The System 2.4.6-Trinitrotoluene–2.4.6-Trinitro-m-xylene.

“…One can perform Fourier transforms of the Fock state wavefunctions in impact space b ⊥ and in x − = x 0 − x 3 space to obtain the spatial form of Fock wavefunctions in coordinate space. See also: [11,12] The DVCS amplitudes also enter the two-photon exchange contribution to elastic electron-proton scattering, which in turn produces a significant correction to the Rosenbluth method used for separating form factors [13,14].…”

Section: Wavefunction Representation Of Dis and Dvcsmentioning

confidence: 99%

Deep Inelastic Scattering at the Amplitude Level

Brodsky¹

2005

AIP Conference Proceedings

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Abstract. The deep inelastic lepton scattering and deeply virtual Compton scattering cross sections can be interpreted in terms of the fundamental wavefunctions defined by the light-front Fock expansion, thus allowing tests of QCD at the amplitude level. The AdS/CFT correspondence between gauge theory and string theory provides remarkable new insights into QCD, including a model for hadronic wavefunctions which display conformal scaling at short distances and color confinement at large distances.Keywords: Quantum Chromodynamics, Deep Inelastic Scattering, Gauge/String Duality PACS: 12.38.Aw,13.60.Hb,11.25.Tq WAVEFUNCTION REPRESENTATION OF DIS AND DVCSThe primary goal of deep inelastic lepton scattering is to resolve the fundamental structure of the nucleon. In fact, by combining measurements of DIS with measurements of deeply virtual Compton scattering, elastic lepton-hadron scattering, and other hard exclusive channels, it is possible to obtain information on the fundamental form of quark and gluon bound-state wavefunctions. Thus, for the first time, we have the potential to test QCD at the amplitude level.If one quantizes QCD at fixed light-front time x + = x 0 + x 3 , the bound state hadronic solutions | Ψ H are eigenstates of the light-front Heisenberg equation. The spectrum of QCD is given by the eigenvalues M 2 H . The projection of each hadronic eigensolution on the free Fock basis: n | Ψ H ≡ ψ n/H (x i , k ⊥i , λ i ) defines the LF Fock expansion in terms of the quark and transversely polarized gluon constituents in A + = 0 light-cone gauge. The light-front wavefunctions are frameindependent functions of the constituent light-cone fractions x i , relative transverse momenta k ⊥i , and spin projections S z i = λ i . Observables in DIS and DVCS can be calculated directly from the hadron LFWFs. For example, the quark and gluon distributions measured in DIS are defined from the squares of the LFWFS summed over all Fock states n. Form factors, exclusive weak transition amplitudes [2] and the generalized parton distributions [3] measured in DVCS are overlaps of the initial and final LFWFS with n = n and n = n + 2. The resulting distributions obey DGLAP, BFKL, and ERBL evolution as a function of the maximal invariant mass, thus providing a physical factorization scheme [4]. It is important to note that at large x where the struck quark is far-off shell, DGLAP evolution is quenched [5], so that the fall-off of the DIS cross sections in Q 2 satisfies inclusive-exclusive duality at fixed W 2 . The gauge-invariant distribution amplitude φ H (x i , Q) defined from the integral over the transverse momenta k 2 ⊥i ≤ Q 2 of the valence (smallest n) Fock state provides a fundamental measure of the hadron at the amplitude level [6,7]; they are the nonperturbative input to the factorized form of hard

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“…In structure functions such a singular piece is generated at Bjorken x = 0. In QCD on the light cone [19,20] the negative energy states obey a constraint equation which allows a constant x − independent solution. Therefore we assume that the fermion negative energy states develop an expectation value < ψ † − ψ − > c 0 .…”

Section: Introductionmentioning

confidence: 99%

Critical correlations of Wilson lines in SU(3) and the high energyγ*pcross section

Pirner

Yuan

2002

Phys. Rev. D

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We discuss deep inelastic scattering at high energies as a critical phenomenon in 2 + 1 space -time dimensions. In the limit of Bjorken x → 0, QCD SU (3) with quark fields becomes a critical theory with a diverging correlation length ξ(x) ∝ x − 1 2λ 2 where the exponent λ 2 = 2.52 is obtained from the center group Z(3) of SU (3). We conjecture that the dipole wave function of the virtual photon for transverse sizes 1/Q < x ⊥ < ξ obeys correlation scaling Ψ ∝ (x ⊥ ) −(1+n) before exponentially decaying for distances larger than the correlation length. Using this behavior combined with different x -independent dipole proton cross sections we calculate the proton structure function and compare with the experimental data. We take the good agreement with the measured proton structure function F 2 (x, Q 2 ) as an indication that at high energies dimensional reduction to an effective three dimensional theory with a critical point occurs. *

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The System 2.4.6-Trinitrotoluene–2.4.6-Trinitro-m-xylene.

Cited by 71 publications

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Virtual Compton scattering in the generalized Bjorken region and positivity bounds on generalized parton distributions

Virtual Compton scattering in the generalized Bjorken region and positivity bounds on generalized parton distributions

Deep Inelastic Scattering at the Amplitude Level

Critical correlations of Wilson lines in SU(3) and the high energyγ*pcross section

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