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]

Factorization of low-energy gluons in exclusive processes

We outline a proof of factorization in exclusive processes, taking into account the presence of soft and collinear modes of arbitrarily low energy, which arise when the external lines of the process are taken on shell. Specifically, we examine the process of e^+e^- annihilation through a virtual photon into two light mesons. In an intermediate step, we establish a factorized form that contains a soft function that is free of collinear divergences. In contrast, in soft-collinear effective theory, the low-energy collinear modes factor most straightforwardly into the soft function. We point out that the cancellation of the soft function, which relies on the color-singlet nature of the external hadrons, fails when the soft function contains low-energy collinear modes.Comment: 18 pages, 10 figures, 2 tables, version published in Physical Review

Universality of soft and collinear factors in hard-scattering factorization

Universality in QCD factorization of parton densities, fragmentation functions, and soft factors is endangered by the process dependence of the directions of Wilson lines in their definitions. We find a choice of directions that is consistent with factorization and that gives universality between e^+e^- annihilation, semi-inclusive deep-inelastic scattering, and the Drell-Yan process. Universality is only modified by a time-reversal transformation of the soft function and parton densities between Drell-Yan and the other processes, whose only effect is the known reversal of sign for T-odd parton densities like the Sivers function. The modifications of the definitions needed to remove rapidity divergences with light-like Wilson lines do not affect the results.Comment: 4 pages. Extra references. Text and references as in published versio

Factorization in exclusive quarkonium production

We present factorization theorems for two exclusive heavy-quarkonium production processes: production of two quarkonia in e^+e^- annihilation and production of a quarkonium and a light meson in B-meson decays. We describe the general proofs of factorization and supplement them with explicit one-loop analyses, which illustrate some of the features of the soft-gluon cancellations. We find that violations of factorization are generally suppressed relative to the factorized contributions by a factor v^2m_c/Q for each S-wave charmonium and a factor m_c/Q for each L-wave charmonium with L>0. Here, v is the velocity of the heavy quark or antiquark in the quarkonium rest frame, Q=sqrt{s} for e^+e^- annihilation, Q=m_B for B-meson decays, sqrt{s} is the e^+e^- center-of-momentum energy, m_c is the charm-quark mass, and m_B is the B-meson mass. There are modifications to the suppression factors if quantum-number restrictions apply for the specific process.Comment: 69 pages, 12 figures, 2 tables. v2: Version published in Physical Review

Inclusive double-quarkonium production at the Large Hadron Collider

Based on the nonrelativistic QCD (NRQCD) factorization formalism, we investigate inclusive productions of two spin-triplet S-wave quarkonia pp->2J/psi+X, 2Upsilon+X, and J/psi+Upsilon+X at the CERN Large Hadron Collider. The total production rates integrated over the rapidity (y) and transverse-momentum (p_T) ranges |y|<2.4 and p_T<50 GGeV are predicted to be sigma[pp->2J/psi+X] = 22 (35) nb, sigma[pp->2Upsilon+X] = 24 (49) pb, and sigma[pp->J/psi+Upsilon+X] = 7 (13) pb at the center-of-momentum energy sqrt{s} = 7 (14) TeV. In order to provide predictions that can be useful in both small- and large-p_T regions, we do not employ the fragmentation approximation and we include the spin-triplet S-wave color-singlet and color-octet channels for each quarkonium final state at leading order in the strong coupling. The p_T distributions of pp->2J/psi+X and 2Upsilon+X in the low-p_T region are dominated by the color-singlet contributions. At leading order in the strong coupling, the color-singlet channel is absent for pp->J/psi+Upsilon+X. Therefore, the process pp->J/psi+Upsilon+X may provide a useful probe to the color-octet mechanism of NRQCD.Comment: 26 pages, 7 figures, 3 tables, version published in JHE

Factorization theorems for exclusive heavy-quarkonium production

We outline the proofs of the factorization theorems for exclusive two-body charmonium production in B-meson decay and e^+e^- annihilation to all orders in perturbation theory in quantum chromodynamics. We find that factorized expressions hold up to corrections of order m_c/m_b in B-meson decay and corrections of order m_c^2/s in e^+e^- annihilation, where m_c is the charm-quark mass, m_b is the bottom-quark mass, and root-s is the e^+e^- center-of-momentum energy.Comment: 4 pages, 2 figure

The Lattice Schwinger Model: Confinement, Anomalies, Chiral Fermions and All That

In order to better understand what to expect from numerical CORE computations for two-dimensional massless QED (the Schwinger model) we wish to obtain some analytic control over the approach to the continuum limit for various choices of fermion derivative. To this end we study the Hamiltonian formulation of the lattice Schwinger model (i.e., the theory defined on the spatial lattice with continuous time) in $A_0=0$ gauge. We begin with a discussion of the solution of the Hamilton equations of motion in the continuum, we then parallel the derivation of the continuum solution within the lattice framework for a range of fermion derivatives. The equations of motion for the Fourier transform of the lattice charge density operator show explicitly why it is a regulated version of this operator which corresponds to the point-split operator of the continuum theory and the sense in which the regulated lattice operator can be treated as a Bose field. The same formulas explicitly exhibit operators whose matrix elements measure the lack of approach to the continuum physics. We show that both chirality violating Wilson-type and chirality preserving SLAC-type derivatives correctly reproduce the continuum theory and show that there is a clear connection between the strong and weak coupling limits of a theory based upon a generalized SLAC-type derivative.Comment: 27 pages, 3 figures, revte

Factorization in hard diffraction

In this talk, I reviewed the role of factorization in diffraction hard scattering.Comment: Talk presented at the Ringberg Workshop on ``New Trends in HERA Physics 2001''. 10 pages, 6 postscript figures. Misprints correcte

Colour Screening, Quark Propagation in Nuclear Matter and the Broadening of the Momentum Distribution of Drell-Yan Pairs

We calculate the broadening of the transverse momentum distribution of a quark propagating through nuclear matter. Colour screening plays a fundamental role in that it cuts off quark-nucleon interactions with soft gluons. The mean transverse momentum of the quark acquired along its trajectory, observed via Drell-Yan pairs, is related to it the ratio of the total inelastic meson-nucleon cross section it to the meson mean squared radius. Parameter-free calculations agree with the data.Comment: LaTex file, 7 pages + 2 figs (not included, available by fax) Heidelberg , HD-TVP-93-

Double charmonium production at B-factories within light cone formalism

This paper is devoted to the study of the processes e^+e^- \to J/\Psi \eta_c, J/\Psi \eta_c', \psi' \eta_c, \psi' \eta_c' within light cone formalism. It is shown that if one disregards the contribution of higher fock states, the twist-3 distribution amplitudes needed in the calculation can be unambiguously determined from the twist-2 distribution amplitudes and equations of motion. Using models of the twist-2 distribution amplitudes the cross sections of the processes under study have been calculated. The results of the calculation are in agreement with Belle and BaBar experiments. It is also shown that relativistic and radiative corrections to the cross sections play crucial role in the achievement of the agreement between the theory and experiments. The comparison of the results of this paper with the results obtained in other papers has been carried out. In particular, it is shown that the results of papers where relativistic and radiative corrections were calculated within NRQCD are overestimated by a factor of ~1.5.Comment: 14 pages, 1 figur