Related papers: Master integrals with 2 and 3 massive propagators …
We develop a method to obtain $\epsilon$-expansions of massless two-point integrals in position space, based on the constraints implied by symmetries of the asymptotic expansion of conformal four-point integrals. Together with parametric…
We calculate the complete set of two-loop Master Integrals with two off mass-shell legs with massless internal propagators, that contribute to amplitudes of diboson $V_1V_2$ production at the LHC. This is done with the Simplified…
We consider the two-loop amplitude of $gg\rightarrow HH$ mediated by bottom quarks, which provides a correction of percent level at leading order in the low invariant mass region. In order to compute the corresponding master integrals, we…
We discuss progress in SM two-loop calculations of the pole position of the massive gauge-boson propagators.
We compute the complete two-loop electroweak corrections to the Higgsstralung process $e^+e^-\rightarrow HZ$ at the future Higgs factory. The Feynman integrals involved in the computation are decomposed into linear combinations of a minimal…
I obtain identities satisfied by the 3-loop self-energy master integrals with four or five propagators with generic masses, including the derivatives with respect to each of the squared masses and the external momentum invariant. These…
We calculate master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals,…
We present the electroweak corrections for the production of a photon pair through gluon fusion, focusing on the contribution from the first two generations of quarks. The two-loop amplitude is calculated using a series of projection…
Formulae are provided to express any two-loop scalar integral with arbitrary masses and arbitrary external momenta in terms of an integral of one fairly simple function or of its derivatives. Such integrals can be calculated numerically…
We present the analytic calculation of all master integrals for 3-, 4-, and 5-particle semi-inclusive cuts of four-loop massless propagators by means of differential equations. We fix the integration constants by reducing the semi-inclusive…
We compute all master integrals for massless three-loop four-particle scattering amplitudes required for processes like di-jet or di-photon production at the LHC. We present our result in terms of a Laurent expansion of the integrals in the…
We present analytic results for the two tennis-court integral families relevant to $2\to2$ scattering processes involving one massive external particle and massless propagators in terms of Goncharov polylogarithms of up to transcendental…
A general one-loop scattering amplitude may be expanded in terms of master integrals. The coefficients of the master integrals can be obtained from tree-level input in a two-step process. First, use known formulas to write the coefficients…
Based on the Simplified Differential Equations approach, we present results for the two-loop non-planar hexa-box families of master integrals. We introduce a new approach to obtain the boundary terms and establish a one-dimensional integral…
The general lines of the derivation and the main properties of the master equations for the master amplitudes associated to a given Feynman graph are recalled. Some results for the 2-loop self-mass graph with 4 propagators are then…
We present numerical results which are needed to evaluate all non-trivial master integrals for four-loop massless propagators, confirming the recent analytic results of[1]and evaluating an extra order in $\ep$ expansion for each master…
In this paper we consider weakly holomorphic modular forms (i.e. those meromorphic modular forms for which poles only possibly occur at the cusps) of weight $2-k\in 2\Z$ for the full modular group $\SL_2(\Z)$. The space has a distinguished…
We use dimensional recurrence relations and analyticity to calculate four-loop propagator-type master integrals in the heavy-quark effective theory. Compared to previous applications of the DRA method, we apply a new technique of fixing…
This article displays a proof of concept of the mixed analytical/numerical method, presented in previous publications, to compute two-loop functions with up to five massive propagators in a scalar theory having three- and four-leg vertices…
We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the $\rho$-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be…