Hard exclusive processes at EIC

Andrzej SandaczSołtan Institute for Nuclear

Studies, Warsaw

Introduction

DVCS – from Central Detector only

Exclusive Meson production

DVCS – including fast ‘recoil’ proton

- experimental aspects -

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

The same final state in DVCS and Bethe-Heitler

interference I

( )DVCS*BH

*DVCSBH

2

DVCS

2

BH TTTTT +++Τ∝σ

up to twist-3 BMK (2002)

interference + structure of azimuthal distributions

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

P1 (Φ), P2 (Φ) BH propagators

harmonics with twist-2 DVCS amplitudes (related to GPDs) c0

DVCS, c1I, s1

I and c0I (the last one Q suppresed)

Towards extraction of full set of GPDs

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

measure e p → e p γ cross sections both for e+ and e-

for unpolarized, longitudinally and transversely polarized protons

σ+(φ) – σ -(φ) IΛ(φ) σ+(φ) + σ -(φ) – 2 σBH(φ) 2 σDVCS,Λ(φ)

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

1,Λ

Λ = {unp, LP, TnP, TsP}

from these determine all 4 DVCS amplitudes (including their phases) which depend on GPDs E

~,E,H

~,H

another 8 leading-twist harmonics cDVCS0,Λ and cI

0,Λ cross check

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

Aim for DVCS - go beyond measurements of unpolarized cross sections, access interference term and exploit azimuthal angle dependence

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)

φφσφσ sin]Im[),(),( 1 ⋅∝− HFededsr

φφφπφφσφφσ cos)sin(]Im[),(),( 12 SSS FFdd −⋅−∝+− EHφφφξ sin)cos(]

~~Im[ 12 SFF −⋅−+ EH

φφσφσ sin]~

Im[),(),( 1 ⋅∝− HFPdPdrs

F1 and F2 are Dirac and Pauli proton form factors

φφσφσ cos]Re[),(),( 1 ⋅∝− −+ HFeded

*

2

**

42)

~~(4 EEHHHH

Mtunp

DVCS −+∝σ

Unpolarized cross sections for DVCS

cross section σDVCS averaged over φ for unpolarised protons

H1 and ZEUS

DIS 2006

at small xB ( < 0.01) Hsea, Hg

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

Distributions of events within acceptance of Central Detector

log10(xBj)

HE setup

LE setup

log10(xBj) Q2 [GeV2]

Q2 [GeV2]

W [GeV]

W [GeV]

Nu

mb

er o

f ev

ent

[arb

itra

ry u

nit

s]

DVCSBH

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

good coverage for 3 < W < 90 GeV and 1.5 · 10-4 < xBj < 0.2

Precision of DVCS unpolarized cross sections at eRHIC (1)

Lint = 530 pb-1

Assume 2 weeks for each setup

σ(ep→epγ) = 292 pb

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

Q2 [GeV2]

eRHIC HE setup

<W> = 37 GeV

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

eRHIC LE setup

Q2 > 1 GeV2

10 < W < 95 GeV

0.05 < |t| < 1.0 GeV2

Q2 > 1 GeV2

0.05 < |t| < 1.0 GeV2

2.5 < W < 28 GeV

σ(ep→epγ) = 173 pb

Lint = 530 pb-1 Lint = 180 pb-1

Δσ

/σ

Reconstructed: ≈ 133 000 events ≈ 28 000 events

Precision of DVCS unpolarized cross sections at eRHIC (2)

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]

Precision of DVCS unpolarized cross sections at eRHIC (3)

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

An example: Lepton charge asymmetry precision at eRHIC

φσσφσσφσσππ

π

π

πdddAC ∫∫∫ −+−+

−

−+ +−−−=2

0

2/3

2/

2/

2/

)(/})()({

Lint = 530 pb-1 divided in half between e+ and e-

cross section in 6x6 bins of Q2 and W

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

Determination of smearing and acceptance as a function of φcrucial for the Fourier analysis, asymmetry also for φ-integrated cross sections

Nb

of

even

ts [

arb

. un

its]

(φrec-φgen) [º] φgen[º]A

ccep

tan

ce

HE setup

RMS = 15º

Lepton charge asymmetry precision at eRHIC

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

s(1)

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

Detection of scattered fast protons (‘recoils’) 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 beam pipe and follow trajectories determined by magnetic fileds of accelarator

Note different θrec scales for HE and LE setups

θr [rad]

pr [GeV]

θr [rad]

pr [GeV]

HE

HE

LE

LE

Nb

of

even

ts [

arb

. un

its]

A method for detection of recoil protons

(or horizontally)

=yD

D

xD

D

y

x

Θ

Θ

*0

*0

y

x

y

x

Θ

Θ

4443

33

2221

11

00

00

00

00

aa

La

aa

La

yeff

xeff

Beam transport matrix

at the detector at the IP

10 cm

σx ≈ σy ≈ 30 μm

Elements of TM depend on distance L

from IP and on δ = (pr –pb)/pb

Requirements

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

protons ε* = 9.5 nm β*x/y = 0.26 m σ0x/y = 50 μm σ0

θx/y = 191 μrad

Considered option: linac-ring for 10 GeV e + 250 GeV ptransport program written by Christoph Montag (CAD-BNL)

electrons ε* = 2.5 nm β*x/y = 1 m σ0x/y = 50 μm σ0

θx/y = 50 μrad

12 σ beam envelope

Dis

tan

ce f

rom

bea

m o

rbit

[m

]

L [m]

RP 1 @ 23.3 m RP 2 @ 57.4 m

Transverse coordinates of recoil protons at positions of RP’sL = 23.3 m L = 57.4 m

xD [m]xD [m]

y D [

m]

y D [

m]

all

in acceptance of RP

Full acceptance including Roman Pots

RP 1 @ L = 23.3 m RP 2 @ L = 57.4 m

Nb

of

even

ts [

arb

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its]

Acc

epta

nce

generated

accepted (CD + RP)

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

-t [GeV2] -t [GeV2]

-t [GeV2] -t [GeV2] ‘reasonable’ acceptance

|t| > 0.35 GeV2 for RP 1 |t| > 0.15 GeV2 for RP 2

average acceptancefor 0.05 < |t| < 1.0 GeV2

12% for RP 125% for RP 2

Determination of recoil angles θ and φ at the IP

pr [GeV] pr [GeV]

a 11 o

r a 33

Lef

f [m

]

TM elements relevant for determination of θ*x and θ*

y

Effect of transverse smearing of IP ( ≈ 70 μm) small at RP’s because of small a11 and a33

θ*x ≈ xD / Lx

eff

θ*y ≈ yD / Ly

effθ* and φ of recoil at IP

With RP1 significantly higher sensitivity to angle at IP

because of larger Leff

Resolution for reconstructed recoil and tagging of exclusive events

Nb

of

even

ts [

arb

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its]

(θrrec-θr

gen) [rad] (θrrec-θr

gen) [rad] (trrec – tgen) [GeV2]

21 μradRMS

124 μrad

0.046

RMS

RMSRP 2RP 1 RP 1

trrec ≈ - (pbeam· θr

rec) 2

No measurement of pr

Nb

of

even

ts [

arb

. un

its]

RP 1RMS RMS RMS5.7 º 2.8 º 6.4 º

(φeγrec-φeγ

gen) [º] (φrrec-φr

gen) [º] (φeγrec-φr

rec) [º]

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

Conclusions for resolution and tagging recoil protons

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 eRHICResults of previous simultations of ρ0 and J/ψ exclusive production at eRHIC

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

Main ingredients of those simulations

e (10 GeV) + p (250 GeV)

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

ρ0 production at large Q2

Lint = 330 pb-1

Lint = 330 pb-1

Exclusive production of mesons at eRHIC (2)

J/ψ production at large Q2 J/ψ photo-production

Nb of accepted events ≈ 5200 Nb of accepted events ≈ 67 000

Tagging spectator protons from deteron beam

spectator protons traced down to RP1 or RP2

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

Assumed settings of magnets for 250 GeV deuteron beam

Nb

of

even

ts

Results below – for RP1

xD [m]xD [m]

y D [

m]

yD [m]

allin acceptance of RP

in acceptance of RP

efficiency ≈ 0.96Nb

of

even

ts

Tagging of proton spectators feasible, with high efficiency

Summary for DVCS at eRHIC

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