Techniques of GPD extraction from data

Transcription

1 Techniques of GPD extraction from data Krešimir Kumerički University of Zagreb, Croatia INT-17-3 Workshop: Tomography of Hadrons and Nuclei at Jefferson Lab August 28 September 29, 2017 Seattle, WA

2 Outline Introduction DVCS φ vs. harmonics Global fits Neural nets Conclusion 2 Krešimir Kumerički : GPD extraction

3 Probing the proton with two photons Deeply virtual Compton scattering (DVCS) [Müller 92, et al. 94] γ q 2 1 = Q2 q 2 2 = 0 γ DVCS P 1 P 2 P = P 1 + P 2, t = (P 2 P 1 ) 2 q = (q 1 + q 2 )/2 Generalized Bjorken limit: q 2 Q 2 /2 ξ = q2 2P q const To leading twist-two accuracy cross-section can be expressed in terms of Compton form factors (CFFs) H(ξ, t, Q 2 ), E(ξ, t, Q 2 ), H(ξ, t, Q 2 ), Ẽ(ξ, t, Q 2 ),... 3 Krešimir Kumerički : GPD extraction

4 Factorization of DVCS GPDs γ γ q 2 1 = Q2 q2 2 = 0 C a x + ξ x ξ 2 2 H a P 1 P 2 P = P 1 + P 2, t = (P 2 P 1 ) 2 q = (q 1 + q 2 )/2 q 2 Q 2 /2 ξ = q2 2P q const Compton form factor is a convolution: a H(ξ, t, Q 2 ) = dx C a (x, ξ, Q 2 /Q 2 0) H a (x, η = ξ, t, Q 2 0) a=ns,s(σ,g) H a (x, η, t, Q 2 0 ) Generalized parton distribution (GPD) 4 Krešimir Kumerički : GPD extraction

5 DVCS experimental coverage 5 Krešimir Kumerički : GPD extraction

6 Experimental coverage (fixed target) Collab. Year Observables Kinematics No. of points xb Q 2 [GeV 2 ] t [GeV 2 ] total indep. HERMES 2001 A sin φ LU CLAS 2001 A sin φ LU CLAS 2006 A sin φ UL HERMES 2006 A cos φ C Hall A 2006 σ(φ), σ(φ) CLAS 2007 ALU(φ) A cos(0,1)φ C, A sin(φ φs ) UT,DVCS, sin(φ φs HERMES 2008 ) cos(0,1)φ AUT,I, cos(φ φs ) sin φ AUT,I < CLAS 2008 ALU(φ) HERMES 2009 A sin(1,2)φ LU,I, A sin φ LU,DVCS, A cos(0,1,2,3)φ C HERMES 2010 A sin(1,2,3)φ UL, HERMES 2011 A cos(0,1,2)φ LL cos(φ φs ) cos(0,1,2)φ ALT,I, sin(φ φs ) sin(1,2)φ ALT,I, cos(φ φs ) cos(0,1)φ ALT,BH+DVCS, sin(φ φs ) sin φ ALT,BH+DVCS HERMES 2012 A sin(1,2)φ LU,I, A sin φ LU,DVCS, A cos(0,1,2,3)φ C < < < < CLAS 2015 ALU(φ), AUL(φ), ALL(φ) CLAS 2015 σ(φ), σ(φ) Hall A 2015 σ(φ), σ(φ) Hall A 2017 σ(φ), σ(φ) [0.36] [ ] Krešimir Kumerički : GPD extraction

7 Electroproduction of photon dσ T 2 = T BH 2 + T DVCS 2 + I. { T BH 2 =K BH 1 c0 BH + P 1 (φ)p 2 (φ) { I =K I e l 3 c0 I + P 1 (φ)p 2 (φ) T DVCS 2 =K DVCS { c DVCS 0 + c I 1,unpol. [ F 1 Re H t 4M 2 p 2 n=1 n=1 2 n=1 } cn BH cos(nφ) + s1 BH sin φ, [ c I n cos(nφ) + s I n sin(nφ) ] }, [ c DVCS n cos(nφ) + sn DVCS sin(nφ) ] }, F 2 Re E + c DVCS n quadratic in H, E, H, x ] B (F 1 + F 2 ) Re 2 x H B [Belitsky, Müller et. al 01 14] 7 Krešimir Kumerički : GPD extraction

8 Separation of form factors One would like to obtain separation between: 1. different terms in cross section: T BH 2, T DVCS 2, I 2. then different harmonic coefficients: c0 I, si 1, cdvcs 0, then different CFFs: H, E, H, and then one could try to extract GPDs To do that in experiments one chooses 1. different beam charges 2. different beam and target polarizations 3. different beam energies, utilizing dependence of harmonics c n and kinematical factors K on y ( Rosenbluth separation ): K = K(x B, Q 2 Q 2, t y), y = x B (s Mp) 2 8 Krešimir Kumerički : GPD extraction

9 Case #1: CLAS cross-section (φ-space) dσ =dσ +dσ KM15 prelim. KMM12 CLAS 2015 x B = 0.335, Q 2 = 2.78, t = -0.2 x B = 0.335, Q 2 = 2.78, t = x B = 0.335, Q 2 = 2.78, t = σ =dσ dσ x B = 0.335, Q 2 = 2.78, t = x B = 0.335, Q 2 = 2.78, t = x B = 0.335, Q 2 = 2.78, t = φ [deg] φ [deg] φ [deg] KM15 model (global refit including this data): χ 2 /npts = /1014 for dσ and 936.1/1012 for σ looks excellent 9 Krešimir Kumerički : GPD extraction

10 Going from φ- to n-space Because of simple dependence of cross-section σ on φ, harmonics (Fourier transforms) of σ provide very direct access to coefficients c 0, c 1,... It is often convenient to work with weighted harmonics σ sin nφ,w 1 π π π dw sin(nφ) σ(φ), with specialy weighted Fourier integral measure dw 2πP 1(φ)P 2 (φ) π π dφ P 1(φ)P 2 (φ) dφ, thus cancelling strongly oscillating factors 1/(P 1 (φ)p 2 (φ)) in Bethe-Heitler and interference terms in dσ. (Since P 1,2 (φ) depend also on y, weighting may be undesirable if you are after Rosenbluth separation, see [Achenauer, Fazio, K.K., Müller 13] for EIC case.) 10 Krešimir Kumerički : GPD extraction

11 Weighted harmonics Series of such weighted harmonic terms converges then faster with increasing n than normal Fourier series. Example of first four bins of Hall A (2015) cross-section measurement: cos(n ) cos(n ), w n bin #1 n bin # bin # n 11 Krešimir Kumerički : GPD extraction bin # n

12 Case #1: CLAS cross-section (n-space) Q 2 =1.63 x B =0.18 Q 2 =1.64 x B =0.21 Q 2 =1.88 x B =0.21 Q 2 =1.79 x B =0.24 Q 2 =2.12 x B = Q 2 =1.63 x B =0.18 Q 2 =1.64 x B =0.21 Q 2 =1.88 x B =0.21 Q 2 =1.79 x B =0.24 Q 2 =2.12 x B =0.24 σ sinφ,w dσ cos0φ,w Q 2 =2.35 x B =0.28 Q 2 =2.58 x B =0.30 Q 2 =2.78 x B =0.34 Q 2 =2.97 x B =0.36 Q 2 =3.18 x B = Q 2 =2.35 x B =0.28 Q 2 =2.58 x B =0.30 Q 2 =2.78 x B =0.34 Q 2 =2.97 x B =0.36 Q 2 =3.18 x B = σ sinφ,w dσ cos0φ,w t [GeV 2 ] t [GeV 2 ] dσ cosφ,w Q 2 =1.63 x B =0.185 Q 2 =1.64 x B =0.214 Q 2 =1.88 x B =0.215 Q 2 =1.79 x B =0.244 Q 2 =2.12 x B =0.245 χ 2 /npts = 62.2/48 for dσcos φ,w (O.K. but not so perfect as in φ-space) 0.01 dσ cosφ,w Q 2 =2.35 x B =0.275 Q 2 =2.58 x B =0.305 Q 2 =2.78 x B =0.335 Q 2 =2.97 x B =0.365 Q 2 =3.18 x B = t [GeV 2 ] 12 Krešimir Kumerički : GPD extraction

13 Case #1: CLAS cross-section (n-space) Q 2 =1.63 x B =0.18 Q 2 =1.64 x B =0.21 Q 2 =1.88 x B =0.21 Q 2 =1.79 x B =0.24 Q 2 =2.12 x B = Q 2 =1.63 x B =0.18 Q 2 =1.64 x B =0.21 Q 2 =1.88 x B =0.21 Q 2 =1.79 x B =0.24 Q 2 =2.12 x B =0.24 σ sinφ,w dσ cos0φ,w Q 2 =2.35 x B =0.28 Q 2 =2.58 x B =0.30 Q 2 =2.78 x B =0.34 Q 2 =2.97 x B =0.36 Q 2 =3.18 x B = Q 2 =2.35 x B =0.28 Q 2 =2.58 x B =0.30 Q 2 =2.78 x B =0.34 Q 2 =2.97 x B =0.36 Q 2 =3.18 x B = σ sinφ,w dσ cos0φ,w t [GeV 2 ] t [GeV 2 ] dσ cosφ,w Q 2 =1.63 x B =0.185 Q 2 =1.64 x B =0.214 Q 2 =1.88 x B =0.215 Q 2 =1.79 x B =0.244 Q 2 =2.12 x B =0.245 χ 2 /npts = 62.2/48 for dσcos φ,w (O.K. but not so perfect as in φ-space) 0.01 dσ cosφ,w Q 2 =2.35 x B = Q 2 =2.58 x B = Q 2 =2.78 x B = t [GeV 2 ] Q 2 =2.97 x B = Q 2 =3.18 x B = Krešimir Kumerički : GPD extraction In addition to χ 2 /d.o.f. use: pull 1 N N f (x i ) y i i=1 y i

14 Case #2: Sine toy model 1.0 χ 2 /n pts = model data cos data sin χ 2 /1 = target = 1.0 sin(phi) model = 1.1 sin(phi) data (15% noise) φ φ-space view can be misleading harmonics 13 Krešimir Kumerički : GPD extraction

15 Extraction of harmonics General model for cross section or any other observable f (φ) = c max k=0 s max c k cos(kφ) + k=1 s k sin(kφ) c max + s max + 1 real parameters to be determined from N equidistantly measured values f (φ i=1,...,n ). least-squares optimization gives standard Fourier formulas, e.g., for k 1, c k = 2 N N f (φ i )cos(kφ i ) i=1 c k and their uncertainties are independent of c max, s max, thanks to orthogonality of trig functions (but only if you have measured full set of φ bins!) 14 Krešimir Kumerički : GPD extraction

16 How many harmonics are there? Case #3: Target function is f (φ) = cos(φ) cos(2φ) cos(3φ) 0.13 sin(φ) 0.03 sin(2φ) sin(3φ) and is used to generate data with variable noise Fitting Fourier series with increasing number of harmonics until χ 2 /d.o.f. w.r.t. target function starts to deteriorate 3 cos sin no. of visible harmonics noise amplitude 15 Krešimir Kumerički : GPD extraction

17 How many harmonics are there? Case #3: Target function is f (φ) = cos(φ) cos(2φ) cos(3φ) 0.13 sin(φ) 0.03 sin(2φ) sin(3φ) and is used to generate data with variable noise Fitting Fourier series with increasing number of harmonics until χ 2 /d.o.f. w.r.t. target function starts to deteriorate no. of visible harmonics cos sin But in real life we don t know target function! How to determine number of harmonics using only data? noise amplitude 15 Krešimir Kumerički : GPD extraction

18 Bias-variance trade-off target data FT φ φ φ 0.4 target cos sin n n n 16 Krešimir Kumerički : GPD extraction

19 Cross-validation procedure To determine the optimal number of harmonics using only data: Divide data randomly in n subsets Leave one out and fit the model to remaining n 1 subsets Evaluate model (calculating χ 2 ) on the left-out set Repeat with leaving out other n 1 sets and average the error Repeat with increasing number of harmonics until description of left-out sets starts to deteriorate 3 cos optimal cos cross-valid. sin optimal sin cross-valid. no. of visible harmonics noise amplitude noise amplitude 17 Krešimir Kumerički : GPD extraction

20 Cross-validation procedure To determine the optimal number of harmonics using only data: Divide data randomly in n subsets Leave one out and fit the model to remaining n 1 subsets Evaluate model (calculating χ 2 ) on the left-out set Repeat with leaving out other n 1 sets and average the error Repeat with increasing number of harmonics until description of left-out sets starts to deteriorate 3 cos optimal cos cross-valid. sin optimal sin cross-valid. no. of visible harmonics Finaly, determine just optimal harmonics using all data noise amplitude noise amplitude 17 Krešimir Kumerički : GPD extraction

21 Propagation of uncertainties to harmonics Consider three types of uncertainty: 1. uncorrelated point-to-point uncertainty (absolute size ɛ) 2. correlated normalization uncertainty (relative size ɛ) 3. correlated modulated (φ-dependent) uncertainty (e.g., relative size ɛ cos(φ)) Uncorrelated uncertainty: c k = 2/N ɛ Normalization uncertainty: c k /c k = ɛ Correlated modulated uncertainty: more complicated, but for hierarchical case c 0 c 1 one obtains c 0 c 0 = c 1 2c 0 ɛ, c 1 c 1 = c 0 c 1 ɛ i.e. we have enhancement of uncertainty for subleading harmonics! ( (c 0 +c 1 cos φ+ ) (1+ɛ cos φ) = c c ( 1 ɛ )+c c ) 0 ɛ cos φ 2c 0 c 1 18 Krešimir Kumerički : GPD extraction

22 Modulated correlated error in the wild Hall A [M. Defurne et. al 2015] discussing systematic uncertainties: 19 Krešimir Kumerički : GPD extraction

23 Hall A cos(φ) harmonics cos φ,w dσ KM15 syst enh. stat syst t [GeV 2 ] (Syst added linearly on top of stat.) t [GeV 2 ] 20 Krešimir Kumerički : GPD extraction

24 Hybrid GPD models for global fits Sea quarks and gluons modelled using SO(3) partial wave expansion in conformal GPD moment space + Q 2 evolution. Valence quarks model CFFs directly (ignoring Q 2 evolution): [ 4 Im H(ξ, t) = π 9 Hu val (ξ, ξ, t) Hd val (ξ, ξ, t) + 2 ] 9 Hsea (ξ, ξ, t) ( ) 2x α(t) ( ) 1 x b H(x, x, t) = n r 2 α 1 ( ) 1 + x 1 + x p. 1 1 x t 1+x M 2 Re H determined by dispersion relations 15 free parameters in total for H, H, E, Ẽ. 21 Krešimir Kumerički : GPD extraction

25 Model KM09a KM09b KM10 KM10a KM10b KMS11 KMM12 KM15 free params. {3}+(3)+5 {3}+(3)+6 {3}+15 {3}+10 {3}+15 NNet {3}+15 {3}+15 χ 2 /d.o.f. 32.0/ / / / / / / /275 F 2 {85} {85} {85} {85} {85} {85} {85} σ DVCS (45) (45) dσ DVCS/dt (56) (56) A sin φ LU A sin φ LU,I cos 0φ AC 6 6 A cos φ C σ sin φ,w σ cos 0φ,w σ cos φ,w σ cos φ,w /σ cos 0φ,w 4 4 A sin φ UL cos 0φ ALL 4 14 A cos φ LL 10 sin(φ φs ) cos φ AUT,I 4 4 [K.K., Müller, et al ] These models are publicly available (google for gpd page ) 22 Krešimir Kumerički : GPD extraction

26 KM GPD server Plots of all CFFs available; numerical values soon to come Krešimir Kumerički : GPD extraction

27 2006 vs 2015 Hall A cross-sections σ sinφ, w Q 2 = x B = Q 2 = x B = Q 2 = x B = σ sinφ, w Q 2 = x B = Q 2 = x B = Q 2 = x B = t [GeV 2 ] t [GeV 2 ] t [GeV 2 ] KM15 KMM12 dσ cos0φ, w KM15 KMM12 dσ cos0φ, w dσ cosφ, w dσ cosφ, w t [GeV 2 ] t [GeV 2 ] t [GeV 2 ] Improvement of global χ 2 /d.o.f / / Krešimir Kumerički : GPD extraction

28 2015 vs 2017 Hall A cross-sections (1/2) 0.08 KM15 only 2017 data Hall A 2017 d cos0, w Q 2 = 1.98 E = Q 2 = 1.74 E = Q 2 = 1.51 E = d cos0, w Q 2 = 1.99 E = t [GeV 2 ] Q 2 = 1.74 E = t [GeV 2 ] Q 2 = 1.50 E = t [GeV 2 ] Predictions of KM15 model fail for low-q Hall A measurements! 25 Krešimir Kumerički : GPD extraction

29 2015 vs 2017 Hall A cross-sections (2/2) 0.06 KM15 only 2017 data Hall A KM15 only 2017 data Hall A d cos, w 0.02 sin, w Q 2 = 1.98 E = Q 2 = 1.74 E = Q 2 = 1.51 E = Q 2 = 1.98 E = Q 2 = 1.74 E = Q 2 = 1.51 E = d cos, w 0.02 sin, w Q 2 = 1.99 E = 4.46 Q 2 = 1.74 E = 4.46 Q 2 = 1.50 E = Q 2 = 1.74 E = 4.46 Q 2 = 1.50 E = t [GeV 2 ] t [GeV 2 ] t [GeV 2 ] t [GeV 2 ] t [GeV 2 ] 26 Krešimir Kumerički : GPD extraction

30 H1 (2007), ZEUS (2008) 27 Krešimir Kumerički : GPD extraction

31 2007 CLAS beam spin asymmetry ALU(90 ) ALU(90 ) ALU(90 ) Q 2 = x B = Q 2 = x B = Q 2 = x B = t [GeV 2 ] Q 2 = x B = Q 2 = x B = Q 2 = x B = t [GeV 2 ] Only data with t 0.3 GeV 2 used for fits. Q 2 = x B = KM15 Q 2 = x B = Q 2 = x B = t [GeV 2 ] 28 Krešimir Kumerički : GPD extraction

32 2015 CLAS asymmetries 29 Krešimir Kumerički : GPD extraction

33 χ 2 /npts and pull values Collaboration Observable n pts KMM12 KM15 χ 2 /n pts pull χ 2 /n pts pull ZEUS σ DVCS ZEUS,H1 dσ DVCS /dt HERMES cos 0φ A C HERMES A cos φ C HERMES A sin φ LU,I CLAS A sin φ LU CLAS A sin φ LU CLAS σ sin φ,w CLAS dσ cos 0φ,w CLAS dσ cos φ,w Hall A σ sin φ,w Hall A dσ cos 0φ,w Hall A dσ cos φ,w Hall A σ sin φ,w Hall A dσ cos 0φ,w Hall A dσ cos φ,w HERMES,CLAS A sin φ UL HERMES cos 0φ A LL HERMES A sin(φ φ S ) cos φ UT,I CLAS A sin φ UL CLAS cos 0φ A LL CLAS A cos φ LL Krešimir Kumerički : GPD extraction

34 Problems with standard fitting approaches 1. Choice of fitting function introduces theoretical bias leading to systematic error which cannot be estimated (and is likely much larger for GPDs(x, η, t) than for PDFs(x). 2. Propagation of uncertainties from experiment to fitted function is difficult. Errors in actual experiments are not always Gaussian. 31 Krešimir Kumerički : GPD extraction

35 Problems with standard fitting approaches 1. Choice of fitting function introduces theoretical bias leading to systematic error which cannot be estimated (and is likely much larger for GPDs(x, η, t) than for PDFs(x). NNets 2. Propagation of uncertainties from experiment to fitted function is difficult. Errors in actual experiments are not always Gaussian. Monte Carlo error propagation 31 Krešimir Kumerički : GPD extraction

36 Multilayer perceptron 32 Krešimir Kumerički : GPD extraction

37 Multilayer perceptron Essentially a least-square fit of a complicated many-parameter function. f (x) = tanh( w i tanh( w j )) no theory bias 32 Krešimir Kumerički : GPD extraction

38 Function fitting by a neural net Theorem: Given enough neurons, any smooth function f (x 1, x 2, ) can be approximated to any desired accuracy. Single hidden layer is sufficient (but not always most efficient). 33 Krešimir Kumerički : GPD extraction

39 Function fitting by a neural net Theorem: Given enough neurons, any smooth function f (x 1, x 2, ) can be approximated to any desired accuracy. Single hidden layer is sufficient (but not always most efficient). With simple training of neural nets to data there is a danger of overfitting (a.k.a. overtraining) 33 Krešimir Kumerički : GPD extraction

40 Function fitting by a neural net Theorem: Given enough neurons, any smooth function f (x 1, x 2, ) can be approximated to any desired accuracy. Single hidden layer is sufficient (but not always most efficient). With simple training of neural nets to data there is a danger of overfitting (a.k.a. overtraining) 33 Krešimir Kumerički : GPD extraction

41 Function fitting by a neural net Theorem: Given enough neurons, any smooth function f (x 1, x 2, ) can be approximated to any desired accuracy. Single hidden layer is sufficient (but not always most efficient). With simple training of neural nets to data there is a danger of overfitting (a.k.a. overtraining) Solution: Divide data (randomly) into two sets: training sample and validation sample. Stop training when error of validation sample starts increasing. 33 Krešimir Kumerički : GPD extraction

42 Monte Carlo propagation of errors H, E, Neural Net x 100 x B, t, Q 2 34 Krešimir Kumerički : GPD extraction

43 Monte Carlo propagation of errors H, E, Neural Net x 100 x B, t, Q 2 34 Krešimir Kumerički : GPD extraction

44 Monte Carlo propagation of errors H, E, Neural Net x 100 x B, t, Q 2 34 Krešimir Kumerički : GPD extraction

45 Monte Carlo propagation of errors H, E, Neural Net x 100 x B, t, Q 2 34 Krešimir Kumerički : GPD extraction

46 Monte Carlo propagation of errors H, E, Neural Net x 100 x B, t, Q 2 34 Krešimir Kumerički : GPD extraction

47 Monte Carlo propagation of errors H, E, Neural Net x 100 x B, t, Q 2 34 Krešimir Kumerički : GPD extraction

48 Monte Carlo propagation of errors H, E, Neural Net x 100 x B, t, Q 2 34 Krešimir Kumerički : GPD extraction

49 Monte Carlo propagation of errors H, E, Neural Net x 100 x B, t, Q 2 Set of N rep NNs defines a probability distribution in space of possible CFF functions: F[H] = DH P[H] F[H] = 1 N rep F[H (k) ], (1) N rep k=1 Experimental uncertainties and their correlations are preserved [Giele et al. 01] 34 Krešimir Kumerički : GPD extraction

50 Take some (fake) data Fitting example Fit with 1. Standard Minuit fit with ansatz f (x) = x a (1 x) b 2. Neural network fit 35 Krešimir Kumerički : GPD extraction

51 Take some (fake) data Fitting example Fit with 1. Standard Minuit fit with ansatz f (x) = x a (1 x) b 2. Neural network fit 35 Krešimir Kumerički : GPD extraction

52 Take some (fake) data Fitting example Fit with 1. Standard Minuit fit with ansatz f (x) = x a (1 x) b 2. Neural network fit 35 Krešimir Kumerički : GPD extraction

53 Fit to HERMES BSA+BCA data 50 neural nets with 13 neurons in a single hidden layer 36 Krešimir Kumerički : GPD extraction

54 Resulting neural network CFFs 37 Krešimir Kumerički : GPD extraction

55 CFFs from various fits t = 0.28 GeV 2 Q 2 2 GeV Im H 10 Re H Im H KM15 prelim. KMM12 GK07 NNet 14 Moutarde 09 Boër/Guidal 14 Re E xb xb (from [K.K., Moutarde and Liuti 16]) 38 Krešimir Kumerički : GPD extraction

56 CFFs from various fits (II) Comparing Im H and D-term for a typical JLab kinematics: 39 Krešimir Kumerički : GPD extraction

57 CFFs from various fits (II) Comparing Im H and D-term for a typical JLab kinematics: We need access to ERBL region. 39 Krešimir Kumerički : GPD extraction

58 Going beyond first approximations Published DVCS data (apart from new 2017 Hall A) is well described within leading order, leading twist and other approximations. Some available corrections: NLO evolution and NLO coefficient functions finite-t and target mass corrections [Braun et al. 14] twist-3 GPDs massive charm [Noritzsch 03] small-x resummation can maybe be absorbed in redefinition of GPDs (think DVCS scheme factorization), but have to be taken into account when working with more processes (striving towards universal GPDs) and with more precise future data. 40 Krešimir Kumerički : GPD extraction

59 Summary Global fits of all proton DVCS data using flexible hybrid models were in healthy shape until 2017 (some tension for first cos(φ) harmonic of JLab cross sections). New Hall A 2017 data present a challenge Standard global model fitting and neural networks approach are complementing each other 41 Krešimir Kumerički : GPD extraction

60 Summary Global fits of all proton DVCS data using flexible hybrid models were in healthy shape until 2017 (some tension for first cos(φ) harmonic of JLab cross sections). New Hall A 2017 data present a challenge Standard global model fitting and neural networks approach are complementing each other The End 41 Krešimir Kumerički : GPD extraction