4 th EIC Workshop Hampton University 19 23

4 th EIC Workshop Hampton University 19 --23 May 2008 DVCS in an ep Collider Charles Earl Hyde Université Blaise Pascal and Old Dominion University

DVCS • High CM energy less important than high Luminosity. § Factor of two range in CM energy can resolve BH • DVCS from |DVCS|2 without positron beams. • Precision Cross sections (1% from each independent contribution, 4% total) § Spin Observables for H, E, … separations § Cannot test factorization (only test models) with relative asymmetries. • High Resolution • Forward proton tagging essential § § Exclusivity; Transverse imaging ( resolution). Spectator nucleons in D N final state at threshold ==> Soft Pion Theorems

H(e, e’ ) Exclusivity Jlab Hall A E 00 -110 [ H(e, e’ )X - H(e, e’ ) Y ]: Missing Mass 2 H(e, e’ p H(e, e’ … H(e, e’ p) sample <2% in estimate of H(e, e )N … below threshold MX 2<(M+m)2 H(e, e’ p) simulation, Normalized to data

JLab Hall A Cross Sections C. Munoz Camacho et al PRL 97 (2006) Im[BH*DVCS] BH 2 Re[BH*DVCS] + |DVCS|2 • • Isolation of Re and Im parts of Twist-2 DVCS-BH interference. Kinematic weight of DVCS 2 term is ≤ 1% in Im[BH*DVCS], 4. 5% in Re. § DVCS 2 term in VGG ≈ 20.

BH-DVCS & Bilinear DVCS terms 2. Variable energy Collider: Scaling with CM energy se = [(k+p)2]1/2 3. Subtract BH 2 term by direct calculation. Isolate BH-DVCS from bilinear DVCS terms I with two or more collider CM energies, with variation in se of at least a factor of 2. 4. Complete set of Proton and electron spin observables will separate all DVCS GPDs and bilinear DVCS terms. 5. Test in Hall. A e 07 -007 expected 2010

Detector notions / Design Questions • Five Detector Segments § § § • Ultraforward hadron projectile tagging in beam lattice Forward “hadrons” Central Detector (least important? ? ) Forward “electrons” ≈0˚ tagging of quasi-real photons in electron beam lattice. Where are the angular boundaries between elements? § Central Forward (Electrons, Hadrons) § Mininum Forward and Maximum ultra-forward angles • (maximum angle obstructed by final focus lattice elements) • Maximum Ultra-forward angle acceptance of final focus elements. P Quasi-real photon tagging k Forward “Electrons” « Central » Forward “Hadrons” Ultraperipheral, tagging

(e, e’) Kinematics 5 Ge. V electrons 50 Ge. V/c Protons • k<k’ for x. B<k/P • e<30 deg for Q 2≤ 4 Ge. V 2

(e, e’) Kinematics 10 Ge. V electrons 100 Ge. V/c Protons • k<k’ for x. B<k/P • e<30˚ for Q 2≤ 16 Ge. V 2 • Push “Electron Endcap” to 45˚

Collider vs. Fixed Target Kinematics at equal s • s M 2 = 2 k. FM=2 k. C [E+P]C≈4 k. CPC § k. F = k. C [E+P]C/M ≈ 4 k. C P. • DVCS: Fixed Target § 2 minimized for q’||q • q’, q, p’ all co-linear at 2 min. • Boost by P >>1 along (-)electron beam direction to collider frame. § Non-parallel boost to q, q’, p’ • q 2 < 0 = q’ 2 < p’ 2 § Very different rotations of q, q’, p’ into collider frame

DVCS Kinematics Where are the Photons? • Boost =P/E from target rest-frame to Collider frame at same s=(k+P)2. § (Electron in z direction) • In rest frame at ∆2 min, q’||q. • q’z ≈ q’Rest( cos q. Rest+ ) § q’z>0 For >cos( Rest) § Photon is boosted into “hadronic hemisphere”

5 x 50 Ge. V 2 Collider, Q 2=5 Ge. V 2 Angle of Final Real Photon, Relative to Proton Axis Forward Hadronic Forward Electron Side Central Electron Central Hadronic Calorimeters in shadow of FF Quads

10 x 100 Ge. V 2 Collider, Forward Hadronic Forward Electron Central Hadronic Calorimeters in shadow of Final Focus Quads

Where does the DVCS Proton Go? • DVCS variables § =(q-q’) = (P’-P) • = Component of perp. to (P’+P) • C = Component of perp. to P. § x. B=Q 2/(2 q • P) § = (q+q’)2/[4(q+q’) • (P+P’)] x. B / (2 - x. B) § 2 = (2 • P)/(2 k • P) ≈ 2 • All variables are equivalent, to order 2/Q 2 §. x. B / (2 - x. B) § C • 2= [4 M 2+ C]/(1 -2 ) (exact) • For design study, assume C ≤ 1 Ge. V 2 § tan (P’)] =[ | C | / P(1 -2 ) ] § Constraint of Final Focus Aperture is independent of Q 2.

Final Focus Aperture R at Distance L & DVCS “Recoil” Protons • Constraint [R/L] > [ | C | / P(1 -2 ) ] § 5 mr limits | C | < 500 Me. V/c at P=100 Ge. V/c § 5 mr limits | C | < 250 Me. V/c at P=50 Ge. V/c § Pion p from N final state p < 60 Me. V/c ≈ [ 5 mr] [m P/(M+m )]

DVCS Recoil Proton Tagging • Large aperture Lattice for tagging P’ is more important to DVCS than small angle detection in the forward hadron side (final photon). • Large Aperture Final Focus Quadrupoles (≥ 10 mr) § Compact Calorimetry in front of Quadrupole “shadow” to catch the narrow range of x. B≈2 z for which final DVCS photon is occluded by Final Focus Quadrupoles

Exclusivity, for $1 B, we better deliver • Exclusivity means different things to different people. • “Photon Exclusivity” § Resolve P(e, e’ )P’ from P(e, e’ )P’ • Distance to calorimeter and granularity is sufficient to separate opening angle of m /E ≈ m /q’ • Detector is sufficiently hermetic to detect decays with good efficiency (including asymmetric decays over ≈ 50% of CM) • “Baryon Exclusivity” § Resolve P(e, e’ )P’ from P(e, e’ )N etc. § Missing Mass Squared (k+P-k’-q’)2 < (M+ m )2=1. 15 Ge. V 2 § Tag final proton P’ in lattice.

Exclusivity Resolution Study • Incident Beam Spread § p||/p = 0. 001 § p /p = [ p *]1/2 • (k, P) = (70, 0. 7) • 10 -6 m • * =5 mm (ELIC, maximum luminosity Ø P =160 Me. V/c @ 100 Ge. V/c • Scattered Electron § k’ /k’ = 1 mrad § k’||/k’ = 1% 1%[1 Ge. V/k’]1/2 • Internal pre- and post-bremsstrahlung • Final Photon § q’ /q’ = 1 mrad § q’/q’ = 1% 4%[1 Ge. V/q’]1/2 • Final Proton (for Study) § p /p = 200 m / 10 m = 20 rad § p||/p = 200 m / 2 m = 0. 01%

5 Ge. V 50 Ge. V/c (e P) • Q 2=4 Ge. V 2 • 2 = 0. 2 • P’ tagging required § Exclusivity § Resolution • ( ) ≈ 0. 3 Ge. V 2 without tagging • Transverse Imaging

10 Ge. V 100 Ge. V/c (e P) (Turn off beam spread) • Q 2=8 Ge. V 2 • 2 = 0. 05 § q’ ≈ 5 Ge. V • P’ tagging required • [Missing Mass]2 resolution terrible at high energy • Resolution unchanged from 5 50 § Transverse Imaging

Conclusions: EIC-DVCS • Forward (|q|<45˚) region more important than central § High energy final photon in “forward hadron” side of detector • Full Ultra-forward tagging of final proton essential: § Exclusivity § Transverse Imaging • Transverse emittance of beams cannot be neglected at ultimate luminosity § Tagged proton and neutron DVCS in Deuteron • e+d --> e’+ +NDVCS+Nspectator § Large aperture Final Focus Quads required.