Nuclear GPDs and DVCS in Collider kinematics. Vadim Guzey. Theory Center, Jefferson Lab. Outline

Transcription

1 Nuclear GPDs and DVCS in Collider kinematics Vadim Guzey Theory Center, Jefferson Lab Introduction Outline Nuclear PDFs Nuclear GPDs Predictions for DVCS Conclusions

2 Introduction e(k ) Deeply Virtual Compton Scattering (DVCS) is the cleanest example of hard exclusive process. e(k) γ (Q 2 ) γ GPDs A A In collider kinematics, hard exclusive processes (DVCS) on nuclear targets will address the following physics problems: Interaction of small-size q q dipoles with nuclear matter, related to the phenomenon of Color Transparency Quark and gluon 3D (transverse) imaging through the studies (extraction) of generalized parton distributions (GPDs) Approach to the regime of high parton densities (saturation)

3 Introduction More specifically, DVCS on nuclear targets: Will naturally continue studies of nuclear Parton Distribution Functions (PDFs) carried out with fixed nuclear targets Will complete studies of DVCS on the nucleon initiated at HERA in DVCS on the proton Might access novel nuclear effects not present in DIS on nuclear targets (effects associated with the real part of the DVCS amplitude) Will put stringent constaints on theoretical models of the nuclear structure. DVCS is more sensitive to details of small-x physics (shadowing, antishadowing, black disk limit) than inclusive DIS on nuclear targets In my talk, I will concentrate on the last point.

4 Nuclear PDFs Unpolarized Inclusive Deep Inelastic Scattering (DIS) measures the structure function F2 A (x, Q 2 ) e(k) A e(k ) γ (Q 2 ) PDFs X DIS on fixed nuclear targets, R F2 = F A 2 (x, Q 2 )/F D 2 (x, Q 2 ) F 2 A F 2 d (b) nuclear shadowing antishadowing EMC effect Li, NMC C, NMC Xe, E665 x

5 Using QCD factorization theorem, nuclear Parton Distribution functions (PDFs) can be extracted from F A 2 (x, Q 2 ) and other data (DY, RHIC) by global fits. Nuclear PDFs R G = g A (x, Q 2 )/[Ag N (x, Q 2 )] Main drawbacks: insufficient kinematic coverage; small x correspond to small Q 2. Hence, small-x is either excluded from fits or contain large uncertainty (HT corrections) large uncertainties at small-x K. Eskola et al., arxiv: [hep-ph]

6 Nuclear PDFs An alternative to fitting is the leading twist (LT) model of nuclear shadowing (NS) L. Frankfurt, V.G, M. Strikman, Phys. Rev. D7, (2005) LT model of NS is based on: γ γ γ X X X γ γ γ connection between NS and diffraction due to V. Gribov QCD factorization theorem for inclusive and hard diffractive scattering in DIS QCD analysis of the HERA diffractive data by H and ZEUS A N N A A N N a) b) c) xf j/a (x, Q 2 0 ) = A xf j/n (x, Q2 0 ) ( iη)2 0. 8πA(A )Re + η 2 dx IP βf D(4) x j (β, Q 2 0, x IP, t min ) d 2 b dz dz 2 ρ A ( b, z )ρ A ( b, z 2 )e i(z z 2 )x IP m N z e A 2 ( iη)σj eff (x,q2 ) z 2 z dz ρ A ( b,z ) A A N N N A

7 Nuclear PDFs Predictions of LT model of NS, L. Frankfurt, V.G, M. Strikman, in preparation, based on 2006 H analysis of diffraction at HERA LT model of NS also predicts: nuclear diffractive PDFs impact parameter dependent PDFs f j/a /(Af j/n ) f j/a /(Af j/n ) Q 2 =2.5 GeV 2 Q 2 =0 GeV 2 Q 2 =00 GeV 2 u-quark Pb charm x x.3.2. gluon F x x

8 Nuclear GPDs Quark GPD of a spinless nucleus dz H q (x, ξ, t,µ 2 ) = 4π eix P + A z P A ψ ( z 2 ) γ + ψ ( ) z P A 2 z +, z =0 x longit. momentum fraction µ 2 factorization scale P + A = (P A + P A )/2 x ± ξ longit. momentum fractions ξ = x B /(2 x B ) = P A P A enters via convolution!

9 Nuclear GPDs Nuclear impact parameter dependent PDFs are nuclear GPDs at ξ = 0 (from the definition and from the fact that b is conjugate to, M. Burkardt, Int. J. Mod.Phys. A 8, 73 (2003) for proton) LT theory of NS gives nuclear GPDs at ξ = 0 for free. R q = q A (x, b)/[at A (b)q N (x)] H q A (x, ξ = 0,b) for 208 Pb at Q 2 0 = 2.5 GeV 2 Interesting feature: NS introduces correlations between x and b Such correlations are absent in the nucleon GPDs at small x b [fm] x

10 Nuclear GPDs How to nuclear GPDs for ξ 0? Two possible ways: Generalize the LT theory of NS to the case of off-forward kinematics V.G and M. Siddikov, in progress Using experience with modeling nucleon GPDs in terms of nucleon PDFs, relate nuclear GPDs to nuclear PDFs Double Distibution A. Radyushkin, Phys. Rev. D 56, 5524 (997) Align-jet model motivated A. Freund, M. McDermott, M. Strikman, Phys. Rev. D 67, (2003) Dual parameterization V.G. and T. Teckentrup, Phys. Rev. D 74, (2006)

11 Nuclear GPDs I will use the dual parameterization, which: essensially small-x B expansion of nucleon GPDs simple expressions at LO σ DVCS [nb] Regge Exponential H ZEUS Q 2 = 8 GeV 2 leads to good description of all 4 high-energy DVCS data on proton (HERA, Hermes) 2 V.G. and T. Teckentrup, (2006) Generalization of the dual parameterization to the case of nuclear GPDs allows to express A LO DVCS(ξ, t, Q 2 ) in terms of q A (x, Q 2 ) q A (x, Q 2 ) are given by LT theory of NS W [GeV]

12 Predictions for DVCS Predictions of the resulting model of nuclear GPDs for DVCS on nuclear targets R DVCS 0.2 Q 2 =4 GeV 2 Ca-40 Pb x Bj Ratio of t-integrated DVCS cross sections, A DVCS (nucleus)/a DVCS (proton) Q 2 =4 GeV 2 Pb x Bj Ratio of nucleus/proton DVCS amplitudes Im Re R DVCS = σ DVCS σ DVCS (no NS) R = AA DVCS (t min) A p DVCS (t min)

13 Predictions for DVCS Contributions of the imaginary and real parts of DVCS amplitudes can be separated by measuring DVCS asymmetries arising due to the interference with the purely EM Bethe-Heitler process: Beam-spin asymmetry A LU (φ): dσ( e,φ) dσ( e,φ) ImH sinφ Beam-charge asymmetry A C (φ): dσ(e +, φ) dσ(e, φ) ReH cosφ

14 Predictions for A LU (φ) and A C (φ) Predictions for DVCS A LU (φ) GeV/c 00 GeV/c 40 Ca 208 Pb proton Q 2 =4 GeV 2 φ=π/2 t=-0.0 GeV 2 A C (φ) GeV/c 00 GeV/c 40 Ca 208 Pb proton Q 2 =4 GeV 2 φ=0 t=-0.0 GeV x B x B

15 Conclusions Studies of DVCS and other hard exclusive processes with nuclei and extraction of nuclear GPDs is a natural continuation of studies of small-x physics with fixed nuclear targets. In particular, GPDs contain information on the distribution of quarks and gluons both in the longitudinal and transverse directions. DVCS appears to be rather sensitive to LT nuclear shadowing and antishadowing at small-x. This is observed both in DVCS cross sections and in DVCS asymmetries. (A C which probes the real part of DVCS amplitude is especially sensitive.)

16 Back-up σ [nb] 0000 DVCS BH Interference σ [nb] 0000 DVCS BH Interference Ca-40 Coherent cross sections x Bj 00 Pb-208 Coherent cross sections x Bj