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. 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

4. 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 Q strong W-dep.
dipole transv. size W-dep t-dep.
large weak steep
small strong shallow

5. + 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

6. 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

7. 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

8. 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

9. 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

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 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

11. 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 – π or e p → e p π+ π - π0
L. Morand et al. EPJ A24, 445 (2005)
J.P. Santoro et al. PR C78, (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 -

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+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

14. 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

15. 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

16. <xB> = 0.08, <Q2> = 1.95 GeV2, <-t’> = 0.13 GeV2
SDMEs
combined 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. 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); ° ± 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 = ± ± (p); ± ± (d)
τ2UPE = ± ± (p); ± ± (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

18. selected results on helicity amplitudes from H1 and ZEUS
among SCHS non-conserving SDMEs significantly ≠ 0 r ~ Re(T01 T*00)
smaller Re r0411 , Re r110 , Im r ~ 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)

19. R = σL/σT several models able to desribe the data wellGK
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. 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

21. 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

22. | 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 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

23. 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

24. Exclusive π+ production at Hall C
experiments Fπ – 2 [*] and π - CT [**]
e p → e n π+
T. Horn et al. PRL 97, (2006)
T. Horn et al. PR C78, (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. 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, (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

26. Exclusive π0 production at Hall A
preliminary
e p → e p π0 → e p γ γ
at 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

27. 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
E taking data now
for components σTL, σTT, σTL’ respectively

28. Exclusive π0 and η production at CLAS
preliminary
e p → e p π0 → e p γ γ
at 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

29. 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 = , very weak dependence on Q2 and xB
increases with | t |
V. Kubarovsky xB

30. 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

31. 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% 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

32. 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) = ± 0.103
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 and Jd = 0 consistent with ρ0 data, although within large errors
W.-D. Nowak

33. exclusive ρ0 production on p↑ and d↑ at COMPASS
preliminary
Transversely polarised deuteron target (6LiD), PT ≈ 50%, 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)

34. AUTsin(ϕ-ϕs) for transversely polarised protons compatible with 0
COMPASS ρ0 off p↑ and d↑ p↑
< Q2 > ≈ 2.2 (GeV/c) < xBj > ≈ < 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. | 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%, 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

36. 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

37. 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