Observation of Exclusive γγ Production in CDF (and other exclusive states)
Hard exclusive processes -
description
Transcript of Hard exclusive processes -
Hard exclusive processes -
Andrzej Sandacz
Sołtan Institute for Nuclear Studies, Warsaw
DVCS at fixed target experiments and HERA
Transverse target spin asymmetry for ρ0 production
Vector Meson production at HERA
EIC Collaboration Meeting, Stony Brook University, December 8, 2007
experimental results and simulations for EIC
DVCS at EIC
Exclusive π+ and π0 production
GGeneralizedeneralized P Partonarton D Distributionsistributions
GPDs
x+ x-
P1 P2
hard
soft
* Factorisation:Q2 large, -t<1 GeV2
t
4 Generalised Parton Distributions : H, E, H, Efor each quark flavour and for gluons
depending on 3 variables: x, x, , t, t~~
for DVCS gluons contribute only at higher orders in αs
GPDs properties, link to DIS and form factors
)()(2
1tJEHxdx qqq Ji’s sum rule
)0(qJ total angular momentum carried by quark flavour q(helicity and orbital part)
'~
, ssHH qq
'~
, ssEE qq
for P1 = P2 recover usual parton densities
0)()0,0,(~
),()0,0,( xforxqxHxqxH qq
no similar relations; these GPDs decouple for P1 = P2
0)()0,0,(~
),()0,0,( xforxqxHxqxH qq
0~
, qq EE needs orbital angular momentum between partons
)(),,( 1 tFtxHdx qq
)(),,( 2 tFtxEdx qq
)(),,(~
tgtxHdx qA
q
)(),,(~
tgtxEdx qP
q
Dirac axial
pseudoscalar Pauli
GPD= a 3-dimensional picture of the partonic nucleon structure or spatial parton distribution in the transverse plane H(x, =0, t) → H(x,, rx,y ) probability interpretation Burkardt
‘Holy Grails’ or the main goals
Contribution to the nucleon spin puzzle
E related to the angular momentum
2Jq = x (Hq (x,ξ,0) +Eq (x,ξ,0) ) dx
½ = ½ ΔΣ + ΔG + < Lzq > + < Lz
g >
t
p p
q q
x P
x
y
r
z
E
The imaginary part of amplitude T probes GPD at x =
1
1
1
1
( , , ) +
( , ,
- i + ( , )
, )
DVCS
GPD x t
GPD x tT dx
x
GPD x tdx
i
P x
The real part of amplitude T depends on the integral of GPD over x
Observables and their relationship to GPDs
DG
LAP
DGLAP
ERBL
T
UT ~ sin(s)cos∙Im{k(H - E) + … }
C ~ cos∙Re{ H + H +… }~
LU ~ sin∙Im{H + H + kE}~
UL ~ sin∙Im{H + H + …}~
polarization polarization observables:observables:
kinematically suppressedkinematically suppressed
H
H
H, E
~
different charges: edifferent charges: e++ e e-- (only (only @HERA!):@HERA!):
H
DVCS Asymmetries measured up to now
= xB/(2-xB ),k = t/4M2
* 2 2*~ | | | |BH DVCS DVC BS HB DVCSHd
CLAS: DVCS - BSA
Integrated over tIntegrated over t
<-t> = 0.18 GeV2 <-t> = 0.30 GeV2 <-t> = 0.49 GeV2 <-t> = 0.76 GeV2
Accurate data in a Accurate data in a large kinematical large kinematical domaindomain
Difference of polarized cross sectionsDifference of polarized cross sections
Unpolarized cross sectionsUnpolarized cross sections
Q2 = 2.3 GeV2 xB = 0.36
Results from JLAB Hall A E00-100
Twist-2Twist-3
PRL97, 262002 (2006)
extracted twist-3 contribution small
1 1 2 22()
2 4( )
B
I BCx t
F F Fx
F FM
2 ( , , ) ( , )I ,m q qq
q
e H t H t
No Q2 dependence: strong indication for scaling and handbag dominance
GPD !!!
dominant term at small |t|
s1int ~
Towards E and Ju, Jd
2 1Im( )F H F E
sin( )cos( ) ~sUTA
Hermes DVCS-TTSA:Hermes DVCS-TTSA:
Hall A nDVCS-BSA:Hall A nDVCS-BSA:
x=0.36 and Qx=0.36 and Q22=1.9GeV=1.9GeV22
Neutron obtained combining Neutron obtained combining deuterdeuteronon and proton and proton
FF11 small small and and u & d cancel in u & d cancel in H
1 1 2 22~ ( )4LU
tF H x F F H F E
MA
Present status of the MODEL-DEPENDENT Ju-Jd extraction
With VGG Code
Lattice hep-lat 07054295
Unpolarised DVCS cross sections from HERA σDVCS at small xB (< 0.01) mostly sensitive to
Hg, Hsea
Q² and W dependence: NLO predictions
bands reflect experimental error on slope b: 5.26 < b < 6.40 GeV-2
- Wide range of Q2 - sensitivity to QCD evolution of GPDs
- Difference between MRS/CTEQ due to different xG at low xB
- Meaurements of b significantly constrain uncertainty of models
t dependence of DVCS cross section
New H1 results on slopes - DIS07
DIS06
Lessons from DVCS at H1/ZEUS
Skewing parameter R=Im DIS / Im DVCS ~ 0.5
Good agreement with NLO predictions
GPDs ≡ PDFs at low scale; skewing generated by QCD evolution
Sensitivity to Hg ; 15% change of Hg => 10% change of cross section
Real part of DVCS amplitude – small effect, few%
Low sensitivity to b(Q2) vs. b(const.)
Interplay of Rs (sea) and Rg (gluons)
Color dipole phenomenology (no GPDs) also a satisfacory description
Hard exclusive meson production
necessary to extract longitudinal contribution to observables (σL , …)
allows separation and wrt quark flavours
ρ0 2u+d, 9g/4
ω 2u-d, 3g/4
φ s, g
ρ+ u-d
J/ψ g
Flavour sensitivity of DVMP on the proton
factorisation proven only for σL
4 Generalised Parton Distributions (GPDs)for each quark flavour and for gluons
GPDs depend on 3 variables: x, x, , t, t
conserve flip nucleon helicity
H E Vector mesons (ρ, ω, φ)
H E Pseudoscalar mesons (π, η)~~
σT suppressed of by 1/Q2
wave function of meson (DA Φ)
additional information/complication
quarks and gluons enter at the same order of αS
Dipole models for exclusive VM production at small x
at very small x huge NLO corrections, large ln(1/x) terms (BFKL type logs)
pQCD models to describe colour dipole-nucleon cross sections and meson WF
• Martin-Ryskin-Teubner (MRT) Phys.Rev. D62 (2000) 014022
• Farshaw-Sandapen-Shaw (FSS) Phys.Rev. D69 (2004) 094013
• Kowalski-Motyka-Watt (KMW) Phys.Rev. D74 (2006) 074016
• Dosch-Fereira (DF) hep-ph/0610311 (2006)
• Frankfurt-Koepf-Strikman (FKS) Phys.Rev. D57 (1998) 512
sensitivity to different gluon density distibutions
sensitivity to ρ0 wave function
at small x sensitivity mostly to gluons
dipole transv. size W-dep. t-dep.
large weak steep
small strong shallow
Recent ZEUS results on exclusive ρ0 production
W-dependence σ ∞ Wδ
steeper energy dependence with increasing Q2
96-00 data: 120 pb-1 2 < Q2 < 160 GeV2 32 < W < 180 GeV 2∙10-4 < xBj < 10-2
| t | < 1 GeV2
significant increase of precision + extended Q2 range
arXiv:0708.1478[hep-ex]
W-dependence for hard exclusive processes at small x
ϕϕ J/J/ψψ ϒϒ
steep energy dependence for all vector mesons in presence of hard scale
Q2 and/or M2
‘universality’ of energy dependence at small x?
at Q2+M2 ≈ 10 GeV2 still significant difference between ρ and J/ψ
dσ / dt - ρ0
ZEUS
example (1 out of 6)
||tbedt
d
Fit
shallower t-dependence with increasing Q2
t-dependence for hard exclusive processes at small x
b-slopes decrease with increasing scale
approximate ‘universality’ of slopes as a function of (Q2 + M2)
Q2 and/or M2
approaching a limit ≈ 5 GeV-2 at large scales
recent data suggestive of possible ≈ 15% difference between ρ and J/ψ
Selected results on R = σL/σT for ρ0 production
the same W- and t-dependence for σL and σT
i.e. contribution of large qqbar fluctuations of transverse γ* suppressed
the same size of the longitudinal and transverse γ* involved in hard ρ0 production
δL ≈ δT bL ≈ bT
Comparison to ‘dipole models’
extensive comparison of the models to recent ZEUS ρ0 data inbelow just selected examples
considered models describe qualitatively all features of the data reasonably well
recent ZEUS data are a challenge; none of the models gives at the momentsatisfactory quantitative description of all features of the data
arXiv:0708.1478[hep-ex]
Comparison to GPD model
• Goloskokov-Kroll ‘Hand-bag model’; GPDs from DD using CTEQ6 power corrections due to kt of quarks included
both contributions of γ*L and γ*
T calculated
■ H1 □ ZEUS
ZEUS (recent)
W=75 GeV
W=90 GeV
W=90 GeV
σ/10
complete calculation
leading twist only (in collinear approx.)
leading twist prediction above full calculation, even at Q2 = 100 GeV2
≈ 10% sea quark contribution, including interference with gluons, non-negligible
25% at Q2 = 4 GeV2
contribution of σT decreases with Q2, but does not vanish even at Q2 = 100 GeV2
≈ 20%
arXiv:0708,3569[hep-ph]
Transverse target spin asymmetry for exclusive ρ0 production
So far GPD E poorly constrained by data; mostly by Pauli form factors
Give access to GPD E related to the orbital angular momentum of quarks
Ji’s sum ruleqq
The asymmetry defined as
),(),(
),(),(1),(
ss
ss
TsUT dd
dd
SA
to disentangle contributions from γL and γT the
distribution of ρ0 decay polar angle needed in addition Diehl and Sapeta
Eur. Phys. J.C 41, 515 (2005)
The asymmetry defined as
),(),(
),(),(1),(
ss
ss
TsUT dd
dd
SA
to disentangle contributions from γL and γT the
distribution of ρ0 decay polar angle needed in addition Diehl and Sapeta
Method for L/T separation used by HERMES
Angular distribution W(cos θ, φ, φs) and Unbinned Maximum Likelihood fit
)},()(1{cos[),,(cos ,,04
002
SLUTTLUUS ASArW
)}],()(1{)1(sin2
1,,
0400
2STUTTTUU ASAr
Assuming SCHC
)sin()(,
SmTLUTA
Simultaneous fit of 12 parameters of azimuthal distributions
~Im 00)sin(
,L
LUTSA
Im (E*H) / |H|2
a prerequisite for the method: determination of acceptance correction as a function of cos θ, φ and φs
A. Rostomyan and J. Dreschler arXiv:0707.2486
ρ0 transverse target spin asymmetry from HERMES
Transversely polarised proton target, PT ≈ 75% 2002-2005 data, 171.6 pb-1
for the first time ρ0 TTSA extracted separately for γ*L and γ*
T
ρ0 transverse target spin asymmetry from HERMES
in a model dependent analysis data favours positive Ju
in agreement with DVCS results from HERMES
ρ0 transverse target spin asymmetry from COMPASS
Transversely polarised deuteron target (6LiD), PT ≈ 50% 2002-2004 data
2
2
)]sin(1[
)]sin(1[
)()(
)()(
)()(
)()()(
du
du
du
du
aa
aa
NN
NNDRin bins of ϑ = φ – φS:
)]sin(41[ C
obtained using Double Ratio Method
)sin( SUTA
raw asymmetry ε from the fit to DR(η)
TUT Pf
A S )sin(
dilution factor f ≈ 0.38
u (d) are for upstream (downstream) cell of polarised targetarrows indicate transverse polarisation of corresponding cells
ρ0 transverse target spin asymmetry from COMPASS
asymmetry for deuteron target consistent with zero
ongoing work on:
longitudinal/transverse separation separation of incoherent/coherent
in 2007 data taken with transversely polarised proton target (NH3)
new
Exclusive π+ production from HERMES
σL VGG LO σL VGG LO+power corrections σT + ε σL Regge model (Laget)
LO calculations strongly underestimate the data
data support magnitude of the power corrections (kt and soft overlap)
Regge calculations provides good description of the magnitude of σtot
and of t’ and Q2 dependences
at leading twist σL sensitive to GPDs H and E ~ ~
at small |t’| E dominates as it contains t-channel pion-pole~
L/T separation not possible at HERMES, σT expected to be supressed as 1/Q2
e p → e n π+
Beam spin asymmetry in exclusive π0 production from CLAS
a fit α sinφ Regge model (Laget) pole terms (ω, ρ, b1) + box diagrams (cuts)
first measurement of BSA for exclusive π0 production above resonance region
sizeable BSA (0.04 – 0.11) indicate that both T and L amplitudes contribute necessity for L/T separation and measurements at higher Q2
prelim
inary
at leading twist σL sensitive to GPD H
no t-channel pion-pole (in contrast to exclusive π+ production) any non-zero BSA would indicate L-T interference, i.e. contribution not described
in terms of GPD’s
~ e p → e p π0
Cross sections for exclusive π0 production from JLAB HALL A DVCS Collab.
from P. Bertin, Baryon-07
t-slope close to 0, maybe even small negative
E00-110
dt
dh
dt
d
dt
d
dt
d
dt
d
ddt
dTLTLTTLTpp '*
2
sin)1(2cos)1(22cos2
10
h = ±1 is the beam helicity
dashed – prediction for σL from VGG model using GPDs
Vanderhaeghen, Guichon, Guidal
Summary for existing measurements
New precise data on cross sections result in significantly more stringent constraints on the models for GPDs
To describe present data on DVMP, both at large and small x, including power corrections (or higher order pQCD terms) is essential
First experimental efforts to constrain GPD E and quark orbital momentum
Results on DVCS promissing;
good agreement with NLO for HERA data
indication of scaling and handbag dominance in valence region
Precision of DVCS unpolarized cross sections at eRHIC (1)
eRHIC measurements of cross section will provide significant constraints
For one out of 6 W intervals (30 < W < 45 GeV)
Lint = 530 pb-1
(2 weeks)
Q2 [GeV2]
eRHIC HE setup
<W> = 37 GeV
σ(γ*
p →
γ p
) [n
b]
HE setup: e+/- (10 GeV) + p (250 GeV) L = 4.4 · 1032 cm-2s-1 38 pb-1/day
EIC measurements of cross section will provide significant constraints
For one out of 6 Q2 intervals (8 < Q2 < 15 GeV2)
W [GeV]
<Q2> = 10.4 GeV2
σ(γ*
p →
γ p
) [n
b]
also significantly extend the range towards small W
Precision of DVCS unpolarized cross sections at eRHIC (2)
LE setup: e+/- ( 5 GeV) + p ( 50 GeV) L = 1.5 · 1032 cm-2s-1 13 pb-1/day
eRHIC
Lint = 530 pb-1
Lint = 180 pb-1
HE setup: e+/- (10 GeV) + p (250 GeV) L = 4.4 · 1032 cm-2s-1 38 pb-1/day
Towards 3D mapping of parton structure of the nucleon at EIC
|)|exp()(/ * tBppdtd
)/ln('2)()( 0 xxxBxB o α’ = 0.125 GeV-2
(assumed for illustration)
simultaneous data in several (6) Q2 bins
Sufficient luminosity to do triple-differential measurements in x, Q2, t at EIC!
Lint = 4.2 fb-1
Lepton charge asymmetry at eRHIC
BMK use ‘improved’ charge asymmetries ACcosφ and AC
sinφ
model of Belitsky, Mueller, Kirchner (2002) for GPDs at small xB
parameters of sea-quark sector fixed using H1 DVCS data (PL B517 (2001))except magnetic moment κsea (-3 < κsea < 2), which enters Ji’s sum rule for Jq
κsea = 2
κsea = 2
κsea = -3
κsea = -3
measurements of asymmetries at EIC sensitive tool to validate models of GPDs
Q2 [GeV2]
W = 75 GeV , -t = 0.1 GeV2
W [GeV]
Q2 =4.5 GeV2 , -t = 0.1 GeV2
HE setup, Lint = 530 pb-1 divided equally between e+ and e-
Summary for DVCS at eRHIC
Wide kinematical range, overlap with HERA and COMPASS 1.5 ·10-4 < xB < 0.2 - sensitivity to quarks and gluons
1 < Q2 < 50 GeV2 - sensitivity to QCD evolution
DVCS cross sections - significant improvement of precision wrt HERA
Intereference with BH - pioneering measurements for a collider
powerfull tool to study DVCS amplitudes full exploratory potential, if e+ and e- available as well as longitudinaly and transversely polarized protons
Sufficient luminosity to do tripple-differential measurements in xB, Q2, t
Backup slide
A simulation of DVCS at eRHIC
HE setup: e+/- (10 GeV) + p (250 GeV) L = 4.4 · 1032 cm-2s-1 38 pb-1/day
acceptance of Central Detector (improved ZDR) 2° < θlab < 178°
diam. of the pipe - 20 cm, space for Central Detector: ≈ +/- 280 cm from IP
event generator: FFS (1998) parameterization with R=0.5, η = 0.4 and b = 6.2 GeV-2
DVCS + BH + INT cross section
due to acceptance and to ‘reasonably’ balance DVCS vs. BH following kinematical range chosen
acceptance simulated by kinematical cuts
kinematical smearing: parameterization of resolutions of H1 (SPACAL, LArCal) + ZEUS (θγ, φγ) + expected for LHC (θe’ , φe’ )
LE setup: e+/- ( 5 GeV) + p ( 50 GeV) L = 1.5 · 1032 cm-2s-1 13 pb-1/day
Ee’ > Emin GeV Eγ > 0.5 GeV 2° < θe’ < 178° 2° < θγ < 178°
Emin = 2 GeV (HE) or 1 GeV (LE)
2.5 < W < 28 GeV
1 < Q2 < 50 GeV2
0.05 < |t| < 1.0 GeV2
1 < Q2 < 50 GeV2
10 < W < 90 GeV
0.05 < |t| < 1.0 GeV2
HE setup LE setup