Twarde procesy ekskluzywne i partonowa struktura nukleonu
Andrzej SandaczInstytut Problemów Jądrowych, Warszawa
Seminarium Fizyki Wielkich Energii, Uniwersytet Warszawski
11 stycznia 2008
DVCS – głęboko wirtualne rozpraszanie Comptona
Spinowa asymetria w produkcji ρ0 z poprzecznie spolaryzowaną tarczą
Ekskluzywna produkcja mezonów wektorowych na akceleratorze HERA
Projekt pomiarów DVCS i produkcji mezonów w COMPASS-ie
Ekskluzywna produkcja pionów
GGeneralizedeneralized P Partonarton D Distributionsistributions
GPDs
x+ x-
p (P1, s)
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
p (P2, s’)
≈ xB/(2-xB )
GPDs properties and links to ‘standard’ physics
'~
, 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
x P
x
y
r
z
t
p p
q q
E
Contribution to the nucleon spin puzzle
E related to the orbital angular momentum
2Jq = x (Hq (x,ξ,0) +Eq (x,ξ,0) ) dx
½ = ½ ΔΣ + ΔG + < Lzq > + < Lz
g >
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
}~~
{ EE,,HH,DVCST}
~,,
~,{ EEHHGPD
notation:
UT ~ sin(s)cos∙Im{(F2H –F1E) + … }
polarization polarization observables:observables:
kinematically suppressedkinematically suppressed
LU ~ sin∙Im{H + H + kE}~
H
H
H, E
UL ~ sin∙Im{H + H + …}~ ~
different charges: edifferent charges: e++ e e-- (only (only @HERA!):@HERA!):
C ~ cos∙Re{ H + H +… }~
H
DVCS Asymmetries measured up to now
≈ xB/(2-xB ),k = t/4M2
* 2 2*~ | | | |BH DVCS DVC BS HB DVCSHd
e
pe
pBH calculableDVCS
+
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 LHPC hep-lat 0705.4295
2007 results from LHPC Collaboration (Lattice)
Lq = Jq – ΔΣq / 2extrapolations to mπ,phys using ChPT (numbers below for covariant barion ChPT)
Ju+d = 0.213(26) Ju = 0.214(16) Jd = -0.001(16)
Lu+d = 0.006(38) Lu = -0.195(38) Ld = 0.200(38)
quarks account for about 43% of the proton spin
for d quarks the spin and OAM (L) conributions almost cancel
Lu and Ld large, but nearly complete cancellation of quarks OAMs
μ2 = 4 GeV2
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
‘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 and asymmetries → 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
Generalized Parton Distributions @
Roadmap:
Now with 6LiD or NH3 polarized target and no recoil detector
After 2010 with H2 or D2 target with a recoil detector and an additional calorimetry
« Expression of Interest » SPSC-EOI-005 and presentation to SPSC
writing of the proposal, preparation of the future GPD program ~2010
E=
190,
100
GeV
HERA
Competition in the world and COMPASS role
Gluons valence quarks valence quarks and sea quarks and gluons
COMPASS JLab 12 GeV, FAIR,… 2010 2014
Ix2
COMPASS at CERN-SPS
High energy muon beam100/190 GeV
μ+ or μ- change once per day
polar(μ+)=-0.80polar(μ-)=+0.80
2.108 μ per SPS cycle
in 2010 ?new Linac4 (high intensity H- source)as injector for the PSB + improvements on the muon line
dσ(μpμp) = dσBH + dσDVCSunpol
+ Pμ dσDVCSpol
+ eμ aBH Re ADVCS + eμ Pμ aBH Im ADVCS
Twist-3 M01
)coscos()()(
),,(
2
21021
2BHBHBHBBH cCc
PP
tQxd
DVCS + BH with polarized and charged leptons and unpolarized target
Twist-2 M11 Twist-2 gluon M-11
known
DVCSBH Aa m
DVCSBH Aa e
eμ Pμ
eμ
Pμ
>>
)sinsin()()(
221
213
6IntInt ss
PtPxye
φ
θμ’μ
*
p
)coscos( 221022
6DVCSDVCSDVCSDVCS
unpolcCc
Qye
d
)sin( DVCSDVCSpol
sQy
ed
122
6
μ
pμ
pBH calculableDVCS
+
Belitsky,Müller,Kirchner
)coscoscos()()(
323210
213
6IntIntIntInt cccc
PtPxye
)~)(( EHH22211 4
Fmt
FFF m e
Int
Int
sc
1
1
11 e
ξx
t)ξ,H(x,dxP H
t)ξ,ξ,H(x H mq
q qe HH 2
F1H dominance with a proton target
F2E dominance with a neutron target (F1<<) very attractive for Ji’s sum rule study
with
Both c1Int and s1
Int accessible at COMPASS with + and -
Q2
xBj
7
6
5
4
3
2
0.05 0.1 0.2
6 month data taking in 201025 % global efficiency
Muon Beam Asymmetry at E = 100 GeV
COMPASS predictionWith a 2.5m H2 target
μ’μ
*
p
μ’μ
*
p
Muon Beam Asymmetry at E = 100 GeV
COMPASS prediction
model 1: H(x,ξ,t) ~ q(x) F(t)
VGG: double-distribution in x,
<b2> = α’ ln 1/x
H(x,0,t) = q(x) e t <b
2> = q(x) / xα’t
α’ slope of Regge traject.
α’=0.8 α’=1.1
model 2 and 2*: correl x and t
Guzey: Dual parametrization model 3: also Regge-motivated
t-dependence with α’=1.1
Design :2 concentric barrels of 24 scintillators counters read at both sides
Goals: Detect protons of 250-750 MeV/c t resolution => TOF < 300 ps exclusivity => Hermetic detector
European funding through a JRA for studies and construction of a prototype ( Bonn, Mainz, Saclay, Warsaw )
Recoil detector design
Recoil Detector Prototype Tests (2006)
i
CHTarget
Inner Layer
Outer Layer
A0
A1
A2
B0
B1
25cm
110cm
15°
All scintillators are BC 408A: 284cm x 6.5cm x 0.4cm Equiped with XP20H0 (screening grid)B: 400cm x 29cm x 5cm Equiped with XP4512
Use 1GHz sampler (300ns window) Design by CEA-Saclay/LAL-Orsay
Trigger:A&B coincidencesfinger pairs
Installed downstream of COMPASS
Resolution on TOFCenter 340ps HV lowCenter 310ps HV high Expected resolution 280 ps
Light brought by LS fibers to Avalanche Micro-Pixel PhotodiodeVery Challenging development for new and cheap AMPDs - magnetic field, low threshold detection, high rate environment
Studies for a new ECAL0 (Dubna,…)
ECAL0 modules dimesions: ~ 50x50 mm2 (inner), ~ 70x70 mm2 (middle and outer)Inner part - 1200 modules (7200 AMPDs) Middle part - 980 modules (3920 AMPDs)Outer part - 1372 modules (4116 AMPDs)The first scint – 3552 AMPDsTotal 3552 modules (15236+3552=18788 AMPDs)
requiremens on ECAL0
large transverse size:
small depth: ~ 25 cm
~ 400 x 400 cm2
geometry
The AMPD (1)The AMPD (1)
~ 1 mm
Depletion region ~ 2 m Substrate
Si Resistor
substrate p+
p-
Guard ring n-
Al conductorp+ n+Vbias
• High Gain (105~106)• Good Photon Detection Efficiency (15~65%)• Compact (package size ~ a few mm)• Relatively Low Cost • Magnetic-field tolerant• High dark noise
(order of 100-1000 kHz)• Response against input light yield is non-linear
Conclusions & prospects for future COMPASS measurements
• Possible physics ouput– Sensitivity to total spin of partons : Ju & Jd
– Sensitivity to spatial distribution of partons– Testing a variety of GPD models (VGG, Müller, Guzey, FFS-
Sch) to quantify the Physics potential of DVCS and HEMP
• Experimental challenges– Recoil Detection for proton (and neutron) – High performance and extension of the EM calorimetry
• Roadmap– Now with the transversely polarized targets: 6LiD ( 2006) and NH3 (2007)– 2008-9: A small RPD and a liquid H2 target will be available for the hadron program (ask for 2 shifts + and -)– > 2010: A complete GPD program at COMPASS with a long RPD + large liquid H2 target
before the availability of JLab 12 GeV, FAIR, EIC…