Massimo Passera

All-purpose numerical evaluation of one-loop multi-leg Feynman diagrams

Abstract A detailed investigation is presented of a set of algorithms which form the basis for a fast and reliable numerical integration of one-loop multi-leg (up to six) Feynman diagrams, with special attention to the behavior around (possibly) singular points in phase space. No particular restriction is imposed on kinematics, and complex masses (poles) are allowed.

Two-loop renormalization in the Standard Model. Part I: Prolegomena ☆

In this paper the building blocks for the two-loop renormalization of the Standard Model are introduced with a comprehensive discussion of the special vertices induced in the Lagrangian by a particular diagonalization of the neutral sector and by two alternative treatments of the Higgs tadpoles. Dyson resummed propagators for the gauge bosons are derived, and two-loop Ward–Slavnov–Taylor identities are discussed. In part II, the complete set of counterterms needed for the two-loop renormalization will be derived. In part III, a renormalization scheme will be introduced, connecting the renormalized quantities to an input parameter set of (pseudo-)experimental data, critically discussing renormalization of a gauge theory with unstable particles.

Precise mass-dependent QED contributions to leptonic g − 2 at order α 2 and α 3

Improved values for the two- and three-loop mass-dependent QED contributions to the anomalous magnetic moments of the electron, muon, and tau lepton are presented. The Standard Model prediction for the electron (g-2) is compared with its most precise recent measurement, providing a value of the fine-structure constant in agreement with a recently published determination. For the tau lepton, differences with previously published results are found and discussed. An updated value of the fine-structure constant is presented in Note added after publication.

Two-loop vertices in quantum field theory: infrared convergent scalar configurations

Abstract A comprehensive study is performed of general massive, scalar, two-loop Feynman diagrams with three external legs. Algorithms for their numerical evaluation are introduced and discussed, numerical results are shown for all different topologies and comparisons with analytical results, whenever available, are performed. An internal cross-check, based on alternative procedures, is also applied. The analysis of infrared divergent configurations, as well as the treatment of tensor integrals, will be discussed in two forthcoming papers.

Two-loop tensor integrals in quantum field theory ☆

Abstract A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed. Integral representations, supporting the same class of smoothness algorithms already employed for the numerical evaluation of ordinary scalar functions, are introduced for each family of diagrams.

Simple formulae for sin**2 Theta (eff)(lept), M(W), Gamma(l), and their physical applications

The calculation of the partial widths of the Z boson in the effective scheme is discussed. Simple formulae for Sin^2 theta_eff^lept, M_W, and Gamma_l in the on-shell, MS, and effective renormalization schemes are presented. Their domain of validity extends to low M_H values probed by current experiments, and to the range of Delta alpha_hadr results from recent calculations. Physical applications of these formulae are illustrated. A comparative analysis of the above mentioned schemes is presented. The paper includes a discussion of the discrepancy of the Sin^2 theta_eff^lept values derived from the leptonic and hadronic sectors and of the shortcomings of theoretical error estimates of Sin^2 theta_eff^lept based solely on those affecting M_W.

A frontier in multi-scale multi-loop integrals: the algebraic–numerical method

Fast and efficient ways to compute multi-loop and multi-leg Feynman diagrams are discussed.

The Muon g‐2 in the Standard Model

The Standard Model prediction of the anomalous magnetic moment of the muon is reviewed. QED, electroweak and hadronic contributions are presented, and open questions discussed.The Standard Model prediction of the anomalous magnetic moment of the muon is reviewed. QED, electroweak and hadronic contributions are presented, and open questions discussed.

The frontier of multi-loop Feynman diagrams: (Semi-) numerical techniques

Abstract Fast and efficient ways to compute multi-loop and multi-leg Feynman diagrams are discussed.