119327590
Semi-exclusive DVCS
We consider Semi-Exclusive Deeply Virtual Compton Scattering, gamma* p \to gamma Y (SECS), where Y is an inclusive state of intermediate mass, \Lambda_QCD<<m_Y<<Q. When the photon is produced with a large transverse momentum k_T \sim m_Y the subprocess is hard and the struck quark fragments independently of the target spectators. Using completeness this allows to express the SECS cross section in terms of ordinary parton distributions. Apart from direct comparisons with data (yet to come) new information on Bloom-Gilman duality may be obtained through comparisons of resonance production via DVCS (gamma* p \to gamma N*) with the SECS scaling distribution in m_Y.
118260296
Introduction to QCD - A Bound State Perspective
These lecture notes focus on the bound state sector of QCD. Motivated by data which suggests that the strong coupling \alpha_s(Q) freezes at low Q, and by similarities between the spectra of hadrons and atoms, I discuss if and how QCD bound states may be treated perturbatively. I recall the basic principles of perturbative gauge theory bound states at lowest order in the \hbar expansion. Born level amplitudes are insensitive to the i\epsilon prescription of propagators, which allows to eliminate the Z-diagrams of relativistic, time-ordered Coulomb interactions. The Dirac wave function thus describes a single electron which propagates forward in time only, even though the bound state has any number of pair constituents when Feynman propagators are used. In the absence of an external potential, states that are bound by the Coulomb attraction of their constituents can be analogously described using only their valence degrees of freedom. The instantaneous A^0 field is determined by Gauss' law for each wave function component, i.e., for each position of the valence constituents. Solutions for A^0 obtained with a boundary condition that imposes an asymptotically constant energy density give rise to a linear potential for color singlet q\bar q and qqq states. The strength of the linear potential is determined by the boundary condition and is of lower order in \alpha_s than the gluon exchange interaction, which may then be treated as a higher order perturbative correction. Bound states evaluated to a given order in \alpha_s and \hbar must have the full symmetry of the exact theory, including the dynamic boost invariance of states quantized at equal time. The wave functions are indeed found to have such a hidden invariance, which ensures the correct dependence of the energy eigenvalues on the center of mass momentum. Thus relativistic bound states can be studied using perturbative methods.
18528565
Factorization at fixed Q^2(1-x)
We consider QCD factorization between hard and soft subprocesses in inclusive reactions where the momentum fraction x of one parton approaches unity as the hard scale Q^2 -> \infty, such that Q^2(1-x) is fixed. In this ``BB limit'' the entire (multi-parton) Fock state containing the high x parton is coherent with the hard subprocess. The soft contribution is given by a forward multiparton matrix element. The BB limit corresponds to a fixed (large or small) missing mass and is thus closely connected to exclusive production. We analyze the Drell-Yan process h + N -> \gamma^* + X in detail, explaining why the virtual photon is longitudinally polarized for h = \pi and transversely polarized for h = p. The BB limit may be relevant also for other phenomena observed at high x, such as the large single spin asymmetries of p p -> \Lambda^\uparrow X and in p p^\uparrow -> \pi X.
117547375
Filling Perturbative Ground States
I discuss a degree of freedom in formulating perturbation theory that is often neglected: the in- and out-states need not be empty. The inclusion of (free) particles in the asymptotic states modifies the on-shell prescription of the free propagator. This affects loop contributions -- but the modified expansion is {\it a priori} as justified as the standard one with Feynman prescription. 
It is possible to dress the quark propagator to all orders with zero-momentum gluons from the perturbative ground state. The dressed quark has no pole and thus cannot appear as an external particle in the S-matrix. Chiral symmetry may be spontaneously broken, but Lorentz and gauge symmetry is exact. Adding loop corrections to this ``dressed tree approximation'' gives a formally exact PQCD expansion.
829521
The Unexpected Role of Final State Interactions in Deep Inelastic Scattering
Rescattering of the struck quark in Deep Inelastic Scattering implies that measured parton distributions are not directly related to the Fock state probabilities of the target wave function. The production amplitudes acquire dynamical phases, which gives rise to shadowing and diffraction in DIS. I review the kinematics and dynamics of DIS as seen in various frames and gauges.
119081579
Perturbative QCD with quark and gluon condensates
The quark 〈 ψ ¯ ψ 〉 and gluon ( F μν F μν ) vacuum expectation values are non-vanishing at low orders in α s when the perturbative ground state includes quark and gluon pairs. This offers possibilities of studying the effects of a non-trivial vacuum using formally exact perturbative methods. The QCD Feynman rules are modified only for the free, on-shell quark and gluon propagators at zero four-momentum. Gauge and lorentz invariance is maintained, while chiral symmetry is spontaneously broken by the ground state.
119846230
Fermion Bound States by the Method of Stationary Phase
The stationary phase method is applied to gauge theory path integrals, taking into account the fermion determinant. This approximation is shown to lead to a unique bound state equation in QED. In the nonrelativistic limit, the equation reduces to the usual Schrodinger form. In 1 + 1 dimensions it leads to "bag"-type wave functions and an energy spectrum which agrees with known exact results. An analytic expression is given for the wave function of states with two massless fermions connected by an unbroken string.
10635169
Nuclear dependence of structure functions in coordinate space
The momentum distributions of partons in bound nucleons are known to depend significantly on the size of the nucleus. The Fourier transform of the momentum (xBj) distribution measures the overlap between Fock components of the nucleon wave function which differ by a displacement of one parton along the light cone. The magnitude of the overlap thus determines the average range of mobility of the parton in the nucleon. By comparing the Fourier transforms of structure functions for several nuclei we study the dependence of quark mobility on nuclear size. We find a surprisingly small nuclear dependence (< 2% for He, C and Ca) for displacements t = z ≲ 2.5 fm, after which a nuclear suppression due to shadowing sets in. The nuclear effects observed in momentum space for xBj ≲ 0.4 can be understood as a reflection of only the large distance shadowing in coordinate space.
14901386
Rapidity gaps in perturbative QCD
We analyze diffractive deep inelastic scattering within perturbative QCD by studying lepton scattering on a heavy quark target. Simple explicit expressions are derived in impact parameter space for the photon wave function and the scattering cross sections corresponding to single and double Coulomb gluon exchange. At limited momentum transfers to the target, the results agree with the general features of the {open_quotes}aligned jet model.{close_quotes} The color-singlet exchange cross section receives a leading twist contribution only from the aligned jet region, where the transverse size of the photon wave function remains finite in the Bjorken scaling limit. In contrast with inclusive DIS, in diffractive events there is no leading twist contribution to {sigma}{sub L}/{sigma}{sub T} from the lowest order (q{bar q}) photon Fock state, and the cross section for heavy quarks is power suppressed in the quark mass. There are also important contributions with large momentum transfer to the target, which corresponds to events having high transverse momentum production in both the projectile and target rapidity regions, separated by a rapidity gap. {copyright} {ital 1997} {ital The American Physical Society}
121132431
Photon interaction with matter: Is there a threshold at multi-TeV energy?
Abstract Claims of new phenomena at multi-TeV energy, which cannot be accounted for by the sub-TeV particle physics based on accelerator experiments, come from (a) observations of muons from cosmic point sources (such as Cygnus X-3) and (b) anomalies in cosmic ray interactions with primary energies in excess of 100 TeV (such as Centauro events). In examining these claims we find a common pattern emerging from these seemingly unrelated phenomena pointing at a novel interaction mechanism of photons with matter. The features of this new threshold possibly observed with cosmic photon beams of O(10 TeV), are reflected in the behavior of secondary photons from π 0 decays in hadronic collisions of O(100 TeV) primary energy. We try to define the precise issues implied by these observations so that they can be scrutinized by future accelerator or non-accelerator experiments.
120494867
Parton evolution as a branching process
Abstract The evolution of parton distributions in high-energy scattering is described using the methods of branching processes. Exclusive, inclusive and multiplicity distributions can be simply obtained from a functional form of the evolution equations. Previous results derived from leading logarithmic terms in perturbation theory are verified. As a new application, we calculate the multiplicity distribution of partons with momenta above a given cutoff.