Tau Kinematics from Impact Parameters

The momenta of $\tau$ decay products in the reaction $e^+e^-\to\tau^+\tau^-$ do not constrain the $\tau$ direction unambiguously. It is shown how the measurement of tracks of hadrons from semileptonic $\tau$ decays, in particular their relative impact parameters, allows to resolve this ambiguity.Comment: 4[pag]es, 1 figure available by FAX, TTP93-1

The Drell-Hearn Sum Rule at Order Alpha**3

The Drell-Hearn-Gerasimov-Iddings (DHGI) sum rule for electrons is evaluated at order $\alpha^3$ and shown to agree with the Schwinger contribution to the anomalous magnetic moment.Comment: 3 pages, 1 figur

Small xx Contributions to the Structure Function FL(x,Q2)F_L(x,Q^2)

The gluon contributions to $F_L(x,Q^2)$ in ${\cal O}(\alpha_s)$ are calculated taking into account the transverse momentum of the initial state parton. In comparison with collinear factorization $F_L(x,Q^2)$, is not affected at large $x$ but takes smaller values in the small $x$ range. The onset of the $k_{\perp}$ effect is a function of $Q^2$.Comment: 4 p., postscript encoded with uufiles; DESY 94--14

Structure Functions are not Parton Probabilities

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.Comment: Talk at ICHEP 2002, Amsterdam (July 2002). 3 pages, 1 figur

Fixed Point Actions for Lattice Fermions

The fixed point actions for Wilson and staggered lattice fermions are determined by iterating renormalization group transformations. In both cases a line of fixed points is found. Some points have very local fixed point actions. They can be used to construct perfect lattice actions for asymptotically free fermionic theories like QCD or the Gross-Neveu model. The local fixed point actions for Wilson fermions break chiral symmetry, while in the staggered case the remnant $U(1)_e \otimes U(1)_o$ symmetry is preserved. In addition, for Wilson fermions a nonlocal fixed point is found that corresponds to free chiral fermions. The vicinity of this fixed point is studied in the Gross-Neveu model using perturbation theory.Comment: 6 pages, figures 1 and 4 included, figures 2,3,5,6,7 can be obtained from [email protected]

The Parton Model and its Applications

This is a review of the program we started in 1968 to understand and generalize Bjorken scaling and Feynman's parton model in a canonical quantum field theory. It is shown that the parton model proposed for deep inelastic electron scatterings can be derived if a transverse momentum cutoff is imposed on all particles in the theory so that the impulse approximation holds. The deep inelastic electron-positron annihilation into a nucleon plus anything else is related by the crossing symmetry of quantum field theory to the deep inelastic electron-nucleon scattering. We have investigated the implication of crossing symmetry and found that the structure functions satisfy a scaling behavior analogous to the Bjorken limit for deep inelastic electron scattering. We then find that massive lepton pair production in collisions of two high energy hadrons can be treated by the parton model with an interesting scaling behavior for the differential cross sections. This turns out to be the first example of a class of hard processes involving two initial hadrons.Comment: Contribution to a book to be published by World Scientific for the occasion of 50 Years of Quarks. 17 pages, 4 figure

How Do Fermions Behave on a Random Lattice?

Comparing random lattice, naive and Wilson fermions in two dimensional abelian background gauge field, we show that the doublers suppressed in the free field case are revived for random lattices in the continuum limit unless gauge interactions are implemented in a non--invariant way.Comment: updated contribution to LAT92 conference; UM-P-92/90 and OZ-92/33; 4 pages; shar archive LaTex document with figures included, requires espcrc2.sty fil

Chiral symmetry on a lattice with hopping interactions

The species doubling problem of the lattice fermion is resolved by introducing hopping interactions that mix left- and right-handed fermions around the momentum boundary. Approximate chiral symmetry is realized on the lattice. The deviation of the fermion propagator from the continuum one is small.Comment: 3 pages, 2 figures, talk presented at Lattice2003 (chiral fermions