Perturbative QCD with Quark and Gluon Condensates

QCD perturbation theory using quark and gluon propagators that have an extra term at zero four-momentum is equivalent to standard PQCD in the presence of massless quark and gluon pairs in the perturbative vacuum. We verify at low orders in perturbation theory that $\neq 0$ and that quarks acquire a constituent mass. Thus chiral symmetry is spontaneously broken, and the conservation of the axial vector current ensures a massless pion. The gluon pairs generate an $$ expectation value and a tachyonic gluon mass. Lorentz and gauge symmetry is preserved, and the short-distance structure of PQCD is unaffected. The modified perturbative expansion thus contains relevant elements of QCD at both short and long distances.Comment: 12 pages, 2 figure

Efficient Quantum Transforms

Quantum mechanics requires the operation of quantum computers to be unitary, and thus makes it important to have general techniques for developing fast quantum algorithms for computing unitary transforms. A quantum routine for computing a generalized Kronecker product is given. Applications include re-development of the networks for computing the Walsh-Hadamard and the quantum Fourier transform. New networks for two wavelet transforms are given. Quantum computation of Fourier transforms for non-Abelian groups is defined. A slightly relaxed definition is shown to simplify the analysis and the networks that computes the transforms. Efficient networks for computing such transforms for a class of metacyclic groups are introduced. A novel network for computing a Fourier transform for a group used in quantum error-correction is also given.Comment: 30 pages, LaTeX2e, 7 figures include

Measuring transverse size with virtual photons

Fourier transforming the virtual photon transverse momentum in \gamma*(q)+N \to f processes allows new insight into hadron dynamics as a function of impact parameter b. I discuss how previous analyses of charge density based on elastic and transition form factors (f=N, N*) can be generalized to any multi-hadron final state (f=\pi N, \pi\pi N, \bar D \Lambda_c,...). The b-distribution determines the transverse positions of the quarks that the photon couples to, and can be studied as a function of multiplicity, the relative transverse momenta, quark masses and polarization. The method requires no factorization nor leading twist approximation. Data with spacelike photon virtualities in the range 0 1/Q_{max} in impact parameter.Comment: Talk at the Third International Workshop on Transverse Polarization Phenomena in Hard Scattering (Transversity 2011), in Veli Losinj, Croatia, 29 August - 2 September 2011. 7 page

Are hadrons simpler than they seem?

I briefly review a systematic approximation scheme of QCD in which the quark model picture of hadrons emerges at lowest order. A linear A^0 potential arises if Gauss' law is solved with a non-vanishing boundary condition at spatial infinity. Similarly to the Dirac case one can describe relativistic states including any number of particle pairs (sea quarks) using valence wave functions, whose norms give {\em inclusive} probability densities. Provided \alpha_s(Q^2) freezes in the infrared, perturbative corrections to the S-matrix can be calculated in the usual way, but with states bound by the linear \order{\alpha_s^0} potential instead of plane waves in the in and out states.Comment: 4 pages. Talk presented at the 3rd Workshop on the QCD Structure of the Nucleon (QCD-N'12), 22-26 October 2012 in Bilbao, Spai

Duality in Semi-Exclusive Processes

Bloom-Gilman duality relates parton distributions to nucleon form factors and thus constrains the dynamics of exclusive processes. The quark electric charge dependence implies that exclusive scattering is incoherent on the quarks even at high momentum transfers. Data on semi-exclusive meson production exceeds the duality prediction by more than an order of magnitude and violates quark helicity conservation. This suggests that the subprocess is dominated by soft `endpoint' contributions which obey dimensional scaling. The large transverse size of the subprocess may explain the absence of color transparency in fixed angle processes.Comment: Talk at the ``Workshop on Exclusive Processes at High Momentum Transfer'' at Jefferson Laboratory, Newport News, USA (May 2002). 7 page

Summary Talk on Quark-Hadron Duality

I ascribe the origin of Bloom-Gilman duality in DIS to a separation of scales between the hard subprocess and soft resonance formation. The success of duality indicates that the subprocesses of exclusive form factors are the same as in DIS. The observed dominance of the longitudinal structure function at large x in \pi N \to \mu^+\mu^- X can explain why local duality works for DIS with a pion target. The failure of duality in semi-exclusive processes indicates that high momentum transfer t is not sufficient to make the corresponding subprocesses compact.Comment: 8 pages, 5 figures. Summary talk at the First Workshop on Quark-Hadron Duality and the Transition to pQCD, Frascati, 6-8 June 200