A zz in Quasielastic and Deep Inelastic Scattering at x>1

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1 A zz in Quasielastic and Deep Inelastic Scattering at x>

2 Fantasia on a theme of tensor polarizations Main Motivation: To use Tensor Polarizations to study short range distances in the deuteron & large final state interaction effects - Relativistic Description of the Deuteron: (a) exclusive reactions (b) exclusive reaction - Color Transparency

3 ~s d(k,k )= X hk,s p,s n d, ~sihd, ~s k,s p,s ni s p,s p,s n,s n apple ~a d(k,k )=u(k )u(k ) k a k (k a)(k a) (k k ) k k apple u(k )w(k ) p + 3 k a k 3 3 k a u(k )w(k ) k p k a + w(k )w(k ), k where the components of ~a are defined through the deuteron spin wave function as: = i a z, i = p (a x + ia y ), = p i (a x ia y ), () where µ is the projection of the deuteron s spin on the the µ direction.

4 ~s d(k,k )= X s p,s p,s n,s n hk,s p,s n d, ~sihd, ~s k,s p,s ni Paris Deuterum wave function fm 3/ - - U(p) W(p) Unpolarized p, GeV/c

5 Deuterum wave function fm 3/ - - Different Potentials p, GeV/c

6 ~s d(k,k )= X hk,s p,s n d, ~sihd, ~s k,s p,s ni s p,s p,s n,s n apple ~a d(k,k )=u(k )u(k ) k a k (k a)(k a) (k k ) k k apple u(k )w(k ) p + 3 k a k 3 3 k a u(k )w(k ) k p k a + w(k )w(k ), k where the components of ~a are defined through the deuteron spin wave function as: = i a z, i = p (a x + ia y ), = p i (a x ia y ), () where µ is the projection of the deuteron s spin on the the µ direction.

7 d (k,k ) d 3 apple = 3 k z + k 3 p i (a x+ia y) p i (a x ia y) (k,k )+ d (k,k ) i az u(k apple )w(k ) p + 3 k z k apple (k k ) ((k k ) 3k z k z ) k k u(k )w(k ) p + k z k + k z k d (k,k ) w(k )w(k ). () GeV -3 unp = ( )/3 ( )/3 - Compressing the deuteron p, GeV/c

8 Exclusive disintegration of the deuteron d(e,e N)N (I) Theory of high energy semi- inclusive electro- nuclear processes: Exclusiveness of the reaction as an advancement in probing smaller distances in nuclei: not entirely true: final state hadronic interactions are never dynamically small Experience from low to medium energy exclusive experiments at Q << GeV was that It is impossible to probe nuclear internal momenta above 3 MeV: (large final state interaction(fsi),intermediate Delta s and Meson Exchange Currents (MEC) In High Energy and Momentum Transfer limit: Q > GeV : MEC is dynamically suppressed, Delta is possible to suppress both kinematically and dynamically For FSI eikonal regime is established: allowed to develop self-consistent theoretical framework that allows to account for the short distance nuclear dynamics

9 Impossibility to Probe Deuteron at Small Distances at low Q 4 5 6! red (GeV -3 ) 3 d 5 /d d e d p [fm /MeV sr ] p m [MeV/c] p, (GeV/c) Mainz, Q =.33 GeV JLab, Q =.66 GeV

10 Generalized Eikonal Approximation (GEA) The theory is formulated in the form of the effective Feynman diagram rules with effective vertices that can be parameterized based on NN elastic scattering amplitudes. q P A p p +q p F... F F F p p k p n+ p n+ A k+ n p n+ p f P A Frankfurt, Sargsian, Strikman PRC 997 Sargsian (review) IJMP For the case of e+ A à e + p f + X Small Parameter: E p z E + p z P D q DNN N Pf Ps q N P f DNN P s Ps P D M. Sargsian PRC For the case of e+ d à e + p f + p s (a) (b)

11 p(p ) i q p(p ) f p(p ) i p(p ) f p(p ) f (a) n(p ) r n(p ) (b) r n(p ) r n n p N R N (c) s f, s r A µ s d = p n N N (d) ū(p r, s r ) µ p /p i +m p i m ū(p f, s f ) DNN s d s f, s r A µ s d = d 4 p r ū(p f, s f )ū(p r, s r )F NN [/p r + m][/p d /p r + /q + m i( ) 4 (p d p r + q) m + i N[/p d /p r + m] DNN s d ((p d p r ) m + i )(pr m + i ), (

12 s f, s r A µ s d = ( ) 3 E r s i J µ N (s f, p f ; s i, p i ) s d d (s i, p i, s r, p r ) s f, s r A µ s d = i ( ) 3 4 s f,s r,s i d p r ( ) Ẽr s(s 4m ) Ẽr q p f, s f ; p r, s r f NN,on (t, s) p r, s r ; p f, s f J µ N (s f, p f ; s i, p i ) ( ) 3 dpr,z d p r Er s(s 4m ) ( ) E r q s f,s r,s i P p f, s f ; p r, s r f NN,off (t, s) p r, s r ; p f, s f p r,z p r,z J µ N (s f, p f ; s i, p i ) s d d (s i, p i, s r, p r ) s d d (s i, p i, s r, p( r ) p r,z = p r,z = q q (E r E r ) + M d q (E r E r )

13 Generalized Eikonal Approximation (GEA) e + d à e + p + n reactions: M. S PRC W. Ford, J.W. Van Orden S. Jeschonnek PRC 3 Some intereswng features of GEA: (i) differs from convenwonal Glauber theory for the case of large internal momenta being probed in the nucleus, (ii) demonstrated the existence of the window in probing the internal nuclear momenta beyond 3 MeV/c " PWIA+FSI /" PWIA " PWIA+FSI /" PWIA ! r, Deg Q = GeV GA Q = 6 GeV ! r, Deg. d"/dq dp n d# n (pb/gev 3, Sr ) K. Egiyan et al PRL 8 d"/dq dp n d# n (pb/gev 3,Sr ) x.5 - x ! r, (Deg.)! r, (Deg.) 3 4 5

14 Probing Deuteron at Small Distances at large Q W. Boeglin et al PRL (a) (a) (b) (c) R = exp/ pwia (b) (c) (fm 3 ) red = exp k cc (iii) (ii) (i) nq = 35 nq = 45 nq = 75 nq(deg) JLab, Q = 3.5 GeV p m (GeV/c)

15 Extension of GEA for Inelastic and Deep-Inelastic Processes W.Cosyn & M.S, PRC For the DIS processes of e+ d à e + X + p s For quasielaswc of e+ d à e + p f + p s (a) R = exp/ pwia (b) (c) (iii) (ii) (i) nq(deg)

16 Extension of GEA for Inelastic and Deep-Inelastic Processes W.Cosyn & M.S., PRC For the DIS processes of e+ d à e + X + p s For quasielaswc of e+ d à e + p f + p s

17 GEA for Vector Meson Electroproduction from Deuteron A.Freese & M.S. PRC 3 (J/Psi) T.Rogers, M.S, Mark Strikman PRC 6 (omega) G. Piller, M.S., L. Frankfurt, M.Strikman NP A 997 (rho meson) d /dt [nb/(gev) ] t [GeV ] Figure

18 (I) Good accuracy in descrip<ng QE d(e,e N)N reac<on Enhances the exploration potential of QE Exclusive Reactions in studying short range phenomena in the deuteron (a) Probing relativistic wave effects in deuteron electrodisintegration (b) Probing Color Transparency Phenomena (II) First successes in describing Inelas<c d(e,e N R )X in Resonance Region FSI effects in b (Wim Cosyn s talk) (III) Vector Meson Electroproduc<on from the Deuteron Color Transparence in vector meson electroproduction in Azz)

19 A zz in d(e,e p)n Reaction: Large FSI Effects T 3 ( (, ) + (, ) (, )) A zz = A d = T d (k,k ) d 3 apple = 3 k z + k 3 i p (a x +ia y ) i p (a x ia y ) (k,k )+ d (k,k ) i a z u(k apple )w(k ) p + 3 k z k apple (k k ) ((k k ) 3k z k z ) k k u(k )w(k ) p + k z k + k z k d (k,k ) w(k )w(k ). ()

20 A zz in d(e,e p)n Reaction T 3 ( (, ) + (, ) (, )) A zz = A d = T

21 Azz in d(e,e p)n Reaction: Relativistic Effects: Suppress FSI T 3 ( (, ) + (, ) (, )) A zz = A d = T ps = 8 T.5 Solid Light Cone Dashed Virtual Nucleon -.5 Curves with triangles Include FSI M.S & M.Strikman, p s, GeV/c

22 Azz in d(e,e V)d Reaction: Large FSI Effects T 3 ( (, ) + (, ) (, )) A zz = A d = T s,m ( ~ l, ~ l ) = X S s,mm d ( ~ l )S s,mm d ( ~ l ) = F C (l )F C (l ) m (" + p 3 ~ l ~ s m l + " 9 (~ l ~ s m # )( ~ l ~ m s ) ~ l ~l l l F C (l )F Q (l )+ 3 ~ l ~ m s l " 3 ~ l ~ m s l 3 ~ l ~ m s l L. Frankfurt, G.Piller & M.S, M. Strikman, NP 997 # + F C (l )F Q (l ) # ) F Q (l )F Q (l ). F C (l) = F Q (l) = Z Z dr u (r)+w (r) j (lr), dr apple u(r) p 8 w(r) w(r)j (lr).

23 Azz in d(e,e V)d Reaction T 3 ( (, ) + (, ) (, )) A zz = A d = T A d Q [GeV ] =,, 5, x = PWIA.5 FSI t [GeV ] Figure

24 Azz in d(e,e p)n Reaction: Color Transparency Effect T 3 ( (, ) + (, ) (, )) A zz = A d = T L. Frankfurt, W.Greenberg, G.PMiller & M.S, M. Strikman, ZPhys

25 Azz in d(e,e p)n Reaction: Color Transparency Effect T 3 ( (, ) + (, ) (, )) A zz = A d = T A d PWIA CT GEA Q (GeV/c)

26 A zz in d(e, e )d T ( (, ) + (, ) (, )) 3 Reaction: Color Transparency A zz = A d = T A d.75.5 Q [GeV ] =,, 5, x =. PWIA FSI t [GeV ] Figure

27 A zz in d(e, e )d T ( (, ) + (, ) (, )) 3 A zz = A d = T Reaction: Color Transparency A d A d Figure 6 (a) Q =., 3.,. GeV, x = t [ GeV ] (b) FSI FSI PWIA PWIA t [ GeV ]

28 A zz in T ( (, ) + (, ) (, )) 3 A zz = A d = T Dashed line Solid Line d(e, e )d N = mb N = 5mb Reaction: Color Transparency d /dt(t)/ d /dt(t=t min ) Ratio (a) t [GeV ] (b) - Figure t [GeV ]

29 Color Transparency in pp scattering T pp.6 (c) CM = 9 deg p + C p+p+x.4. A nn (%) (b) p + p p+p pqcd QIM. s d /dt (a) p + p p+p s (Gev )

30 Color Transparency in pp scattering T pp.6 (c) CM = 9 deg p + C p+p+x.4 M.S. 4, arxiv: A nn (%) (b) p + p p+p pqcd QIM. s d /dt (a) p + p p+p s (Gev )

31 Azz in Inclusive d(e,e )X Reaction T 3 ( (, ) + (, ) (, )) A zz = A d = T Solid Line Light Cone Dashed Light Cone + EMC Dash- Doker Virtual Nucleon d /d dee e nb/gev/st - d(e,e I )X, E =.999 GeV, e =, Q (x=) = GeV T nb/gev/st x x

32 Azz in inclusive d(e,e )X Reaction T 3 ( (, ) + (, ) (, )) A zz = A d = T T /.8 d(e,e / )X Q = Gev solid - light cone dashed - virtual nucleon Solid Line Light Cone Dashed Virtual Nucleon x

33 Conclusions: - Tensor polarization prepares deuteron in a compact state - It enhances the relativistic effect & FSI effects - Can be used to study the deuteron wave function: onset of Light-Cone dynamics, non-nucleonic degrees - Can be used to study effects sensitive to the FSI: Color Transparency, or the total VN cross section

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