Stefano Laporta
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Stefano Laporta has a total of 249 co-authors. Here are the top co-authors by number of shared publications:
- Pierpaolo Mastrolia
Università di Padova
5 shared publications - Amedeo Primo
Department of Physics University of Zürich CH-8057 Zürich Switzerland
2 shared publications - Elisa Balzani
Dipartimento di Fisica e Astronomia "G. Galilei" Università di Padova Via F. Marzolo 8 35131 Padova Italy
2 shared publications - Federico Gasparotto
Dipartimento di Fisica e Astronomia Università di Padova Via Marzolo 8 35131 Padova Italy
2 shared publications - Hjalte Frellesvig
Dipartimento di Fisica e Astronomia, Università di Padova, Padova, Italy
2 shared publications - Luca Mattiazzi
Dipartimento di Fisica e Astronomia Università di Padova Via Marzolo 8 35131 Padova Italy
2 shared publications
Latest Publications
- Top Cited PapersOpen Access
- 10 September 2025
- Published by Elsevier in Physics Reports
- Vol. 1143, 1-158
The anomalous magnetic moment of the muon in the Standard Model: an update
- 10 September 2025
- Published by Elsevier in Physics Reports
- Vol. 1143, 1-158
Top Cited PapersOpen AccessThe anomalous magnetic moment of the muon in the Standard Model: an update
- Open Access
- 1 October 2024
- Published by Elsevier in Physics Letters B
- Vol. 858
Time-kernel for lattice determinations of NLO hadronic vacuum polarization contributions to the muon g-2
- 1 October 2024
- Published by Elsevier in Physics Letters B
- Vol. 858
Open AccessTime-kernel for lattice determinations of NLO hadronic vacuum polarization contributions to the muon g-2
- Open Access
- 13 May 2024
- Published by American Physical Society (APS) in Physical Review D
- Vol. 109 (9) , 096020
Dimensional regularization and two-loop vacuum polarization operator: Master integrals, analytic results, and energy shifts
We present a complete reevaluation of the irreducible two-loop vacuum-polarization correction to the photon propagator in quantum electrodynamics, i.e. with an electron-positron pair in the fermion propagators. The integration is carried out by reducing the integrations to a limited set of master integrals, which are calculated using integration-by-parts identities. Dimensional regularization is used in dimensions, and on-mass shell renormalization is employed. The one-loop effect is given to order , to be combined with the divergence of the two-loop amplitude. Master integrals are given. Final evaluations of two-loop energy shifts for , , and states are done analytically, and results are presented, with an emphasis on muonic hydrogen. For relativistic Dirac-Coulomb reference states, higher-order coefficients are obtained for the -expansion. We compare the results obtained to the existing literature.- 13 May 2024
- Published by American Physical Society (APS) in Physical Review D
- Vol. 109 (9) , 096020
Open AccessDimensional regularization and two-loop vacuum polarization operator: Master integrals, analytic results, and energy shifts
We present a complete reevaluation of the irreducible two-loop vacuum-polarization correction to the photon propagator in quantum electrodynamics, i.e. with an electron-positron pair in the fermion propagators. The integration is carried out by reducing the integrations to a limited set of master integrals, which are calculated using integration-by-parts identities. Dimensional regularization is used in dimensions, and on-mass shell renormalization is employed. The one-loop effect is given to order , to be combined with the divergence of the two-loop amplitude. Master integrals are given. Final evaluations of two-loop energy shifts for , , and states are done analytically, and results are presented, with an emphasis on muonic hydrogen. For relativistic Dirac-Coulomb reference states, higher-order coefficients are obtained for the -expansion. We compare the results obtained to the existing literature. - Top Cited PapersOpen Access
- 2 March 2021
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2021 (3) , 1-55
Decomposition of Feynman integrals by multivariate intersection numbers
We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master integrals, employing multivariate intersection numbers. We discuss a recursive algorithm for the computation of multivariate intersection numbers, and provide three different approaches for a direct decomposition of Feynman integrals, which we dub the straight decomposition, the bottom-up decomposition, and the top-down decomposition. These algorithms exploit the unitarity structure of Feynman integrals by computing intersection numbers supported on cuts, in various orders, thus showing the synthesis of the intersection-theory concepts with unitarity-based methods and integrand decomposition. We perform explicit computations to exemplify all of these approaches applied to Feynman integrals, paving a way towards potential applications to generic multi-loop integrals.
- 2 March 2021
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2021 (3) , 1-55
Top Cited PapersOpen AccessDecomposition of Feynman integrals by multivariate intersection numbers
We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master integrals, employing multivariate intersection numbers. We discuss a recursive algorithm for the computation of multivariate intersection numbers, and provide three different approaches for a direct decomposition of Feynman integrals, which we dub the straight decomposition, the bottom-up decomposition, and the top-down decomposition. These algorithms exploit the unitarity structure of Feynman integrals by computing intersection numbers supported on cuts, in various orders, thus showing the synthesis of the intersection-theory concepts with unitarity-based methods and integrand decomposition. We perform explicit computations to exemplify all of these approaches applied to Feynman integrals, paving a way towards potential applications to generic multi-loop integrals.
- 19 February 2021
- Published by American Physical Society (APS) in Physical Review D
- Vol. 103 (4) , 044038
Gravitational scattering at the seventh order in : Nonlocal contribution at the sixth post-Newtonian accuracyA recently introduced approach to the classical gravitational dynamics of binary systems involves intricate integrals (linked to a combination of nonlocal-in-time interactions with iterated -potential scattering) which have so far resisted attempts at their analytical evaluation. By using computing techniques developed for the evaluation of multiloop Feynman integrals (notably harmonic polylogarithms and Mellin transform) we show how to analytically compute all the integrals entering the nonlocal-in-time contribution to the classical scattering angle at the sixth post-Newtonian accuracy, and at the seventh order in Newton’s constant, (corresponding to six-loop graphs in the diagrammatic representation of the classical scattering angle).- 19 February 2021
- Published by American Physical Society (APS) in Physical Review D
- Vol. 103 (4) , 044038
Gravitational scattering at the seventh order in : Nonlocal contribution at the sixth post-Newtonian accuracyA recently introduced approach to the classical gravitational dynamics of binary systems involves intricate integrals (linked to a combination of nonlocal-in-time interactions with iterated -potential scattering) which have so far resisted attempts at their analytical evaluation. By using computing techniques developed for the evaluation of multiloop Feynman integrals (notably harmonic polylogarithms and Mellin transform) we show how to analytically compute all the integrals entering the nonlocal-in-time contribution to the classical scattering angle at the sixth post-Newtonian accuracy, and at the seventh order in Newton’s constant, (corresponding to six-loop graphs in the diagrammatic representation of the classical scattering angle).- Open Access
- 27 April 2020
- Published by EDP Sciences in EPJ Web of Conferences
- Vol. 234, 01009
The 4-loop slope of the Dirac form factor
The 4-loop contribution to the slope of the Dirac form factor in QED has been evaluated with 1100 digits of precision. The value is . We have also obtained a semi-analytical fit to the numerical value. The expression contains harmonic polylogiπ2iπ iπ arithms of argument , one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits. We show the correction to the energy levels of the hydrogen atom due to the slope.
- 27 April 2020
- Published by EDP Sciences in EPJ Web of Conferences
- Vol. 234, 01009
Open AccessThe 4-loop slope of the Dirac form factor
The 4-loop contribution to the slope of the Dirac form factor in QED has been evaluated with 1100 digits of precision. The value is . We have also obtained a semi-analytical fit to the numerical value. The expression contains harmonic polylogiπ2iπ iπ arithms of argument , one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits. We show the correction to the energy levels of the hydrogen atom due to the slope.
- Open Access
High-precision four-loop mass and wave function renormalization in QED
The 4-loop QED mass and wave function renormalization constants $Z_2$ and $Z_m$ have been evaluated in the on-shell subtraction scheme with 1100 digits of precision. We also worked out the coefficients of the five color structures of the QCD renormalization constants $Z_2^{OS}$ and $Z_m^{OS}$ which can obtained from QED-like diagrams. The results agree with lower precision results available in the literature. Analytical fits were also obtained for all these quantities.Open AccessHigh-precision four-loop mass and wave function renormalization in QED
The 4-loop QED mass and wave function renormalization constants $Z_2$ and $Z_m$ have been evaluated in the on-shell subtraction scheme with 1100 digits of precision. We also worked out the coefficients of the five color structures of the QCD renormalization constants $Z_2^{OS}$ and $Z_m^{OS}$ which can obtained from QED-like diagrams. The results agree with lower precision results available in the literature. Analytical fits were also obtained for all these quantities. - Open Access
- 19 December 2019
- Published by Sissa Medialab Srl
- Vol. 375, 016
The four-loop slope of the Dirac form factor
We have evaluated with 1100 digits of precision the 4-loop contribution to the slope of the Dirac form factor in QED. The value is $$ m^2 F_1^{(4)'}(0) = 0.886545673946443145836821730610315359390424032660064745{\ldots} \left(\frac{\alpha}{\pi}\right)^4 \ . $$ We have also obtained a semi-analytical fit to the numerical value. The expression contains harmonic polylogarithms of argument $e^{\frac{i\pi}{3}}$, $e^{\frac{2i\pi}{3}}$, $e^{\frac{i\pi}{2}}$, one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits. We show the correction to the energy levels of the hydrogen atom due to the slope.- 19 December 2019
- Published by Sissa Medialab Srl
- Vol. 375, 016
Open AccessThe four-loop slope of the Dirac form factor
We have evaluated with 1100 digits of precision the 4-loop contribution to the slope of the Dirac form factor in QED. The value is $$ m^2 F_1^{(4)'}(0) = 0.886545673946443145836821730610315359390424032660064745{\ldots} \left(\frac{\alpha}{\pi}\right)^4 \ . $$ We have also obtained a semi-analytical fit to the numerical value. The expression contains harmonic polylogarithms of argument $e^{\frac{i\pi}{3}}$, $e^{\frac{2i\pi}{3}}$, $e^{\frac{i\pi}{2}}$, one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits. We show the correction to the energy levels of the hydrogen atom due to the slope. - Open Access
High-precision calculation of the 4-loop QED contribution to the slope of the Dirac form factor
We have evaluated with 1100 digits of precision the contribution of all the 891 mass-independent four-loop Feynman diagrams contributing to the slope of the Dirac form factor in QED. The total 4-loop contribution is $ m^2 F_1^{(4)'}(0) = 0.886545673946443145836821730610315359390424032660064745... \left(\frac{\alpha}{\pi}\right)^4$. We have fit a semi-analytical expression to the numerical value. The expression contains harmonic polylogarithms of argument $e^{\frac{i\pi}{3}}$, $e^{\frac{2i\pi}{3}}$, $e^{\frac{i\pi}{2}}$, one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits. I show the correction on the shift of the energy levels of the hydrogen atom due to the slope.Open AccessHigh-precision calculation of the 4-loop QED contribution to the slope of the Dirac form factor
We have evaluated with 1100 digits of precision the contribution of all the 891 mass-independent four-loop Feynman diagrams contributing to the slope of the Dirac form factor in QED. The total 4-loop contribution is $ m^2 F_1^{(4)'}(0) = 0.886545673946443145836821730610315359390424032660064745... \left(\frac{\alpha}{\pi}\right)^4$. We have fit a semi-analytical expression to the numerical value. The expression contains harmonic polylogarithms of argument $e^{\frac{i\pi}{3}}$, $e^{\frac{2i\pi}{3}}$, $e^{\frac{i\pi}{2}}$, one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits. I show the correction on the shift of the energy levels of the hydrogen atom due to the slope. - Open Access
Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
We elaborate on the recent idea of a direct decomposition of Feynman integrals onto a basis of master integrals on maximal cuts using intersection numbers. We begin by showing an application of the method to the derivation of contiguity relations for special functions, such as the Euler beta function, the Gauss ${}_2F_1$ hypergeometric function, and the Appell $F_1$ function. Then, we apply the new method to decompose Feynman integrals whose maximal cuts admit 1-form integral representations, including examples that have from two to an arbitrary number of loops, and/or from zero to an arbitrary number of legs. Direct constructions of differential equations and dimensional recurrence relations for Feynman integrals are also discussed. We present two novel approaches to decomposition-by-intersections in cases where the maximal cuts admit a 2-form integral representation, with a view towards the extension of the formalism to $n$-form representations. The decomposition formulae computed through the use of intersection numbers are directly verified to agree with the ones obtained using integration-by-parts identities.Open AccessDecomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
We elaborate on the recent idea of a direct decomposition of Feynman integrals onto a basis of master integrals on maximal cuts using intersection numbers. We begin by showing an application of the method to the derivation of contiguity relations for special functions, such as the Euler beta function, the Gauss ${}_2F_1$ hypergeometric function, and the Appell $F_1$ function. Then, we apply the new method to decompose Feynman integrals whose maximal cuts admit 1-form integral representations, including examples that have from two to an arbitrary number of loops, and/or from zero to an arbitrary number of legs. Direct constructions of differential equations and dimensional recurrence relations for Feynman integrals are also discussed. We present two novel approaches to decomposition-by-intersections in cases where the maximal cuts admit a 2-form integral representation, with a view towards the extension of the formalism to $n$-form representations. The decomposition formulae computed through the use of intersection numbers are directly verified to agree with the ones obtained using integration-by-parts identities.