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Hard exclusive processes at EIC. - experimental aspects -. Andrzej Sandacz. Sołtan Institute for Nuclear Studies, Warsaw. Introduction. DVCS – from Central Detector only. DVCS – including fast ‘recoil’ proton. Exclusive Meson production. Tagging spectator protons for deuteron beam.

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Hard exclusive processes at EIC

- experimental aspects -

Andrzej Sandacz

Sołtan Institute for Nuclear Studies, Warsaw

  • Introduction

  • DVCS – from Central Detector only

  • DVCS – including fast ‘recoil’ proton

  • ExclusiveMeson production

  • Tagging spectator protons for deuteron beam

  • Conclusions

workshop on ‘Hard Exclusive Process at JLab 12 GeV and a Future EIC’

University of Maryland College Park, October 29-30, 2006

Deeply virtual compton scattering e p e p g
Deeply Virtual Compton Scattering ep→epg

The same final state in DVCS and Bethe-Heitler


interference + structure of azimuthal distributions

a powerful tool to disantangle leading- and higher-twist effects and extract DVCS amplitudes including their phases

up to twist-3 BMK (2002)

P1 (Φ), P2 (Φ) BH propagators

harmonics with twist-2 DVCS amplitudes (related to GPDs)

c0DVCS, c1I, s1Iand c0I(the last one Q suppresed)

Towards extraction of full set of gpds
Towards extraction of full set of GPDs

Aim for DVCS - go beyond measurements of unpolarized cross sections,

access interference term and exploit azimuthal angle dependence

example: method proposed by Belitsky, Mueller, Kirchner (2002)

  • measuree p → e p γ cross sections both for e+ and e-

for unpolarized, longitudinally and transversely polarized protons

  • σ+(φ) – σ-(φ) IΛ(φ)

Λ = {unp, LP, TnP, TsP}

σ+(φ) + σ-(φ) – 2 σBH(φ) 2 σDVCS,Λ(φ)

  • from φ-dependence of IΛ’s extract 8 leading-twist harmonics cI1,Λ sI1,Λ

  • from these determine all 4 DVCS amplitudes (including their phases)

which depend on GPDs

  • another 8 leading-twist harmonics cDVCS0,Λ and cI0,Λcross check

in experiment asymmetries simpler than cross sections, but extraction of DVCS amplitudes more involved

Available measurements of asymmetries for dvcs
Available measurements of asymmetries for DVCS

lepton charge or single spin asymetries at moderate and large xB

HERMES and JLAB results

  • beam-charge asymmetry AC(φ)

  • beam-spin asymmetry ALU(φ)

  • longitudinal target-spin asymmetry AUL(φ)

  • transverse target-spin asymmetry AUT(φ,φs)

F1and F2 are Dirac and Pauli proton form factors

Unpolarized cross sections for dvcs
Unpolarized cross sections for DVCS

cross section σDVCS averaged over φ for unpolarised protons

H1 and ZEUS

Hsea, Hg

at small xB ( < 0.01)

DIS 2006

2° <θe’< 178° 2° < θγ < 178°

Ee’ > Emin GeVEγ > 0.5 GeV

Emin = 2 GeV (HE) or 1 GeV (LE)

1 < Q2 < 50 GeV2

1 < Q2 < 50 GeV2

10 < W < 90 GeV

0.05 < |t| < 1.0 GeV2

0.05 < |t| < 1.0 GeV2

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

LE setup: e+/-( 5 GeV) + p ( 50 GeV) L = 1.5 · 1032 cm-2s-1 13 pb-1/day

diam. of the pipe - 20 cm, space for Central Detector: ≈ +/- 280 cm from IP

acceptance of Central Detector(improved ZDR)2° <θlab< 178°

acceptance simulated by kinematical cuts

event generator: FFS (1998) parameterization with R=0.5, η = 0.4 and b = 6.2 GeV-2

DVCS + BH + INT cross section

kinematical smearing: parameterization of resolutions of H1 (SPACAL, LArCal) + ZEUS (θγ, φγ) + expected for LHC (θe’, φe’)



due to acceptance and to ‘reasonably’ balance DVCS vs. BH following kinematical range chosen

2.5 < W < 28 GeV

Distributions of events within acceptance of Central Detector




Number of event [arbitrary units]



W [GeV]


W [GeV]



Complementarity of HE and LE setups for covered W and xBj ranges

good coverage for3 < W < 90 GeVand 1.5 · 10-4 < xBj < 0.2

Q Detector2 > 1 GeV2

Q2 > 1 GeV2

2.5 < W < 28 GeV

10 < W < 95 GeV

0.05 < |t| < 1.0 GeV2

0.05 < |t| < 1.0 GeV2

Precision of DVCS unpolarized cross sections at eRHIC (1)

eRHIC HEsetup


σ(ep→epγ) = 173 pb

σ(ep→epγ) = 292 pb

Assume 2 weeks for each setup

Lint = 180 pb-1

Lint = 530 pb-1

Reconstructed: ≈ 133 000 events ≈ 28 000 events

Events divided into 6x6 bins of Q2 and W for each setup

Lint = 530 pb-1

<W> = 37 GeV

Δσ /σ

For one out of 6 W intervals: 30 < W < 45 GeV


eRHIC Detector HEsetup

σ(γ*p →γ p) [nb]

Lint = 530 pb-1

(2 weeks)

<W> = 37 GeV


Precision of DVCS unpolarized cross sections at eRHIC (2)

For one out of 6 W intervals (30 < W < 45 GeV)

  • eRHIC measurements of cross section will provide significant constraints

Precision of DVCS unpolarized cross sections at eRHIC (3) Detector

For one out of 6 Q2 intervals (8 < Q2 < 15 GeV2)

σ(γ*p →γ p) [nb]

<Q2> = 10.4 GeV2


  • EIC measurements of cross section will provide significant constraints

also significantly extend the range towards small W

Dependence on azimuthal angle Detectorφ for (DVCS+BH+INT)

Determination of smearing and acceptance as a function of φ

crucial for the Fourier analysis, asymmetry also for φ-integrated cross sections

RMS = 15º

HE setup

Nb of events [arb. units]



(φrec-φgen) [º]

An example: Lepton charge asymmetry precision at eRHIC

Lint = 530 pb-1 divided in half betweene+ande-

cross section in 6x6 bins of Q2 and W

model of DetectorBelitsky, Mueller, Kirchner(2002) forGPDs at small xB

parameters of sea-quark sector fixed using H1 DVCS data (PL B517 (2001))

except magnetic momentκsea(-3 < κsea< 2),whichenters Ji’s sum rule for Jq

BMK use ‘improved’ charge asymmetries CoAunpc(1) and CoAunps(1)

W= 75 GeV , -t = 0.1 GeV2

Q2 =4.5 GeV2 , -t = 0.1 GeV2

Q2 [GeV2]


Lepton charge asymmetry precision at eRHIC

κsea= 2

κsea= -3

κsea= -3

κsea= 2

  • measurements of asymmetries at EIC sensitive tool to validate models of GPDs

Detection of scattered fast protons (‘recoils’) Detector

  • Aim: clean subsample of exclusive events => control of effects of DD in main sample

Since scattering angles of fast protons are small they stay within the beampipe and follow trajectories determined by magnetic fileds of accelarator

Note different θrec scales for HE and LE setups



Nb of events [arb. units]







= Detector

A method for detection of recoil protons

Beam transport matrix

(or horizontally)

10 cm

at the detector

at the IP

Elements of TM depend on distance L from IP and on δ= (pr –pb)/pb

σx ≈ σy ≈ 30 μm


  • Distance from the nominal beam orbit > 12 σ beam envelope

  • High sensitivity to the angles at the IP

  • No strong dependence of TM elements on δ

Beams characteristics and transport Detector

Considered option: linac-ring for 10 GeV e + 250 GeV p

transport program written by Christoph Montag (CAD-BNL)

protons ε*= 9.5 nm β*x/y = 0.26 m σ0x/y=50 μmσ0θx/y= 191 μrad

electrons ε*= 2.5 nm β*x/y = 1 m σ0x/y=50 μmσ0θx/y= 50 μrad

12 σ beam envelope

RP 1 @ 23.3 m

RP 2 @ 57.4 m

Distance from beam orbit [m]


Transverse coordinates of recoil protons at positions of RP’s

L = 23.3 m

L = 57.4 m

yD [m]


yD [m]

in acceptance of RP

xD [m]

xD [m]

‘reasonable’ acceptance RP’s

|t| > 0.35 GeV2 for RP 1

|t| > 0.15 GeV2 for RP 2

Full acceptance including Roman Pots

RP 1 @ L = 23.3 m

RP 2 @ L = 57.4 m



(CD + RP)

Nb of events [arb. units]

-t [GeV2]

-t [GeV2]


average acceptance

for 0.05 < |t| < 1.0 GeV2

12% for RP 1

25% for RP 2

-t [GeV2]

-t [GeV2]

For RP 2 range of t with reasonable acceptance wider ,but …

θ RP’s*x ≈xD / Lxeff

θ*y ≈yD / Lyeff

Determination of recoil angles θand φat the IP

TM elements relevant for determination of θ*xandθ*y

Leff [m]

a11 or a33

pr [GeV]

pr [GeV]

  • Effect of transverse smearing of IP ( ≈ 70 μm) small at RP’s

because of small a11and a33

θ*and φ of recoil at IP

  • With RP1significantly higher sensitivity to angle at IP

because of larger Leff

Resolution for reconstructed recoil and tagging of exclusive events

Full simulation incl. smearing of CD and RP, size of IP and angular beam divergence

RP 2

RP 1

RP 1



21 μrad


No measurement ofpr

Nb of events [arb. units]

trrec ≈ - (pbeam·θrrec)2


124 μrad

(θrrec-θrgen) [rad]

(θrrec-θrgen) [rad]

(trrec – tgen) [GeV2]

RP 1




5.7 º

2.8 º

6.4 º

Nb of events [arb. units]

(φeγrec-φeγgen) [º]

(φrrec-φrgen) [º]

(φeγrec-φrrec) [º]

Conclusions for resolution and tagging recoil protons events

  • Detection of fast recoil protons possible at moderate |t| (above ≈ 0.3 GeV2)

  • Good precision of reconstructed angles at IP for recoils

  • Accuracy of t derived from recoil limited by beam angular divergence

and unmeasured recoil momentum

  • A possible method to tag exclusive process by correlation of azimuthal angles

  • Extension of |t| range (down to ≈ 0.12 GeV2) with detected recoil possible

but with poor precision of recoil angles

Exclusive production of mesons at eRHIC events

Results of previous simultations of ρ0 andJ/ψexclusive production at eRHIC

shown at ‘Current and Future Directions at RHIC’ - 2002

ρ0production at large Q2

Main ingredients of those simulations

Lint = 330 pb-1

e(10 GeV) + p(250 GeV)

Lint = 330 pb-1

Detector angular acceptance

between ZDR (± 1m) and

‘updated ZDR’ (± 3m)

Ranges of W and xbj for hard production similar as shown for DVCS

Nb of accepted events ≈ 650 000

Exclusive production of mesons at eRHIC (2) events


J/ψproduction at large Q2

Nb of accepted events ≈ 5200

Nb of accepted events ≈ 67 000

Tagging spectator protons from deteron beam events

Assumed settings of magnets for 250 GeV deuteron beam

in deuteron rest frame each component with Gaussian distribution σ = 35 MeV

spectator protons traced down to RP1 or RP2

Results below – for RP1


in acceptance of RP

in acceptance of RP

yD [m]

Nb of events

Nb of events

efficiency ≈ 0.96

yD [m]

xD [m]

xD [m]

  • Tagging ofproton spectators feasible, with high efficiency

Summary for DVCS at eRHIC events

  • Wide kinematical range, overlap with HERA and COMPASS

1.5 ·10-4 < xB < 0.2- sensitivity to quarks (mostly u+ubar) 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

  • Feasibility of using RP detectors at range of moderate to large t for

selection of exclusive events