PoS(LC2008)044 http://pos.sissa.it/ modes on anti-de Sitter (AdS) J matrix calculated from the QCD light-front T which allows the separation of the dynamics ζ † ∗ [email protected] [email protected] Speaker. This research was supported by the Department of Energy contract DE–AC02–76SF00515. SLAC–PUB–13428. of quark and gluon bindinglar momentum. from the The kinematics result of isdetermines a constituent the single-variable eigenspectrum spin light-front and and Schrödinger the internal equation light-frontorbital orbital wavefunctions for angular of QCD angu- momentum. hadrons which for This generalthe spin frame-independent equations and light-front of motion wave which equation describespace. is the equivalent propagation Light-front to of spin- holography istudes in a the remarkable AdS fifth feature dimension of tohadrons be AdS/CFT: in mapped it physical to space-time, frame-independent allows light-front thus hadronic wavefunctions providingtude of ampli- a level. relativistic In description principle, the of model hadrons canlight-front at be Hamiltonian the systematically on ampli- improved the by AdS/QCD diagonalizing basis. theat Quark full and the QCD gluon amplitude hadronization level can by be convoluting computed Hamiltonian the with off-shell the hadronic light-frontstatic wavefunctions. observables such We as also the probability note distributions the computedwavefunctions from versus distinction the dynamical between square observables of such the as light-front thesingle-spin structure functions asymmetries and measured the in leading-twist deep inelasticand scattering final-state which interactions. include the effects of initial We identify an invariant light-front coordinate ∗ † Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. c

LIGHT CONE 2008: Relativistic Nuclear andJuly 7-11 Particle Physics 2008, Mulhouse, France Guy F. de Téramond Universidad de Costa Rica, San José,E-mail: Costa Rica Stanley J. Brodsky The AdS/CFT Correspondence and Light-Front QCD Stanford Linear Accelerator Center, Stanford University, Stanford,E-mail: California 94309, USA PoS(LC2008)044 2 n M since , z J = – the “front z i c L The light-front / 1 1 z . The light-front . i − Stanley J. Brodsky = n i ⊥ λ + P ∑ t + which specifies the = z i and ) τ S i 3 1 then has eigenvalues λ , P = i n i 2 ⊥ ⊥ + ∑ P k 0 . , i − t P x − ( 1. Thus one has a direct physical = n P ± ψ + + P P zero modes. For example, in the case and spin projections = ; i.e., the Drell-Yan-West formula. This i ] replaces the vacuum condensate of the z g n + = 2 ⊥ S k 0 is particularly useful in that there are no k = LF 0 = n H + A 2 with 0 n -particle LF Fock state: ψ n and n and then evolve the system using the light-front Hamiltonian . In contrast, setting the initial condition using conventional ψ τ transverse momenta τ ) 3 P ] – rather than at fixed ordinary time + 1 0 P The invariant Hamiltonian ( / . -number LF zero mode constant [ ) c τ 3 d k / + id 0 k = requires simultaneous scattering of photons on each constituent. Thus it is natural 1 relative orbital angular momentum. Since the plus momenta are conserved and 3 t is not sufficient to determine the form factors and other properties of the hadron. In = ( P − t is the physical mass. Its eigenfunctions are the light-front (LF) eigenstates whose Fock + n − P 0 / M P + k Light-front wavefunctions are the fundamental process-independent amplitudes which encode One of the most important theoretical tools in atomic physics is the Schrödinger equation, When a flash from a camera illuminates a scene, each object is illuminated along the light- A remarkable feature of LFWFs is the fact that they are frame independent; i.e., the form of = = − i ghosts and the gluon polarizationinterpretation is of purely orbital angular transverse: momentum.properties of The the constituent hadrons spin are also and encodedangular orbital in momentum the angular LFWFs. is momentum For conserved example, for the each internal spin and orbital is in dramatic contrast to thewhere usual instant the form current result couples which requires tofixed the vacuum time inclusion processes. of contributions Thus knowing the wavefunction of a hadron at addition, one must also be able to compute the boosted instant form wavefunction, which requires formalism for gauge theories in light-cone gauge there are positive, the vacuum in frontof form the Higgs is theory, trivial a except for hadron properties in terms of their quarktities and gluon such degrees as of spin freedom, predicting correlations, dynamicaland form quan- exclusive scattering factors, amplitudes. structure Meson functions, and generalizedin baryon parton light-front diffractive di-jet wavefunctions distributions, can and be tri-jet measured reactions,light-front respectively. formalism One is of that the spacelike mostof form important the factors advantages LF of can Fock the be state represented wavefunctions as simple overlap integrals instant form. The simple structurethe of partonic the content light-front of a vacuum hadron. allows an unambiguous definition of instant time to set boundary conditions at fixed P which describes the quantum-mechanical structure of atomicfront systems at wavefunctions the (LFWFs) amplitude level. play Light- ing a a similar fundamental role description of inconstituent the quantum quarks structure chromodynamics and and (QCD), internal gluons.field dynamics provid- of theories The hadrons such natural in as terms concept of QCD of their is a the wavefunction light-front for relativistic wavefunction quantum front of the flash; i.e., at a given the LFWF is independent of the hadron’s total momentum Light-Front AdS/QCD Holography 1. Introduction where state projections define the light-front wavefunctions. quark and gluon constituentsx of a hadron’s Fock state as a function of the light-cone fractions form” introduced by Dirac [ wavefunctions of bound states in QCD aretions relativistic generalizations of of atomic the Schrödinger physics, wavefunc- but they are determined at fixed light-cone time PoS(LC2008)044 = 2 n (2.1) M . Similarly in 2 in the handbag n . 0 p Stanley J. Brodsky M ) ] k − 4 ( 2 determine the bound- γ ) ]. . Thus, to first approxi- and hadronic properties r M 3 → 2 ⊥ ( ζ p b L interactions , and light front QCD at its ) ) n x q or 5 ψ ( ) + n − ∗ ⊥ γ 1 . To prove this, we show that the M ( b 5 , x x ( = ψ 2 . The essential dynamics of the atom
ζ . We choose the normalization of the LF ` interactions L ) ⊥ 2 b ζ + ( 2 ∇ | φ ) Comparing with the LFWF normalization, we − . ⊥ → 1 ) k , ) 3 ⊥ = x ⊥ b ( 2 , k x , ψ i| | ( x ∗ φ ( ) | x ψ ψ ζ 2 ⊥ : ⊥ − |h ) k b 1 ζ ζ 2 ( ( d x d R φ 3 Z ⊥ the measure of the off-mass shell energy π = k ) , 2 x i ) x 16 d φ which separates the dynamics of Coulomb binding from the kinemat- 2 ⊥ − | − dx k 1 Z 1 φ ( φ ( x h , x dx θ 1 1 , modes on AdS space. This allows us to formally establish a gauge/gravity → 0 0 r Z Z a J with a 2 ⊥ x i = = k φ 2 a | ∑ ζ h M which allows one to separate the essential dynamics of quark and gluon binding from which encode the hadronic properties. This LF wave equations carry the orbital angu- = ) 2 ζ ) =  ζ ( ζ µ a ( k φ φ 1 A key step in the analysis of an atomic system such as positronium is the introduction of the The connection between light-front QCD and the description of hadronic modes on AdS space To simplify the discussion we will consider a two-parton hadronic bound state. In the case of = n a ∑ impact space the relevant variable for a two-parton state is mation LF dynamics depend only onare the encoded boost in the invariant variable hadronic mode mode approximation can be written as the overlap of light-front wavefunctions [ spherical coordinates Light-Front AdS/QCD Holography solving a complex dynamical problem.coupling and In even then fact, are boostedtions more wavefunctions of complicated are the than only individual the known constituentare product spinors. at independent of of weak Melosh the In momentum or contrast, of Wigner the theparton transforma- hadron, distributions light-front measured and in wavefunctions they deep are of inelastic thus a Compton boost scattering invariant. hadron The generalized 2. A Single-Variable Light-Front Schrödinger Equation for QCD [ is specified by the radial Schrödinger equation whose eigensolutions The functional dependence for a given Fock state is given in terms of the invariant mass ical effects of the quantized orbital angular momentum state wavefunction and eigenspectrum. Here we show thatcoordinate there is an analogous invariant light-front is physically compelling and phenomenologicallyQCD successful. is formally To equivalent a to first an approximation effective gravity light-front theory on AdS the kinematical physics ofis constituent a spin single-variable and light-front internaltrum Schrödinger and orbital the equation angular light-front for wavefunctions momentum. of QCDConversely, hadrons this which for The general analysis determines result spin can and the orbitalrelativistic be eigenspec- angular atoms. momentum. applied to atomic physics, providing an elegant formalism for correspondence between an effective gravity theory defined on AdS massless constituents the LF Hamiltonian equation of motion of QCD leads to the equation LF Hamiltonian equations of motionmodes of QCD lead tolar an momentum effective quantum LF numbers wave and equation arepropagation equivalent for of to physical the spin- equations of motion which describe the asymptotic boundary. PoS(LC2008)044 . 0. = ζ ~ ≥ QCD (2.3) (2.2) 2 Λ ] from k 6 , L , M with 5 β ) ) ϕ = ζ ] which have , ]. Likewise a ( The AdS/CFT k 7 , 9 ζ ~ . φ 2 L , ] and theoretical ) 2 Stanley J. Brodsky 6 ζ Q M 12 = ( , is thus a light-front ( 5 0 and thus i ζ U , , not on the bag radius ) φ | 4 ζ ζ 2 is equivalent to the soft- ( i ≥ ∗ 2 φ , | M ) ζ ζ ζ φ LF = ( ∼ d i H φ | ) 2 φ Z | φ ζ h ( + , ] where the partons are free inside . However, unlike the standard bag M LF ) 8 U ) H ζ ζ ζ 1 ( QCD ( ) = Λ p φ φ ζ (  >  ) φ 2 2 ζ ζ ( L  ζ , which is the same result found in [ ] between string states in anti-de Sitter (AdS) ) is equivalent to an AdS wave equation, the ) if 2 U | ζ + ) 11 ( ∞ 2.3 4 + ⊥ ζ d U 2 has an infrared fixed point at low b d of orbital angular momentum in the transverse plane: , L ) 2 + ) = 1 x ζ 4 2 2 ( ζ 2 ζ L Q 4 ( , and factor out the angular dependence of the modes in − L − ψ 2 ( 2 | 4 s 1 2 2 U ζ ) 0, Eq. ( 2 ∂ x α 4 ζ ∂ϕ − d − π 0. The mode spectrum follows from the boundary conditions − d 2 2 1 1 1 → 2 ζ ( and 2 = x − ) ζ − d + L ζ d  2 = 1 ( QCD 2  ζ ζ − 2 Λ d | U ζ d d ζ  d φ p | ) ) ≤ − ζ ζ ζ  ζ  ( ( ∗ ∗ ζ . The light-front eigenvalue equation d d ) ] which reproduce the usual linear Regge trajectories. 0 the LF Hamiltonian is positive definite 1 0 if ζ ζ . We find ζ φ ζ φ ( ) 10 ≥ 0, and is given in terms of the roots of Bessel functions: d d Casimir representation ζ φ = U 2 ]. ( ) ) = Z Z 2 L 7 2 φ ζ ( ) = ∇ = = ϕ ( ] that the QCD coupling 2 : iL U SO ⊥ ± 13 QCD e b M Λ ) ], boundary conditions are imposed on the boost-invariant variable x / ∼ 0 the LF Hamiltonian is unbounded from below and the particle “falls towards the center”. 8 1 ) − < ϕ = Our analysis follows from recent developments in light-front QCD [ We can write the Laplacian operator in circular cylindrical coordinates As the simplest example we consider a bag-like model [ 1 , 2 ( ζ ζ x ~ L ( ( an effective single-variable light-frontanalytically Schrödinger tractable. equation One which can is readilymassive quarks relativistic, generalize [ the covariant equations and to allow for the kinetic energy of wall model of Ref. [ p where all the complexityeffective of potential the interaction termswave in equation for the QCD Lagrangian is summed up in the model [ If The critical value corresponds to φ hard-wall LF model discussed here is equivalent to the hard wall model of Ref. [ been inspired by the AdS/CFT correspondence [ 3. Light-Front Holography the mapping of transition matrix elements for arbitrary values of the momentum transfer. φ the hadron and the interactiona terms hard will wall: effectively build confinement. The effective potential is at fixed time. If two-dimensional transverse oscillator with effective potential space and conformal field theoriesand conformal (CFT) methods in to physical QCD can space-time.arguments be [ motivated The from the application empirical of evidencecorrespondence [ AdS has space led to insightshadronic into light-front the wavefunctions. confining dynamics Asbetween of we the QCD description have and of shown hadronic the modes recently, analytic in there form AdS is space of and a the remarkable Hamiltonian formulation mapping of QCD Light-Front AdS/QCD Holography find the functional relation: terms of the Since in the conformal limit 1 PoS(LC2008)044 y deca in the ) y z ( ρπ Φ hadron deca → " dy 375 GeV) model. . ρπ also specifies the 32 GeV) and (red) . This mapping is Stanley J. Brodsky ψ o . 0 ) ρπ ζ 0 hadron r ζ b 0 = ( → 0 → = " φ fo κ o- dy ) ρπ ψ ψ x o w / r b − πζ QCD → t 1 2 J ( -2 fo o- Λ x ) ψ -0.5 w / 2 st t J q er value ) ) 2 st er -4 value 2 ev ) rge ) = which measures the separation of q all 2 ev -1 GeV rge (b) a w ⊥ q all ( l GeV a ( w ζ ( b l o ). The coordinate ( π o , π 2 2 1 -6 x F q H is Sm ρ π π F q H is Sm ρ ( ψ ], thus providing an important consistency -1.5 ) -8 14 x (a)] displays confinement at large interquark 2 − -2

1 0 ) for the AdS/QCD soft wall ( 5 -10 1 0 0.4 0.2 0.8 0.6 ⊥ (1 0.8 0.6 0.4 0.2 b x , Q x ! ( 2 π in light-front QCD allows the separation of the dynamics Untitled-1 ∝ ψ < ζ ) ) R 0 2 ⊥ R µ ) k Q (b). 1.5 µ Q ⊥ 2 k < x, x, 0.2 ( = = ( x, 2 (a) ( 0.4 1.4 M F − R R M ψ to be precisely mapped to the light-front wave functions of hadrons in 0.6 µ φ ψ µ µ µ Q/ ) (GeV) z 0.8 1.3 ⊥ k 00 5 0.1 0.2 0.05 0.15 x, ( ψ 375 GeV) models. . 0 = Light-front holography for meson wavefunctions: (a) Pion light-front wavefunction ]. More recently we have shown that one obtains the identical holographic mapping using κ 6 , 5 The use of the invariant coordinate light-front kinetic energy and invariant mass ofby constituents. matching This mapping the was expression originally obtained corresponding for expression electromagnetic for the current current matrix matrixtime elements element [ using in light-front AdS theory in spacethe physical matrix with space elements the of the energy-momentum tensor [ test and verification oflight holographic front. mapping from The resultingseparation AdS and wavefunction to conformal [see symmetry physical at fig. observables shorthard distances, defined exclusive reproducing amplitudes. dimensional on The counting predictions the rules for for soft-wall the models spacelike is pion shown form in factor for fig. the hard-wall and Figure 2: Figure 1: Light-Front AdS/QCD Holography (b) Holographic prediction the space-likesoft pion wall form ( factor: (blue) hard wall ( in physical space-time quantized on the light-front. This procedure allows string modes derived from the equality of the LF and AdS formulae for current matrix elements. AdS holographic variable the quark and gluonic constituents within the hadron (see fig. physical space-time in terms of a specific light-front variable PoS(LC2008)044 ]. ∼ 2 15 (4.1) M 2. This > limit is not J C . The event N QCD LF Stanley J. Brodsky H ··· + 2 are not incompatible with LF > I modes on anti-de Sitter (AdS) J H J ε . The LFWFS of AdS/QCD can i 3 + in fig. X 2 1 intermediate probability distributions. The LF Hamiltonian → M ∗ 6 − γ → 2 Initial ad hoc , and thus the light-front excitation spectrum of hadrons − e J M is the invariant mass squared of the intermediate state and + i e LF x I / H ) 2 i . In the soft-wall model the usual Regge behavior is found + L m + LF I + i n H 2 2 ⊥ k = ∼ ( 1 n LF = N i M T ∑ = , then one coalesces the virtual partons into a hadron state using the AdS/QCD 2 QCD Λ < -matrix element is evaluated between the out and in eigenstates of 2 i ]. As in this approximation there are no interactions up to the confining scale, there are no intermediate x 4 LF / M i . One can systematically improve the AdS/QCD approximation by diagonalizing the QCD is the set of interactions of the QCD LF Hamiltonian in the ghost-free light-cone gauge [ T The conversion of quark and gluon partons is usually discussed in terms of on-shell hard- 2 ⊥ L k LF i I + Here H The amplitude generator is illustrated for be used as the interpolating amplitudeshadrons. between the off-shell Specifically, quark if and at gluons∑ and any the stage bound-state a set of color-singlet partons has light-front kinetic energy formulation of quantum field theory providesamplitude a level. natural formalism In to this computelight-front hadronization case Hamiltonian at to one generate the uses the off-shell light-frontthe quark and time-ordered LF gluon generalization perturbation T-matrix of helicity theory the amplitude Lippmann-Schwinger for using formalism: the QCD LFWFs. This provides aperturbative specific and nonperturbative scheme physics. for determining the factorization scale which matches scattering cross sections convoluted with n LF Hamiltonian on themethods AdS/QCD used basis in chemistry or and by nuclearinteraction generalizing physics. Hamiltonian generates the The the action variational form of and of theWe emphasize, the non-diagonal other that terms higher in systematic in Fock contrast with state the the QCD structurerequired original of to AdS/CFT hadronic connect correspondence, light-front LFWFs. the QCD large to an effective dual gravity approximation. 4. Hadronization at the Amplitude Level anomalous dimensions. This mayexclusive explain reactions the where experimental there success are of nosame power-law reason indication scaling we of also in the expect hard little effects effect of of anomalous anomalous dimensions dimensions. on the For gravity the side for Light-Front AdS/QCD Holography of quark and gluonmomentum. binding from The result the is kinematics aeigenspectrum of single-variable and light-front constituent Schrödinger the spin equation light-front and which wavefunctionsmomentum. internal determines of This the orbital light-front hadrons wave angular equation for serves as generalto a first the spin approximation equations and to of QCD orbital motion and is which angular space. equivalent describe Remarkably the the propagation AdS of equations spin- corresponda to hadron, whereas the the kinetic interaction energy terms termsspace build of [ confinement the and partons correspond inside to the truncation of AdS depend only on the orbital and principaldependence is quantum linear: numbers. In the hard-wall holographic model the also explains why physical hadrons lying on Reggea trajectories string with description. In the hardmomentum wall model from there the is total a total hadronic decoupling spin of the internal orbital angular PoS(LC2008)044 1 physical + in 3 Stanley J. Brodsky ) i ⊥ b , i for a given process only x ( n for hadronization processes at ψ g computed in the AdS fifth di- X modes on anti-de Sitter (AdS) ) ordered diagrams. (b) The com- z J → ( − in the AdS/QCD hard wall model of ∗ τ Φ which allows the separation of the γ ζ → 2 QCD − Λ e / 1 + e > 2 ⊥ b ) 7 x . To prove this, we have shown that there exists a ) − i increases, all particles propagate as forward-moving 1 where the partons are far off-shell. (g) Color confine- ⊥ ( τ i b x x , i = x ( 2 . -matrix computation allows for the effects of initial and final ζ ζ LF 2 QCD T Λ ], rendering all amplitudes UV finite. (d) The renormalization scale < ) 16 x maps to 2 ⊥ − z k 1 ( x = ]. 2 13 0. There are thus relatively few contributing M ≥ + i k Illustration of an event amplitude generator for ]. Light-Front Holography is one of the most remarkable features of AdS/CFT. It allows 4 This scheme has a number of important computational advantages: (a) Since propagation in We have identified an invariant light-front coordinate LF Hamiltonian theory only proceeds as one to project the functional dependence of the wavefunction puter implementation can be highly efficient: an amplitude of order dynamics of quark andbital gluon angular momentum. binding The from resultwhich is the determines a kinematics the single-variable light-front eigenspectrum of Schrödinger and constituent equation theand for light-front spin orbital wavefunctions QCD angular of and momentum. hadrons internal This forthe frame-independent general or- light-front spin equations wave of equation motion is equivalent whichspace to describe [ the propagation of spin- mension to the hadronic frame-independentspace-time. light-front wavefunction The variable partons with 5. Conclusions needs to be computed once.nator” (c) counterterm Each method amplitude [ can bein renormalized using a the given “alternate renormalization denomi- multiple scheme physical can scales. be (e) The determined for each skeleton graph even if there are Figure 3: state interactions of the active and spectatoras partons. diffractive This DIS, allows the for Sivers leading-twist spin phenomenain asymmetry such Drell-Yan and processes. the (f) breakdown ERBL of the andquenching PQCD DGLAP of Lam-Tung evolution DGLAP relation are evolution naturally at incorporated, large including the Light-Front AdS/QCD Holography the amplitude level. Capture occurs if ment can be incorporated atquark every and stage gluons by [ limiting the maximum wavelength of the propagating confinement; i.e. if PoS(LC2008)044 ) x ( π ]: the φ ]. This 20 is related -behavior 13 x ζ ] of the pion ] by including 17 ], the moments 7 Stanley J. Brodsky 18 . A new perspective on ϒ has a broader distribution than and ) x , has a quite different ⊥ ψ − k / 1 J ( ]. x over . Given the nonpertubative LFWFs one 19 p i ) π x f / ⊥ ) 3 k 2 i , √ x m ( + 8 ψ ) = i x 2 ⊥ ( k π ( i φ ∑ valence LFWF q q ] and pion form factor data [ 7 . 4 , in analogy to the limited physical extent of superconductor phases. This picture π m / ]. The agreement of the results for both electromagnetic and gravitational hadronic tran- 14 Presented by SJB at Light Cone 2008: Relativistic Nuclear And Particle Physics (LC2008) It is interesting to note that the form of the nonperturbative pion distribution amplitude Nonzero quark masses are naturally incorporated into the AdS predictions [ We also note the importance of distinguishing between static observables such as the prob- Color confinement and its implementation in AdS/QCD implies a maximal wavelength for 7-11 Jul 2008, Mulhouse,Durham, France. UK for He its thanks hospitality.sions. the We also Institute thank for Robert Particle Shrock Physics and James Phenomenology, Vary for helpful discus- Acknowledgments to the invariant mass squared of thekinetic constituents energy, in and the it LFWF is and thus its the off-shellness natural in variable the to light-front characterize theobtained hadronic from wavefunction. integrating the strengthens our understanding of the narrow widths of the ability distributions computed from theobservables square such as of the the structure light-front functions andin wavefunctions the versus deep leading dynamical inelastic twist single-spin scattering asymmetries which measured summarized include in the fig. effects of final state interactions. This distinction is distribution amplitude. The AdS prediction obtained from lattice QCD [ the nature of quark andspatial gluon support condensates of in QCD quantum condensates chromodynamicsthe is interactions is restricted of presented to confined in the quarks and interior [ gluons.of of Chiral hadrons, size symmetry since is 1 they thus arise brokenexplains in due recent a to limited results domain which find no significant signal for the vacuum gluon condensate. sition amplitudes provides an importantfrom consistency AdS test to and physical observables verification defined of on holographic the mapping light-front. The transverse coordinate confined quarks and gluons and thus a finite IR fixed point for the QCD coupling [ Light-Front AdS/QCD Holography correspondence between the matrix elementshadronic of constituents the energy-momentum in tensor QCD ofmodes with the in the fundamental anti-de transition Sitter amplitudesrior describing space [ the with interaction an of external string graviton field which propagates in the AdS inte- expected from solving the ERBL evolution equationto in perturbative be QCD. This consistent observation appears with the results of the Fermilab diffractive dijet experimentthem [ explicitly in the LFcan predict kinetic many energy interesting phenomenological quantities suchparton as distributions heavy quark and decays, generalized partonthus structure only functions. predicts the The lowestmodel valence can AdS/QCD Fock be model state systematically is improved structurethe by semiclassical of AdS/QCD diagonalizing basis. the and the hadron full LFWF. QCD In light-front principle, Hamiltonian the on than the asymptotic distribution amplitude predicted from the PQCD evolution [ PoS(LC2008)044 , 3471 (1974). 9 Stanley J. Brodsky , 1113 (1999)] 38 .) DDIS etc Saturation on: ISI & FSI om Collision etation , 015005 (2006) wing, der Phases , 74 , 349 (2008) [arXiv:0803.4119 -Mulders, 665 , 99 (2001) [arXiv:hep-ph/0009254]. , 4768 (2001) [arXiv:hep-ex/0010043]. Boer , 299 (1998) [arXiv:hep-ph/9705477]. on and Od Anti-Shado 86

olution ers, y Rescattering: , 201601 (2006) [arXiv:hep-ph/0602252]. 596 en Wilson Line 301 v , 4574 (1973). 96 o omer , 056007 (2008) [arXiv:0707.3859 [hep-ph]]. , 025032 (2008) [arXiv:0804.0452 [hep-ph]]. 8 obabilistic Interpr wing, d (Siv , 031601 (2002) [arXiv:hep-th/0109174]. 77 78 d P ocess-Dependent - Fr , 045019 (2002) [arXiv:hep-ph/0202141]. 88 -Od Not Pr T , 359 (1979). 66 9 , 95 (2008) [arXiv:0806.1535 [hep-th]]. 87 , 231 (1998) [Int. J. Theor. Phys. mo- 666 2 r z a wing Shado , 093010 (2006) [arXiv:hep-ph/0608148]. ngul 74 at large x DGLAP Ev a Dynamic versus static observables. , 392 (1949). rbital mod. o 21 Anti-Shado ⊥

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