Towards an improved understanding of eta --> gamma^* gamma^*

We argue that high-quality data on the reaction $e^+e^-\to \pi^+\pi^-\eta$ will allow one to determine the double off-shell form factor $\eta \to \gamma^*\gamma^*$ in a model-independent way with controlled accuracy. This is an important step towards a reliable evaluation of the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon. When analyzing the existing data for $e^+e^- \to \pi^+\pi^-\eta$ in the range of total energies $1\text{GeV}^2<Q_2^2<(4.5\text{GeV})^2$, we demonstrate that the double off-shell form factor $F_{\eta\gamma^*\gamma^*}(Q_1^2,Q_2^2)$ is consistent with the commonly employed factorization ansatz at least for $Q_1^2<1\text{GeV}^2$, if the effect of the $a_2$ meson is taken into account. However, better data are needed to draw firm conclusions.Comment: 7 pages, 3 figure

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

Theory for the FCC-ee : Report on the 11th FCC-ee Workshop

The Future Circular Collider (FCC) at CERN, a proposed 100-km circular facility with several colliders in succession, culminates with a 100 TeV proton-proton collider. It offers a vast new domain of exploration in particle physics, with orders of magnitude advances in terms of Precision, Sensitivity and Energy. The implementation plan foresees, as a first step, an Electroweak Factory electron-positron collider. This high luminosity facility, operating between 90 and 365 GeV centre-of-mass energy, will study the heavy particles of the Standard Model, Z, W, Higgs, and top with unprecedented accuracy. The Electroweak Factory $e^+e^-$ collider constitutes a real challenge to the theory and to precision calculations, triggering the need for the development of new mathematical methods and software tools. A first workshop in 2018 had focused on the first FCC-ee stage, the Tera-Z, and confronted the theoretical status of precision Standard Model calculations on the Z-boson resonance to the experimental demands. The second workshop in January 2019, which is reported here, extended the scope to the next stages, with the production of W-bosons (FCC-ee-W), the Higgs boson (FCC-ee-H) and top quarks (FCC-ee-tt). In particular, the theoretical precision in the determination of the crucial input parameters, alpha_QED, alpha_QCD, M_W, m_t at the level of FCC-ee requirements is thoroughly discussed. The requirements on Standard Model theory calculations were spelled out, so as to meet the demanding accuracy of the FCC-ee experimental potential. The discussion of innovative methods and tools for multi-loop calculations was deepened. Furthermore, phenomenological analyses beyond the Standard Model were discussed, in particular the effective theory approaches. The reports of 2018 and 2019 serve as white papers of the workshop results and subsequent developments

Unsubtractions at NNLO

Computations in perturbative Quantum Field Theory (pQFT) feature several aspects which, although intrinsically non-physical, are traditionally successfully eluded by modifying the dimensions of the space-time. Closed loops in pQFT implicitly extrapolate the validity of the Standard Model (SM) to infinite energies – equivalent to zero distance–, much above the Planck scale. We should expect this to be a legitimate procedure if the loop scattering amplitudes that contribute to the physical observables are either suppressed at very high energies, or if there is a way to suppress / renormalise their contribution in this limit. In gauge theories like QCD, massless particles can be emitted with zero energy, and pQFT treats the quantum state with N external partons as different from the quantum state with emission of extra massless particles at zero energy, while these two states are physically identical. In addition, partons can be emitted in exactly the same direction, or in other words at zero distance. All these unphysical features have a price and lead to the emergence of infinities in the four dimensions of the space-time