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.
7794876
QCD Green functions in a gluon field
We formulate a dressed perturbative expansion of QCD, where the standard diagrams are evaluated in the presence of a constant external gluon field whose magnitude is gaussian distributed. The approach is Poincare and gauge invariant, and modifies the usual results for hard processes only by power suppressed contributions. Long distance propagation of quarks and gluons turns out to be inhibited due to a branch point singularity instead of a pole at p 2 = 0 in the quark and gluon propagators. The dressing keeps the (massless) quarks in q fluctuations of the photon at a finite distance from each other.
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.
412880
Duality in Semi-Exclusive Processes
Semi-exclusive processes like \gamma p \to \pi^+ Y are closely analogous to DIS, ep \to eX, in the limit where the momentum transfer |t| to the pion and the mass of the inclusive system Y are large but still much smaller than the total CM energy. We apply Bloom-Gilman duality to this semi-exclusive process. The energy dependence of the \gamma p \to \pi^+ n cross section given by semi-local duality agrees with data for moderate values of |t|, but its normalization is underestimated by about two orders of magnitude. This indicates that rather high momentum transfers are required for the validity of PQCD in the hard subprocess \gamma u \to \pi^+ d. In the case of Compton scattering \gamma p \to \gamma p the analogous discrepancy is about one order of magnitude. In electroproduction the virtuality of the incoming photon can be used to directly measure the hardness of the subprocess.
15070652
The static PQCD potential with modified boundary conditions
We calculate the potential between two static quarks in QCD using modified boundary conditions for the perturbative expansion. Through a change of the Feynman ie-prescription we effectively add a ``sea'' of gluons to the asymptotic states with energies below a given scale Λ. We find that the standard result for the static potential gets corrections of order Λ2/Q2 both at small and large momentum transfers Q2. After resummation of the infrared sensitive corrections we find that the running coupling αs(Q2) freezes in the infrared and that the exchanged gluon gets an effective tachyonic mass. We verify that identical results are obtained in the Coulomb and Feynman gauges.
121421461
Perturbative QED; The Schrodinger picture
A derivation of ordinary QED perturbation theory is given in the Schrodinger picture. The path integral is restricted to fields in a finite time interval, ti ≤ t ≤ tf, with explicit boundary conditions given by vacuum state functionals at the initial and final times. The free photon vacuum functional is uniquely specified by the requirement of stationarity in time. For the free electron vacuum further conditions need to be imposed, e.g., the occupation of all negative energy states. The calculations are carried out using a discretized time interval of finite spacing dt, and exact results (to all orders in dt) are obtained for the free generating functionals in Coulomb gauge. Hence Feynman diagrams may be evaluated before the limits of continuous and infinite time are taken, with 1/dt and 1/(tf − ti) providing, respectively, an ultraviolet and an infrared cut-off on the energy integrals. The method may also be used for studying the time evolution of interacting states, in particular of bound states.
119362358
Charmonium Production at ELFE Energies
I discuss issues related to charmonium production, in view of physics possibilities at a 15 ... 30 GeV continuous beam electron facility. High energy photo- and hadroproduction of heavy quarkonia presents several challenges to QCD models concerning cross sections, polarization and nuclear target dependence. Theoretical approaches based on color evaporation as well as on color singlet and color octet mechanisms have met with both successes and failures, indicating that charmonium production is a sensitive probe of color dynamics. Experiments close to charm kinematic threshold will be sensitive also to target substructure since only unusual, compact target configurations contribute. In particular, subthreshold production on nuclei should identify nuclear hot spots of high energy density. At low energies, charmonium will form inside the target nucleus, allowing a determination of c cbar bound state interactions in nuclear matter.
14560984
Monte Carlo sensitivity in jet studies - what is the physics
Tests of perturbative QCD in hard processes involving jets have been found to depend on the jet fragmentation model used. We emphasize the need for testing the factorization of hard and soft processes, i.e., the independent fragmentation of jets. A method of analysis is suggested, which allows a model-independent determination of the gluon fragmentation function from e/sup +/e/sup -/ data. We also comment on some simple features expected in anti pp ..-->.. (2 or 3 jets) + X events. 19 references.
17059488
Subprocess size in hard exclusive scattering
The interaction region of hard exclusive hadron scattering can have a large transverse size due to endpoint contributions, where one parton carries most of the hadron momentum. The endpoint region is enhanced and can dominate in processes involving multiple scattering and quark helicity flip. The endpoint Fock states have perturbatively short lifetimes and scatter softly in the target. We give plausible arguments that endpoint contributions can explain the apparent absence of color transparency in fixed angle exclusive scattering and the dimensional scaling of transverse ρ photoproduction at high momentum transfer, which requires quark helicity flip. We also present a quantitative estimate of Sudakov effects.