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تسجيل مستخدم جديدA novel approach to the computation of one-loop three- and four-point functions. I -- The real mass case
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تأليف
J. Ph. Guillet
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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.
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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.
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 fe
atures 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.
A framework to represent and compute two-loop $N$-point Feynman diagrams as double-integrals is discussed. The integrands are generalised one-loop type multi-point functions multiplied by simple weighting factors. The final integrations over these tw
o variables are to be performed numerically, whereas the ingredients involved in the integrands, in particular the generalised one-loop type functions, are computed analytically. The idea is illustrated on a few examples of scalar three- and four-point functions.
In the context of a left-right extension of the standard model of quarks and leptons with the addition of a gauged $U(1)_D$ dark symmetry, it is shown how the electron may obtain a radiative mass in one loop and two Dirac neutrinos obtain masses in three loops.
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 par
ticular 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.
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