1. Andrzej Sandacz Sołtan Institute for Nuclear Studies, Warsaw ECT*, Trento, Italy, October 10-15, 2010 recent experimental results GPD 2010 Workshop Review on exclusive meson production

2. Introduction Exclusive and proton-dissociative production of VM at small |t| Meson production on transversely polarised nucleons Conclusions Production of pseudoscalar mesons Helicity amplitudes for VM production on unpolarised nucleons

3. GPDHEMP GPDs and Hard Exclusive Meson Production  allows separation and wrt quark flavours Flavour sensitivity of HEMP on the proton  factorisation proven only for σ L  4 Generalised Parton Distributions (GPDs) for each quark flavour and for gluons conserve flip nucleon helicity H E Vector mesons ( ρ, ω, φ) H E Pseudoscalar mesons ( π, η) ~~ σ T suppressed by 1/ Q 2  wave function of meson (DA Φ ) additional nonperturbative component  quarks and gluons enter at the same order of α S  at Q 2 ≈ few GeV 2 power corrections/higher order pQCD terms are essential ρ0ρ0 2u  d, 9g/4 ω 2u  d, 3g/4  s, g ρ+ρ+ udud J/ψg 00 2  u  d  2  u  d  applicable at DIS region, |t| << Q 2 and any x B

4.  at small x sensitivity mostly to gluons universal dipole-nucleon cross section Colour dipole models an alternative description of VM production at small x applicable at small x both for photoproduction and DIS region for heavy mesons or γ * L z ≈ ½ and dipole-nucleon cross section related to inclusive photo- and DIS production the link exploited in certain colour dipole models  cross section for VM production ~ | g ( x B )| 2 (at LO) hardening of the gluon distribution g ( x B ) ~ x B - λ at large Q 2 strong W -dep. dipole transv. size W-dep. t-dep. large weak steep small strong shallow

5. γ*γ* M R pp’ M’ R1R1 M N, Δ γ*γ* p p’ R2R2 Regge models another alternative description of meson photo- and electroproduction t-channel exchange of Reggeon(s) based on general properties of amplitudes analiticity at |t| << s (W) Regge polesRegge cuts R (R 1, R 2 ) : Ƥ, ρ, ω, σ, f 2, π, b 1 … ρ0ρ0 Ƥ, σ, f 2 ω Ƥ, π 0  Ƥ ρ+ρ+ π +, ρ + π0π0 ω, ρ 0, b 1 M R factorisation of vertices for a Regge pole exchange; g RNN (t) at nucleon vtx. and meson form factor energy dependence determined by the Reggeon trajectory: α R (t) ≈ α R (0) + α’ R t except Ƥ, contributions of other Reggeons decrease with W + applicable from photoproduction to moderate Q 2

6. Elastic and proton-dissociative small |t| VM production at HERA 10 -4 ≤ x B ≤ 10 -2 0 ≤ Q 2 < 160 GeV 2 | t | < 3 GeV 2 30 < W < 180 GeV VM measured in central detectors no other activity, apart from forward detectors elastic sample - scattered proton inside the beam pipe; ‘no-tag events’ proton-dissociative sample - remnants of the proton hit forward detectors; ‘tag events’ Main sources of background: cross-contaminations between tag and no-tag samples ≈ 10% diffractive ρ’ production with not all decay particles being mesured - several % π + π - background in ϕ samples ≈ 5% semi-inclusive events suppressed by large rapidity gap between VM and forward detectors VM: ρ 0, ω, ϕ, J/ψ, ψ(2s), Υ

7.  Q 2 dependence KMW (Kowalski, Motyka, Watt) dipole approach MRT (Martin, Ryskin, Teubner) parton-hadron duality shape similar for ρ & ϕ and for elastic & dissoc. shape reasonably well described by models normalization; some (< 20%) differences between exps similar level of agreement with models for the ratios σ V rescaled according to quark charge content  SU(4) universality (?) universality qualitative (within 20%) scaling factors from VM electronic decay widths expected to encompass wave function and soft effects power low fits 1/(Q 2 +M V 2 ) n with n ≈ 2.4

8.  t dependence for elastic (| t | < 0.5(1.0) GeV 2 ) and dissoc. (| t | < 3 GeV 2 ) b = b Y + b qq + b Ƥ ( + b V ?) some discrepancy between experiments, due to subtraction of dissoc. background significant decrease from photoproduction already at μ 2 ≈ 0.5 GeV 2 and levelling at μ 2 ≈ 5 GeV 2 decrease of dipole transverse size with increasing scale light mesons slightly above J/ψ ( effect of VM form factors ?) slopes in diffractive dissociation significantly smaller μ 2 = (Q 2 +M V 2 )/4 ( = Q 2 for DVCS ) related to ‘transverse imaging’ of the proton b Ƥ expected small and Q 2 independent

9.  W dependence σ ∞ W δ faster growth at large mass or large Q 2 photoproduction DIS hardening of the gluon distribution g ( x B ) ~ x B - λ pQCD models reproduce W dependence well, sensitivity to assumed gluon PDFs GK - (Goloskokov, Kroll) GPD model KMW INS-L - (Ivanov, Nikolaev, Savin) dipole model with large meson wave function

10. at large μ 2 scales W dependence (α Ƥ (0)) significantly stronger than in soft hadronic diffraction  Interplay between W and t dependences effective Pomeron trajectory determined either by measuring W evolution of t -slope b or t evolution of W δ (more accurate) increase of α Ƥ (0) with the scale due to hardening of gluon distribution α’ Ƥ smaller than for ‘soft Pomeron’, even at Q 2 ≈ 0 a hint that α’ Ƥ may vanish at very large Q 2, as expected for BFKL dynamics L. Schoeffel

11. Exclusive VM production at CLAS 0.16 ≤ x B ≤ 0.7 1.6 ≤ Q 2 < 5.6 GeV 2 0.1 < | t | < 4.3 GeV 2 1.8 < W < 2.8 GeV ‘Typical’ kinematic domain missing mass used to ensure exclusivity VM: ρ 0, ω, ϕ, ρ + preliminary, first results ever S. Morrow et al. EPJ A39, 5 (2009) L. Morand et al. EPJ A24, 445 (2005) J.P. Santoro et al. PR C78, 025210 (2008) ρ 0 : e p → e p π + π - ω : e p → e p π + π – π 0 or e p → e p π + π - π 0 ϕ : e p → e p K + K - ρ + : e p → e n π + π 0 missing mass M X [epX] for selected (Q 2, x B ) bins ρ0 ρ0 fitted sum of ρ 0, f 0, f 2 and nonresonant π + π -

12.  W dependence of σ(γ * p → ρ 0 p L ) J.M. Laget (Regge) GK VGG (‘hand-bag’) VGG with ‘meson exchange’ Laget (Regge) able to describe data up to Q 2 ≈ 4 GeV 2 GPD models using ‘hand-bag’ mechanism + power corrections OK at W ≥ 5 GeV fail by an order of magnitude at the lowest W at small W (large x B ) in the framework of GPDs important contrib. of exchange

13.  W dependence for ρ + L and ϕ L for ρ + (not shown) qualitatively similar trends as for ρ 0 ϕ for ϕ GPD model describes data well in all W range GK ϕ production through gluon and sea quark exchanges (Pomeron in Regge formalism) in contrast, for other mesons at small W also valence quark exchanges important (subleading Reggeons)  b slope probing more compact object at large x B courtesy of M. Guidal

14. VM angular distributions W(cosθ, φ, Φ) depend on the spin density matrix elements (SDME)  23 (15) observables with polarized (unpolarized) beam SDMEs are bilinear combinations of the helicity amplitudes Spin Density Matrix Elements for VM production on unpolarised nucleons  check s-channel helicity conservation  describe parity of t-channel exchange  impact on GPD studies – determination of σ L SDMEs NPE vs. UPE for SCHS the only non-vanishing are T 00, T 11, U 11 F λm λN’;λγ λN (γ*N → mN’) F = T + U (natural + unnatural PE) convention T λm λγ, U λm λγ implies λ N’ =λ N = +½  determine hierarchy of T λm λγ, U λm λγ amplitudes in Regge formalism - NPE: Ƥ, ρ, ω, f 2, a 2 ; UPE: π, a 1, b 1 exchanges in GPD formalism - NPE: H, E ; UPE: H, E GPDs ~ at leading order only SCHC & NPE

15.  SDMEs from HERMES for ρ 0 production on protons and deuterons comprehensive measurement and analysis of 15(8) unpolarised (polarised) SDMEs ! 1 < Q 2 < 7 GeV 2 | t’ | < 0.4 GeV 2 (**) 3.0 < W < 6.3 GeV t’ = t – t 0 selections and background 0.6 < M ππ < 1.0 GeV (*) Main sources of systematic errors: ΔE = (M X 2 -M p 2 )/2<M p -1.0 < ΔE < 0.6 GeV (**) (*) non-resonant π + π – background 4-8% (unsubtracted) SIDIS background 3-12% (subtracted bin-by-bin) proton-dissociative background ≈4% (unsubtracted) (**) similar results (not shown here) also for ϕ uncertainties of parameters in exclusive MC background subtraction PYTHIA A. Airapetian et al. EPJ C 62, 659 (2009)

16.  SDMEs combined 1996-2005 data over whole kinematic range = 0.08, = 1.95 GeV 2, = 0.13 GeV 2 ~ |T 11 | 2 ~ Re{T 11 T* 00 } ~ |T 01 | 2 ~ Im{T 11 T* 00 } ~ Re{T 01 T* 11 } ~ Im{T 01 T* 11 } ~ Re{T 01 T* 00 } ~ Re{T 10 T* 11 } ~ Im{T 10 T* 11 } ~ Re{T 1-1 T* 11 } ~ Im{T 1-1 T* 11 } leading contributions observed hierarchy of NPE ampllitudes: |T 00 | ~ |T 11 | >> |T 01 | > |T 10 | ≈ |T 1-1 | EPJ C 62, 659 (2009) ρ0 ρ0

17.  for φ no s-channel helicity violation and no UPE  for proton and deuteron SDMEs (mostly) the same  small contribution of unnatural-parity exchanges for ρ 0  selected results on helicity amplitudes from HERMES W.-D. Nowak phase difference between T 11 and T 00 : δ = +26.4° ± 2.3 ± 4.9 (p); +29.3° ± 1.6 ± 3.6 (d) increases (20°→ 38°) with Q 2 (1 → 7 GeV 2 ) relative magnitude of SCHC non-conserving amplitudes and UPE amplitudes relative contributions to cross section, τ 2 T and τ 2 UPE, of NPE SCHC non-conserving τ 2 T = 0.025 ± 0.003 ± 0.003 (p); 0.028 ± 0.002 ± 0.002 (d) τ 2 UPE = 0.063 ± 0.011 ± 0.025 (p); 0.046 ± 0.008 ± 0.023 (d)  for ρ 0 small (≈ 10%) but statistically significant SCHS violating amplitudes T 01 and T 10

18.  selected results on helicity amplitudes from H1 and ZEUS  phase difference δ between T 11 and T 00  UPE consistent with 0 (checked for transverse photons )  among SCHS non-conserving SDMEs significantly ≠ 0 r 5 00 ~ Re(T 01 T* 00 ) smaller Re r 04 11, Re r 1 10, Im r 2 10 ~ Re(T 01 T* 11 )  extracted ratios of helicity amplitudes T 11 /T 00, T 01 /T 00, T 10 /T 00, T 1-1 /T 00 vs. Q 2 and t example HERMES ρ 0 however opposite trend for HERMES only observed hierarchy of amplitudes |T 00 | > |T 11 | >> |T 01 | > |T 10 | ≈ |T 1-1 | reflection of possible x B dependence ? in HERMES data) (due to Q 2 -x B correlation ?

19.  R = σ L /σ T several models able to desribe the data well GK qualitative universality of R vs. Q 2 /M V 2 no significant W-dependence of R within single experiment an indication of moderate increase between low energies (HERMES) and HERA S. Goloskokov, more comparison of GK model vs. data

20.  t -dependence of R ( or r 04 00 ) HERMES ρ 0 t -dependence of R would indicate different transverse sizes probed by γ * L and γ * T no significant t-dependence of R within total (statistical + systematic) errors however from another H1 estimate of R using ratios of helicity amplitudes 3 σ from 0 Surprising ! needed to check by ZEUS and sensitivity to assumptions

21. Exclusive pseudoscalar meson production π + (HERMES, Hall C), π 0 (Hall A, CLAS), η (CLAS) challenging at higher energies – small cross section for γ * L at leading order sensitivity to GPDs H, E ~ flavour separation π+π+ Δu−Δd 00 2  u  d  2  u  d for π + important contribution to E of pion-pole exchange in t -channel ~ dominates σ L at small t no pion-pole exchange for π 0 ; expected sizeable higher twist corrections: π 0 from the pion cloud cannot couple directly to γ * a) transverse momenta of partons b) soft overlap diagrams leading order soft-overlap

22. 0.02 ≤ x B ≤ 0.55 1 < Q 2 < 11 GeV 2 | t | ≲ 2 GeV 2 = 4 GeV selection of exclusive π + sample: A. Airapetian et al. PL B 659, 486 (2008)  Exclusive π + production from HERMES e p → e n π + to ensure good efficiency and purity of pion identification 7 < p π < 15 GeV data collected in 1996-2005 from unpolarised and polarised proton target cut: M X 2 < = 1.2 GeV 2 Main sources of systematic errors: estimate of detection probability background subtraction ‘double subtraction method’ L - T separation not possible

23. σ L VGG LO σ L VGG LO+power corrections σ T + ε σ L Regge model (Laget) σ L Regge model (Laget) HERMES π + GPD LO calculations underestimate the data data support the order of the magnitude of the power corrections at low – t’ region Regge calculations for unseparated xsec. provides good description of magnitude and t’ and Q 2 dependences

24.  Exclusive π + production at Hall C e p → e n π + T. Horn et al. PRL 97, 192001 (2006) Rosenbluth separation of σ L and σ T VGL(Regge) VGG(GPD with power corrections) Regge calculations also reproduce σ L well σ T underestimated by factor ~ 3 - 6 GPD model describes σ L well Q 2 dependence of σ T significantly softer than ~Q -8 experiments F π – 2 [*] and π - CT [**] T. Horn et al. PR C78, 058201 (2008) = 1.60, 2.45 GeV 2 [*] ≈ 2.2 GeV = 2.15, 3.91 GeV 2 [**]

25. Hall C π + A model for solving longstanding problem of observed large σ T M.M. Kaskulov, K. Gallmeister, U. Mosel PR D78, 114022 (2008) combined description of longitudinal and transverse components: σ L dominated by hadronic exchanges (Regge) and pion form factor σ T at moderate and large Q 2 mostly hard scattering process (DIS) γ * q → q followed by fragmentation into π + n Regge (KGM) DIS + LM with fitted = 1.2 GeV 0.4 GeV fit to SIDIS by Anselmino et al. (2005) results in = 0.5 GeV

26.  Exclusive π 0 production at Hall A e p → e p π 0 → e p γ γ kinematic domain preliminary two values of x B (= 0.40, 0.33 ) at fixed Q 2 = 2.1 GeV 2 two values of Q 2 (= 1.9, 2.3 GeV 2 ) at fixed x B = 0.36 at 5.75 GeV electron energy high resolution spectrometer + PbF 2 calorimeter E γ > 1 GeV missing mass M X [e π 0 X] resolution results given for: exclusivity cut M X 2 < 1.0 GeV 2 | t’ | < 0.22 GeV 2 Main sources of systematic errors (≈ 3.4%): HRS acceptance beam polarisation radiative corrections

27. ε (ε L ) degree of linear (longitudinal) polarisation of γ * Kin2: Q 2 = 1.9 GeV 2, x B = 0.36 Kin3: Q 2 = 2.3 GeV 2, x B = 0.36 Hall A π 0 no depletion at t’=0 slow Q 2 -dependence of σ T + ε σ L ~ (Q 2 ) -1.35±0.10 far from the QCD leading twist prediction for σ L ~ (Q 2 ) -3 need σ L - σ T separation E07-007 taking data now bands show fits ~ sin θ π CM, sin 2 θ π CM, sin θ π CM for components σ TL, σ TT, σ TL’ respectively and no significant t-dependence of σ T + ε σ L reasonable agreement (within ≈ 15%) between Regge model (Laget) and σ T + ε σ L no agreement for interference terms

28.  Exclusive π 0 and η production at CLAS e p → e p π 0 → e p γ γ preliminary at 5.78 GeV electron energy e p → e p η → e p γ γ 1 ≤ Q 2 < 4.5 GeV 2 0.09 < | t | < 2.0 GeV 2 0.1 < x B < 0.58 various cuts to ensure exclusivity ☺ θ (M X [ep], γγ ) M X [e γγ ] E miss [ep γγ ] M γγ M X 2 [ep]

29. V. Kubarovsky CLAS π 0 example: 2 out of 25 (Q 2,x B ) bins compared to Regge model (Laget) Q 2 = 1.38 GeV 2 x B = 0.17Q 2 = 2.25 GeV 2 x B = 0. 34 - t [GeV] Regge model exhibit s similar trends as the data but quantitative differences, in paricular at |t| (< 0.5 GeV 2 ) t-slope [GeV -2 ] xBxB t-slope almost independent of Q 2, decreases with x B ratio σ η / σ π = 0.2 -0.4, very weak dependence on Q 2 and x B increases with | t |

30. Ji’s sum rule q q Exclusive meson production on transversely polarised targets for vector mesons weights depend on contributions of various quark flavours and of gluons to the production of meson M transverse target spin dependent cross section so far GPD E poorly constrained by data (mostly by Pauli form factors) access to ‘elusive’ GPD E and the orbital angular momentum of quarks are weighted sums of convolutions of hard scattering kernels, corresponding GPDs of quarks and gluons, and meson DAs at leading twist cross section sensitive to GPD E and E ~ for pseudoscalar mesons H M, E M (H M, E M ) ~~

31. A. Airapetian et al. PL B 679, 100 (2009)  exclusive ρ 0 production on p ↑ at HERMES 30 new SDMEs determined for the first time ! and from W UT ( ϕ, ϕ s, φ, ϑ ) ( similarly from W UU ( ϕ, φ, ϑ ) ) μ, μ’(ν, ν’) helicities of γ * (ρ 0 ). one spin-flip amplitude two spin-flip amplitudes α (β) correspond to helicity signal of UPE; related to H, E ~, > 2.5 σ from 0 > 2.5 σ from 0 another indication of SCHC violation in γ T * →ρ L of initial (final) proton Diehl’s convention: For amplitudes T(U) μ ν α β = 0.08, = 1.95 GeV 2, = 0.13 GeV 2 Transversely polarised proton target, P T ≈ 73% 2002-2005 data Q 2 > 1 GeV 2 W > 2 GeV 2 | t’ | < 0.4 GeV 2

32. HERMES ρ 0 off p ↑ for ρ 0 L for ρ 0 T if SCHC (in Schilling-Wolf notation) a few GPD model calculations for A UT sin( ϕ - ϕ s ) for ρ 0 Goeke, Polyakov, Vanderhaegen (2001) Ellinghaus, Nowak, Vinnikov, Ye (2006) A UT LL, sin( ϕ - ϕ s ) = - 0.035 ± 0.103 E q parameterised in terms of J u and J d ENVY includes also E g J u in the range 0.2 - 0.4 and J d = 0 consistent with ρ 0 data, although within large errors W.-D. Nowak

33.  exclusive ρ 0 production on p ↑ and d ↑ at COMPASS Transversely polarised deuteron target ( 6 LiD), P T ≈ 50%, 2002-2004 data Transversely polarised proton target (NH 3 ), P T ≈ 90%, 2007 data Target segmented in 2 (3 in 2007) cells with opposite polarisationsSpins reversed regularly by DNP Q 2 > 1 GeV 2 W > 5 GeV 0.005 < x Bj < 0.1 0.05 < p t 2 < 0.5 GeV 2 [NH 3 ] 0.01 < p t 2 < 0.5 GeV 2 [ 6 LiD] Kinematic domain dominant coherent on N dominant non-exclusive bkg. -0.3 < M ππ – M ρ(PDG) < 0.3 GeV/c 2 A UT extracted with the double ratio (DR) method; in DR( ϕ - ϕ s ) counts from different cells for the data before and after spin reversal combined such that in the ratio muon flux, numbers of target nucleons and unpolarised cross section σ 0 cancel also acceptance cancels provided no changes between spin reversals fit to DR( ϕ - ϕ s ) preliminary

34. ≈ 2.2 (GeV/c) 2 ≈ 0.04 ≈ 0.18 (GeV/c) 2 in progress: L/T ρ 0 separation A sin( ϕ - ϕ s) A UT sin( ϕ - ϕ s) for transversely polarised protons compatible with 0 COMPASS ρ 0 off p ↑ and d ↑ GK (2008) Preliminary p↑p↑ compatible with predictions of the GPD model of GK for protons for transversely polarised deuterons A UT sin( ϕ - ϕ s) also compatible with 0 in 2010 data with transverse polarisation with NH 3 target3-fold increase of statistics for the proton target errors ≈ 2x smaller than for HERMES coherent/incoherent separation for deuteron data estimate effects of the non-exclusive background

35.  exclusive π + production on p ↑ at HERMES Transversely polarised proton target 0.03 ≤ x B ≤ 0.35 1 < Q 2 < 10 GeV 2 | t | ≲ 0.7 GeV 2 = 4 GeV selection of exclusive π + sample: 7 < p π < 15 GeV -1.2 < M X 2 < = 1.2 GeV 2 estimate of detection probability background subtraction ‘double subtraction method’ determination of target polarisation Main systematic errors P T ≈ 73%, 2002-2005 data A. Airapetian et al. PL B 682, 345 (2010) determined for the first time ! LT contrib from γ * L HT contrib from γ * T W.-D. Nowak

36. HERMES π + off p ↑ C. Bechler, D. Müller more t-channel exchanges pion pole dominates E ~ K. Kumericki, D. Müller S. Goloskokov, P. Kroll π n γ * p in LT ~ higher twist contributions involving H T and H T doesn’t have to vanish ~ H T (x,0,0) = h 1 (x) A sin( ϕ - ϕ s) A UT,l sin( ϕ - ϕ s) consistent with zero within errors excluding pure pion-pole contribution to GPD E ~ A sin( ϕ s) A UT,l sin( ϕ s) signal of γ * T → π + transitions interesting link to transversity and chiral odd GPDs S. Goloskokov

37. Significant progress on meas. of cross sections, SDME’s and spin asymmetries provide more stringent constraints on the models for DVMP Description of the present data on DVMP in terms of GPDs more complex Conclusions than LT handbag approach: quark-antiquark exchanges, semiinclusive-like contribution etc. power corrections, higher order pQCD terms, For DVMP program at future facilities: JLAB12, COMPASS-II, EIC high luminosity, hermetic detector (or recoil detector), γ * L – γ * T separation essential experimental requirements for further progress: