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…