GENERALIZED PARTON DISTRIBUTIONS

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1 Exploring fundamental questions of NUCLEON STRUCTURE with GENERALIZED PARTON DISTRIBUTIONS Florian Herrmann Corfu Summer School

2 LHC COMPASS SPS Versatile facility for hadron structure studies hadron spectroscopy

3 The COMPASS CERN NIM A 577 (2007) 455 µ +, µ - or hadron (p, K, p) beam - changeover within < 1h momentum: GeV/c 80% polarization µ + & µ - with opposite polarization Two stage magnetic spectrometer large angular & momentum acceptance Particle identification - Ring Imaging Cerenkov Counter - Electromagnetic calorimeters - Hadronic calorimeters - Hadron absorbers

4 GPDs - a 3-dimensional picture of the partonic nucleon structure Deep Inelastic Scattering Hard Exclusive Scattering Deeply Virtual Compton Scattering γ* Q²x Bj x ep ex γ* Q² γ ep epγ p z p x+ξ GPDs t x-ξ p z x P x P r x boost y x boost y 0 x 1 Parton Density q ( x ) P x Generalized Parton Distribution H( x,ξ,t ) ( P x, r y,z ) Burkard,Belitsky,Müller,Ralston,Pire

5 Why GPDs are promising? What can we learn from a 3D picture? Goal: correlation between the 2 pieces of information: -distribution of longitudinal momentum carried by the partons -distribution in the transverse plane r p Contribution of orbital angular momentum to the total spin of a nucleon r in the context of the COMPASS program p Knowledge of transverse size of nucleon as function of parton momentum in hadron-hadron collisions such as at LHC, RHIC

6 Approaches to access GPDs x+ξ γ, π, ρ, ω x-ξ factorization t The observables are some integrals of GPDs over x Dynamics of partons in the Nucleon Models: Parametrization ~ ~ H,H,E,E (x,ξ,t) Fit of Parameters to the data Elastic Form Factors Ji s sum rule 2J q = x(h+e)(x,ξ,0)dx ordinary parton density x 1/2 = 1/2 Δ Σ + Lq + ΔG + Lg x H(x,ξ,t)dx = F(t) H(x,0,0) = q(x) ~ H(x,0,0) = q(x)

7 Necessity of factorization to access GPDs Deeply Virtual Compton Scattering (DVCS): γ* Q 2 γ γ* Q 2 4 GPDs: γ ~ ~ H,H,E,E (x,ξ,t) hard x + ξ x - ξ x + ξ x - ξ soft GPDs p p t = 2 GPDs p p t = 2 Q2 large t << Q 2 Hard Exclusive Meson Production (HEMP): hard soft γ* L x + ξ Q 2 GPDs p p t = 2 meson x - ξ Quark contribution Q 2 meson γ* L + γ* L x + ξ x - ξ GPDs p p t = 2 Gluon contribution

8 Hard Exclusive Meson Production Cross section measurements: ~ ~ Pseudo-scalar: π, η, H & E Vector meson: ρ, ω, φ H & E Allows for flavor separation: Eρ 0 = 1/ 2 (2/3 E u + 1/3 E d + 3/8 E g ) ρ : ω : φ 9 : 1 : 2 (at large Q 2 ) Eω = 1/ 2 (2/3 E u 1/3 E d + 1/8 E g ) Eφ = -1/3 E s 1/8 E g Vector meson production from transversely polarized target asymmetry E/H

9 HEMP with transversely polarized Targets A sin UT ( φ φ ) S t ' * Im ( E H ) H 2 E and H are weighted sums of GPD E q,g & H q,g Provide access to GPD E Constrain total angular momentum using Ji's relation: J + 1 f f f = 1 lim (,, ) (,, ) 2 dxx H x ξ t + E x ξ t t 0 1

10 Exclusivity Cuts No recoil detector assuming π and p masses Missing Energy Technique: E miss 2 2 MX Mp = = E E + γ * 0 ρ 2M 2 p t M p 14% contamination of diffractive dissociation (no attempt to remove it) Final sample: NH 3 : events 6 LiD: events but still strong SIDIS background

11 SIDIS Background Subtraction Two examples: total exclusive SIDIS still 5 40% background from SIDIS x Q p φ 2 2 Bj,, T, S (depending on target cell, ) Fix shape of background using Data/MC like- sign events φ Estimate SIDIS background from fit to data Assume Gaussian shape for signal total exclusive SIDIS ( ) A sin φ φ S UT by a binned max. likelihood

12 Exclusive ρ 0 production on transverse polarized Targets COMPASS proton Goloskokov & Kroll, EPJ C59 (2009) COMPASS deuteron Nuclear Physics B 865 (2012) 1 20

13 Bethe-Heitler & DVCS Cross Sections at 160GeV DVCS : Bethe-Heitler : dσ α T DVCS 2 + T BH 2 + Interference Term Low x B : BH dominates Large x B : DVCS dominates Reference yield from almost pure BH Study DVCS through interference term Re T DVCS & Im T DVCS Study dσ DVCS /dt Transverse Imaging

14 Observables (Phase 1) unpolarized Target Beam Charge & Spin Sum: S CS U dσ ( µ p µ pγ ) = dσ BH + dσ + DVCS unpol P µ dσ DVCS pol + e a Re T + e BH DVCS BH DVCS µ µ µ 2( BH DVCS BH DVCS ), = dσ + + dσ = dσ + dσ unpol + eµ Pa µ Im T Beam Charge & Spin Difference: P a Im T D CS U + 2( DVCS BH DVCS ), = dσ dσ = Pd µ σ pol + eµ a Re T

15 Beam Charge & Spin Sum S CS,U - Transverse imaging S CS U 2( BH DVCS BH DVCS ), = dσ + + dσ = dσ + dσ unpol + eµ Pa µ Im T Using S CS,U Integrating over ϕ Subtracting BH No Modell dependence dσ e dt Bt r 2 ( x ) ~ 2 Bx ( ) B B Ansatz at x B <<1: (x ~ x B ) x Bx ( ) = b + 2 α'ln B 0 measure α with accuracy >2.5 σ for: α > 0.26 (with ECAL 1+2 ) α > (with ECAL 0+1+2) 0 x B L = 1222 pb -1 ε global = 10 % 2 < r > 0.65 ±0.02 fm H1 PLB659(2008)? x COMPASS B

16 S CS,U - Transverse imaging S CS U 2( BH DVCS BH DVCS ), = dσ + + dσ = dσ + dσ unpol + eµ Pa µ Im T Projection for commissioning run 10/2012

17 Beam Charge & Spin Difference D CS,U D + 2( DVCS BH DVCS ), = dσ dσ = Pd µ σ pol + eµ a Re T CS U Phys. Rev. D60 (1999) arxiv: L = 1222 pb -1 ε global = 10 % Control detector acceptance and beam flux with high precision Error band assumes a 3% systematic uncertainty between µ + and µ - Use inclusive events and BH for check

18 Beam Charge & Spin Asymmetry D CS,U /S CS,U BCSA = D CS,U /S CS,U = A 0 + A CS,U cos ϕ + A 2 cos2ϕ Measurement of Int c 1 Using VGG B B B Kumericki, Müller Incl. HALL A Without HALL A arxiv:

19 First DVCS Signal COMPASS Global detection efficiency : ε global = / µ+p µ+p+γ efficiency - SPS & COMPASS availability - Dead time - Trigger efficiency Conclusion: Projections of errors are realistic

20 2008 & 2009 Beam COMPASS Target Setup for the Hadron Programme Ring B Ring A Target : 40 cm LH2 Recoil Detector (1m long) ECAL 1 & ECAL 2

21 New Target & Recoil-Proton Detector New: 2.5 m LH2 Target d=4 cm; ρ/ρ<3% 4 m ToF Barrel (CAMERA) σt<300ps for TOF ECAL m 1 GHz digitization of PMT signal Resolution >10 ENOB real-time feature extraction 1st level trigger detector signal digitization

22 Conclusions Generalized Parton Distibution allow access to contribution of angular momentum of quarks to total spin Study nucleon transverse dimension as function of x B (Tomography) Azimuthal Asymmetries in polarized exclusive ρ 0 production small & compatible with zero reasonable agreement with Goloskokov&Kroll prediction (GPD E) COMPASS II: investigate quark GPDs using DVCS Measure the spatial dimension of the nucleon Constrain GPD H through φ dependence of D CS,U Future Phase 2: DVCS & HEMP with polarized Target inside RPD Use knowledge of GPD H as input to constrain GPD E Requires highly sophisticated recoil detection & polarized target systems Changeover to DVCS physics starts next week!! Stay tuned for results!