737 research outputs found
Integrand reduction of one-loop scattering amplitudes through Laurent series expansion
We present a semi-analytic method for the integrand reduction of one-loop
amplitudes, based on the systematic application of the Laurent expansions to
the integrand-decomposition. In the asymptotic limit, the coefficients of the
master integrals are the solutions of a diagonal system of equations, properly
corrected by counterterms whose parametric form is konwn a priori. The Laurent
expansion of the integrand is implemented through polynomial division. The
extension of the integrand-reduction to the case of numerators with rank larger
than the number of propagators is discussed as well.Comment: v2: Published version: references and two appendices added. v3:
Eq.(6.11) corrected, Appendix B updated accordingl
Single Cut Integration
We present an analytic technique for evaluating single cuts for one-loop
integrands, where exactly one propagator is taken to be on shell. Our method
extends the double-cut integration formalism of one-loop amplitudes to the
single-cut case. We argue that single cuts give meaningful information about
amplitudes when taken at the integrand level. We discuss applications to the
computation of tadpole coefficients.Comment: v2: corrected typo in abstrac
Temperature inversion symmetry in the Casimir effect with an antiperiodic boundary condition
We present explicitly another example of a temperature inversion symmetry in
the Casimir effect for a nonsymmetric boundary condition. We also give an
interpretation for our result.Comment: 4 page
Avaliação preliminar, por zona de inibição, da atividade antimicrobiana de quitosanas hidrossolúveis.
Spinor formalism for massive fields with half-integral spin
In this article, we extend the %Weyl-van der Waerden spinor technique for
calculating helicity amplitudes to general massive fields of half-integer
spins. We find that the little group generators can be represented as
first-order differential operators in the spinor formalism. We use the spinor
forms of the generators to get the explicit form of the massive fields of any
spin and any helicity. We also deal with the three-particle S-matrix by these
spinor form generators, and find that we are able to extend the explicit form
of the three-particle vertex obtained by Benincasa and Cachazo to the massive
case. We present the explicit expressions for the amplitudes with external
particles of the lowest helicities up to -3/2. Group theory, in the form of
raising operators of the little group, then dictates other amplitudes with
higher helicity in the same spin multiplets. The formalism allows, in
principle, to determine the electromagnetic form-factors of charged particles
of arbitrary helicities, without additional assumptions about the underlying
lagrangian. We find that restrictions which follow from gauge and Lorentz
invariance are nearly as restrictive as in the massless case.Comment: 21 pages, 1 figure
Optimizing the Reduction of One-Loop Amplitudes
We present an optimization of the reduction algorithm of one-loop amplitudes
in terms of master integrals. It is based on the exploitation of the polynomial
structure of the integrand when evaluated at values of the loop-momentum
fulfilling multiple cut-conditions, as emerged in the OPP-method. The
reconstruction of the polynomials, needed for the complete reduction, is rended
very versatile by using a projection-technique based on the Discrete Fourier
Transform. The novel implementation is applied in the context of the NLO QCD
corrections to u d-bar --> W+ W- W+
Hepta-Cuts of Two-Loop Scattering Amplitudes
We present a method for the computation of hepta-cuts of two loop scattering
amplitudes. Four dimensional unitarity cuts are used to factorise the integrand
onto the product of six tree-level amplitudes evaluated at complex momentum
values. Using Gram matrix constraints we derive a general parameterisation of
the integrand which can be computed using polynomial fitting techniques. The
resulting expression is further reduced to master integrals using conventional
integration by parts methods. We consider both planar and non-planar topologies
for 2 to 2 scattering processes and apply the method to compute hepta-cut
contributions to gluon-gluon scattering in Yang-Mills theory with adjoint
fermions and scalars.Comment: 37 pages, 6 figures. version 2 : minor updates, published versio
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