Anomalous decay and scattering processes of the eta meson

We amend a recent dispersive analysis of the anomalous $\eta$ decay process $\eta\to\pi^+\pi^-\gamma$ by the effects of the $a_2$ tensor meson, the lowest-lying resonance that can contribute in the $\pi\eta$ system. While the net effects on the measured decay spectrum are small, they may be more pronounced for the analogous $\eta'$ decay. There are nonnegligible consequences for the $\eta$ transition form factor, which is an important quantity for the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment. We predict total and differential cross sections, as well as a marked forward-backward asymmetry, for the crossed process $\gamma\pi^-\to\pi^-\eta$ that could be measured in Primakoff reactions in the future.Comment: 12 pages, 11 figures; v2 matches version published in EPJ

Asymptotic expansions through the loop-tree duality

First results towards a general method for asymptotic expansions of Feynman amplitudes in the loop-tree duality (LTD) formalism are presented. The asymptotic expansion takes place at integrand-level in the Euclidean space of the loop three-momentum, where the hierarchies among internal and external scales are well-defined. Additionally, the UV behaviour of the individual contributions to the asymptotic expansion emerges only in the first terms of the expansion and is renormalized locally in four space-time dimensions. These two properties represent an advantage over the method of Expansion by Regions (EbR). We explore different approaches in different kinematical limits, and derive general guidelines with several benchmark examples.Comment: 23 pages, 7 figure

Asymptotic expansions and causal representations through the loop-tree duality

Large-scale particle physics experiments have provided a vast amount of high-quality data during the last decades. A leading role has been played by the Large Hadron Collider where the evaluation and analysis of its second run is currently still in progress while the third run is about to start, promising ever higher precision data of particle collisions and subsequent decays. The agreement between experimental observations and theoretical predictions using the Standard Model of Particle Physics is excellent. Indeed, this is a problem since there are currently few clues for how genuine shortcomings of the model can be overcome. New physics phenomena can appear either at higher energies, which would require the construction of an even larger particle collider, or as small deviations accessible only through precision calculations. These involve higher-order quantum corrections which pose technical challenges. An alternative to the traditional method has been proposed in the form of the loop-tree duality theorem. A derivation of the theorem based on the application of the Cauchy residue theorem is presented and the application of the loop-tree duality to the two loop sunrise amplitude is demonstrated in detail. Further, the appearance of singularities in the dual integrands is analyzed. Cancellations between unphysical singularities are demonstrated. In this work a newly found purely causal representation of the dual integrands and the definitions of several classes of multiloop topologies as well as their loop-tree duality representations are presented. The main part of this work is focused on the development of a framework for using asymptotic expansions in the context of the loop-tree duality. Previously found expansions in the leading order Higgs boson decay are analyzed and their limitations pointed out. A general method is derived for defining asymptotic expansions of scattering amplitudes within the loop-tree duality framework. This method involves the expansion of the dual propagator in a general form that is easily applicable to any given kinematic limit. This expanded propagator is used in the calculation of the scalar two-point function. Upon integration a master expansion is obtained, which can be evaluated for a variety of kinematic limits. Convergence is obtained both at the level of the integrand as well as for the integrated result. The tested limits are: one large mass, a large external momentum, and the threshold limit (both below and above threshold). A separate method for expanding the dual integrand is derived by dividing the integration range into two dual regions such that the integrand can be expanded separately using a Taylor series. This method takes direct advantage of the Euclidean nature of the dual integrand. It has been successful for the scalar two-point function. In the following, the method is applied to the scalar three-point function and tested for two different limits. A multiloop expansion has been achieved for the case of the maximal-loop-topology. Finally, an application to a physical amplitude is shown: the process q q -> H g, which is one of the amplitudes contributing to highly boosted Higgs boson production. Also for this process one limit below and one above threshold were tested successfully

Open loop amplitudes and causality to all orders and powers from the loop-tree duality

Multiloop scattering amplitudes describing the quantum fluctuations at high-energy scattering processes are the main bottleneck in perturbative quantum field theory. The loop-tree duality is a novel method aimed at overcoming this bottleneck by opening the loop amplitudes into trees and combining them at integrand level with the real-emission matrix elements. In this Letter, we generalize the loop-tree duality to all orders in the perturbative expansion by using the complex Lorentz-covariant prescription of the original one-loop formulation. We introduce a series of mutiloop topologies with arbitrary internal configurations and derive very compact and factorizable expressions of their open-to-trees representation in the loop-tree duality formalism. Furthermore, these expressions are entirely independent at integrand level of the initial assignments of momentum flows in the Feynman representation and remarkably free of noncausal singularities. These properties, that we conjecture to hold to other topologies at all orders, provide integrand representations of scattering amplitudes that exhibit manifest causal singular structures and better numerical stability than in other representations.Comment: Final version to appear in Physical Review Letter

A Stroll through the Loop-Tree Duality

The Loop-Tree Duality (LTD) theorem is an innovative technique to deal with multi-loop scattering amplitudes, leading to integrand-level representations over a Euclidean space. In this article, we review the last developments concerning this framework, focusing on the manifestly causal representation of multi-loop Feynman integrals and scattering amplitudes, and the definition of dual local counter-terms to cancel infrared singularities