Scattering amplitudes with massive fermions using BCFW recursion

We study the QCD scattering amplitudes for and where q is a massive fermion. Using a particular choice of massive fermion spinor we derive compact expressions for the partial spin amplitudes for the 2→2 process. We then investigate the corresponding 2→3 amplitudes using the BCFW recursion technique. For the helicity conserving partial amplitudes we present new expressions, but we were unable to treat the helicity-flip amplitudes recursively, except for the case where all the gluon helicities are the same. We therefore evaluate the remaining partial amplitudes using standard Feynman diagram techniques.     

On the computation of one-loop amplitudes with external fermions in 4D heterotic superstrings

We present the technical tools needed to compute any one-loop amplitude involving external spacetime fermions in a four-dimensional heterotic string model à la Kawai-Lewellen-Tye. As an example, we compute the one-loop three-point amplitude with one “photon” and two external massive fermions (“electrons”). As a check of our computation, we verify that the one-loop contribution to the Anomalous Magnetic Moment vanishes if the model has spacetime supersymmetry, as required by the supersymmetric sum rules.     

The singular behavior of one-loop massive QCD amplitudes with one external soft gluon

We calculate the one-loop correction to the soft-gluon current with massive fermions. This current is process independent and controls the singular behavior of one-loop massive QCD amplitudes in the limit when one external gluon becomes soft. The result derived in this work is the last missing process-independent ingredient needed for numerical evaluation of observables with massive fermions at hadron colliders at the next-to-next-to-leading order.     

Quark scattering amplitudes with quasi-elastic unitarity

We consider quark-quark scattering at high energies and fixed momentum transfer. In a model where in the s and u channel intermediate states only gluons with sufficiently small transverse momenta are emitted, the scattering amplitudes are expressed in terms of the S-matrix elements for exactly soluble two-dimensional field theories.     

Massless and massive one-loop three-point functions in negative dimensional approach

In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive, two massive with the same mass m and three equal masses for the virtual particles. Our results are given in terms of hypergeometric and hypergeometric-type functions of the external momenta (and masses for the massive cases) where the propagators in the Feynman integrals are raised to arbitrary exponents and the dimension of the space-time is D. Our approach reproduces the known results; it produces other solutions as yet unknown in the literature as well. These new solutions occur naturally in the context of NDIM revealing a promising technique to solve Feynman integrals in quantum field theories. Received: 14 April 2002 / Revised version: 18 July 2002 / Published online: 7 October 2002 RID="a" ID="a" e-mail: suzuki@ift.unesp.br RID="b" ID="b" e-mail: esdras@ift.unesp.br RID="c" ID="c" e-mail: schmidt@fisica.ufpr.br     

A class of scattering amplitudes which satisfy the unitarity condition

The unitarity condition is applied to the Regge representation of the scattering amplitude. This leads to a linear inhomogeneous algebraic equation for the residua of Regge poles and to a linear inhomogeneous integral equation (with Cauchy kernel) for the conical amplitude which can be solved exactly.     

Chiral Schwinger model with massive fermions

We study the chiral Schwinger model with massive fermions. By bosonizing it within the path integral framework, we find an equivalent bosonic lagrangian with an interaction term of the sine-Gordon type. The consistency of the theory is discussed.     

The holographic fermions dual to massive gravity

We investigate the properties of the spectral function of the fermionic operator in the field theory which is dual to a 4-dimensional massive gravity. We first study the Fermi surface and the dispersion relation in the dual boundary theory. We find that as the massive parameters is decreased, the Fermi momentum becomes lower and the low energy excitation near Fermi surface behaves more like non-Fermi liquid. Then, we introduce a dipole coupling in the bulk theory and explore the emergence of a gap in the fermionic spectral function. It is found that larger critical dipole coupling is needed to open the gap than that in Einstein gravity. Accordingly, in the field theory dual to massive gravity, it requires stronger negative dipole coupling to generate the marginal Fermi liquid.     

Two particle unitarity for helicity amplitudes with particles of arbitrary spin

The two particle unitarity contribution to the double spectral function of the scattering amplitude for any 2 → 2 process is explicitly calculated for the case of arbitrary spins of the initial, intermediate and final particles. A closed, simple result is obtained which is a generalization of the Mandelstam result for spinless particles. The results should be of value in calculations of the contribution of the exchange of pairs of high spin particles to the nucleon-nucleon force.     

Compact multigluonic scattering amplitudes with heavy scalars and fermions

Combining the Berends-Giele and on-shell recursion relations we obtain an extremely compact expression for the scattering amplitude of a complex massive scalar-antiscalar pair and an arbitrary number of positive helicity gluons. This is one of the basic building blocks for constructing other helicity configurations from recursion relations. We also show explicitly that the scattering amplitude of massive fermions to gluons, all with positive helicity, is proportional to the scalar one, confirming in this way the recently advocated SUSY-like Ward identities relating both amplitudes.     

Algebraic algorithm for the computation of one-loop Feynman diagrams in lattice QCD with Wilson fermions

We describe an algebraic algorithm which allows us to express every one-loop lattice integral with gluon or Wilson-fermion propagators in terms of a small number of basic constants which can be computed with arbitrary high precision. Although the presentation is restricted to four dimensions the technique can be generalized to every space dimension. Various examples are given, including the one-loop self-energies of the quarks and gluons and the renormalization constants for some dimension-three and dimension-four lattice operators. We also give a method to express the lattice free propagator for Wilson fermions in coordinate space as a linear function of its values in eight points near the origin. This is an essential step in order to apply the recent methods of Lüscher and Weisz to higher-loop integrals with fermions.     

Application of the unitarity conditions to calculating interaction amplitudes for Ramond states in superstring theory

The unitarity conditions for superstring amplitudes of boson interaction are used to calculate the Green's function for Ramond states—that is, for 10-spinor states and Ramond bosons. It is shown that, from the unitarity conditions, it follows, among other things, that local quantities specifying the sought amplitudes satisfy some integral relations. The amplitude for the transition of two massless Neveu-Schwarz bosons into a system of two massless Ramond states is obtained in an arbitrary order in the number of loops. For this amplitude, the aforementioned integral relations are verified in the tree approximation.