Deeply Virtual Meson Production Cynthia Hadjidakis 6 th

Deeply Virtual Meson Production Cynthia Hadjidakis 6 th research conference on Electromagnetic Interactions with Nucleon and Nuclei Milos, 19 -24 September, 2005 ü Generalized Parton Distributions ü Experimental results ü Future measurements Deeply Virtual Meson Production Cynthia Hadjidakis

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. GPDs PERSPECTIVES GPDs Hard exclusive meson production 4 Generalized Parton Distributions (GPDs) ~ H H conserve nucleon helicity ~ E E flip nucleon helicity -2 x x+x x-x t Vector mesons ( , , ) GPDs depend on 3 variables: x, x, t for each quark flavour Hq, for gluon Hg quark flavour decomposition possible from meson production Deeply Virtual Meson Production Cynthia Hadjidakis Pseudoscalar mesons ( , ) ρ0 2 u+d, 9 g/4 ω 2 u-d, 3 g/4 s, g ρ+ u-d

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. GPDs PERSPECTIVES GPDs Factorization for hard meson production Q 2>>, t<< wave function for meson production: additional information/uncertainty hard scale t factorization for longitudinal photons only s. T suppressed by 1/Q 2 → at large Q 2, s. L dominates asymptotically for fixed x. B and t Deeply Virtual Meson Production Cynthia Hadjidakis « scaling law »

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. GPDs PERSPECTIVES Experimental facilities DESY: H 1, ZEUS, HERMES: 27. 5 Ge. V e+ H 1, ZEUS: HERMES: p (920 Ge. V) p, d CERN SPS: Compass 160 Ge. V m+ Compass: H 1, ZEUS collider 10 -4<x. B<0. 021: gluons in the proton distinct signature d Jlab: CLAS up to 5. 7 Ge. V fixed target experiments COMPASS, HERMES 0. 006/0. 02<x. B<0. 3: gluons/valence and sea quarks CLAS 0. 15<x. B<0. 75: valence quarks signature of exclusive process with missing mass/energy technique missing energy ep→er 0 X e- CLAS: p Deeply Virtual Meson Production Cynthia Hadjidakis

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. VECTOR MESONS GPDs PERSPECTIVES H, E Vector Mesons cross sections s~ | ∫ 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 Q 2 Deeply Virtual Meson Production Cynthia Hadjidakis

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. GPDs PERSPECTIVES Hg, Eg Total cross section vs W at HERA J/Y s ~ Wd(Q 2) with d=0. 7 no dependence on Q 2 hard scale provided by MJ/Y Deeply Virtual Meson Production Cynthia Hadjidakis , , J/Y general transition to hard behaviour at high Q 2+M 2

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. GPDs PERSPECTIVES Hg, Eg GPD based model comparison NLO calculations for s. L [Ivanov et. al. (2004)] 0 M=MRST 2001 C=CTEQ 6 M different renormalization scale m. R Deeply Virtual Meson Production Cynthia Hadjidakis GPD combined with Modified Perturbative Approach corrections to LO: quark transverse momenta, Sudakov suppression [Goloskokov et. al. (2005)] 0 calculations of s. L, s. TL, s. TT

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. GPDs PERSPECTIVES H, E 0 → + - angular distributions: extraction of s. L if SCHC holds (VM retains g* helicity): from polarized lepton beam: → weak violation of SCHC Deeply Virtual Meson Production Cynthia Hadjidakis

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. GPDs PERSPECTIVES H, E 0 → + - angular distributions: extraction of s. L if SCHC holds (VM retains g* helicity): 2002 → at Q 2 = 2 Ge. V 2, s. L=s. T Deeply Virtual Meson Production Cynthia Hadjidakis

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. GPDs PERSPECTIVES Hq, Eq Cross sections at HERMES [EPJC 17, 2000] GPD model calculations for s. L: [Vanderhaegen et. al. (1999)] --- 2 -gluon exchange --- quark exchange corrections to LO: quark transverse momenta → quark exchange dominates Deeply Virtual Meson Production Cynthia Hadjidakis → indication of a larger gluon contribution [Diehl et. al. (2005)] [Vinnikov et. al. (2005)] → talk by Markus Diehl

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. GPDs PERSPECTIVES Hq, Eq 0 cross sections at CLAS (4. 2 Ge. V) CLAS: analysis of s. L for 0 ( +, ) from 5. 7 Ge. V data (higher W, higher Q 2) s An is lys ro p in s gre a r+ [Vanderhaegen et. al. (1999)] frozen coupling constant at 0. 56 to average out non perturbative effect Deeply Virtual Meson Production Cynthia Hadjidakis Two-pion invariant mass spectra

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. GPDs PERSPECTIVES Hq, Eq production at CLAS (5. 7 Ge. V) Analysis of ω decay angular distributions: SCHC does not seem to hold → not possible to extract σL Evidence for unnatural parity exchange 0 exchange very probable even at high Q 2 (4 Ge. V 2) Cross sections described by REGGE model [Laget (2005)] Deeply Virtual Meson Production Cynthia Hadjidakis

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. VECTOR MESONS GPDs PERSPECTIVES Hq, Eq 0 transverse target spin asymmetry s. S ~ |ST| sin ( - S) E∙H [Goeke et. al. (2001)] 2002 -04 x. B E related to Jq TSA sensitive to Jq + Hg : smaller AUT same x. B-dependence behaviour as GPD calculations [Vinnikov et. al. (2005)] no s. L/s. T separation yet 2 times more data for 2005 0 TSA can be investigating at COMPASS Deeply Virtual Meson Production Cynthia Hadjidakis

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. PION PAIRS GPDs PERSPECTIVES Hq, Eq Pion pairs production: e p (d)→ e’ p (d) + - Legendre moment: <P 1> sensitive to the interference between different + - isospin states Deeply Virtual Meson Production Cynthia Hadjidakis

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. PION PAIRS GPDs PERSPECTIVES Hq, Eq Legendre Moment: M dependence interference between S-wave and lower 0 tail m < 0. 6 Ge. V minimum interference between S-P waves m ~ 0. 77 Ge. V indication of 0 –f 2 interference m ~ 1. 3 Ge. V GPD model calculations for s. L: [Lehmann-Dronke et. al. (2001)] ■▲ quark exchange ― quark + 2 -gluon exchange Deeply Virtual Meson Production Cynthia Hadjidakis [PLB 599, 2004]

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. GPDs PERSPECTIVES ~ ~ H, E Pseudoscalar Mesons cross sections ~ ~ s~ | ∫ 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 + production: ~ At low t and large x, E dominated by the pion pole ~ E related to F target spin asymmetry ~ ~ AUT~ Im( H. E ) Deeply Virtual Meson Production Cynthia Hadjidakis

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. PS MESONS s GPDs PERSPECTIVES ~ ~ Hq, Eq + cross section at HERMES L/T separation not possible s. T suppressed by 1/Q 2 → at large Q 2, s. L dominates supported by REGGE model [Laget (2005)] GPD model calculations for s. L: [Vanderhaegen et. al. (1999)] Q 2 dependence is in general agreement with theoretical expectation Corrections to LO (k┴ and soft overlap) calculations overestimate the data Deeply Virtual Meson Production Cynthia Hadjidakis

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. PS MESONS s GPDs PERSPECTIVES ~ ~ Hq, Eq Cross section ratios 0 production: no -pole e p→e + n / e p→e 0 p measure at HERMES Jlab: [Mankiewicz et al. (1999)] e p → e + X CLAS (5. 7 Ge. V) Q 2~2. 3 Ge. V 2 x~0. 3 x. B Deeply Virtual Meson Production Cynthia Hadjidakis Missing mass (Ge. V)

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. PS MESONS asym. GPDs PERSPECTIVES ~ ~ Hq, Eq + transverse TSA ~~ TARGET SPIN ASYMMETRY s. S ~ |ST| sin ( - S) E∙H g*L p → + n HERMES COMPASS Deeply Virtual Meson Production Cynthia Hadjidakis [Frankfurt et al. (1999)] [Belitsky et al. (2001)]

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. PERSPECTIVES GPDs PERSPECTIVES HERMES with a recoil detector 2006/2007 Detection of the recoiling proton clean reaction identification improve statistical precision (unpolarised data with high density target) improve detector resolution: multi-dimensional binning in x. B and t → poster by Yves Van Haarlem Deeply Virtual Meson Production Cynthia Hadjidakis

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. PERSPECTIVES GPDs PERSPECTIVES Jlab upgrade to 12 Ge. V beam energy Projections for 11 Ge. V (sample kinematics) TARGET SPIN ASYMMETRY AUT x. B = 0. 3 -0. 4 -t = 0. 2 -0. 3 Ge. V 2 s. L s. Tot s. T Other bins measured concurrently Deeply Virtual Meson Production Cynthia Hadjidakis r 0 COMPASS: 2010 CERN proton luminosity upgrade proposal for a recoil detector x. B up to Q 2= 20 Ge. V 2 up to Q 2= 7 Ge. V 2

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. GPDs PERSPECTIVES ~~ HE HE CONCLUSION GPDs can be probed by hard exclusive meson production Reaction ep→epρ0 ep→epρ+ ep→epf ep→epω ep→epp+p- ep→epp+ ep→epp 0 Observable σL Exploration H (2 u+d) Experiment H 1, ZEUS, HERMES, CLAS TSA H. E HERMES σL H (u-d) σL H (s) H 1, ZEUS, HERMES σL H (2 u-d) CLAS Legendre Moment H HERMES ~ σtot E (u-d) HERMES ~~ TSA H. E ~ σtot H (2 u+d) Corrections to leading order are needed to describe the cross sections Scaling region expected to be reached at lower Q 2 for TSA, cross section ratios Combining all the measurements will allow to constrain GPD models Deeply Virtual Meson Production Cynthia Hadjidakis

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. GPDs PERSPECTIVES Factorization theorem prediction asymptotically for fixed x. B and t fit: 1/Qp p=1. 9± 0. 5 p=1. 7± 0. 6 p=1. 5± 1. 0 Deeply Virtual Meson Production Cynthia Hadjidakis

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. GPDs PERSPECTIVES SDME from GPD model Modified Perturbative Approach [Goloskokov et. al. (2005)] Good agreement with the data (s. L, SDME) for Q 2>5 Ge. V 2 t-dependence can be different for stot and s. L no separate measurements for the t-slope on the data Deeply Virtual Meson Production Cynthia Hadjidakis

VECTOR MESONS s asym. | PION PAIRS | PS MESONS s asym. GPDs PERSPECTIVES Sum Rules and Limited cases Forward limit (t → 0, x→ 0) ~q H (x, x=0, t=0) = Dq(x) ~ Hq(x, x=0, t=0) = x. G(x) Hq(x, x=0, t=0) = x. DG(x) Hq(x, x=0, t=0) = q(x) Sum rules dx Hq(x, x, t) = Fq 1 (t) dx Eq(x, x, t) = Fq 2 (t) ~ dx Hq(x, x, t) = gq. A (t) ~ dx Eq(x, x, t) = hq. A (t) Ji sum rules 30%(DIS) 1 ( H(x, x, t=0) + E(x, x, t=0) ) x dx = Jquark =1/2 DS + D Lz -1 Deeply Virtual Meson Production Cynthia Hadjidakis