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

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

GPDs and Hard Exclusive Meson Production 4 Generalised Parton Distributions (GPDs) for each quark flavour and for gluons factorisation proven only for σL σT suppressed by 1/Q2 applicable at DIS region, |t| << Q2 and any xB allows separation and wrt quark flavours conserve flip nucleon helicity H E Vector mesons (ρ, ω, φ) H E Pseudoscalar mesons (π, η) ~ Flavour sensitivity of HEMP on the proton p0 2Du+Dd h 2Du-Dd quarks and gluons enter at the same order of αS ρ0 2u+d, 9g/4 ω 2u-d, 3g/4 f s, g ρ+ u-d J/ψ g at Q2 ≈ few GeV2 power corrections/higher order pQCD terms are essential wave function of meson (DA Φ) additional nonperturbative component

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 at small x sensitivity mostly to gluons universal dipole-nucleon cross section 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(xB)|2 (at LO) hardening of the gluon distribution g(xB) ~ xB-λ at large Q2 strong W-dep. dipole transv. size W-dep. t-dep. large weak steep small strong shallow

+ Regge models ρ0 ω f ρ+ R (R1, R2): Ƥ, ρ, ω, σ, f2, π, b1… M R another alternative description of meson photo- and electroproduction based on general properties of amplitudes analiticity at |t| << s (W) applicable from photoproduction to moderate Q2 t-channel exchange of Reggeon(s) R (R1, R2): Ƥ, ρ, ω, σ, f2, π, b1… γ* M R p p’ M’ R1 M N, Δ γ* p p’ R2 + Regge poles Regge cuts M R factorisation of vertices for a Regge pole exchange; ρ0 Ƥ, σ, f2 ω Ƥ, π0 f Ƥ ρ+ π+, ρ+ π0 ω, ρ0, b1 g RNN(t) at nucleon vtx. and meson form factor energy dependence determined by the Reggeon trajectory: αR(t) ≈ αR(0) + α’Rt except Ƥ, contributions of other Reggeons decrease with W

Elastic and proton-dissociative small |t| VM production at HERA VM: ρ0, ω, ϕ, J/ψ, ψ(2s), Υ VM measured in central detectors 10-4 ≤ xB ≤ 10-2 0 ≤ Q2 < 160 GeV2 | t | < 3 GeV2 30 < W < 180 GeV 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

Q2 dependence SU(4) universality (?) KMW (Kowalski, Motyka, Watt) dipole approach MRT (Martin, Ryskin, Teubner) parton-hadron duality SU(4) universality (?) shape similar for ρ & ϕ and for elastic & dissoc. power low fits 1/(Q2+MV2)n with n ≈ 2.4 shape reasonably well described by models normalization; some (< 20%) differences between exps similar level of agreement with models universality qualitative (within 20%) scaling factors from VM electronic decay widths expected to encompass wave function and for the ratios σV rescaled according to quark charge content soft effects

bƤ expected small and Q2 independent t dependence for elastic (| t | < 0.5(1.0) GeV2) and dissoc. (| t | < 3 GeV2) b = bY + bqq + bƤ ( + bV ?) related to ‘transverse imaging’ of the proton bƤ expected small and Q2 independent μ2 = (Q2+MV2)/4 ( = Q2 for DVCS ) some discrepancy between experiments, due to subtraction of dissoc. background significant decrease from photoproduction already at μ2 ≈ 0.5 GeV2 and levelling at μ2 ≈ 5 GeV2 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

σ ∞ Wδ W dependence faster growth at large mass or large Q2 GK - (Goloskokov, Kroll) GPD model KMW σ ∞ Wδ INS-L - (Ivanov, Nikolaev, Savin) dipole model with large meson wave function photoproduction DIS faster growth at large mass or large Q2 hardening of the gluon distribution g(xB) ~ xB-λ pQCD models reproduce W dependence well, sensitivity to assumed gluon PDFs

Interplay between W and t dependences effective Pomeron trajectory determined either by measuring W evolution of t-slope b or t evolution of Wδ (more accurate) increase of αƤ(0) with the scale due to hardening of gluon distribution at large μ2 scales W dependence (αƤ(0)) significantly stronger than in soft hadronic diffraction α’Ƥ smaller than for ‘soft Pomeron’, even at Q2 ≈ 0 a hint that α’Ƥ may vanish at very large Q2, as expected for BFKL dynamics L. Schoeffel

Exclusive VM production at CLAS preliminary, first results ever ρ0 : e p → e p π+ π - S. Morrow et al. EPJ A39, 5 (2009) ω : e p → e p π+ π – π0 or e p → e p π+ π - π0 L. Morand et al. EPJ A24, 445 (2005) J.P. Santoro et al. PR C78, 025210 (2008) ϕ : e p → e p K+ K - ρ+ : e p → e n π+ π0 ‘Typical’ kinematic domain missing mass used to ensure exclusivity 0.16 ≤ xB ≤ 0.7 1.6 ≤ Q2 < 5.6 GeV2 0.1 < | t | < 4.3 GeV2 1.8 < W < 2.8 GeV ρ0 missing mass MX[epX] for selected (Q2, xB) bins fitted sum of ρ0, f0, f2 and nonresonant π+π -

W dependence of σ(γ* p → ρ0 pL) J.M. Laget (Regge) GK VGG (‘hand-bag’) VGG with ‘meson exchange’ Laget (Regge) able to describe data up to Q2 ≈ 4 GeV2 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 xB) in the framework of GPDs important contrib. of exchange

W dependence for ρ+L and ϕL for ρ+ (not shown) qualitatively similar trends as for ρ0 ϕ GK for ϕ GPD model describes data well in all W range 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 courtesy of M. Guidal probing more compact object at large xB

Fλm λN’;λγ λN (γ*N → mN’) Spin Density Matrix Elements for VM production on unpolarised nucleons VM angular distributions W(cosθ, φ, Φ) depend on the spin density matrix elements (SDME)  23 (15) observables with polarized (unpolarized) beam Fλm λN’;λγ λN (γ*N → mN’) SDMEs are bilinear combinations of the helicity amplitudes F = T + U (natural + unnatural PE) convention Tλm λγ , Uλm λγ implies λN’ =λN = +½ determine hierarchy of Tλm λγ , Uλm λγ amplitudes check s-channel helicity conservation for SCHS the only non-vanishing are T00, T11, U11 describe parity of t-channel exchange NPE vs. UPE impact on GPD studies – determination of σL SDMEs in Regge formalism - NPE: Ƥ, ρ, ω, f2, a2 ; UPE: π, a1, b1 exchanges in GPD formalism - NPE: H, E ; UPE: H, E GPDs ~ ~ at leading order only SCHC & NPE

ΔE = (MX2-Mp2)/2<Mp | t’ | < 0.4 GeV2 (**) t’ = t – t0 SDMEs from HERMES for ρ0 production on protons and deuterons comprehensive measurement and analysis of 15(8) unpolarised (polarised) SDMEs ! A. Airapetian et al. EPJ C 62, 659 (2009) similar results (not shown here) also for ϕ selections and background 1 < Q2 < 7 GeV2 0.6 < Mππ < 1.0 GeV (*) 3.0 < W < 6.3 GeV ΔE = (MX2-Mp2)/2<Mp -1.0 < ΔE < 0.6 GeV (**) | t’ | < 0.4 GeV2 (**) t’ = t – t0 (*) non-resonant π+π – background 4-8% (unsubtracted) SIDIS background 3-12% (subtracted bin-by-bin) (**) proton-dissociative background ≈4% (unsubtracted) Main sources of systematic errors: background subtraction uncertainties of parameters in exclusive MC PYTHIA

<xB> = 0.08, <Q2> = 1.95 GeV2, <-t’> = 0.13 GeV2 SDMEs combined 1996-2005 data over whole kinematic range EPJ C 62, 659 (2009) ρ0 <xB> = 0.08, <Q2> = 1.95 GeV2, <-t’> = 0.13 GeV2 leading contributions ~ |T11|2 ~ Re{T11 T*00} ~ Im{T11 T*00} ~ Re{T01 T*11} ~ |T01|2 ~ Re{T01 T*00} ~ Im{T01 T*11} ~ Re{T10 T*11} ~ Im{T10 T*11} ~ Re{T1-1 T*11} ~ Im{T1-1 T*11} observed hierarchy of NPE ampllitudes: |T00| ~ |T11| >> |T01| > |T10| ≈ |T1-1|

small contribution of unnatural-parity exchanges for ρ0 selected results on helicity amplitudes from HERMES phase difference between T11 and T00 : δ = +26.4° ± 2.3 ± 4.9 (p); +29.3° ± 1.6 ± 3.6 (d) increases (20°→ 38°) with Q2 (1 → 7 GeV2) relative magnitude of SCHC non-conserving amplitudes relative contributions to cross section, τ2T and τ2UPE , of NPE SCHC non-conserving and UPE amplitudes τ2T = 0.025 ± 0.003 ± 0.003 (p); 0.028 ± 0.002 ± 0.002 (d) τ2UPE = 0.063 ± 0.011 ± 0.025 (p); 0.046 ± 0.008 ± 0.023 (d) for ρ0 small (≈ 10%) but statistically significant SCHS violating amplitudes T01 and T10 small contribution of unnatural-parity exchanges for ρ0 for φ no s-channel helicity violation and no UPE for proton and deuteron SDMEs (mostly) the same W.-D. Nowak

selected results on helicity amplitudes from H1 and ZEUS among SCHS non-conserving SDMEs significantly ≠ 0 r500 ~ Re(T01 T*00) smaller Re r0411 , Re r110 , Im r210 ~ Re(T01 T*11) UPE consistent with 0 (checked for transverse photons ) extracted ratios of helicity amplitudes T11/T00, T01/T00, T10/T00, T1-1/T00 vs. Q2 and t example observed hierarchy of amplitudes |T00| > |T11| >> |T01| > |T10| ≈ |T1-1| phase difference δ between T11 and T00 HERMES ρ0 however opposite trend reflection of possible for HERMES only xB dependence ? (due to Q2-xB correlation ? in HERMES data)

R = σL/σT several models able to desribe the data well GK several models able to desribe the data well qualitative universality of R vs. Q2/MV2 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

t-dependence of R ( or r0400 ) t-dependence of R would indicate different transverse sizes probed by γ*L and γ*T HERMES ρ0 no significant t-dependence of R within total (statistical + systematic) errors however from another H1 estimate of R Surprising ! using ratios of helicity amplitudes needed to check by ZEUS 3 σ from 0 and sensitivity to assumptions

π+ p0 h Exclusive pseudoscalar meson production π+ (HERMES, Hall C), π0 (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+ Δu−Δd p0 2Du+Dd h 2Du-Dd for π+ important contribution to E of pion-pole exchange in t-channel ~ dominates σL at small t no pion-pole exchange for π0; π0 from the pion cloud cannot couple directly to γ* expected sizeable higher twist corrections: a) transverse momenta of partons b) soft overlap diagrams leading order soft-overlap

| t | ≲ 2 GeV2 Exclusive π+ production from HERMES e p → e n π+ A. Airapetian et al. PL B 659, 486 (2008) e p → e n π+ data collected in 1996-2005 from unpolarised and polarised proton target 0.02 ≤ xB ≤ 0.55 L - T separation not possible 1 < Q2 < 11 GeV2 | t | ≲ 2 GeV2 to ensure good efficiency and purity of pion identification 7 < pπ < 15 GeV < W > = 4 GeV selection of exclusive π+ sample: ‘double subtraction method’ cut: MX2 < = 1.2 GeV2 Main sources of systematic errors: background subtraction estimate of detection probability

σL VGG LO+power corrections σT + ε σL Regge model (Laget) HERMES π+ σL VGG LO σL Regge model (Laget) σL VGG LO+power corrections σT + ε σL Regge model (Laget) 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 Q2 dependences

Exclusive π+ production at Hall C experiments Fπ – 2 [*] and π - CT [**] e p → e n π+ T. Horn et al. PRL 97, 192001 (2006) T. Horn et al. PR C78, 058201 (2008) < Q2 > = 1.60, 2.45 GeV2 [*] Rosenbluth separation of σL and σT = 2.15, 3.91 GeV2 [**] < W > ≈ 2.2 GeV GPD model describes σL well Regge calculations also reproduce σL well VGL(Regge) σT underestimated by factor ~ 3 - 6 VGG(GPD with power corrections) Q2 dependence of σT significantly softer than ~Q-8

A model for solving longstanding problem of observed large σT Hall C π+ A model for solving longstanding problem of observed large σT M.M. Kaskulov, K. Gallmeister, U. Mosel PR D78, 114022 (2008) combined description of longitudinal and transverse components: σL dominated by hadronic exchanges (Regge) and pion form factor σT at moderate and large Q2 mostly hard scattering process (DIS) γ*q → q followed by fragmentation into π+n Regge (KGM) DIS + LM with fitted 0.4 GeV = 1.2 GeV fit to SIDIS by Anselmino et al. (2005) results in = 0.5 GeV

Exclusive π0 production at Hall A preliminary e p → e p π0 → e p γ γ at 5.75 GeV electron energy kinematic domain high resolution spectrometer + PbF2 calorimeter Eγ > 1 GeV results given for: two values of Q2 (= 1.9, 2.3 GeV2) at fixed xB = 0.36 two values of xB (= 0.40, 0.33) at fixed Q2 = 2.1 GeV2 | t’ | < 0.22 GeV2 missing mass MX[eπ0X] resolution exclusivity cut MX2 < 1.0 GeV2 Main sources of systematic errors (≈ 3.4%): HRS acceptance beam polarisation radiative corrections

ε (εL) degree of linear (longitudinal) polarisation of γ* Hall A π0 ε (εL) degree of linear (longitudinal) polarisation of γ* Kin2: Q2 = 1.9 GeV2, xB = 0.36 Kin3: Q2 = 2.3 GeV2, xB = 0.36 no depletion at t’=0 and no significant t-dependence of σT + ε σL slow Q2-dependence of σT + ε σL ~ (Q2)-1.35±0.10 far from the QCD leading twist prediction for σL ~ (Q2)-3 reasonable agreement (within ≈ 15%) between Regge model (Laget) and σT + ε σL no agreement for interference terms need σL - σT separation bands show fits ~ sinθπCM, sin2θπCM, sinθπCM E07-007 taking data now for components σTL, σTT, σTL’ respectively

Exclusive π0 and η production at CLAS preliminary e p → e p π0 → e p γ γ at 5.78 GeV electron energy e p → e p η → e p γ γ various cuts to ensure exclusivity ☺ θ (MX[ep], γγ) MX[eγγ] Emiss[epγγ] Mγγ MX2[ep] 1 ≤ Q2 < 4.5 GeV2 0.1 < xB < 0.58 0.09 < | t | < 2.0 GeV2

Regge model exhibits similar trends as the data CLAS π0 example: 2 out of 25 (Q2,xB) bins compared to Regge model (Laget) Q2 = 1.38 GeV2 xB = 0.17 Q2 = 2.25 GeV2 xB = 0.34 -t [GeV] -t [GeV] Regge model exhibits similar trends as the data t-slope [GeV-2] but quantitative differences, in paricular at |t| (< 0.5 GeV2) t-slope almost independent of Q2, decreases with xB ratio ση/σπ = 0.2 -0.4, very weak dependence on Q2 and xB increases with | t | V. Kubarovsky xB

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

exclusive ρ0 production on p↑ at HERMES <xB> = 0.08, <Q2> = 1.95 GeV2, <-t’> = 0.13 GeV2 A. Airapetian et al. PL B 679, 100 (2009) one spin-flip amplitude two spin-flip amplitudes Q2 > 1 GeV2 W > 2 GeV2 | t’ | < 0.4 GeV2 Transversely polarised proton target, PT ≈ 73% 2002-2005 data 30 new SDMEs determined for the first time ! and from WUT( ϕ, ϕs, φ, ϑ ) ( similarly from WUU( ϕ, φ, ϑ ) ) Diehl’s convention: μ, μ’(ν, ν’) helicities of γ*(ρ0). For amplitudes T(U)μναβ α (β) correspond to helicity of initial (final) proton , > 2.5σ from 0 signal of UPE; related to H, E ~ ~ > 2.5σ from 0 another indication of SCHC violation in γT*→ρL

Eq parameterised in terms of Ju and Jd HERMES ρ0 off p↑ for ρ0L (in Schilling-Wolf notation) for ρ0T if SCHC AUTLL,sin(ϕ-ϕs) = - 0.035 ± 0.103 a few GPD model calculations for AUTsin(ϕ-ϕs) for ρ0 Goeke, Polyakov, Vanderhaegen (2001) Eq parameterised in terms of Ju and Jd Ellinghaus, Nowak, Vinnikov, Ye (2006) ENVY includes also Eg Ju in the range 0.2 - 0.4 and Jd = 0 consistent with ρ0 data, although within large errors W.-D. Nowak

exclusive ρ0 production on p↑ and d↑ at COMPASS preliminary Transversely polarised deuteron target (6LiD), PT ≈ 50%, 2002-2004 data Transversely polarised proton target (NH3), PT ≈ 90%, 2007 data Target segmented in 2 (3 in 2007) cells with opposite polarisations Spins reversed regularly by DNP Kinematic domain Q2 > 1 GeV2 W > 5 GeV 0.005 < xBj < 0.1 0.05 < pt2 < 0.5 GeV2 [NH3] 0.01 < pt2 < 0.5 GeV2 [6LiD] -0.3 < Mππ – Mρ(PDG) < 0.3 GeV/c 2 dominant coherent on N dominant non-exclusive bkg. AUT extracted with the double ratio (DR) method; in DR(ϕ-ϕs) 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 σ0 cancel also acceptance cancels provided no changes between spin reversals fit to DR(ϕ-ϕs)

AUTsin(ϕ-ϕs) for transversely polarised protons compatible with 0 COMPASS ρ0 off p↑ and d↑ p↑ < Q2 > ≈ 2.2 (GeV/c)2 < xBj > ≈ 0.04 < pt2 > ≈ 0.18 (GeV/c)2 Preliminary GK (2008) AUTsin(ϕ-ϕs) for transversely polarised protons compatible with 0 compatible with predictions of the GPD model of GK for protons for the proton target errors ≈ 2x smaller than for HERMES for transversely polarised deuterons AUTsin(ϕ-ϕs) also compatible with 0 in progress: L/T ρ0 separation coherent/incoherent separation for deuteron data estimate effects of the non-exclusive background in 2010 data with transverse polarisation with NH3 target 3-fold increase of statistics

| t | ≲ 0.7 GeV2 exclusive π+ production on p↑ at HERMES determined for the first time ! A. Airapetian et al. PL B 682, 345 (2010) Transversely polarised proton target PT ≈ 73%, 2002-2005 data LT contrib from γ*L 0.03 ≤ xB ≤ 0.35 1 < Q2 < 10 GeV2 | t | ≲ 0.7 GeV2 < W > = 4 GeV HT contrib from γ*T selection of exclusive π+ sample: 7 < pπ < 15 GeV ‘double subtraction method’ -1.2 < MX2 < = 1.2 GeV2 Main systematic errors background subtraction estimate of detection probability determination of target polarisation W.-D. Nowak

AUT,lsin(ϕ-ϕs) consistent with zero within errors HERMES π+ off p↑ pion pole dominates E ~ C. Bechler, D. Müller more t-channel exchanges K. Kumericki, D. Müller S. Goloskokov, P. Kroll π n γ* p in LT ~ higher twist contributions involving HT and HT doesn’t have to vanish ~ AUT,lsin(ϕ-ϕs) consistent with zero within errors excluding pure pion-pole contribution to GPD E ~ AUT,lsin(ϕs) signal of γ*T → π+ transitions interesting link to transversity and chiral odd GPDs HT (x,0,0) = h1(x) S. Goloskokov

Conclusions γ*L – γ*T separation 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 than LT handbag approach: power corrections, higher order pQCD terms, quark-antiquark exchanges, semiinclusive-like contribution etc. For DVMP program at future facilities: JLAB12, COMPASS-II, EIC essential experimental requirements for further progress: high luminosity, hermetic detector (or recoil detector), γ*L – γ*T separation