0000000000870864
AUTHOR
German F. R. Sborlini
Causal representation of multi-loop Feynman integrands within the loop-tree duality
The numerical evaluation of multi-loop scattering amplitudes in the Feynman representation usually requires to deal with both physical (causal) and unphysical (non-causal) singularities. The loop-tree duality (LTD) offers a powerful framework to easily characterise and distinguish these two types of singularities, and then simplify analytically the underling expressions. In this paper, we work explicitly on the dual representation of multi-loop Feynman integrals generated from three parent topologies, which we refer to as Maximal, Next-to-Maximal and Next-to-Next-to-Maximal loop topologies. In particular, we aim at expressing these dual contributions, independently of the number of loops an…
Four-dimensional unsubtraction with massive particles
We extend the four-dimensional unsubtraction method, which is based on the loop-tree duality (LTD), to deal with processes involving heavy particles. The method allows to perform the summation over degenerate IR configurations directly at integrand level in such a way that NLO corrections can be implemented directly in four space-time dimensions. We define a general momentum mapping between the real and virtual kinematics that accounts properly for the quasi-collinear configurations, and leads to an smooth massless limit. We illustrate the method first with an scalar toy example, and then analyse the case of the decay of a scalar or vector boson into a pair of massive quarks. The results pr…
Polarized triple-collinear splitting functions at NLO for processes with photons
We compute the polarized splitting functions in the triple collinear limit at next-to-leading order accuracy (NLO) in the strong coupling $\alpha_{\rm S}$, for the splitting processes $\gamma \to q \bar{q} \gamma$, $\gamma \to q \bar{q} g$ and $g \to q \bar{q} \gamma$. The divergent structure of each splitting function was compared to the predicted behaviour according to Catani's formula. The results obtained in this paper are compatible with the unpolarized splitting functions computed in a previous article. Explicit results for NLO corrections are presented in the context of conventional dimensional regularization (CDR).
Two-loop QED corrections to the Altarelli-Parisi splitting functions
We compute the two-loop QED corrections to the Altarelli-Parisi (AP) splitting functions by using a deconstructive algorithmic Abelianization of the well-known NLO QCD corrections. We present explicit results for the full set of splitting kernels in a basis that includes the leptonic distribution functions that, starting from this order in the QED coupling, couple to the partonic densities. Finally, we perform a phenomenological analysis of the impact of these corrections in the splitting functions.
Double collinear splitting amplitudes at next-to-leading order
We compute the next-to-leading order (NLO) QCD corrections to the $1 \to 2$ splitting amplitudes in different dimensional regularization (DREG) schemes. Besides recovering previously known results, we explore new DREG schemes and analyze their consistency by comparing the divergent structure with the expected behavior predicted by Catani's formula. Through the introduction of scalar-gluons, we show the relation among splittings matrices computed using different schemes. Also, we extended this analysis to cover the double collinear limit of scattering amplitudes in the context of QCD+QED.
Triple collinear splitting functions at NLO for scattering processes with photons
We present splitting functions in the triple collinear limit at next-to-leading order. The computation was performed in the context of massless QCD+QED, considering only processes which include at least one photon. Through the comparison of the IR divergent structure of splitting amplitudes with the expected known behavior, we were able to check our results. Besides that we implemented some consistency checks based on symmetry arguments and cross-checked the results among them. Studying photon-started processes, we obtained very compact results.
Combining QED and QCD transverse-momentum resummation for W and Z boson production at hadron colliders
In this article, we consider the transverse momentum ($q_T$) distribution of $W$ and $Z$ bosons produced in hadronic collisions. We combine the $q_T$ resummation for QED and QCD radiation including the QED soft emissions from the $W$ boson in the final state. In particular, we perform the resummation of enhanced logarithmic contributions due to soft and collinear emissions at next-to-leading accuracy in QED, leading-order accuracy for mixed QED-QCD and next-to-next-to-leading accuracy in QCD. In the small-$q_T$ region we consistently include in our results the next-to-next-to-leading order (i.e.\ two loops) QCD corrections and the next-to-leading order (i.e.\ one loop) electroweak correctio…
Mathematical properties of nested residues and their application to multi-loop scattering amplitudes
Journal of high energy physics 02(2), 112 (2021). doi:10.1007/JHEP02(2021)112