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.

A possible way to relate the covariantization and the negative dimensional integration method in the light-cone gauge

Here we present a possible way to relate the method of covariantizing the gauge-dependent pole and the negative dimensional integration method for computing Feynman integrals pertinent to the light-cone gauge fields. Both techniques are applicable to the algebraic light-cone gauge and dispense with prescriptions to treat the characteristic poles.

Negative-dimensional integration revisited

Feynman diagrams are the best tool we have to study perturbative quantum field theory. For this very reason the development of any new technique that allows us to compute Feynman integrals is welcome. By the middle of the 1980s, Halliday and Ricotta suggested the possibility of using negative-dimensional integrals to tackle the problem. The aim of this work is to revisit the technique as such and check on its possibilities. For this purpose, we take a box diagram integral contributing to the photon-photon scattering amplitude in quantum electrodynamics using the negative-dimensional integration method. Our approach enables us to quickly reproduce the known results as well as six other solutions as yet unknown in the literature. These six new solutions arise quite naturally in the context of negative-dimensional integration method, revealing a promising technique to handle Feynman integrals.

Notes on the overall coefficient of the two-loop superstring amplitude using pure spinor

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Do tadpoles vanish in the light-front?

In covariant gauges (CG) regularized with dimensional regularization (DR) it is a standard procedure to set all tadpole Feynman integrals to zero, though; explicitly, they diverge quadratically as the space-time volume. on the other hand, in the notoriously subtle light-front gauge (LTG) some divergent tadpole integrals are said to be nonvanishing, i.e., cannot be set to zero as in the CC case. In this article we analyse the reasons behind this seemingly ambiguous results.

J/Psi mass shift in nuclear matter

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Extension of the Nambu-Jona-Lasinio model predictions at high densities and temperatures using an implicit regularization scheme

Traditional cutoff regularization schemes of the Nambu-Jona-Lasinio model limit the applicability of the model to energy-momentum scales much below the value of the regularizing cutoff. In particular, the model cannot be used to study quark matter with Fermi momenta larger than the cutoff. In the present work, an extension of the model to high temperatures and densities recently proposed by Casalbuoni, Gatto, Nardulli, and Ruggieri is used in connection with an implicit regularization scheme. This is done by making use of scaling relations of the divergent one-loop integrals that relate these integrals at different energy-momentum scales. Fixing the pion decay constant at the chiral symmetry breaking scale in the vacuum, the scaling relations predict a running coupling constant that decreases as the regularization scale increases, implementing in a schematic way the property of asymptotic freedom of quantum chromodynamics. If the regularization scale is allowed to increase with density and temperature, the coupling will decrease with density and temperature, extending in this way the applicability of the model to high densities and temperatures. These results are obtained without specifying an explicit regularization. As an illustration of the formalism, numerical results are obtained for the finite density and finite temperature quark condensate and applied to the problem of color superconductivity at high quark densities and finite temperature.

Predictive formulation of the Nambu-Jona-Lasinio model

A novel strategy to handle divergences typical of perturbative calculations is implemented for the Nambu-Jona-Lasinio model and its phenomenological consequences investigated. The central idea of the method is to avoid the critical step involved in the regularization process, namely, the explicit evaluation of divergent integrals. This goal is achieved by assuming a regularization distribution in an implicit way and making use, in intermediary steps, only of very general properties of such regularization. The finite parts are separated from the divergent ones and integrated free from effects of the regularization. The divergent parts are organized in terms of standard objects, which are independent of the ( arbitrary) momenta running in internal lines of loop graphs. Through the analysis of symmetry relations, a set of properties for the divergent objects are identified, which we denominate consistency relations, reducing the number of divergent objects to only a few. The calculational strategy eliminates unphysical dependencies of the arbitrary choices for the routing of internal momenta, leading to ambiguity-free, and symmetry-preserving physical amplitudes. We show that the imposition of scale properties for the basic divergent objects leads to a critical condition for the constituent quark mass such that the remaining arbitrariness is removed. The model becomes predictive in the sense that its phenomenological consequences do not depend on possible choices made in intermediary steps. Numerical results are obtained for physical quantities at the one-loop level for the pion and sigma masses and pion-quark and sigma-quark coupling constants.

CAUSAL PRESCRIPTION FOR THE LIGHT-CONE GAUGE

We present a prescription for light-cone gauge singularities which embeds in it causality and show that it results in simpler and less demanding integrals to be performed.

A RIEMANN INTEGRAL APPROACH TO FEYNMANS PATH-INTEGRAL

It is a well known result that the Feynman's path integral (FPI) approach to quantum mechanics is equivalent to Schrodinger's equation when we use as integration measure the Wiener-Lebesgue measure. This results in little practical applicability due to the great algebraic complexibity involved, and the fact is that almost all applications of (FPI) - ''practical calculations'' - are done using a Riemann measure. In this paper we present an expansion to all orders in time of FPI in a quest for a representation of the latter solely in terms of differentiable trajetories and Riemann measure. We show that this expansion agrees with a similar expansion obtained from Schrodinger's equation only up to first order in a Riemann integral context, although by chance both expansions referred to above agree for the free. particle and harmonic oscillator cases. Our results permit, from the mathematical point of view, to estimate the many errors done in ''practical'' calculations of the FPI appearing in the literature and, from the physical point of view, our results supports the stochastic approach to the problem.

COMPLEX KOHN VARIATIONAL PRINCIPLE FOR 2-NUCLEON BOUND-STATE AND SCATTERING WITH THE TENSOR POTENTIAL

Complex Kohn variational principle is applied to the numerical solution of the fully off-shell Lippmann-Schwinger equation for nucleon-nucleon scattering for various partial waves including the coupled S-3(1), D-3(1), channel. Analytic expressions are obtained for all the integrals in the method for a suitable choice of expansion functions. Calculations with the partial waves S-1(0), P-1(1), D-1(2), and S-3(1)-D-3(1) of the Reid soft core potential show that the method converges faster than other solution schemes not only for the phase shift but also for the off-shell t matrix elements. We also show that it is trivial to modify this variational principle in order to make it suitable for bound-state calculation. The bound-state approach is illustrated for the S-3(1)-D-3(1) channel of the Reid soft-core potential for calculating the deuteron binding, wave function, and the D state asymptotic parameters. (c) 1995 Academic Press, Inc.

Green functions of the Dirac equation with magnetic-solenoid field

Various Green functions of the Dirac equation with a magnetic-solenoid field (the superposition of the Aharonov-Bohm field and a collinear uniform magnetic field) are constructed and studied. The problem is considered in 2+1 and 3+1 dimensions for the natural extension of the Dirac operator (the extension obtained from the solenoid regularization). Representations of the Green functions as proper time integrals are derived. The nonrelativistic limit is considered. For the sake of completeness the Green functions of the Klein-Gordon particles are constructed as well. (C) 2004 American Institute of Physics.

NONADIABATIC NEUTRINO OSCILLATIONS REEXAMINED

Employing the Feynman procedure of ordered exponential operators and the stationary phase method to evaluate the multiple integrals involved, we calculate the level-crossing probability and analyze the role of a resonance in the evolution of a two-level neutrino system. We compare this procedure with more conventional ones, such as Landau's method and the ansatz of Kuo and Pantaleone and Petcov. We verify that our results reproduce the correct extreme nonadiabatic limit and give the standard solutions in the adiabatic regime for any arbitrary matter density distributions. We discuss in particular the case of solar neutrino propagation using the standard solar model predictions for the matter distribution in the Sun.

Causal propagators for algebraic gauges

Applying the principle of analytic extension for generalized functions we derive causal propagators for algebraic non-covariant gauges. The so-generated manifestly causal gluon propagator in the light-cone gauge is used to evaluate two one-loop Feynman integrals which appear in the computation of the three-gluon vertex correction. The result is in agreement with that obtained through the usual prescriptions.

Some superstring amplitude computations with the non-minimal pure spinor formalism

We use the non-minimal pure spinor formalism to compute in a super-Poincare covariant manner the four-point massless one and two-loop open superstring amplitudes, and the gauge anomaly of the six-point one-loop amplitude. All of these amplitudes are expressed as integrals of ten-dimensional superfields in a pure spinor superspace which involves five theta coordinates covariantly contracted with three pure spinors. The bosonic contribution to these amplitudes agrees with the standard results, and we demonstrate identities which show how the t(8) and epsilon(10) tensors naturally emerge from integrals over pure spinor superspace.