance) ?
Goloskokov & Kroll, 2005-2011
k?
10 100101
102
� L(�
* p->�
p) [
nb]
W[GeV]4 6 8 20 40 60
Consequence: model tuned for rather low values of xB
Break-down of handbag description
Transverse target spin asymmetry for ρ0
COMPASS (12)
- Small asymmetry measured by both COMPASS and HERMES
- In GK model, gluon and sea contributions for E cancel each other for ρ0
- Dominated by valence quark contributions from E but small at these xB values
Goloskokov & Kroll, 2005-2011
Near future : COMPASS-II and JLab12
COMPASS-II
CLAS12
HallA12
q Mixed charge and spin observables at COMPASS-II
q JLab12 : dealing with statistical errors ~1% q x10-100 more data expected in the next few years