Generalized Parton Distributions: A general unifying tool for exploring
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Transcript of Generalized Parton Distributions: A general unifying tool for exploring
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Generalized Parton Distributions:
A general unifying toolfor exploring
the internal structure of hadrons
INPC, 06/06/2013
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1/ Introduction to GPDs
2/ From data to CFFs/GPDs
3/ CFFs/GPDs to nucleon imaging
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1/ Introduction to GPDs
2/ From data to CFFs/GPDs
3/ CFFs/GPDs to nucleon imaging
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)(),( 11 xgxfep a eX
yxp
xz(Parton Distribution
Functions: PDF)(DIS)
)(),(),(),( 21 tGtGtFtF PAep a ep
y
xz
b
(Form Factors: FFs)(elastic)
),,(~),,,(~),,,(),,,(
txEtxH
txEtxH
ep a epgxp
xz
b(Generalized Parton Distributions: GPDs)(DVCS)
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x+ : relative longitudinal momentum of initial quarkx- : relative longitudinal momentum of initial quark
t=D2 : total squared momentum transfer to the nucleon (transverse component: )
In the light-cone frame:
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GPDs
DVCS
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GPDs FFs
DVCS ES
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PDFs
GPDs FFs
DVCS ES
DIS
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PDFs
GPDs FFs
DVCS ES
DIS
Impact parameter
Transverse momentum
Longitudinal momentum
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TMDs PDFs
GPDs FFs
DVCS ES
SIDIS DIS
Impact parameter
Transverse momentum
Longitudinal momentum
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GTMDs
TMDs PDFs
GPDs FFs
DVCS ES
SIDIS DIS
Impact parameter
Transverse momentum
Longitudinal momentum
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GTMDs
TMDs PDFs
GPDs FFs
DVCS ES
SIDIS DIS
Impact parameter
Transverse momentum
Longitudinal momentum
(thanks to C. Lorcéfor the graphs)
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Extracting GPDs from DVCS observables
A complex problem:
There are 4 GPDs (H,H,E,E)~~
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Extracting GPDs from DVCS observables
A complex problem:
There are 4 GPDs (H,H,E,E)
They depend on 4 variables (x,xB,t,Q2)
One can access only quantities such as
and (CFFs)
~~
1
1
),,( dxx
txGPD ),,( tGPD
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Hq(x,,t) but only and t accessible experimentally
1
1
1
1
),,(),,(~),,(~ tHidxx
txHPdxixtxHT DVCS
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In general, 8 GPD quantities accessible (Compton Form Factors)
with
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Extracting GPDs from DVCS observables
A complex problem:
There are 4 GPDs (H,H,E,E)
They depend on 4 variables (x,xB,t,Q2)
One can access only quantities such as
and (CFFs)
~~
1
1
),,( dxx
txGPD ),,( tGPD
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Extracting GPDs from DVCS observables
A complex problem:
There are 4 GPDs (H,H,E,E)
They depend on 4 variables (x,xB,t,Q2)
One can access only quantities such as
and (CFFs)
They are defined for each quark flavor (u,d,s)
~~
1
1
),,( dxx
txGPD ),,( tGPD
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Extracting GPDs from DVCS observables
A complex problem:
There are 4 GPDs (H,H,E,E)
They depend on 4 variables (x,xB,t,Q2)
One can access only quantities such as
and (CFFs)
They are defined for each quark flavor (u,d,s)
~~
Measure a series of (DVCS) polarized observables
over a large phase space on the proton and on the neutron
1
1
),,( dxx
txGPD ),,( tGPD
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gf
leptonic planehadronic
planeN’
e’
e
Unpolarized beam, longitudinal target (lTSA) :DsUL ~ sinfIm{F1H+(F1+F2)(H + xB/2E) –kF2 E+…}df~ Im{Hp, Hp}
~~
Polarized beam, longitudinal target (BlTSA) :DsLL ~ (A+Bcosf)Re{F1H+(F1+F2)(H + xB/2E)…}df~ Re{Hp, Hp}
~
Unpolarized beam, transverse target (tTSA) :DsUT ~ cosfIm{k(F2H – F1E) + ….. }df Im{Hp, Ep}
= xB/(2-xB) k=-t/4M2
DsLU ~ sinf Im{F1H + (F1+F2)H -kF2E}df~Polarized beam, unpolarized target (BSA) :
Im{Hp, Hp, Ep}~
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The experimental actors
p-DVCSBSAs,lTSAs
p-DVCS(Bpol.) X-sec
Hall BHall AJLab CERN
COMPASSp-DVCS
X-sec,BSA,BCA,tTSA,lTSA,BlTSA
p-DVCSX-sec,BCA
p-DVCSBSA,BCA,
tTSA,lTSA,BlTSA
H1/ZEUSHERMESDESY
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1/ Introduction to GPDs
2/ From data to CFFs/GPDs
3/ CFFs/GPDs to nucleon imaging
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JLabHall A
JLabCLAS
HERMES
DVCS BSA
DVCS lTSA
DVCS BSA,lTSA,tTSA,BCA
DVCSunpol. X-section
DVCSB-pol. X-section
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Given the well-established LT-LO DVCS+BH amplitude
DVCS Bethe-HeitlerGPDs
Obs= Amp(DVCS+BH) CFFs
Can one recover the 8 CFFs from the DVCS observables?
Two (quasi-) model-independent approaches to extract, at fixed xB, t and Q2 (« local » fitting),
the CFFs from the DVCS observables
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1/ «Brute force » fitting
c2 minimization (with MINUIT + MINOS) of the available DVCS observables at a given xB, t and Q2 pointby varying the CFFs within a limited hyper-space (e.g. 5xVGG)
M.G. EPJA 37 (2008) 319 M.G. & H. Moutarde, EPJA 42 (2009) 71
M.G. PLB 689 (2010) 156 M.G. PLB 693 (2010) 17
The problem can be (largely) undersconstrained:JLab Hall A: pol. and unpol. X-sectionsJLab CLAS: BSA + TSA
2 constraints and 8 parameters !
However, as some observables are largely dominated bya single or a few CFFs, there is a convergence (i.e. a well-definedminimum c2) for these latter CFFs.
The contribution of the non-converging CFF entering in the error bar of the converging ones.
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DsUL ~ sinfIm{F1H+(F1+F2)(H + xB/2E) –kF2 E+…}df~ ~DsLU ~ sinf Im{F1H + (F1+F2)H -kF2E}df~
2/ Mapping and linearization
If enough observables measured, one has a system of 8 equations with 8 unknowns
Given reasonnable approximations (leading-twist dominance, neglect of some 1/Q2 terms,...), the system can be linear(practical for the error propagation)
K. Kumericki, D. Mueller, M. Murray, arXiv:1301.1230 hep-ph, arXiv:1302.7308 hep-ph
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unpol.sec.eff.
+
beam pol.sec.eff.
c2 minimization
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unpol.sec.eff.
+
beam pol.sec.eff.
c2 minimization
beam spin asym.
+
long. pol. tar. asym
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unpol.sec.eff.
+
beam pol.sec.eff.
c2 minimization
beam spin asym.
+
long. pol. tar. asym
beam charge asym.
+
beam spin asym
+
…
linearization
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unpol.sec.eff.
+
beam pol.sec.eff.
c2 minimization
beam spin asym.
+
long. pol. tar. asym
beam charge asym.
+
beam spin asym
+
…
linearization
VGG modelKM10 model/fit
Moutarde 10 model/fit
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1/ Introduction to GPDs
2/ From data to CFFs/GPDs
3/ CFFs/GPDs to nucleon imaging
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How to go from momentum coordinates (t) to space-time coordinates (b) ?
(with error propagation)
Burkardt (2000)
From CFFs to spatial densities
Applying a (model-dependent) “deskewing” factor:
and, in a first approach, neglecting the sea contribution
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1/Smear the data according to their error bar2/Fit by Aebt
3/Fourier transform (analytically) } ~1000 times
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1/Smear the data according to their error bar2/Fit by Aebt
3/Fourier transform (analytically) } ~1000 times
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Thanks to J. VandeWiele
1/Smear the data according to their error bar2/Fit by Aebt
3/Fourier transform (analytically)4/Obtain a series of Fourier transform as a function of b5/For each slice in b, obtain a (Gaussian) distribution which is fitted so as to extract the mean and the standard deviation
} ~1000 times
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1/Smear the data according to their error bar2/Fit by Aebt
3/Fourier transform (analytically)4/Obtain a series of Fourier transform as a function of b5/For each slice in b, obtain a (Gaussian) distribution which is fitted so as to extract the mean and the standard deviation
~1000 times}
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CLAS data (xB=0.25)
“skewed” HIm
“unskewed” HIm
(fits applied to « unskewed » data)
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HERMES data (xB=0.09)
“skewed” HIm
“unskewed” HIm
(fits applied to « unskewed » data)
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xB=0.25 xB=0.09
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Projections for CLAS12 for HIm
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Corresponding spatial densities
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GPDs contain a wealth of information on nucleon structure and dynamics: space-momentum quark correlation, orbital momentum, pion cloud, pressure forces within the nucleon,…
They are complicated functions of 3 variables x,,t , dependon quark flavor, correction to leading-twist formalism,…: extraction of GPDs from precise data and numerous observables, global fitting, model inputs,…
Large flow of new observables and data expected soon (JLab12,COMPASS) will bring allow a precise nucleon Tomography in the valence region
First new insights on nucleon structure already emergingfrom current data with new fitting algorithms
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1) The HERMES Recoil detector. A. Airapetian et al, e-Print: arXiv:1302.6092 2) Beam-helicity asymmetry arising from deeply virtual Compton scattering measured with kinematically complete event reconstruction A. Airapetian et al, JHEP10(2012)0423) Beam-helicity and beam-charge asymmetries associated with deeply virtual Compton scattering on the unpolarised proton A. Airapetian et al, JHEP 07 (2012) 032
Many analysis at JLab in progress (CLAS X-sections and lTSA, new Hall A X-sections at different beam energies, proton and neutron channels,… with publications planned for 2013/2014
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The sea quarks (low x) spread to the periphery of the nucleon while the valence quarks (large x) remain in the center
HIm:the t-slope reflects the size of the probed object (Fourier transf.)
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The axial charge (~Him) appears to be more « concentrated » than the electromagnetic charge (~Him)
~