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Register a new userMultiloop calculations with Implicit Regularization in massless theories
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Antonio Paulo Baeta Scarpelli
Publication date
2009
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and research's language is
English
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We establish a systematic way to calculate multiloop amplitudes of infrared safe massless models with Implicit Regularization (IR), with a direct cancelation of the fictitious mass introduced by the procedure. The ultraviolet content of such amplitudes have a simple structure and its separation permits the identification of all the potential symmetry violating terms, the surface terms. Moreover, we develop a technique for the calculation of an important kind of finite multiloop integral which seems particularly convenient to use Feynman parametrization. Finally, we discuss the Implicit Regularization of infrared divergent amplitudes, showing with an example how it can be dealt with an analogous procedure in the coordinate space.
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We extend a constrained version of Implicit Regularization (CIR) beyond one loop order for gauge field theories. In this framework, the ultraviolet content of the model is displayed in terms of momentum loop integrals order by order in perturbation theory for any Feynman diagram, while the Ward-Slavnov-Taylor identities are controlled by finite surface terms. To illustrate, we apply CIR to massless abelian Gauge Field Theories (scalar and spinorial QED) to two loop order and calculate the two-loop beta-function of the spinorial QED.
The program FIESTA has been completely rewritten. Now it can be used not only as a tool to evaluate Feynman integrals numerically, but also to expand Feynman integrals automatically in limits of momenta and masses with the use of sector decompositions and Mellin-Barnes representations. Other important improvements to the code are complete parallelization (even to multiple computers), high-precision arithmetics (allowing to calculate integrals which were undoable before), new integrators and Speer sectors as a strategy, the possibility to evaluate more general parametric integrals.
Implicit Regularization is a 4-dimensional regularization initially conceived to treat ultraviolet divergences. It has been successfully tested in several instances in the literature, more specifically in those where Dimensional Regularization does not apply. In the present contribution we extend the method to handle infrared divergences as well. We show that the essential steps which rendered Implicit Regularization adequate in the case of ultraviolet divergences have their counterpart for infrared ones. Moreover we show that a new scale appears, typically an infrared scale which is completely independent of the ultraviolet one. Examples are given.
We give the exact solution of classical equation of motion of a quartic scalar massless field theory showing that this is massive and is represented by a superposition of free particle solutions with a discrete spectrum. Then we show that this is also a solution of the classical Yang-Mills field theory that is so proved acquiring mass by dynamical evolution with a corresponding discrete mass spectrum. Finally we develop quantum field theory starting with this solution.
We use the numerical S-matrix bootstrap method to obtain bounds on the two leading Wilson coefficients of the chiral lagrangian controlling the low-energy dynamics of massless pions thus providing a proof of concept that the numerical S-matrix bootstrap can be used to derive non-perturbative bounds on EFTs in more than two spacetime dimensions.
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