1. 1 Nuclear Transparency in Exclusive r 0 Production at HERMES Introduction Diffractive r 0 production Nuclear Effects b N (Q 2 ) variation ( g shrinkage) coherent/incoherent cross section ratios l c -dependence Q 2 -dependence (Color Transparency) Summary W. Lorenzon (Michigan) Collaboration

2. 2 HERMES Experiment at HERA (2003) Canada Germany Italy 29 Institutions Russia United Kingdom USA Armenia Belgium Japan Netherlands Poland China

3. 3 The HERMES Detector Forward Spectrometer: 40    220 mrad,  P/P (0.7-1.3)%,   0.6 mrad Electron Identification: efficiency  98% with hardon contamination  1% Calorimeter:  E/E = 5%/ RICH (1998):  +-, K +-, p separation overfull kinematic range

4. 4 Exclusive Diffractive r 0 Electroproduction  0,  ± have I(J PC ) = 1(1 -- ) [ N.B.:  has 0,1(1 -- )] M  = 770 MeV, G  =150 MeV (c  =1.3 fm)  0 content is Dominant time-ordered diagram (lab frame): Exclusive: M T = M T Diffractive: d s /dt ~ e bt (note t  0) – Incoherent:  * N   0 N, b N  7 GeV -2 (for A > 1, this is nuclear inelastic) – For A > 1, coherent:  * A   0 A, b 14 N  57 GeV -2

5. 5 Evolution of Virtual Quantum States Virtual state such as  *  in  * -induced reaction transverse size of wave packet: coherence length l c : finite propagation distance (lifetime) for – measure interactions with perturbing medium at different l c – study space-time evolution of VQS – for exclusive  0 production: M  domiates and l c  can measure explicit l c -dependence formation length l f : distance needed to evolve to normal-size  0 – governing scale for Color Transparency

6. 6 Color Transparency Vanishing of h – N interaction cross section for h produced in high Q 2 exclusive process Requirements: Quantum Mechanics, Relativity, Nature of Strong Interaction QED analogy in e + e - ( Chudakov-Perkins effect ) unique to QCD ! No unambiguous signature found for the onset of CT yet ! – A(p,2p) Oscillation in Transparency data Leksanov et al. PRL 87, 212301 (2001) – A(e,e’p) Consistent with conventional nuclear physics Garrow et al. PR C66, 044613 (2002) – A(l,l’  0 ) Coherence/Formation length Issues E665, Adams et al. PRL 74, 1525 (1995) – A( ,di-jet) claims full CT at Q 2  10 GeV 2, but only A-dependence E791, Aitala et al. PRL 86, 4773 (2001) There is more at stake: – CT required for strict validity of factorization in deep exclusive processes  essential for access to General Parton Distributions

7. 7 “Charge Screening” Perkins (1955) [  0  e + e -  ] e + e - pairs (~ 200 GeV) make tracks in photographic emulsions Measure ionization density vs. distance from production distance ( m m) Ionization

8. 8 Color Transparency in A(p,2p) – BNL Results E-0850, Leksanov et al. PRL 87, 212301 (2001) Shaded are is Glauber calculation solid line is 1/oscillation in p-p scattering A(p,2p) may remove long-distance component in p-p scattering (Nuclear Filtering)

9. 9 Color Transparency in A(e,e’p) – SLAC/JLab Results E94-139, Garrow et al. PR C66, 044613 (2002) Constant Value fits for Q 2 > 2 GeV 2   2 /df  1 Dashed line is correlated Glauber calculation (Panharipande at al) Q 2 dependence consistent with standard Glauber

10. 10 Color Transparency in A(  ’  0 ) – FNAL Results E665, Adams et al. PRL 74, 1525 (1995) E665 fit: Fit to  A (Q 2 )=  N (Q 2 ) A   “The probability of  being independent of Q 2 is 2.7%.” Skeptical fit: assumes   f(Q 2 ),  2 /df = 10.0/11=0.91, with  =0.69

11. 11 Color Transparency in A( ,di-jet) – FNAL Results E791, Aitala et al. PRL 86, 4773 (2001) Coherent   diffractive dissociation At T  =500 GeV/c Parameterized as  (A)=  0 A , using 12 C and 195 Pt nuclei, with Q 2  4k T 2  from pion-nuleus total cross sections

12. 12 Color Transparency Vanishing of h – N interaction cross section for h produced in high Q 2 exclusive process Requirements: Quantum Mechanics, Relativity, Nature of Strong Interaction QED analogy in e + e - ( Chudakov-Perkins effect ) unique to QCD ! No unambiguous signature found for the onset of CT yet ! – A(p,2p) Oscillation in Transparency data Leksanov et al. PRL 87, 212301 (2001) – A(e,e’p) Consistent with conventional nuclear physics Garrow et al. PR C66, 044613 (2002) – A(l,l’  0 ) Coherence/Formation length Issues E665, Adams et al. PRL 74, 1525 (1995) – A( ,di-jet) claims full CT at Q 2  10 GeV 2, but only A-dependence E791, Aitala et al. PRL 86, 4773 (2001) There is more at stake: – CT required for strict validity of factorization in deep exclusive processes  essential for access to General Parton Distributions

13. 13 Color Transparency and r 0 Leptoproduction Prediction that in exclusive reactions, ISI and FSI vanish at high Q 2, : (p,2p)(e,e’p) (l,l’  0 ) Small size Config. (high Q 2 ) Color Screening t exp =  exp (high n) ? Yes small ? Yes small Yes Large (E m,p m ) sensitivity  (n,Q 2 ) smooth Good QED or QCD model l c ambiguity Yes No Yes No Yes

14. 14 Exclusive Diffractive r 0 Main cuts: exclusive: -0.4 GeV  D E  0.6 GeV diffractive: -t’  0.4 GeV 2 select mass: 0.6 GeV  M pp  1 GeV eliminate background: 1.04 GeV  M KK Kinematics: Q 2 = 0.6 ÷ 6 GeV 2, = 1.7 GeV 2 W = 3.0 ÷ 6.5 GeV, = 4.9 GeV x bj = 0.01 ÷ 0.35, = 0.07 n = 5 ÷ 24 GeV, = 13.3 GeV

15. 15 t’ Distributions For 14 N: – for –t’  0.045 GeV 2 coherent  0 dominates – for –t’  0.09 GeV 2 incoherent  0 dominates incoherent: b N  7 GeV -2 ( e bt represents elastic F.F., squared) b N of various nuclei consistent with hydrogen value Approx. b A r A (GeV) -2 (fm) 57 2.5 30 1.9 29 2.1 7 0.8

16. 16 Size of Nuclei in agreement with world data of nuclear size measurements, H. Alvensleben at al., PRL 24, 786 (1970) r A dominates

17. 17 b N (Q 2 ) – “Photon Shrinkage” d s /dt ~ e -bt size of virtual photon controlled via Q 2 prerequisite for CT

18. 18 Q2 dependence of s coh / s incoh Very strong Q 2 -dependence of ratio  have to study coherence length effects r He =1.9 fm r N =2.5 fm r Ne =2.7 fm r Kr =5.5 fm

19. 19 Coherence Length Dependence of ISI Initial State Interactions (ISI) of photon’s hadronic components Strength of the ISI depend on l c [ K. Gottfried and D.r. Yennie, PR 182, 1595 (1969) ] l c  r A  weak electromagnetic ISI (naïve expectation): l c  r A  hadronic ISI:

20. 20 Incoherent Nuclear Transparency T A Nuclear transparency T  search for Color Transparency Without ISI and FSI, incoherent s A =A s N Incoherent nuclear transparency: T A  s A /A s N – effect of ISI of  *, and FSI of  0 – if ISI and FSI factorize  T A = probability of transmitting  * and  0 unscathed ISI increase with lifetime l c of fluctuation  T A should decrease with onset of hadronic ISI at l c  1 fm (note: s rN  constant for n > 1 GeV expect s n  s H  use s N = s H ) – L A,H from inclusive DIS e events, corrected for h + h - efficiency – N A,H = # of incoherent events CT signature is rise in T A with Q 2 – l c effect can mimic Q 2 -dependence of T A predicted by CT for l c  r A

21. 21 Coherence Length Effects coherent nuclear transparency: T c  s A /A s N – opposite l c dependence  cannot mimic Color Transparency – T c can no longer be associated directly with probability of escape from nucleus  T c is ratio of  A /  N : can exceed unity ! incoherent nuclear transparency: T inc  s A /A s N – ISI increase with l c for l c  r A  can mimic Q 2 -dependence of T inc predicted by Color Transparency study T=T(Q 2 ) while keeping l c fixed  disentangle CL from CT effects

22. 22 HERMES acceptance in Q 2 vs l c allows 2-dim analysis = 1.7 GeV 2 ; = 2.7 fm same kinematics for coherent and incoherent  0, except: – coherent: |t’|  0.045 GeV 2 – incoherent: 0.09  |t’|  0.4 GeV 2 limited region used: – lower l c  acceptance corrections get large – higher l c  Q 2 range gets too small

23. 23 Color Transparency Common fit at fixed l c yields positive slope of Q 2 -dependence of nuclear transparency in nitrogen HERMES collab., PRL 90, 052501 (Feb 2003)  signature of Color Transparency B.Z. Kopeliovich et al., PR C65, 035201 (2002) Data sampleMeasured Q 2 slopePrediction coherent incoherent 0.070 ± 0.021 ± 0.012 0.089 ± 0.046 ± 0.008 0.060 0.048

24. 24 Summary Exclusive  0 production: virtual  *  – lifetime given by Heisenberg assuming – interacts like a  0 t’ slope parameter b agrees with r A 2 ~ A 2/3 size of virtual  * controlled via Q 2 (photon shrinkage) strong coherence length effects in s A coh / s A incoh intricate mixture of coherence and formation length effects – different appearance for coherent and incoherent  0 production – can mimic CT effects (incoherent) – can obscure clean observation of CT effect (coherent) for clean observation of CT: study variation of T with Q 2 for fixed l c new evidence (3.4  ) of CT in exclusive  0 production

25. 25 A and Q2 dependence of s coh / s incoh Plateau for heavy targets as = 2.7 fm  r A r He =1.9 fm; r N =2.5 fm; r Ne =2.7 fm; r Kr =5.5 fm Very strong Q 2 -dependence of ratio  have to study coherence length effects