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Register a new userA novel approach to the computation of one-loop three- and four-point functions. II - The complex mass case
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J. Ph. Guillet
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This article is the second of a series of three presenting an alternative method to compute the one-loop scalar integrals. It extends the results of the first article to general complex masses. Let us remind the main features enjoyed by this method. It directly proceeds in terms of the quantities driving algebraic reduction methods. It applies to the four-point functions in the same way as to the three-point functions. Lastly, it extends to kinematics more general than the one of physical e.g. collider processes relevant at one loop.
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This article is the first of a series of three presenting an alternative method to compute the one-loop scalar integrals. This novel method enjoys a couple of interesting features as compared with the method closely following t Hooft and Veltman adopted previously. It directly proceeds in terms of the quantities driving algebraic reduction methods. It applies to the three-point functions and, in a similar way, to the four-point functions. It also extends to complex masses without much complication. Lastly, it extends to kinematics more general than the one of physical e.g. collider processes relevant at one loop. This last feature may be useful when considering the application of this method beyond one loop using generalised one-loop integrals as building blocks.
This article is the third and last of a series presenting an alternative method to compute the one-loop scalar integrals. It extends the results of first two articles to the infrared divergent case. This novel method enjoys a couple of interesting features as compared with the methods found in the literature. It directly proceeds in terms of the quantities driving algebraic reduction methods. It yields a simple decision tree based on the vanishing of internal masses and one-pinched kinematic matrices which avoids a profusion of cases. Lastly, it extends to kinematics more general than the one of physical e.g. collider processes relevant at one loop. This last feature may be useful when considering the application of this method beyond one loop using generalised one-loop integrals as building blocks.
We compute the two-point functions for chiral matter states in toroidal intersecting D6-brane models. In particular, we provide the techniques to calculate Moebius strip diagrams including the worldsheet instanton contribution.
We present a new Fortran code to calculate the scalar one-loop four-point integral with complex internal masses, based on the method of t Hooft and Veltman. The code is applicable when the external momenta fulfill a certain physical condition. In particular it holds if one of the external momenta or a sum of them is timelike or lightlike and therefore covers all physical processes at colliders. All the special cases related to massless external particles are treated separately. Some technical issues related to numerical evaluation and Landau singularities are discussed.
It has been suggested a long time ago by W. Bardeen that non-vanishing of the one-loop same helicity YM amplitudes, in particular such an amplitude at four points, should be interpreted as an anomaly. However, the available derivations of these amplitudes are rather far from supporting this interpretation in that they share no similarity whatsoever with the standard triangle diagram chiral anomaly calculation. We provide a new computation of the same helicity four-point amplitude by a method designed to mimic the chiral anomaly derivation. This is done by using the momentum conservation to rewrite the logarithmically divergent four-point amplitude as a sum of linearly and then quadratically divergent integrals. These integrals are then seen to vanish after appropriate shifts of the loop momentum integration variable. The amplitude thus gets related to shifts, and these are computed in the standard textbook way. We thus reproduce the usual result but by a method which greatly strengthens the case for an anomaly interpretation of these amplitudes.
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