26 June 2009 Recoil Tagging in Deeply Virtual

26 June 2009 Recoil Tagging in Deeply Virtual Exclusive Reactions on Nuclei Charles Hyde

Conclusions • For Nuclei ≥ 4 He, the recoil nucleus is § INSIDE the transverse admittance of the FF Quads § OUTSIDE the longitudinal admittance of the ring lattice § The Nuclei are detectable at high resolution with far forward tracking in the lattice.

Deep Virtual Exclusive Scattering k' k • • e+ e+ + e + AZ + ( AZ + J/ Hard scale, Q 2 or MJ/ AZ q' q AZ P § Perturbative coupling to quarks and gluons • Soft Recoil § Q P'

ep DVES Collider Kinematics • s=(k+P)2 = 2 k(E+P) • Q 2 = 2 kk’(1 -cos e) § x. B = Q 2/(2 q·P) § 0≤ x. B ≤ 1 • • • P = [P+, 0 T, P ]= [(E+P)/21/2, 0 T, M 2/(2 P+)] P’ = [(1 -2 )P+, T, M 2/(2 P+(1 -2 ))] = P’-P = [ -2 P+, T, 2 M 2/(2 P+(1 -2 ))] = 4 M 2/(1 -2 ) T 2 As Q 2 ∞ and /Q 2 0 § 2 2 x. B/(2 -x. B) = Q 2/(2 q·P) • The beam proton loses longitudinal momentum fraction 2 while receiving a transverse kick T.

e. A DVES Collider Kinematics • PA = ZP § P is defined by ring, P ≤ 60 Ge. V/c § PN=PA/A = P(Z/A). § s. A=(k+PA)2 ≈Zs • x. B = Q 2/(2 q·PN) § 0< x. B <A • PA’ = [(1 -2 )PA+, T, MA 2/(2 PA+(1 -2 ))] § Kinematically, 2 is bounded by • 0<2 < A § Realistically, 2 z is bounded by • 0<2 <1 • = 4 M 2/(1 -2 ) T 2 • The beam ion loses momentum fraction 2 /A

Nuclear Sizes • Nuclear rms radius § RA ≈ (1 fm) A 1/3. • Coherent Cross sections § Exp(2 RA 2 § Cross section drops rapidly for RA 2 =(200 Me. V/c)2 / A 2/3. • This puts a practical upper bound on the acceptance needed in T

Interaction Point Optics • Ultra-High Luminosity Tune § Ion Beam rms angular spread ≈ 1 mr § Transverse momentum spread • Z P (1 mr) ≈ (60 Me. V/c) Z § Transverse admittance ≤ 10 rms. • Admittance ≤ (600 Me. V/c) Z • Coherent cross sections for § PT < (200 Me. V/c) / A 1/3. • For ≥ 4 He, coherent recoil nuclei are within (few x) rms angular spread of ion beam § Detect downstream of FF Quads within FF acceptance

Longitudinal Admittance of Ring • CEBAF long rms spread is 0. 0001 § Admittance ≈ 0. 001 • DVES recoil ions, momentum loss fraction § 2 /A § Typical ELIC physics/detector (e, e’) kinematics • 0. 02 < 1 • Assume ions are detectable somewhere in lattice if 2 /A > 0. 001 § 2 for 20 Ne § 2 for 4 He • Largest (realistic) value is 2 ≈1. § What happens to an ion with momentum loss fraction 2 /A as large as 0. 25?

Ring Lattice • What is longitudinal admittance of FF, Ring ? § High dispersion Ring Lattice, Yuhong Zhang • 1. 3 m at center of supercell = 1. 3 cm per % § Low Dispersion Alex Bogazc. • Need a high dispersion (D/ >1) section § Separate recoil nuclei from beam by ≥ 5 mm • Tagging ions with 2 /A≥ 0. 001 requires (0. 001 D) > (10 x) = 10[ x x]1/2. e. g. D=5 m, x. N=1µm, x. G=33 nm x=6 m Ø 0. 001 D=1 cm > 5 mm ≈ (10 x) § Measure angles to 1 mr to measure momentum to 10 -3. • Need Drift space ≈ 1 m • 10 -4 longitudinal momentum resolution achievable with 100 micron resolution if Dispersion ≥ 1 m § This resolution has large impact on exclusive physics program

Ion Ring – large disp. lattice (100 Ge. V) phase adv. /cell ( x= 600, y=600) Arc dipoles $Lb=200 cm 6 cells superperiod achromat large dispersion ( ~ doubled) $B=81. 6 k. G Arc quadrupoles $Lb=40 cm $G= 14 k. G/cm MEIC Meeting, Alex Bogacz Figure-8 Ion Ring Minimum Dispersion Lattice JLAB-TN-06 -052 Abstract PDF Alex Bogacz March 13, 2009

Minimum disp. Ion Ring – lattice (100 Ge. V) phase adv. /cell ( x= 600, y=600) 3 transition cells with shorter (2/3) dipoles periodic (minimum) dispersion in the arc Arc dipoles $Lb=200 cm $B=81. 6 k. G Arc quadrupoles $Lb=40 cm $G= 14 k. G/cm MEIC Meeting, Alex Bogacz Figure-8 Ion Ring Minimum Dispersion Lattice JLAB-TN-06 -052 Abstract PDF Alex Bogacz March 13, 2009

Discrete ambiguity • More than one tracker for different momentum loss regimes § 0. 01 -- 0. 1 § >0. 1 • Even with multiple IP, it is sufficient to have one set of tracking stations. § Overcompleteness of event will allow experiment to decide if tagged ion came from IP 1 or IP 2, etc.