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DVCS in an ep Collider

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4th EIC Workshop

Hampton University

19--23 May 2008

DVCS in an ep Collider

Charles Earl Hyde

Université Blaise Pascal

and

Old Dominion University

- 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 E00-110

[ H(e,e’)X - H(e,e’)Y ]: Missing Mass2

H(e,e’p

H(e,e’…

H(e,e’p) sample

H(e,e’p) simulation,

Normalized to data

<2% in estimate of

H(e,e)N…

below threshold MX2<(M+m)2

- Isolation of Re and Im parts of Twist-2 DVCS-BH interference.
- Kinematic weight of DVCS2 term is ≤ 1% in Im[BH*DVCS], 4.5% in Re.
- DVCS2 term in VGG ≈ 20.

Im[BH*DVCS]

BH2

Re[BH*DVCS] + |DVCS|2

- Variable energy Collider: Scaling with CM energy se = [(k+p)2]1/2
- Subtract BH2 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.
- Complete set of Proton and electron spin observables will separate all DVCS GPDs and bilinear DVCS terms.
- Test in HallA e07-007 expected 2010

- 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

k

Quasi-real photon tagging

Ultra-peripheral, tagging

« Central »

Forward “Hadrons”

Forward “Electrons”

- k<k’ for xB<k/P
- e<30 deg for Q2≤4 GeV2

- k<k’ for xB<k/P
- e<30˚ for Q2≤16 GeV2
- Push “Electron Endcap” to 45˚

- sM2 = 2kFM=2kC [E+P]C≈4kCPC
- kF = kC [E+P]C/M ≈ 4kCP.

- DVCS: Fixed Target
- 2 minimized for q’||q
- q’, q, p’ all co-linear at 2min.

- 2 minimized for q’||q
- Boost by P >>1 along (-)electron beam direction to collider frame.
- Non-parallel boost to q, q’, p’
- q2 < 0 = q’2 < p’2

- Very different rotations of q, q’, p’ into collider frame

- Non-parallel boost to q, q’, p’

- Boost =P/E from target rest-frame to Collider frame at same s=(k+P)2.
- (Electron in z direction)

- In rest frame at ∆2min, q’||q.
- q’z≈gq’Rest(cosqRest+)
- q’z>0 For >cos(Rest)
- Photon is boosted into “hadronic hemisphere”

Angle of Final Real Photon, Relative to Proton Axis

Central

Hadronic

Forward Hadronic

Forward Electron Side

Calorimeters in shadow of FF Quads

Central

Electron

Central

Hadronic

Forward Hadronic

Forward Electron

Calorimeters in shadow of Final Focus Quads

Central

Electron

- DVCS variables
- =(q-q’) = (P’-P)
- = Component of perp. to (P’+P)
- C = Component of perp. to P.

- xB=Q2/(2q•P)
- = (q+q’)2/[4(q+q’)•(P+P’)] xB / (2- xB)
- 2 = (2•P)/(2k•P) ≈ 2

- =(q-q’) = (P’-P)
- All variables are equivalent, to order 2/Q2
- . xB / (2- xB)
- C

- 2=[4M2+ C]/(1-2)(exact)
- For design study, assume C ≤ 1 GeV2
- tan(P’)] =[ |C | / P(1-2) ]
- Constraint of Final Focus Aperture is independent of Q2.

- Constraint [R/L] > [ |C | / P(1-2) ]
- 5mr limits |C | < 500 MeV/c at P=100 GeV/c
- 5mr limits |C | < 250 MeV/c at P=50 GeV/c
- Pion pfrom N final state p< 60 MeV/c ≈ [ 5 mr] [mP/(M+m)]

- 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 (≥10mr)
- Compact Calorimetry in front of Quadrupole “shadow” to catch the narrow range of xB≈2z for which final DVCS photon is occluded by Final Focus Quadrupoles

- 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)

- Resolve P(e,e’)P’ from P(e,e’)P’
- “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 GeV2
- Tag final proton P’ in lattice.

- Incident Beam Spread
- p||/p = 0.001
- p/p = [p*]1/2
- (k,P) = (70,0.7)•10-6m
- * =5mm (ELIC, maximum luminosity
- P=160MeV/c @ 100 GeV/c

- Scattered Electron
- k’/k’ = 1 mrad
- k’||/k’ = 1% 1%[1GeV/k’]1/2

- Internal pre- and post-bremsstrahlung
- Final Photon
- q’/q’ = 1 mrad
- q’/q’ = 1% 4%[1GeV/q’]1/2

- Final Proton (for Study)
- p/p = 200 m / 10 m = 20 rad
- p||/p = 200 m / 2m = 0.01%

- Q2=4 GeV2
- 2= 0.2
- P’ tagging required
- Exclusivity
- Resolution
- () ≈ 0.3GeV2 without tagging
- Transverse Imaging

(Turn off beam spread)

- Q2=8 GeV2
- 2= 0.05
- q’ ≈ 5 GeV

- P’ tagging required
- [Missing Mass]2 resolution terrible at high energy
- Resolution unchanged from 5 50
- Transverse Imaging

- 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.