Hard exclusive production at HERMES Cynthia Hadjidakis 2nd workshop on the QCD structure of the Nucleon Rome, 12-16 June, 2006 Generalized Parton Distributions Compton scattering (DVCS) Exclusive mesons production Summary and perspectives

Hard exclusive production of photons and mesons p0, r0L, g Q2 Q2>>, t<< 4 Generalized Parton Distributions (GPDs) H H conserve nucleon helicity E E flip nucleon helicity ~ -2 x ~ x+x x-x Vector mesons (r, w, f) Pseudoscalar mesons (p, h) DVCS (g) depends on 4 GPDs t t Add gluon exchange diagram: ZEUS for each quark flavour Hq, for gluon Hg 1 2 q L J D + S = Ji’s sum rule: 0.2-0.3 (DIS) quark flavour decomposition possible from meson production GPDs depend on 3 variables: x, x, t 30%(DIS) 1 ( H(x,x,t=0) + E(x,x,t=0) ) x dx = Jquark =1/2 DS + D Lz -1 ρ0 2u+d, 9g/4 ω 2u-d, 3g/4 f s, g ρ+ u-d

HERMES kinematics coverage GPDs formalism: Q2>>, t<< HERMES: <Q2>=2.4 (1-10) GeV2, -t < 0.5 GeV2 collider experiments H1, ZEUS 10-4<xB<0.021 : gluons in the proton fixed target experiments COMPASS, HERMES  0.006/0.02<xB<0.3 : gluons/valence and sea quarks CLAS  0.15<xB<0.6 : valence quarks

HERMES spectrometer e +/ e - 27.5 GeV PB= 55% → Tracking system: dP/P = 2 %, dq < 1 mrad (charged) Particle Identification: RICH, TRD, preshower, calorimeter Photon: calorimeter: dP/P = 5 % for high energy photon no recoil detection e+ p → e+ g (p) only e+ and g detected Exclusive reaction signed via the missing mass technique MX = ( e + p – e’ – g ) Exclusive reaction selected with a cut on MX Background contamination estimated with non-exclusive MC 1H→ <|Pt|> ~ 85 % 2H→ <|Pt|> ~ 85 % 1H↑ <|Pt|> ~ 75 % Target: polarized H, D / unpolarized H, D, N, Ne, Kr, Xe

Deep Virtual Compton Scattering: e p → e’ p’ g  H, H, E, E ~ DVCS Deep Virtual Compton Scattering: e p → e’ p’ g DVCS Bethe-Heitler for HERMES kinematics: DVCS << Bethe-Heitler DVCS-BH interference leads to non-zero azimuthal asymmetry

DsUT DVCS asymmetries I~Ds ~ DsC ~ cosf Re{ H + x H + k E} ~  H, H, E, E ~ DVCS DVCS asymmetries I~Ds  Different charge : e+ e- (only at HERA!) : DsC ~ cosf Re{ H + x H + k E} ~ H  Different polarisations : DsLU ~ sinf Im{H + x H + k E} ~ DsUT beam target H DsUL ~ sinf Im{H + x(H + …} ~ ~ H, H DsUT ~ sinf Im{H - E + … } H, E Suppressed by kinematical factor x = xB/(2-xB ),k = -t/4M2

Beam spin and charge asymmetry  H, H, E, E ~ DVCS Beam spin and charge asymmetry Beam Spin Asymmetry Beam Charge Asymmetry [PRL87,2001] symmetrization f → |f| (cancel sin f terms from polarized beam) [hep-ex/0605108, subm. to PRL] L=140 pb-1 e+/- p → e+/- p g (MX<1.7 GeV) ─ P1 + P2 cos f + P3 cos 2f + P4 cos 3f L=10 pb-1 P1 = -0.01±0.02 P2 = 0.06±0.03 P3 = 0.02±0.03 P4 = 0.03±0.03 <-t> = 0.12 GeV2,<xB> = 0.1, <Q2> = 2.5 GeV2

Beam charge asymmetry: t-dependence DVCS ~ ~  H, H, E, E Beam charge asymmetry: t-dependence e+/- p → e+/- p g (MX<1.7 GeV) (in HERMES acceptance) Regge, D-term Regge, no D-term fac., D-term fac., no D-term GPD calculation: different parameterization for H [Vanderhaegen et.al. (1999)] H = double distribution ~ q(x) with skewing effect D-term or not t dependence: Regge-inspired t-dependence factorized t-dependence (ebt) BCA: no sensitivty to profile parameter :bsea, bval → AC sensitive to GPD-models tiny e-p sample (L=10 pb-1) HERA: 2004-2005 e- beam (x10) P1 = -0.01±0.02 P2 = 0.06±0.03 P3 = 0.02±0.03 P4 = 0.03±0.03 <-t> = 0.12 GeV2,<xB> = 0.1, <Q2> = 2.5 GeV2 symmetrization f → |f| (cancel sin f terms from polarized beam)

Longitudinal target spin asymmetry DVCS ~ ~  H, H, E, E Longitudinal target spin asymmetry Lp = 50 pb-1 Ld = 170 pb-1 sin f in agreement with GPD models unexpected large sin 2f (NLO contributions): from qGq correlations twist-3 GPDs?

Transverse target spin asymmetry DVCS ~ ~  H, H, E, E Transverse target spin asymmetry ~ AUT ~ sin(f-fS) cos(f) Im{H - E + … }+ cos(f-fS) sin(f) Im{H + … } + 2005: 2 times more statistics GPD calculation: [Goeke et.al. (2001)] , [Ellinghaus et.al. (2005)] H = double distribution Regge-inspired t-dep. D-term E = double distribution ~ sensitive to Jq: Ju (Jd=0) factorized t-dep. (dipole form factor) L = 64 pb-1 → First (model dependent) constraints on Ju and Jd ! talk by Zhenyu Ye

DVCS on nuclear target  H, H, E, E ~ ~  H, H, E, E DVCS on nuclear target GPDs modification in nuclear matter: spatial distribution of energy, angular momentum and shear forces inside the nuclei coherent nuclear DVCS (-t<0.05 GeV2) different from proton DVCS incoherent nuclear DVCS similar to proton DVCS (small BH cross section on neutron at small t) proton and deuteron data consistent highest t-bin may be affected by associated production (30%) 2H (720 pb-1), 4He (30 pb-1), 14N (50 pb-1), Ne (86 pb-1), Kr (135 pb-1), Xe (80 pb-1) study of properties of quarks and gluons inside nuclei

Beam spin asymmetry on nuclear target DVCS ~ ~  H, H, E, E Beam spin asymmetry on nuclear target L=30 pb-1 L=86 pb-1 → clear sin f amplitude in the exclusive region for Ne and Kr → soon: Anucleus/Aproton (He, N, Ne, Kr, Xe ) t-dependence (separation of coherent and incoherent part) A-dependence for coherent production [Guzey et al. (2003)], [Liuti et al. (2005)]

Factorization theorem for meson production Q2 Q2>>, t<< Meson production: wave function: additional information/uncertainty hard scale t Meson production: factorization for longitudinal photons only sT suppressed by 1/Q2 → at large Q2, sL dominates for fixed xB and t asymptotically « scaling law »

Vector Mesons cross sections transverse target spin asymmetry  H, E ~ | ∫ dx H(x,x,t) + E(x,x,t) |2 E kinematically suppressed at low t H = double distribution ~ q(x)/G(x) with skewing effect factorized t-dependence (ebt with slope from data) transverse target spin asymmetry AUT~ Im( H .E ) E = double distribution ~ sensitive to Jq factorized t-dependence (dipole form factor) higher order corrections cancel: scaling region reached at lower Q2

e p → e r0 (p): exclusive r0 selection VECTOR MESONS e p → e r0 (p): exclusive r0 selection r0 →p+ p- : h+h- detected Missing energy DE = (M2X-M2p)/2Mp (MX = e + p – e’ – h+ – h- ) 0.6 < M2h< 1.0 GeV DE < 0.6 GeV -t’=-t+tmin<0.4 GeV2 DE < 0.6 GeV -t’< 0.4 GeV2 Fit with skewed Breit-Wigner 0.6 < M2p< 1.0 GeV -t’< 0.4 GeV2 data non exclusive MC Monte Carlo simulation of non-exclusive (DIS) background

extraction of sL: r0 → p+p- angular distributions VECTOR MESONS extraction of sL: r0 → p+p- angular distributions g*-p CMS 23 SDMEs (15 unpolarised, 8 polarised) extracted in 3-D: F, f, cos q r° rest frame p’ f e’ p g* e r° L=250 pb-1 p+ F q p- if SCHC holds (VM retains g* helicity): → violation of SCHC → at Q2 = 2 GeV2, sL=sT

r0 longitudinal cross sections VECTOR MESONS  H, E r0 longitudinal cross sections [EPJC17,2000] L = 106 pb-1 [Vanderhaegen et.al. (1999)] corrections to LO: quark transverse momenta quark exchange dominates --- 2-gluon exchange --- quark exchange GPD model calculations for sL: H indication of a larger gluon contribution [Diehl et.al. (2005)] [Vinnikov et.al. (2005)] [Frankfurt et.al. (1996)] more data to come: r, f, w, r+

r0 transverse target spin asymmetry VECTOR MESONS  H, E r0 transverse target spin asymmetry interference between E and H [Vinnikov et.al. (2005)] - Goeke, Polyakov & Vanderhaeghen (2001) - E related to Jq  TSA sensitive to Jq sS: |ST| sin (f-fS) E H L=64 pb-1 xB x GPD model calculations (quarks+gluons GPDs) E related to Jq  TSA sensitive to Jq 2 times more data with 2005: sL/sT separation → talk by Armine Rostomyan

Pion pairs production: e p (d)→ e’ p (d) p+ p-  H, E Pion pairs production: e p (d)→ e’ p (d) p+ p- Legendre moment: <P1> sensitive to the interference between different p+p- isospin states

Legendre Moment: Mpp dependence PION PAIRS  H, E Legendre Moment: Mpp dependence interference between S-wave and lower r0 tail mpp < 0.6 GeV [PLB599,2004] minimum interference between S-P waves mpp ~ 0.77 GeV L=250 pb-1 indication of r0 –f2 interference mpp ~ 1.3 GeV GPD model calculations for sL: ■▲ quark exchange ― quark + 2-gluon exchange [Lehmann-Dronke et.al. (2001)]

Pseudoscalar Mesons cross sections target spin asymmetry  H, E ~ ~ PS MESONS  H, E ~ ~ Pseudoscalar Mesons cross sections ~ ~ ~ | ∫ dx H(x,x,t) + E(x,x,t) |2 ~ E kinematically suppressed at low t H = double distribution ~ Dq(x) with skewing effect factorized t-dependence ~ At low t and large x, E dominated by the pion pole E related to Fp ~ p+ production: target spin asymmetry ~ ~ AUT~ Im( H .E )

p+ cross section measurement PS MESONS  H, E ~ ~ p+ cross section measurement L/T separation not possible sT suppressed by 1/Q2 L=250 pb-1 → at large Q2, sL dominates supported by REGGE model [Laget (2005)] GPD model calculations for sL: [Vanderhaegen et.al. (1999)] Q2 dependence is in general agreement with the theoretical expectation Corrections to LO (k┴ and soft overlap) calculations overestimate the data

Transverse target spin asymmetry for exclusive p+ PS MESONS  H, E ~ ~ Transverse target spin asymmetry for exclusive p+ interference between E and H ~ ~ g*L p → p+ n [Frankfurt et al. (1999)] sS: |ST| sin (f-fS) E H ~ ~ [Belitsky et al. (2001)] L = 145 pb-1

Future analysis: recoil detector Jan. 06 - Jun. 07 Detection of the recoiling proton associated prod. ~11% semi-incl. ~5% associated prod. ~1% semi-incl. <<1% clean reaction identification improve statistical precision (Lp = 750 pb-1, Ld = 200 pb-1) → talk by Ralf Kaiser

CONCLUSION Polarisation provides observable sensitive ~ ~  H E ~  H, H, E, E  H E  H E CONCLUSION GPDs probed by hard exclusive photon and meson production H DVCS: BSA, BCA excl. r0: sL excl. pions pairs H DVCS: LTSA ~ E: TTSA DVCS, excl. r0 ~ E excl. p+ : s Corrections to leading order are needed to describe the cross sections Leading order calculations describe asymmetries Jan. 06: polarized target removed, recoil detector installed and under commissioning → HERMES dedicated to exclusive processes! ~ Asymmetries: powerful tool to constrain GPD models H H E E ~ ~ ~ Reaction Observable GPDs ~ ep→epg BCA, BSA, L(T)TSA H (2u+d) ep→epρ0 σL H (2u+d) TTSA H.E ep→epf σL H (s) ep→epω σL H (2u-d) ep→epp+p- Legendre Moment H ep→epp+ σtot E (u-d) TTSA H.E ep→epp0 σtot H (2u+d) ~ ~ ~ Hpp0: 2/3 Hu/p + 1/3 Hd/p Hpp+: Hu/p - Hd/p Polarisation provides observable sensitive to different combinations of GPDS ~ ~ ~ dedicated experiments for exclusive measurements starting soon at HERMES

HERMES at DESY e-beam: e+/e-, Ee=27.5 GeV, PB= 55% spin rotators @ HERMES for longitudinal beam polarization

Longitudinal target spin asymmetry:sin 2f ~ ~  H, H, E, E Longitudinal target spin asymmetry:sin 2f unexpected large sin 2f: from qGq correlations twist-3 GPDs? upper limits for qGq correlations twist-3 GPDs [D. Mueller]

Model dependent constraint on Ju and Jd ~ ~  H, H, E, E Model dependent constraint on Ju and Jd

Exclusive p+ production: e p → e p+(n) Missing Mass2 = (p-g*-p+)2 e p → e p-n : use of p- yield to subtract the non exclusive background e p → e p+ X e p → e p+ n -t (GeV2) 1 Monte Carlo (arbitrary norm.) data #events p+ enhancement Exclusive peak clearly centered at the nucleon mass Mean and width in agreement with exclusive MC Good description of data by MonteCarlo (acceptance determination) - Vanderhaeghen, Guichon & Guidal (1999) -