Exclusive Physics with an EIC

Transcription

1 Exclusive Physics with an EIC Dieter Müller Universität Regensburg K. Kumerički, DM, K. Passek-Kumerički (KMP-K), hep-ph/ GPD fits at NLO and NNLO of H1/ZEUS data KMP-K, [hep-ph] constructive critics on ad hoc GPD model approach [lot of good news] first applications of dispersion integral approach KMP-K, [hep-ph]; KM [hep-ph] flexible GPD model for small x and fits of H1/ZEUS data dispersion integral fits of HERMES and JLAB data

2 What can we learn from GPDs? Strategies to access GPDs Towards a global analysis Exclusive processes at EIC Conclusions

3 GPDs embed non-perturbative physics GPDs appear in various hard exclusive processes, e.g., hard electroproduction of photons (DVCS) [DM et. al (90/94) Radyushkin (96) Ji (96)] p γ (q) DVCS γ p' x + ξ Q 2 > 1GeV 2 GPD t = 2 x ξ fix F(ξ, Q 2, t) = R 1 1 dx C(x, ξ, α s(μ), Q/μ)F (x, ξ, t, μ) + O( 1 Q 2 ) CFF Compton form factor observable hard scattering part perturbation theory (our conventions/microscope) GPD universal (conventional) higher twist depends on approximation

4 GPD related hard exclusive processes scanned area of the surface as a functions of lepton energy Deeply virtual Compton scattering (clean probe) ep e 0 p 0 γ ep e 0 p 0 μ + μ γp p 0 e + e e e' γ (*) γ Hard exclusive meson production (flavor filter) ep e 0 p 0 π ep e 0 p 0 ρ ep e 0 nπ + ep e 0 nρ + etc. e p e' γ M p' p' + μ μ η x + ep e' p' μ μ twist-two observables: cross sections transverse target spin asymmetries

5 exclusive large t hard exclusive processes form factors lattice simulations GPDs LC-wave functions QCD-models Regge-phenom phenom. ``amplitudes 3D-picture spin content duality parton densities (PDs) unintegrated PDs

6 GPDs: : a partonic duality interpretation quark GPD (anti-quark x -x): F = θ( η x 1) ω x, η, 2 + θ(η x 1) ω x, η, 2 ω x, η, 2 = 1 η Z x+η 1+η 0 dy x p f(y, (x y)/η, 2 ) dual interpretation on partonic level: η+x 2 η x 2 support extension is unique [DM et al. 92] x+η 2 x η 2 p p central region - η < x < η mesonic exchange in t-channel ambiguous (D-term) [DM, A. Schäfer (05) KMP-K (07)] p p outer region η < x partonic exchange in s-channel

7 GPD modeling & Evolution outer region governs the evolution at the cross-over trajectory μ 2 d H(x, x, t, μ 2 ) = R 1 dμ 2 x dy x V (1, x/y, α s(μ))h(y, x, μ 2 ) GPD at h = x is `measurable (LO) central region follows (polynomiality of moments) outer region governs evolution x = PV Z 1 h PV 0 dx net contribution of outer + central region is governed by a sum rule: Z 1 2x dx 0 η 2 x 2 H (x, η, t) 2x η 2 x 2 H (x, x, t) + C(t)

8 each representation has its own advantages, however, they are equivalent (clearly spelled out in [Hwang, DM 07]) Overview: GPD representations ``light-ray spectral functions R dκ 2π eiκ(xp + P + 2k + ) diagrammatic α-representation k + p 1 k + p 2 DM, Robaschik, Geyer, Dittes, Hoŕejśi (88 (92) 94) called double distributions A. Radyushkin (96) X diagrams p 1 p 2 light cone wave function overlap (Hamiltonian approach in light-cone quantization) SL(2,R) (conformal) expansion (series of local operators) one version is called Shuvaev transformation, used in `dual (t-channel) GPD parameterization Diehl, Feldmann, Jakob, Kroll (98,00) Diehl, Brodsky, Hwang (00) Radyushkin (97); Belitsky, Geyer, DM, Schäfer (97); DM, Schäfer (05);. Shuvaev (99,02); Noritzsch (00) Polyakov (02,07)

9 DVCS fits for H1 and ZEUS data DVCS cross section measured at small 40GeV. W. 150GeV, 2GeV 2. Q 2. 80GeV 2, t. 0.8GeV 2 predicted by dσ dt (W, t, Q2 ) 4πα2 Q 4 W 2 ξ 2 W 2 + Q 2 H 2 2 x Bj 2ξ = 4M 2 p 2Q2 2W 2 +Q 2 E 2 + eh 2 ξ, t, Q 2 ξ= Q 2 2W 2 +Q 2 suppressed contributions <<0.05>> relative O(ξ) LO data could not be described before 2008 NLO works with ad hoc GPD models [Freund, McDermott (02)] results strongly depend on employed PDF parameterization do a simultaneous fit to DIS and DVCS [KMP-K (07)] use flexible GPD models in a two-step fit [KMP-K (08)]

10 effective functional form at small x: PDFs: GPDs: q sea (ξ, Q) = n(q)ξ α(q), α 1, F sea (0) = 1 H = r(η/x = 1, Q)F sea (t)ξ α0 (t,q) q sea (ξ, Q) skewness transverse distribution? E(ξ, ξ, t, Q) mostly unseen in standard Regge phenomenology chromo-magnetic pomeron might be sizeable (instantons) pqcd suggests pomeron intercept qualitative understanding of E is needed (not only forji`s spin sum rule) B = R 1 dx xe(x, η, t, Q) 0

11 good DVCS fits at LO, NLO, and NNLO with flexible GPD ansatz

12 quark skewness ratio from DVCS LO R = =ma DVCS =ma DIS LO = H(ξ,ξ) H(2ξ,0) 2α r conformal ratio W = 82GeV r = H(ξ,ξ) H(ξ,0) ξ conformal the conformal ratio is ruled out for sea quark GPD a generically zero-skewness effect over a large Q 2 lever arm scaling violation consistent with pqcd prediction this zero-skewness effect is non-trivial to realize in conformal space (SO(3) sibling poles are required)

13 CFF H posses ``pomeron behavior ξ-α(q) - α (Q)t α increases with growing Q 2 α decreases growing Q 2 t-dependence: exponential shrinkage is disfavored (α 0) dipole shrinkage is visible (α 0.15 at Q 2 =4 GeV 2 ) (normalized) profile functions ρ R d 2 ~ e i~ b ~ H(x, 0, t = ~ 2 ) sea quarks gluons essentially differ for b > 1 fm

14 Beam charge asymmetry T Interference BCA = dσ e dσ + e = dσ e + + dσ e F 1 (t)<eh + t 4M 2 F 2(t)<eE T BH 2 + T DVCS 2 set E sea H sea, use anomalous gravitomagnetic moment as parameter the unknown in Ji s nucleon spin sum rule B sea = R 1 0 dx xe sea unfortunately, H1 data do not allow to access B sea

15 Dispersion relation fits to unpolarized DVCS model of GPD H(x,x,t) within DD motivated ansatz at Q 2 =2 GeV 2 fixed: PDF normalization eff. Reage pole large t-counting rules H(x, x, t) = n r 2α 1 + x µ 2x α(t) µ b 1 x x 1 + x ³ 1 1 x 1+x p. t M 2 free: r-ratio at small x large x-behavior p-pole mass sea quarks (taken from LO fits) n = 0.68, r = 1, α(t) = t/GeV 2, m 2 = 0.5GeV 2, p = 2 valence quarks flexible parameterization of subtraction constant + pion-pole contribution n = 1.0, α(t) = t/GeV 2, p = 1 D(t) = data points quality of global fit is good χ 2 /d.o.f. 1 C (1 t/m 2 c )2

16 Global GPD fit example: HERMES & JLAB BCA HERMES BSA CLAS/JLAB HALL A/JLAB

17 extracting GPD from present collider and fixed target DVCS data H(x,x,t,Q 2 =2 GeV 2 ) Electron Ion Collider t=0 t=-0.3 GeV 2 prediction for COMPASS A BCSA = dσ + dσ dσ + +dσ

18 Neural network: extraction of CFF and error estimates BSA HERMES NNwork fit, assuming H dominance Zvonimir Vlah, KK, DM

19 EIC potential for DVCS studies: DVCS: cross section, beam spin, target spin, and double spin flip experiments (disentangling CFF at small x) BSA y F 1 (t)h(ξ, ξ, t, Q 2 ) T SA t 4M F 2 2 E(ξ, ξ, t, Q 2 ) ª n F 1 (t) e H(ξ, ξ, t, Q 2 ) + ξ(f 1 + F 2 )(t)h(ξ, ξ, t, Q 2 ) o off neutron another possibility to access GPD E time-like region (a new field to study) off nuclei (has its own interest) dσ unp dx B dq 2 dt [nbarn/gev2 ] E N = 250GeV E l = 5GeV proton neutron t = 0.1GeV 2 Q 2 = 2GeV 2 x B = φ BSA φ

20 EIC potential for hard exclusive meson production vector meson production (σ L /σ T separation) dσ γ? p V N L dt x2 Bj Q 6 H 2 t 4M 2 E 2 + hard exclusive pion production (GPD Ĥ related to Δq (3) ) dσ γ p πn L dt x2 Bj Q 6 ³ eh 2 t 4M 2 ξ ee 2 + HERMES: differential cross section versus various GPD models H x 1 Bj E x? Bj eh x? Bj ee π pole

21 Remainder: the hole in Regge phenomenology unnatural parity exchanges were never understood as Regge poles from Regge point of view polarized DIS remains mysterious within conjectured a 1 master trajectory and SU(6) symmetry reasonable description of polarized and semi-inclusive DIS our generic GPD model GS, GRSV, BB (only a few data from HERMES) SU(6) not excluded by [de Florian, Sassot, Stratmann, Vogelsang (09)]

22 DVCS observables, so far not addressed at small x: single beam spin asymmetry: pinning down GPD H (unpolarized PDFs) longitudinal target spin asymmetry: addressing Ĥ (polarized PDF) transverse target spin asymmetry: (hopefully) access to E (Ji`s spin sum rule) other exclusive channels: hard exclusive vector meson production, ρ, pseudo scalar mesons? related to the small x-behavior of PDFs leading twist observables: cross section, transverse target spin asymmetry Goloskokov, Kroll model a GPD inspired model description for all observables dipole color models

23 Conclusions Generalized parton distributions form a concept (not only a number) probing the nucleon wave function in terms of partonic degrees of freedom some work to do: to address them one needs next-generation fitting tools realistic models can be set up which embed GPDs and TMDs model predictions for cross sections and asymmetries a high luminosity Electron Ion Collider with polarized beam would be ideal: to study hard exclusive processes and to address GPDs in the small x region it is necessary: to address the small x-behavior of polarized PDFs and GPD E (spin sum rule)