Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections...
Transcript of Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections...
![Page 1: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/1.jpg)
Extracting GPDs from DVCS data: Border and skewness functions at LO
Getting to Grips with QCD - Summer EditionPrimošten, September 18 - 22, 2018
Paweł SznajderNational Centre for Nuclear Research, Warsaw
![Page 2: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/2.jpg)
■ Introduction
■ PARTONS project
■ Global analysis of DVCS
■ Summary
Outline
Paweł Sznajder Getting to Grips with QCD SE 2
![Page 3: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/3.jpg)
factorization for |t|/Q2 ≪ 1
for sum overparton helicities
for difference over parton helicities
nucleon helicity changed
Chiral-even GPDs:(helicity of parton conserved)
nucleon helicity conserved
Deeply Virtual Compton Scattering (DVCS)
Introduction
Paweł Sznajder Getting to Grips with QCD SE 3
![Page 4: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/4.jpg)
■ Nucleon tomography
x
x
b⊥
active quark with momentum x
spectators with momentum 1 - x
center of momentum
■ Study of long. polarization with GPD H ■ Study of distortion in transv. polarized nucleon with GPD E
■ Impact parameter b⊥ defined w.r.t. center of momentum, such as
Introduction
~
Paweł Sznajder Getting to Grips with QCD SE 4
![Page 5: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/5.jpg)
Access to total angular momentum and forces acting on quarks
Energy momentum tensor in terms of form factors:
Introduction
Ji's sum rule
Paweł Sznajder Getting to Grips with QCD SE 5
![Page 6: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/6.jpg)
H. Moutarde, P. S., J. Wagner "Border and skewness functions from a leading order fit to DVCS data"arXiv:1807.07620 [hep-ph]
Goal: global extraction of Compton Form Factors (CFFs) from DVCS data using LO/LT formalism
Analysis done within PARTONS project
Analysis
Paweł Sznajder Getting to Grips with QCD SE 6
![Page 7: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/7.jpg)
PARTONS project
■ PARTONS - platform to study GPDs
■ Come with number of available physics developments implemented
■ Addition of new developments as easy as possible
■ To support effort of GPD community
■ Can be used by both theorists and experimentalists
■ More info in: Eur. Phys. J. C78 (2018) 6, 478
http://partons.cea.fr
DVCS TCS HEMP
Observable Layer
DVCS TCS HEMP
Process Layer
DVCS TCS HEMP
CCF Layer
GPDs and Evolution
GPD Layer
Paweł Sznajder Getting to Grips with QCD SE 7
![Page 8: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/8.jpg)
PARTONS project
■ PARTONS - platform to study GPDs
■ Come with number of available physics developments implemented
■ Addition of new developments as easy as possible
■ To support effort of GPD community
■ Can be used by both theorists and experimentalists
■ More info in: Eur. Phys. J. C78 (2018) 6, 478
http://partons.cea.fr
Hu @ = 0.2, t = -0.1 GeV2, μF2 = μR
2 = 2 GeV2
GK11MPSSW13VGGVinnikov
Paweł Sznajder Getting to Grips with QCD SE 8
![Page 9: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/9.jpg)
Compton Form Factors
■ imaginary part
"−" for
■ real part
"+" for
Paweł Sznajder Getting to Grips with QCD SE 9
![Page 10: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/10.jpg)
Subtraction Constant
Relation between subtraction constant and D-term:
where
Decomposition into Gegenbauer polynomials:
Connection to EMT FF:
Paweł Sznajder Getting to Grips with QCD SE 10
![Page 11: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/11.jpg)
Subtraction Constant
Comparing CFFs evaluated with two methods
for ξ = 0
divergent integral!but
well defined for odd positive j
Paweł Sznajder Getting to Grips with QCD SE 11
![Page 12: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/12.jpg)
Subtraction Constant
Subtraction constant as analytic continuation of Mellin moments to j = -1
Analytic regularization prescription
applicable if f(x) analytic and not-vanishing at x = 0
Paweł Sznajder Getting to Grips with QCD SE 12
![Page 13: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/13.jpg)
Ansatz for H and H
■ modify "classical" log(1/x) term by BGq(1-x)2 in low-x and by CG
q(1-x)x in high-x regions
■ polynomials found in analysis of EFF data → good description of data
■ allows to use the analytic regularization prescription
■ finite proton size at x → 1
~
Paweł Sznajder Getting to Grips with QCD SE 13
![Page 14: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/14.jpg)
■ at x → 0 constant skewness effect
■ at x → 1 reproduce power behavior predicted for GPDs in Phys. Rev. D69, 051501 (2004)
■ t-dependence similar to DD-models with (1-x) to avoid any t-dep. at x = 1
Ansatz for H and H~
Paweł Sznajder Getting to Grips with QCD SE 14
GK GPD model~1/(1 - x2)2
![Page 15: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/15.jpg)
"trouble" with analytic regularization
where in our case
compensating terms singular for and unless at and at , condition provided by:
where are PDF parameterization parameters
Ansatz for H and H~
Paweł Sznajder Getting to Grips with QCD SE 15
![Page 16: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/16.jpg)
Ansatz for E and E~
■ for GPD E
from Eur. Phys.J. C73 (2013) 4, 2397
from Phys. Rev. D69, 051501 (2004)
■ for GPD E~
CFF from GK GPD model
Paweł Sznajder Getting to Grips with QCD SE 16
![Page 17: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/17.jpg)
Steps of analysis:
Step 1Analysis of PDFs
Step 2Analysis of EFF data
Step 3Analysis of DVCS data
Effectively we combine (semi-)inclusive, pp, elastic and exclusive data in a single analysis
Analysis
Paweł Sznajder Getting to Grips with QCD SE 17
![Page 18: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/18.jpg)
uval
Δdsea
Ansatz:
13 parameters:
constrained by NNPDF3.0 and NNPDFpol11 sets (per each flavor and each PDF replica)
where
PDFs
Paweł Sznajder Getting to Grips with QCD SE 18
![Page 19: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/19.jpg)
for the selection of observables and experimental data we follow Eur. Phys.J. C73 (2013) 4, 2397
Elastic FF data
From Dirac and Pauli partonic FFs to Sachs nucleon FFs
Free parameters for valance quarks and GPDs H and E constrained by EFF data
Observables
Paweł Sznajder Getting to Grips with QCD SE 19
![Page 20: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/20.jpg)
GM,Np
GM,Nn
Rp
Rn
rnE2GEn
Performance:
Replication of experimental data to estimate corresponding uncertainties:
Fitted values:
Paweł Sznajder Getting to Grips with QCD SE 20
![Page 21: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/21.jpg)
F1u F1d
F2dF2u
Paweł Sznajder Getting to Grips with QCD SE 21
![Page 22: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/22.jpg)
Kinematic cuts:
All DVCS proton data used in the fit, except:• HERA data • Hall A cross sections
DVCS data
Angles:
Paweł Sznajder Getting to Grips with QCD SE 22
![Page 23: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/23.jpg)
Performance: Fitted values:
Replication of experimental data to estimate corresponding uncertainties:
DVCS data
Paweł Sznajder Getting to Grips with QCD SE 23
![Page 24: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/24.jpg)
Results
Phys. Rev. D91(5), 052014 (2015) Phys. Rev. Lett. 115(21), 212003 (2015)
CLAS data:
this analysisGK modelVGG model
Paweł Sznajder Getting to Grips with QCD SE 24
![Page 25: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/25.jpg)
Results this analysisGK modelVGG modelHERMES data:
JHEP 06, 066 (2008)
Paweł Sznajder Getting to Grips with QCD SE 25
![Page 26: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/26.jpg)
Results this analysisGK modelVGG modelHall A data:
Phys. Rev. C92(5), 055202 (2015)
Paweł Sznajder Getting to Grips with QCD SE 26
![Page 27: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/27.jpg)
Results this analysisGK modelVGG modelCOMPASS and HERA:
arXiv: hep-ex/1802.02739
Paweł Sznajder Getting to Grips with QCD SE 27
![Page 28: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/28.jpg)
Results this analysisGK modelVGG modelCompton Form Factors:
Paweł Sznajder Getting to Grips with QCD SE 28
![Page 29: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/29.jpg)
Results this analysisGK modelVGG modelCompton Form Factors:
Paweł Sznajder Getting to Grips with QCD SE 29
![Page 30: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/30.jpg)
Paweł Sznajder Getting to Grips with QCD SE 30
![Page 31: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/31.jpg)
Results
Subtraction constant:
Paweł Sznajder Getting to Grips with QCD SE 31
![Page 32: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/32.jpg)
no uncertainties!
Results
Nucleon tomography:
Paweł Sznajder Getting to Grips with QCD SE 32
![Page 33: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/33.jpg)
Results this analysisGK modelVGG modelCompton Form Factors:
Paweł Sznajder Getting to Grips with QCD SE 33
![Page 34: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/34.jpg)
Results this analysisGK modelVGG modelCompton Form Factors:
Paweł Sznajder Getting to Grips with QCD SE 34
![Page 35: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/35.jpg)
SUMMARY
Fits to DVCS data■ New parameterizations of border and skewness function proposed
→ basic properties of GPD as building blocks
→ small number of parameters
→ encoded access to nucleon tomography and subtraction constant
■ Successful to fit EFF and DVCS data
→ replica method for a careful propagation of uncertainties
What next?
■ Neural network parameterization of CFFs
■ Include other channels and more observables
■ Include new and already existing theory developments
■ Make consistent analysis of all those ingredients → PARTONS
Paweł Sznajder Getting to Grips with QCD SE 35
![Page 36: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/36.jpg)
Inequalities:
BACKUP | Inqualities
to avoid violation of the positivity in the impact parameter space
Paweł Sznajder Getting to Grips with QCD SE 36
![Page 37: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/37.jpg)
BACKUP | PARTONS PROJECT
Layered structure:
■ one layer = collection of objects designed for common purpose
■ one module = one physical development
■ operations on modules provided by Services, e.g. for GPD Layer
■ what can be automated is automated
■ features improving calculation speed
e.g. CFF Layer Service stores the last calculated values
GPDResult computeGPDModel(const GPDKinematic& gpdKinematic, GPDModule* pGPDModule) const;
GPDResult computeGPDModelRestrictedByGPDType(const GPDKinematic& gpdKinematic, GPDModule* pGPDModule, GPDType::Type gpdType) const;
GPDResult computeGPDModelWithEvolution(const GPDKinematic& gpdKinematic, GPDModule* pGPDModule, GPDEvolutionModule* pEvolQCDModule) const;
...
DVCS TCS HEMP
Observable Layer
DVCS TCS HEMP
Process Layer
DVCS TCS HEMP
CFF Layer
GPDs and Evolution
GPD Layer
Paweł Sznajder Getting to Grips with QCD SE 37
![Page 38: Extracting GPDs from DVCS data: Border and skewness ......• HERA data • Hall A cross sections DVCS data Angles: Paweł Sznajder Getting to Grips with QCD SE 22 Performance: Fitted](https://reader036.fdocuments.us/reader036/viewer/2022081602/6130f2031ecc515869446bc1/html5/thumbnails/38.jpg)
BACKUP | PARTONS PROJECT
Existing modules:
■ GPD: GK11, VGG, Vinnikov, MPSSW13, MMS13
■ Evolution: Vinnikov code
■ CFF (DVCS only): LO, NLO (gluons and
light or light + heavy quarks)
■ Cross Section (DVCS only): VGG, BMJ, GV
■ Running coupling: 4-loop PDG expression, constant value
Hu @ x = 0.2, t = -0.1 GeV2, μF2 = μR
2 = 2 GeV2
GK11MPSSW13VGGVinnikov
Paweł Sznajder Getting to Grips with QCD SE 38