Spin dependence in exclusive o production at COMPASS

Spin dependence in exclusive ρo production at COMPASS Andrzej Sandacz Sołtan Institute for Nuclear Studies, Warsaw On behalf of the Collaboration Ø longitudinal double-spin asymmetry A 1ρ Ø ρo spin density matrix elements and R = σL / σT GPD 2006 Workshop Trento, Italy June 5 - 9, 2006

Physics of exclusive ρ0 production μN μ’N’ρ + π π Q * 2 p. QCD calculations or p. QCD-inspired models with exchange of 2 quarks or 2 gluons (at large Q 2) Diffraction Regge theory: W N N’ t at low energy (W < 5 Ge. V) exchange of Reggeons ρ, ω, a 2, f 2 at higher energies exchange of Pomeron aim of the present analysis: spin structure of cross section / helicity amplitudes for γ*N → ρ0 N natural/unnatural parity of exchanged object is γ* helicity retained by ρ0 (SCHC) ? R = σL/σT vs. Q 2 better understanding of Pomeron’s nature

Properties of helicity amplitudes (1) Wick and Jacob assume γ*N → ρ0 N with t-channel exchanges of natural and unnatural parities natural: P, ρ, ω, a 2, f unnatural: How to assess contribution of unnatural exchanges ? => use longitudinal double spin asymmetries if SCHC π, a 1

Properties of helicity amplitudes (2) if a) nucleon unpolarized (or average over nucleon spins ≈ 0) b) assume only natural parity exchanges contribute only 5 independent helicity amplitudes Tλv λγ helicity conserving T 00, T 11 , single helicity-flip T 10, T 01 , double helicity-flip T 1 -1 hierarchy of helicity amplitudes T 00 , T 11 > T 01 > T 1 -1 > due to the angular momentum conservation all helicity-flip amplitudes vanish at t=0 st small t T 01 , T 10 T 1 -1 T 10

COMPASS experiment trigger-hodoscopes ~ 250 physicists from 28 institutes DW 45 SM 2 dipole RICH_1 straws Muon-filter 2, MW 2 HCAL 1 Gem_11 SM 1 dipole ECAL 2, HCAL 2 MWPC Gems Scifi Polarised Target 6 Li. D Muon-filter 1, MW 1 Veto straws, MWPC, Gems, Sci. Fi, DCs, straws Silicon Sci. Fi Micromegas, DC, Sci. Fi μ 160 Ge. V from CERN SPS Beam Polarization ~ -76% Beam intensity Luminosity 2 · 108 μ+/spill (4. 8 s / 16. 2 s) ~ 5 · 1032 cm-2 s-1

The polarized 6 Li. D-target 3 He – 4 He dilution refrigerator (T~50 m. K) Superconducting Solenoid (2. 5 T) + Dipole(0. 5 T) μ Target Polarization ~ 50% Dilution factor f ~ 0. 36 Two 60 cm long target cells with opposite polarizations 4 possible spin combinations: longitudinal u v transverse Reversed every 8 hours Reversed once a week

Incoherent exclusive ρ0 production * Mpp Assuming both hadrons are p 0. 5 < Mpp< 1 Ge. V Emiss Exclusivity of the reaction Emiss=(M²X-M²N) /2 MN -2. 5 < Emiss < 2. 5 Ge. V p t² Incoherent production 0. 15 < pt²< 0. 5 Ge. V² scattering off a quasi-free nucleon Q 2 W N 6 Li. D N’ t polarized target Kinematics: ν > 30 Ge. V Eμ’ > 20 Ge. V Q² > 0. 01 Ge. V² (Q 2 cut applied only in SDME analysis) Background ~12%

Kinematical domain of the final sample 2002 : 800, 000 evts 2003 : 1, 600, 000 evts Q²> 1 Ge. V² ~60, 000 evts + 2004 : not yet analyzed ~ will double the data sample <pt 2> = 0. 27 Ge. V 2 <W> = 10. 2 Ge. V

Longitudinal double-spin asymmetry for exclusive ρ0 production Both muon beam and target have to be polarized along the beam direction in COMPASS polarized d from 6 Li. D Ultimately one determines σ1/2 (σ3/2) cross section for antiparallel (parallel) spin orientation of γ* and target N can arise from exchange of a 1(1260) trajectory in t-channel (small at 160 Ge. V) from interference of amplitudes for exchange in t-channel of Reggeons with natural parity: ρ, ω, f, a 2(1320), P(pomeron) and unnatural parity: π, a 1(1260) (sensitivity even to small contributions of the latter ones) if only non-perturbative P in p. QCD-inspired models possible Ryskin Goloskokov and Kroll => access to spin dependent GPDs

Evaluation of A 1ρ (γ* N → ρo N) for incoherent exclusive ρ0 production to minimize systematic effects ‘ 2 nd order weighted method’ used v each event assigned weight w = f D Pb v 2 nd order equation for A 1 with coefficients depending on weights w, Pb and acceptance ratios for u and d cells values of A-dependent cross sections (for f) and ratio R (for D) specific for incoherent exclusive ρ0 production

Depolarization factor D for incoherent exclusive ρ° production R: E 665 parametrization

Dilution factor f for incoherent exclusive ρ° production n. D, n. A: numbers of nucleons from deuteron and nucleus A in the target : cross sections per nucleon for incoherent exclusive ρ° production on deuteron and nucleus A finally used f = C 1 · f 0 , where C 1 takes into account that there are 2 deuterons in 6 Li. D molecule f calculated event by event

COMPASS preliminary and HERMES results on A 1ρ (d) COMPASS results on A 1ρ on polarized deuteron target consistent with 0 Extended kinematical range of COMPASS by almost 2 decades down both in Q 2 and x COMPASS : inner bars –stat. outer – total errors HERMES: total errors at small x ( < 0. 01 ) contribution of unnatural parity exchanges small for exclusive ρ0 production

ρ° angular distributions W(cosθ, φ, Φ) depend on the spin density matrix elements (SDME) 23 (15) observables with polarized (unpolarized) beam φ SDMEs are bilinear combinations of the helicity amplitudes A(γ*(λγ) → ρ(λρ)) ≡ Tλρ, λγ λγ = ± 1, 0 λρ = ± 1, 0 This analysis: only one-dimensional angular distributions also used: ψ= φ - Φ

Measurement of r 04 00 0. 01 < Q² < 0. 05 < Q² < 0. 3 < Q² < 0. 6 < Q² < 2. 0 < Q² < 10 Ge. V 2 Distribution : 2002 Spin density matrix element: Tλρ λγ helicity amplitudes meson photon

Determination of R = s. L/s. T If SCHC holds : only T 00≠ 0 T 11≠ 0 Then : 2002 Impact on GPD study: determination of s. L is dominant at Q 2>2 Ge. V 2 - High statitics from quasi-photoproduction to hard production - Better coverage at high Q 2 with 2003 and 2004 data

04 Measurement of r 1 -1 and Im r 31 -1 φ Distribution : 2002 beam polarisation Spin density matrix elements: ak e w If SCHC holds a v l io n tio

Measurement of 1 r 1 -1 If SCHC holds general expression for r 11 -1 : in future independent of SCHC determination of 23 SDMEs including r 11 -1 from 3 D distributions 2002

Summary and outlook Asymmetry A 1ρ (d) consistent with zero over wide range of Q 2 and x small contribution of unnutaral parity exchanges at x < 0. 01 first measurement at small Q 2 and small x High-statistics data on SDM elements and R for incoherent exlusive ρ0 production in a wide Q 2 range (including small Q 2 not covered previously) weak violation of SCHC observed Significant improvement of accuracy expected after including 2004 (and 2003 data) extraction of 23 SDMEs under way Studies of coherent exclusive ρ0 production foreseen Single spin asymmetry for transversely polarized target Analysis of exlusive φ and J/ψ production in progress → E/H GPDs