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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
. un
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
. un
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
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