High Energy Break-Up of Few-Nucleon Systems Misak Sargsian Florida International University
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- Ἀγαμέμνων Γεωργιάδης
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1 High Energy Break-U of Few-Nucleon Systems Misak Sargsian Florida International University Exclusive Worksho, JLab May 2-24, 2007
2 Nuclear QCD
3 Nuclear QCD - identyfy hard subrocess
4 Nuclear QCD - identyfy hard subrocess - aly factorization
5 Nuclear QCD - identyfy hard subrocess - aly factorization - aly QCD to hard subrocess
6 Nuclear QCD - identyfy hard subrocess - aly factorization - aly QCD to hard subrocess - soft art exress through measurable/extractable quatities as PDF s, hadronic amlitudes, FF and calculable nuclear wave functions
7 Nuclear QCD - identyfy hard subrocess - aly factorization - aly QCD to hard subrocess - soft art exress through measurable/extractable quatities as PDF s, hadronic amlitudes, FF and calculable nuclear wave functions - obtain arameter free results
8 Nuclear QCD - EMC effect - Formfactors of Few Nucleon Systems at high momentum transfer Text Energy - Color Transarency - DIS at x > - High Energy Break u of two hadrons in Nuclei
9 Nuclear QCD - EMC effect - Formfactors of Few Nucleon Systems at high momentum transfer Text Energy - Color Transarency - DIS at x > - High Energy Break u of two hadrons in Nuclei
10 N N N N q q q- q g g g
11 N N N N q q q- q g g g
12 - Large CM angle disintegration of nuclei: N γ N D, 3 He(, n) γ Mx N D N s = (k γ + d ) 2 = 2M d E γ + M 2 d Brodsky, Chertock, 976 Holt, 990 Gilman, Gross, 2002 t = (k γ N ) 2 = [cosθ cm ] s M 2 d 2 E γ = 2 GeV, s = 2 GeV 2, t GeV 2, M x = 2 GeV E γ = 2 GeV, s = 4 GeV 2, t GeV 2, M x = 4.4 GeV
13 - Large CM angle disintegration of nuclei: N γ N D, 3 He(, n) γ Mx N D N s = (k γ + d ) 2 = 2M d E γ + M 2 d Brodsky, Chertock, 976 Holt, 990 Gilman, Gross, 2002 t = (k γ N ) 2 = [cosθ cm ] s M 2 d 2 E γ = 2 GeV, s = 2 GeV 2, t GeV 2, M x = 2 GeV E γ = 2 GeV, s = 4 GeV 2, t GeV 2, M x = 4.4 GeV
14 Consider A+B C + D A C f( t s ) B D s A F ( t s ) s n A +n B +n C +n D 2 2 Brodsky, Farrar 975 Matveev, Muradyan, Takhvelidze, 975 dσ dt A 2 s 2 = F 2 ( t s ) s n A+n B +n C +n D 2
15 Consider A+B C + D A C f( t s ) B D additional A F ( t s ) s n A +n B +n C +n D 2 2 s s Brodsky, Farrar 975 Matveev, Muradyan, Takhvelidze, 975 dσ dt A 2 s 2 = F 2 ( t s ) s n A+n B +n C +n D 2
16 γd n Exclusive large-momentum-transfer scattering scaling Dimensional counting rule: d σ -(N= n A + nb + nc + nd -2) dt AB CD S f( t s ) For γ d ( high t ) + n ( high t ) N = = Notice: dσ dσ ( Eγ = GeV/c) / ( Eγ = 4 GeV/c) 0 dt dt 4
17 γd n 20 (GeV 2 ) W 2 # m d x=0 x=0.5 x=.0 x=.5 x= N$ NN ! = E " = Q 2 /2mx (GeV) Gilman, Gross, 2002
18
19 Hard Rescattering Mx Mmax=w > 2 GeV Mx w 2E γ m N q E γ 2.5 GeV d k + q A k 2 k 2 B
20 Hard Rescattering Mx Mmax=w > 2 GeV Mx w 2E γ m N q QCD E γ 2.5 GeV d k + q A k 2 k 2 B
21 Hard Rescattering Mx Mmax=w > 2 GeV Mx w 2E γ m N q QCD E γ 2.5 GeV d k + q A k 2 k 2 B N N N N NN -amlitude
22 l regen k k 2 z l regen Landau, Pameranchuk, Migdal
23 l regen k k 2 z l regen > Z Landau, Pameranchuk, Migdal
24 l regen k k 2 z l regen > Z Landau, Pameranchuk, Migdal
25 l regen k k 2 z l regen > Z l regen E γ R 2 Landau, Pameranchuk, Migdal
26 l regen k k 2 z l regen > Z l regen E γ R 2 E> 2.5GeV Landau, Pameranchuk, Migdal
27 l regen k k 2 z l regen > Z l regen E γ R 2 E> 2.5GeV z Landau, Pameranchuk, Migdal
28 l regen k k 2 z l regen > Z l regen E γ R 2 E> 2.5GeV z > fm Landau, Pameranchuk, Migdal
29 q Frankfurt, Miller, MS, Strikman PRL 2000 d k + q A k 2 k 2 B T = ( ψ N (x 2, B, k 2 ) x ū( B 2 + k 2 ) [ igtc F γ ν] e q 2 u(k + q)ū(k + q) [ ieq (k + q) 2 m 2 ɛ γ ] u(k ) ψ ) N(x,, k ) q + iɛ x { ψ N (x, A, k ) x G µν Ψ d(α, ) α ū( A + k ) [ igt F c γ µ ] u(k2 ) ψ N(x 2, 2, k 2 x 2 dx d 2 k dx 2 d 2 k 2 dα x 2(2π) 3 x 2 2(2π) 3 α d 2 2(2π) 3,
30 We use the reference frame where d = ( d0, dz, ) ( s 2 + M 2 d 2, s s 2 M 2 d 2, 0), s with s = (q + d ) 2, s s MD 2, and the hoton four-momentum is q = ( s 2, s 2, 0). -The knocked-out quark roagator. (k + q) 2 m 2 q = x s [( + s (M d 2 m2 n + 2 ) α ) α x m 2 R + k2 + ] m2 q( x ) ( x )x s 2 2 k x s -We are concerned with momenta such that 2 m2 N s and α 2 neglect terms of order 2, m2 N /s to obtain: () so we (k + q) 2 m 2 q + iɛ x s (α α c + iɛ), α c x m 2 R + k2 ( x )x. looking for α (2) s c 2 contribution Here s s ( + M 2 d s ) and m R is the recoil mass of the sectator quark-gluon system of the first nucleon. - The integration over k in the region k 2 ( x )x s 2 x m 2 R does rovide α c = 2.
31 α c = 2
32 x = ( m2 R α c s ) - Keeing only the imaginary art of the quark roagator (eikonal aroximation) leads to α = α c and corresonds to keeing the contribution from the soft comonent of the deuteron wave function. Next we calculate the hoton-quark hard scattering vertex ū(k +q)[γ ]u(k ) and use Eq. (2) to integrate over α -By taking into account only second term in the decomosition of struck quark roagator: (α α c + ɛ) P(α α c ) iπδ(α α c ): q d k + q A k 2 k 2 B ū β (k + q) [ ieɛ µ (λ γ )γ µ ] u α (k ) = ie q 2 2E 2 E( λ γ )δ β,α δ λ γ,α
33 λ A, λ B A λ γ, λ D = { ψ λ B,η 2 N ( B, x 2, k 2 ) ψ λ A,η x 2 N ( B, x, k ) x Ψ λ D,λ,λ 2 (α, ) ( α)α (η,η 2 ),(ξ 2 ),(λ,λ 2 ) eq 2 [ ( αc )x ]( α c )x x s ū η2 ( B k 2 )[ igt F c γ ν ] u λγ ( k + q) ψλ,λ γ N (, x, k ) x ū η ( A k )[ igt F c γ µ ]u ξ2 ( 2 k 2 ) ψλ 2,ξ 2 N ( 2, x 2, k 2 ) x 2 G µ,ν (r) dx x d 2 k 2(2π) 3 dx 2 x 2 d 2 k 2 2(2π) 3 d 2 4(2π) 2. } () A QIM n = ψ N (x 2, B, k 2 ) x 2 ū( B 2 + k 2 ) [ igt F c γ ν] u(k + q) ψ N(x,, k ) x ψ N (x, F, k ) x ū( A + k ) [ igt F ] c γ µ u(k2 ) ψ N (x 2, 2, k 2 ) G µν x 2 dx x d 2 k 2(2π) 3 dx 2 x 2 d 2 k 2 2(2π) 3 ()
34 Frankfurt, Sargsian, Strikman, Phys.Rev. Lett 2000 λ A, λ B, A Qi λ γ, λ D = (η,η 2 ),(ξ 2 ),(λ,λ 2 ) eqi f(θ cm ) 2s η 2, λ B η, λ A A i QIM (s, l 2 ) λ, λ γ λ 2 ξ 2 Ψ λ D,λ,λ 2 (α c, ) d2 (2π) 2() Notation used λ nucleon, λ quark Assuming λ = λ γ NN NN γn n a b A NN QIM ab = 2 a b i a, j b Brodsky,Carlson,Likin Phys.Rev.D 979 [I i I j + τ i τ j ]F i,j (s, t) ab a b A Q QIM ab a,b D = 2 a b [I i I j + τ i τ j ](Q i +Q j )F i,j (s, t) ab = (Q u +Q d ) a b A n QIM ab i a, j b (Q u + Q d ) a b A n QIM ab = 3 a b A n ab. A n QIM A n
35 λa, n λb A λ γ, λ D = λ 2 f(θ cm ) 3 2s ( λa, n λb A n (s, t n ) λγ, n λ2 λa, n λb A n (s, u n ) n λγ λ2 ) Ψ λ D,λ γ,λ 2 (α c, ) d2 (2π) 2 () Ψ λ D,λ λ 2 = (2π) 3 2 Ψ J D,λ,λ 2 NR m = [u(k) + w(k) 8 S 2]ξ λ D,λ,λ 2 dσ γd n dt = 8α 9 π4 t )dσn n (s, t) C( s s dt Ψ NR d ( z = 0, ) d 2 m N (2π) 2 2, C( t s ) θ cm =90=
36
37
38 NN NN R.Feynman Photon Hadron Interactions
39 NN NN R.Feynman Photon Hadron Interactions
40 NN NN before R.Feynman Photon Hadron Interactions
41 NN NN x x 2 before R.Feynman Photon Hadron Interactions
42 NN NN x x 2 before after R.Feynman Photon Hadron Interactions
43 B NN NN x x 2 x x 2 C before after R.Feynman Photon Hadron Interactions
44 B NN NN x x 2 x x 2 C before after γd n R.Feynman Photon Hadron Interactions
45 B NN NN x x 2 x x 2 C before after γd n R.Feynman Photon Hadron Interactions
46 B NN NN x x 2 x x 2 C before A after γd n x x 2 R.Feynman Photon Hadron Interactions x + x 2 = x γ = 2 B C 2 x x 2 x x 2
47 B NN NN x x 2 x x 2 C before A after γd n x x 2 R.Feynman Photon Hadron Interactions x + x 2 = x γ = 2 when x, x 2 B = B B C 2 x x 2 x x 2
48 dσ γd n dt = 8α 9 π4 t )dσn n (s, t) C( s s dt Frankfurt, Miller, M.S. Sargsian PRL 2000 Ψ NR d ( z = 0, ) d 2 m N (2π) 2 2, s d"/dt (kb-gev 20 ) E! (GeV)
49 s d"/dt (kb-gev 20 ) ! + d # + n s d"/dt (kb GeV 20 ) E!, GeV
50
51 0 Mirazita, et al, Phys. Rev. C 2004 FIG. 7: (Color) Angular distributions of the deuteron hotodisintegration cross section measured by the CLAS (full/red circles) in the incident hoton energy range GeV. Results from Mainz [26] (oen squares, average of the measured values in the given hoton energy intervals), SLAC [5, 6, 7] (full/green down-triangles), JLab Hall A [0] (full/blue squares) and Hall C [8, 9] (full/black u-triangles) are also shown. Error bars reresent the statistical uncertainties only. The solid line and the hatched area reresent the redictions of the QGS [8] and the HRM [27] models, resectively. FIG. 8: (Color) Same as Fig. 7 for hoton energies GeV.
52 Secifics of Hard Rescattering Model Helicity Selection Rule - Photon selects nucleon in the nucleus with helicity = to its own - Due to dominance of Helicity Conserving amlitudes in NN scattering, hoton helicity will roogate to the helicty of one of the final nucleons. q d k + q A k 2 k 2 B
53 Polarization Observables λa, n λb A λ γ, λ D = λ 2 f(θ cm ) 3 2s ( λa, n λb A n (s, t n ) λγ, n λ2 λa, n λb A n (s, u n ) n λγ λ2 ) Ψ λ D,λ γ,λ 2 (α c, ) d2 (2π) 2 C x P y C z Gilman, Gross, 2002
54 { } 2Im φ 5 [2(φ + φ 2 ) + φ 3 φ 4 ] P y = 2 φ φ φ φ φ 5 { } 2 2Re φ 5 [2(φ φ 2 ) + φ 3 + φ 4 ] C x = 2 φ φ φ φ φ φ 2 2 φ φ 3 2 φ 4 2 C z = 2 φ φ φ φ φ 5 [ ] 2 2Re φ 5 2 φ 3 φ 4 Σ = 2 φ φ φ φ φ 5 2, φ (s, t n, u n ) = +, + A n +, + φ 2 (s, t n, u n ) = +, + A n, φ 3 (s, t n, u n ) = +, A n +, φ 4 (s, t n, u n ) = +, A n, + φ 5 (s, t n, u n ) = +, + A n +,. () φ φ 3, φ 4 > φ 5 > φ 2.
55 P y E γ, GeV C x E γ, GeV C z E γ, GeV Σ E γ, GeV Sargsian, Phys. Lett. B 2004 q d k + q A k 2 k 2 B
56 Jiang, PRL2007
57 - Hard Photodisintegration of air: γ + 3 He + n Magnitude of vs. n hard hotodisintegration σ ( γ At low hoton energy For 3 E γ He 0.5 GeV/c ) / σ ( γ 3 He n) % σ γ << σ γn σ γ 0 γ 0 π, ρ MEC is the dominant rocess air : only a neutral ion can be exchanged, its couling to the hoton is weak. Laget NP A497 (89) 39, (Saclay data). - Three Body Processes are Dominant
58 Hard Disintegration of from 3He q Brodsky, Frankfurt, Gilman,Hiller, Miller,Piasetzky,M.S. Strikman Phys.Lett. B 2003 A k k 2 r 2 B n n dσ dtd 3 n = ( ) 2 4 8π 4 α EM 5 s M 2 3 He dσ (s, t N ) dt 2 sins Ψ 3 He (, 2, n ) M N d 2 2T (2π) 2 2, where s = (P γ + P3 He) 2, t = (P P γ ) s t N = ( a α ) 2 2 t. = (P γ + P3 He P n ) 2, and
59 - Hard Photodisintegration of air: MS, Carlos Granados,2007 λ A, λ B A Qi λ γ, λ = ef(θcm ) Q λ 2 2s i λ A, λ B A i QIM (s, l 2 ) λ γ, λ 2 Ψ λ,λ γ,λ 2 (α c, ) d2 (2π) 2 a b A Q QIM ab a,b = 2 a b i a, j b [I i I j + τ i τ j ](Q i +Q j )F i,j (s, t) ab = 4 5 a b A QIM ab A QIM A
60 - Hard Photodisintegration of air: MS, Carlos Granados,2007 λ A, λ B A Qi λ γ, λ = ef(θcm ) Q λ 2 2s i λ A, λ B A i QIM (s, l 2 ) λ γ, λ 2 Ψ λ,λ γ,λ 2 (α c, ) d2 (2π) 2 a b A Q QIM ab a,b = 2 a b i a, j b [I i I j + τ i τ j ](Q i +Q j )F i,j (s, t) ab = 4 5 a b A QIM ab He3 q A QIM A roton(uud) A k k 2 r roton(uud) n neutron 2 B n
61 Ā 2 = const 2 [ φ 2 S + (φ φ 4 )S 34 ] S = 2 ψ 2 3 He (λ, λ 2, λ 3 )m d2 2 (2π) 2 2 λ =λ 2,λ 3 = 2 S 34 = 2 ψ 2 3 He (λ, λ 2, λ 3 )m d2 2 (2π) 2 2 λ = λ 2,λ 3 = 2
62 dσ dtd 3 n = ( ) 2 4 6π 4 α 5 S M 2 3 He ( 2c 2 + 2c 2 )dσ dt (s, t n ) S 34 E n c = φ 3,4 φ 2 s d!/dt (kb GeV 20 ) E g
63 Polarization Observables λ A, λ B A Qi λ γ, λ = ef(θcm ) Q λ 2 2s i λ A, λ B A i QIM (s, l 2 ) λ γ, λ 2 Ψ λ,λ γ,λ 2 (α c, ) d2 (2π) 2 { } 2Im φ 5 [2(φ + φ 2 ) + φ 3 φ 4 ] P y = 2 φ φ φ φ φ 5 { } 2 2Re φ 5 [2(φ φ 2 ) + φ 3 + φ 4 ] C x = 2 φ φ φ φ φ φ 2 2 φ φ 3 2 φ 4 2 C z = 2 φ φ φ φ φ 5 [ ] 2 2Re φ 5 2 φ 3 φ 4 Σ = 2 φ φ φ φ φ 5 2, () Helicity Selection Rule C z = 0!
64 Conclusion and Outlook - High Energy Photodisintegration of Few Nucleon System may eventually rovide a framework of robing the QCD structure of NN force - Hard Rescattering Mechanism reresents one such examle - disintegration data are crucial for verifying the validity of the HR mechanism New Venues - Hard disintegration into Delta airs σ(γd ++ ) σ(γd n) A(NN ++ ) A(NN NN) 2 - Hard Disintegraion into Strange Baryons
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