Status and prospects of GPD extraction from DVCS

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1 Status and prospects of GPD extraction from DVCS Krešimir Kumerički University of Zagreb, Croatia Probing Nucleons and Nuclei in High Energy Collisions October 1 November 16, 18, INT, Seattle

2 Outline 1 Introduction and status of fits to DVCS data Uncertainties? 3 Neural net fits 4 Summary Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 / 7

3 Access to GPDs via DVCS Deeply virtual Compton scattering (DVCS) gold plated process of exclusive physics DVCS is measured via leptoproduction of a photon l l γ γ l γ l γ l γ γ l + + p DVCS p p BH p p BH p Interference with Bethe-Heitler process gives unique access to both real and imaginary part of DVCS amplitude. Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 3 / 7

4 DVCS cross section dσ T = T BH + T DVCS + I. where e. g. interference term is { e l 3 I c I [ + c I P 1 (φ)p (φ) n cos(nφ) + sn I sin(nφ) ] }, where e. g. c1 I [ c1,unpol. I F 1 Re H n=1 harmonic for unpolarized target is t 4M p F Re E + x B x B (F 1 + F ) Re H and at leading order everything depends on four complex Compton form factors (CFFs) H(ξ, t, Q ), E(ξ, t, Q ), H(ξ, t, Q ), Ẽ(ξ, t, Q ) ] Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 4 / 7

5 Factorization of DVCS GPDs γ ( Q ) γ γ ( Q ) γ [Collins et al. 98] DVCS C = + O 1 Q GPD CFFs are convolution: a H(ξ, t, Q ) = p p p p dx C a (x, ξ, Q Q ) H a (x, ξ, t, Q) H a (x, η, t, Q ) Generalized parton distribution (GPD) a=q,g Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 5 / 7

6 Hybrid GPD models for global fits [K.K., Müller 9-15] Sea quarks and gluons modelled using SO(3) partial wave expansion in conformal GPD moment space + Q evolution. Valence quarks model CFFs directly (ignoring Q evolution): [ 4 Im H(ξ, t) = π 9 Hu val (ξ, ξ, t) Hd val (ξ, ξ, t) + ] 9 Hsea (ξ, ξ, t) ( ) x α(t) ( ) 1 x b H(x, x, t) = n r α 1 ( ) 1 + x 1 + x p. 1 1 x t 1+x M Re H determined by dispersion relations 15 free parameters in total for H, H, E, Ẽ. Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 6 / 7

7 Fit examples (1/): H1/ZEUS Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 7 / 7

8 Fit examples (/): JLab s Hall A (15) KM15 global fit is fine. χ /n d.o.f. = 4./75 Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 8 / 7

9 Global fit χ values: KM and PARTONS [K.K., Müller 9-15] [Moutarde, Sznajder, Wagner, 18] Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 9 / 7

10 Including Hall A 17 data in global world fit: fail.6 KM world KM 17 data Hall A KM world KM 17 data Hall A 17.4 d cos, w. sin, w Q = 1.98 E = Q = 1.74 E = Q = 1.51 E = Q = 1.98 E = Q = 1.74 E = Q = 1.51 E = d cos, w. sin, w..1. Q = 1.99 E = 4.46 Q = 1.74 E = 4.46 Q = 1.5 E = Q = 1.74 E = 4.46 Q = 1.5 E = t [GeV ]..3.4 t [GeV ]..3.4 t [GeV ]..3.4 t [GeV ]..3.4 t [GeV ] Global world DVCS data fit before 17 χ /n d.o.f = 4./75 including 17 Hall A χ /n d.o.f =545./337 Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 1 / 7

11 Uncertainties? Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 11 / 7

12 Example: Uncertainty of D-term D-term is a part of GPD that has nice physical interpretation (related to pressure distribution inside nucleon [M. Polyakov 3]), see talk by [P. Schweitzer] tomorrow within some approximations and up to a charge-related prefactor of order one it is equal to subtraction constant in dispersion relation for CFFs H and E [O. Teryaev 5]: D(t) (t) = Re H(ξ, t) 1 1 π P.V. x dx ξ Im H(x, t) x In KM fits [K.K., D. Müller], D(t) = D/(1 t/m D ) and is extracted directly by fits (where Re H is then determined by dispersion relations) Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 1 / 7

13 Extractions of D-term D Q (t) KM15 global fit -.5 JLab data lattice LHPC -3 dispersion relations chiral quark soliton -3.5 Skyrme model bag model t [GeV ] Fit parameter uncertainties of D(t) are %, but systematic uncertainty due to model selection is unknown and presumably much larger! [V. D. Burkert, F.-X. Girod and L. Elouadrhiri 18] use just CLAS dσ and σ DVCS data to extract very precise value of D-term Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 13 / 7

Extractions of D-term D Q (t) -.5-1 -1.5 - KM15 global fit -.5 JLab data lattice LHPC -3 dispersion relations chiral quark soliton -3.

14 Extractions of D-term D Q (t) KM15 global fit -.5 JLab data lattice LHPC -3 dispersion relations chiral quark soliton -3.5 Skyrme model bag model t [GeV ] Fit parameter uncertainties of D(t) are %, but systematic uncertainty due to model selection is unknown and presumably much larger! [V. D. Burkert, F.-X. Girod and L. Elouadrhiri 18] use just CLAS dσ and σ DVCS data to extract very precise value of D-term Data science: total error = bias + variance Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 13 / 7

15 Bias-variance tradeoff: toy example Unknown f (x) = sin(πx) measured at two points. H - rigid (biased) H 1 - flexible [Abu-Mostafa et al. 1] h(x) = a h(x) = ax + b error = bias + variance Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 14 / 7

16 Bias-variance tradeoff: toy example Unknown f (x) = sin(πx) measured at two points. H - rigid (biased) H 1 - flexible [Abu-Mostafa et al. 1] h(x) = a h(x) = ax + b error = bias + variance In DVCS situation is the opposite! We need to decrease bias. Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 14 / 7

1] h(x) = a h(x) = ax + b error = bias + variance In DVCS situation is the opposite!

17 Bias-variance tradeoff: toy example Unknown f (x) = sin(πx) measured at two points. H - rigid (biased) H 1 - flexible [Abu-Mostafa et al. 1] h(x) = a h(x) = ax + b error = bias + variance In DVCS situation is the opposite! We need to decrease bias. Neural networks are proven to be unbiased Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 14 / 7

18 Neural net fits Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 15 / 7

19 Fitting with neural networks Essentially a least-square fit of a complicated many-parameter function. f (x) = tanh( w i tanh( w j )) no theory bias Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 16 / 7

20 Study A: NN fit to CLAS 15 data We start by fitting just to the CLAS 15 dσ and σ measurements [Jo et al. 15], and just H We utilize dispersion relations (one NNet represents Im H, another represents D(t)) Uncertainty is estimated by averaging over ensemble of neural nets: t =. GeV = xb/( xb) = xb/( xb) t =. GeV NNDR-C = xb/( xb) = xb/( xb) Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 17 / 7

21 Comparison to [Burkert et al. 18] ImH t =. GeV ξ ReH KM15 GK NNet H Burkert et al ξ Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 18 / 7

22 Comparison to [Burkert et al. 18] ImH t =. GeV ξ ReH KM15 GK NNet H Burkert et al ξ But what is the effect of using the limited set of data, and assumption of H dominance? χ /n pts = 175/8 (this NNet), 191/8 (KM15), 3/8 (GK) Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 18 / 7

23 More flexible model: H + H t =. GeV NNDR-C15- NNDR-C15-4t t =. GeV ξ ImH ReH KM15 7 GK NNet H, E, H, Ẽ 8 Burkert et al ξ Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 19 / 7

24 Adding more data points Adding HERMES A LU,I data. (Model now includes H and E) t =. GeV NNDR-C15-6 NNDR-C15_ALUI Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 / 7

25 Adding more data points Adding HERMES A LU,I data. (Model now includes H and E) t =. GeV NNDR-C15-6 NNDR-C15_ALUI D Q (t) t[gev ] KM15 global fit CLAS 15 + HERMES BSA CLAS15 data alone is still consistent with zero D-term. Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 / 7

26 Propagating uncertainties back to d σ and σ d = d + d = d d NNDR-C15-6 NNDR-C15_ALUI-6 CLAS 15 xb =.335, Q =.78, t = -. xb =.335, Q =.78, t = -. xb =.335, Q =.78, t = -.6 xb =.335, Q =.78, t = -.45 xb =.335, Q =.78, t = -.6 xb =.335, Q =.78, t = [deg] [deg] [deg] Small propagated error is due to small sensitivity of these observables to CFFs (and D-term). Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 1 / 7

27 Independent simple way to the same conclusion.35.3 Q = 1.63 xb =.18 Q = 1.64 xb =.1 Q = 1.88 xb =.1 Q = 1.79 xb =.4 Q =.1 xb =.4 sin, w KM9a model with subtraction constant C describes CLAS 15 dσ and σ data correctly χ /n pts = 1746/3 d = d + d = d d KM9a(C->) CLAS 15 xb =.335, Q =.78, t = -. sin, w Q =.35 xb = Q =.58 xb = Q =.78 xb = t [GeV ] xb =.335, Q =.78, t = -.6 xb =.335, Q =.78, t = xb =.335, Q =.78, t = xb =.335, Q xb =.335, Q =.78, t = -.6 =.78, t = [deg] [deg] [deg] Q =.97 xb = Q = 3.18 xb =.4 KM9a(C->) Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 / 7

28 Study B: NN fit to world fixed target data Representative subset of world DVCS fixed target data: npt x obs collab harm. ref x ALUI HERMES -1. arxiv: x AUTDVCS HERMES arxiv: x AUTI HERMES 1. arxiv: x BCA HERMES. arxiv: x BCA HERMES 1. arxiv: x BSDw CLAS -1 arxiv: x BSDw HALLA -1 arxiv: x BSSw CLAS. arxiv: x BSSw CLAS 1. arxiv: x BSSw HALLA. arxiv: x BSSw HALLA 1. arxiv: x BTSA HERMES. arxiv:14.177v1 3 x TSA CLAS -1 arxiv:hep-ex/651 6 x TSA HERMES -1. arxiv:14.177v TOTAL = 18 We now use completely unconstrained neural nets representing Im H, Re H, Im E, Re E,... (do not assume dispersion relations) Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 3 / 7

29 Results (1/) Only Im H, Im H and Re E consistently extracted as different from zero, and, with somewhat smaller significance, Re H and Im E: 3 NN-fix-3L-ReE-ImHt NN-fix-4L-ImHt-ReH NN-fix-4L-ImHt-ImE t =. GeV NN-fix-3L-ReE-ImHt NN-fix-4L-ImHt-ReH NN-fix-4L-ImHt-ImE t =. GeV Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 4 / 7

30 Results (/) Other CFFs come out consistent with zero. Only bounds on their size are obtained. E. g. for Im Ẽ: 3 NN-fix-3L-ReE-ImHt NN-fix-4-ImHt-ImEt t =. GeV NN-fix-3L-ReE-ImHt NN-fix-4-ImHt-ImEt NN-fix-4-ImHt-ReHt t =. GeV Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 5 / 7

31 Summary Neural network method has a unique capability of extraction of Compton form factors (and, later, GPDs) with reliable uncertainties Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 6 / 7

32 GPD/CFF server Plots of all CFFs available; numerical values soon to come... Krešimir Kumerički Status of GPD extraction INT 18-3, Week 1 7 / 7

Fitting GPDs and CFFs various approaches. Physics Department University of Zagreb, Croatia

Fitting GPDs and CFFs various approaches Krešimir Kumerički Physics Department University of Zagreb, Croatia Nuclear and Nucleon Structure Through Dileptons Production ECT Trento, Italy, 24 28 October