16490878
The Quark Model via an hbar expansion of QCD
I discuss the possibility that the quark model emerges as the lowest order of an h expansion of QCD bound states. In a hamiltonian approach the instantaneous A0 potential is determined by the field equations separately for each Fock component. These equations allow also a linear potential as a homogeneous solution. Stationarity of the action sets the direction of the ensuing constant electric field to be along the fermion pair separation. States bound by this non-perturbative, linear A0 potential are analogous to the Born term of standard perturbative expansions of scattering amplitudes, in that they represent the dominant contribution at lowest order in h (no loops) and at O (g) in the potential. The Dirac equation for relativistic fermions bound by an external A0 potential is most easily derived using retarded boundary conditions. I demonstrate why this boundary condition does not affect the bound state energies at lowest order in h. Translated to physical Feynman boundary conditions the Dirac bound states are a superposition of Fock states with any number of fermionantifermion pairs. Applying this approach to relativistic quark-antiquark states in QCD results in a bound state equation which was previously proposed without derivation and shown to provide a reasonable description of the meson spectrum, including linear Regge trajectories. The equal-time wave functions have unique Lorentz transformation properties, which ensure the correct dependence of the bound state energy on the center-of-mass momentum. This indicates that the solution is exact at the Born level, i.e., at lowest order in h and at O (g) in the QCD interaction.
120890782
Mesons and baryons from QCD
Abstract We study a gauge covariant method for quark bound states in 3 + 1 dimensions, based on a stationary phase approximation of the gluon path integral. Assuming thet lim | x |→∞ F μν a ( x ) F a μν ( x ) ≠ 0 we find meson (q q ) and baryon (qqq) states bound by a Coulomb + linear potential. The quark wave function is confined, as in the bag model. The high-spin states lie on asymptotically linear Regge trajectories of universal slope.
120877951
Sister trajectories in the dual resonance model
Abstract The existence of a Regge tranjectory γ = α /3 − 1 in the eight-point amplitude of the Dual Resonance Model set of demonstrated. It is suggested that the three presently known trajectories α, β and γ are part of an infinite set of “sister” trajectories, the expected properties of which are discussed.
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.
121596214
Test of duality in baryon--antibaryon amplitudes from Reggeon--particle scattering
Abstract By studying the backward production data for meson resonances we investigate the dual properties of baryon-Reggeised antibaryon elastic scattering. We find strong support for the duality prediction that meson resonances in the baryon antibaryon channel should be dual to an exotic trajectory.
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.
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.
119448188
Structure functions are not Parton probabilities
Abstract Parton distributions given by deep inelastic lepton scattering (DIS) are not equal to the probabilities of finding those partons in the parent wave function. Soft rescattering of the struck parton within the coherence length of the hard process influences the DIS cross section and gives dynamical phases to the scattering amplitudes. This gives rise to diffractive DIS, shadowing in nuclear targets and transverse spin asymmetry.
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.
119307830
Bound states at lowest order in hbar
Bound states poles in scattering amplitudes are generated by the divergence of the perturbative series due to enhanced Coulomb scattering near thresholds. This suggests to organize bound state calculations according to an expansion in hbar, i.e., in the number of loops. I study QED and QCD bound states at lowest order in hbar, which are analogous to Born amplitudes. The absence of loops allows the use of retarded boundary conditions where particles only propagate forward in time, making a hamiltonian approach feasible. The instantaneous A^0 field is determined by the equations of motion separately for each Fock component of the bound state. The field equations are compatible with a linear A^0 potential as a homogeneous, non-perturbative solution. Stationarity of the action determines the direction of the ensuing constant electric field in each Fock state. Applying this approach to relativistic qqbar and qqq states in QCD results in a bound state equation which provides a reasonable description of the spectrum, including linear Regge trajectories. The equal-time wave functions have unique Lorentz transformation properties, which ensure the correct dependence of the bound state energy on the center-of-mass momentum. The qqq potential is gauge covariant and confines the three quarks in a symmetric way.
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.