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Andrzej Sandacz

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|.

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Andrzej Sandacz

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  1. 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

  2. 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

  3. allows separation and wrt quark flavours H E Vector mesons (ρ, ω, φ) ~ ~ H E Pseudoscalar mesons (π, η) conserve flip nucleon helicity 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 Flavour sensitivity of HEMP on the proton • quarks and gluons enter at the same order of αS • at Q2≈ few GeV2power corrections/higher order pQCD terms are essential • wave function of meson (DA Φ) additional nonperturbative component

  4. and dipole transv. size W-dep. t-dep. large weak steep small strong shallow 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 orγ*L z ≈ ½ • at smallxsensitivity 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-λat large Q2 strong W-dep.

  5. γ* γ* M M M’ R R1 R2 N, Δ p p’ p p’ Regge models 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 R (R1, R2):Ƥ, ρ, ω, σ, f2, π, b1… t-channel exchange of Reggeon(s) + Regge poles Regge cuts 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: αR(t) ≈ αR(0) + α’Rt except Ƥ, contributions of other Reggeons decrease with W

  6. 10-4 ≤xB≤ 10-2 0 ≤Q2< 160 GeV2 30 <W< 180 GeV | t |< 3 GeV2 Elastic and proton-dissociative small |t| VM production at HERA VM:ρ0, ω, ϕ, J/ψ, ψ(2s), Υ 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

  7. Q2 dependence KMW(Kowalski, Motyka, Watt) dipole approach MRT(Martin, Ryskin, Teubner) parton-hadron duality • SU(4) universality (?) • shape similar for ρ&ϕand 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 soft effects for the ratios σVrescaled according to quark charge content

  8. 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 bƤexpected small and Q2 independent μ2 =(Q2+MV2)/4 (=Q2for 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

  9. photoproduction DIS • W dependence GK - (Goloskokov, Kroll) GPD model KMW σ∞Wδ INS-L - (Ivanov, Nikolaev, Savin) dipole model with large meson wave function • 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

  10. 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 scaledue 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

  11. 0.16 ≤xB≤ 0.7 1.6 ≤Q2< 5.6 GeV2 1.8 <W< 2.8 GeV 0.1 < | t |< 4.3 GeV2 Exclusive VM production at CLAS VM:ρ0, ω, ϕ, ρ+ 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– π0ore p → e p π+π-π0 L. Morand et al. EPJ A24, 445 (2005) ϕ: e p → e p K+ K- J.P. Santoro et al. PR C78, 025210 (2008) ρ+ : e p → e nπ+ π0 ‘Typical’ kinematic domain missing mass used to ensure exclusivity ρ0 missing mass MX[epX] for selected (Q2, xB) bins fitted sum of ρ0, f0, f2and nonresonantπ+π-

  12. 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

  13. W dependence for ρ+Land 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

  14. SDMEs ~ ~ • in GPD formalism - NPE: H, E ; UPE: H, E GPDs 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’;λγλN (γ*N → mN’) SDMEs are bilinear combinations of the helicity amplitudes F = T + U (natural + unnatural PE) conventionTλm λγ , Uλm λγimplies λN’ =λN= +½ • determine hierarchy of Tλm λγ , Uλm λγamplitudes • 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 • in Regge formalism - NPE: Ƥ, ρ, ω, f2, a2 ; UPE: π, a1, b1 exchanges at leading order only SCHC & NPE

  15. 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-resonantπ+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

  16. 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|

  17. 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, τ2Tandτ2UPE , 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) • forρ0small (≈ 10%) but statistically significant SCHS violating amplitudes T01 and T10 • smallcontribution of unnatural-parity exchangesforρ0 • forφno s-channelhelicity violation and no UPE • for proton and deuteron SDMEs (mostly) the same W.-D. Nowak

  18. selected results on helicity amplitudes from H1 and ZEUS • among SCHS non-conserving SDMEs significantly ≠ 0r500~ Re(T01 T*00) smallerRe 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/T00vs. Q2andt example observed hierarchy of amplitudes |T00| > |T11| >> |T01| > |T10| ≈ |T1-1| • phase difference δbetweenT11 and T00 HERMES ρ0 however opposite trend reflection of possible for HERMES only xB dependence ? (due to Q2-xB correlation ? in HERMES data)

  19. R = σL/σT 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

  20. HERMES ρ0 • t-dependence of R ( or r0400 ) t-dependence of R would indicate different transverse sizes probed by γ*Landγ*T • 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

  21. ~ ~ • for γ*Lat leading order sensitivity to GPDs H, E ~ • for π+ important contribution to E of pion-pole exchange in t-channel Exclusive pseudoscalar meson production π+ (HERMES, Hall C), π0 (Hall A, CLAS), η(CLAS) challenging at higher energies – small cross section • flavour separation dominates σL at small t • no pion-pole exchange for π0; π0from the pion cloud cannot couple directly toγ* • expected sizeable higher twist corrections: a) transverse momenta of partons b) soft overlap diagrams leading order soft-overlap

  22. Exclusive π+production from HERMES A. Airapetian et al. PL B 659, 486 (2008) e p → e nπ+ 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 to ensure good efficiency and purity of pion identification | t |≲ 2 GeV2 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

  23. HERMES π+ σLReggemodel(Laget) σLVGG LO σLVGGLO+power corrections σT+εσLRegge 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

  24. Exclusive π+production at Hall C experimentsFπ – 2 [*] and π - CT [**] e p → e nπ+ 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

  25. with fitted = A model for solving longstanding problem of observed large σT Hall C π+ 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 0.4 GeV 1.2 GeV fit to SIDIS by Anselmino et al. (2005) results in = 0.5 GeV

  26. Exclusive π0production at Hall A preliminary e p → e pπ0 →e pγγ at5.75 GeV electron energy high resolution spectrometer + PbF2 calorimeter kinematic domain Eγ > 1 GeV results given for: two values ofQ2(=1.9, 2.3 GeV2)atfixed xB= 0.36 two values ofxB(= 0.40, 0.33)atfixed 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

  27. 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 + εσL • slow Q2-dependence of σT + εσL~ (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 + εσL 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

  28. MX[eγγ] θ(MX[ep],γγ) Emiss[epγγ] MX2[ep] Mγγ • Exclusive π0and η production at CLAS preliminary e p → e p π0 →e p γγ at5.78 GeV electron energy e p → e p η→e p γγ various cuts to ensure exclusivity ☺ 1 ≤Q2< 4.5 GeV2 0.1 <xB< 0.58 0.09 < | t |< 2.0 GeV2

  29. 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

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

  31. Q2 > 1 GeV2 and from WUT( ϕ, ϕs, φ, ϑ ) W > 2 GeV2 | t’ | < 0.4 GeV2 ( similarly from WUU( ϕ, φ, ϑ ) ) • , > 2.5σ from 0 ~ ~ signal of UPE; related to H, E • > 2.5σ from 0 one spin-flip amplitude two spin-flip amplitudes <xB> = 0.08, <Q2> = 1.95 GeV2, <-t’> = 0.13 GeV2 • exclusiveρ0production on p↑at HERMES A. Airapetian et al. PL B 679, 100 (2009) Transversely polarised proton target, PT≈ 73% 2002-2005 data 30 new SDMEs determined for the first time ! Diehl’s convention: μ, μ’(ν, ν’)helicities ofγ*(ρ0). For amplitudes T(U)μναβ α (β)correspond to helicity of initial (final) proton another indication of SCHC violation in γT*→ρL

  32. Juin the range 0.2 - 0.4 and Jd= 0 consistent with ρ0data, although within large errors 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 Juand Jd Ellinghaus, Nowak, Vinnikov, Ye (2006) ENVY includes also Eg W.-D. Nowak

  33. 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] • exclusiveρ0production on p↑andd↑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 -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)

  34. 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

  35. exclusiveπ+production on p↑at HERMES determined for the first time ! A. Airapetian et al. PL B 682, 345 (2010) Transversely polarised proton target LT contrib from γ*L PT≈ 73%, 2002-2005 data 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

  36. ~ pion pole dominates E in LT ~ πnγ*p ~ higher twist contributions involving HT and HT doesn’t have to vanish ~ excluding pure pion-pole contribution to GPD E HERMES π+ off p↑ C. Bechler, D. Müller more t-channel exchanges K. Kumericki, D. Müller S. Goloskokov, P. Kroll • AUT,lsin(ϕ-ϕs)consistent with zero within errors • 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

  37. Conclusions • 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: γ*L–γ*T separation high luminosity, hermetic detector (or recoil detector),

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