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DiffExp, a Mathematica package for computing Feynman integrals in terms of one-dimensional series expansions [article]

Martijn Hidding
2020 arXiv   pre-print
DiffExp is a Mathematica package for integrating families of Feynman integrals order-by-order in the dimensional regulator from their systems of differential equations, in terms of one-dimensional series  ...  DiffExp is based on the series expansion strategies that were explored in recent literature for the computation of families of Feynman integrals relevant for Higgs plus jet production with full heavy quark  ...  Moriello for introducing me to series expansions methods, for developing the first private implementation of these methods in Ref. [1] , and for numerous useful discussions on the topic.  ... 
arXiv:2006.05510v2 fatcat:5mbc7ir5jrc6honnwlduhfkh2m

Evaluation of Feynman integrals with arbitrary complex masses via series expansions [article]

Tommaso Armadillo, Roberto Bonciani, Simone Devoto, Narayan Rana, Alessandro Vicini
2022 arXiv   pre-print
We present an algorithm to evaluate multiloop Feynman integrals with an arbitrary number of internal massive lines, with the masses being in general complex-valued, and its implementation in the Mathematica  ...  The implementation solves by series expansions the system of differential equations satisfied by the Master Integrals.  ...  Conclusions The solution via series expansion of multi-loop Feynman integrals has received a renewed attention after the work of Ref. [38] and the publication of the package DiffExp [39] .  ... 
arXiv:2205.03345v1 fatcat:vwmef6qdjrco3aeuzidycixazu

One-loop QCD helicity amplitudes for pp→ tt̅ j to O(ϵ^2) [article]

Simon Badger, Matteo Becchetti, Ekta Chaubey, Robin Marzucca, Francesco Sarandrea
2022 arXiv   pre-print
We compute helicity amplitudes for the one-loop QCD corrections to top-quark pair production analytically in terms of a set of uniformly transcendental master integrals.  ...  Analytic forms of the boundary values are obtained in all cases except one where we find a one-dimensional integral representation.  ...  The computation of the boundary terms is described and the numerical evaluation using generalised series expansions with DiffExp is presented.  ... 
arXiv:2201.12188v3 fatcat:zfctqmxyurgqph22h523lxpbga

Two-loop QCD corrections to Wbb̅ production at hadron colliders [article]

Simon Badger, Heribertus Bayu Hartanto, Simone Zoia
2021 arXiv   pre-print
We present an analytic computation of the two-loop QCD corrections to ud̅→ W^+bb̅ for an on-shell W-boson using the leading colour and massless bottom quark approximations.  ...  We perform an integration-by-parts reduction of the unpolarised squared matrix element using finite field reconstruction techniques and identify an independent basis of special functions that allows an  ...  Finally, we evaluate the g (w) i 's by solving the corresponding DEs using the Mathematica package DiffExp [79] .  ... 
arXiv:2102.02516v3 fatcat:3x2ze7crvfhknes3iffodwd3za

Functions Beyond Multiple Polylogarithms for Precision Collider Physics [article]

Jacob L. Bourjaily, Johannes Broedel, Ekta Chaubey, Claude Duhr, Hjalte Frellesvig, Martijn Hidding, Robin Marzucca, Andrew J. McLeod, Marcus Spradlin, Lorenzo Tancredi, Cristian Vergu, Matthias Volk (+5 others)
2022 arXiv   pre-print
Feynman diagrams constitute one of the essential ingredients for making precision predictions for collider experiments.  ...  Yet, while the simplest Feynman diagrams can be evaluated in terms of multiple polylogarithms – whose properties as special functions are well understood – more complex diagrams often involve integrals  ...  A fully automated strategy was described in [339] , and a public implementation was provided in the Mathematica package DiffExp [147] .  ... 
arXiv:2203.07088v1 fatcat:x3vstzj7vjb2zhycym6j75mbs4

Two-loop amplitude for mixed QCD-EW corrections to gg → Hg [article]

Matteo Becchetti, Francesco Moriello, Armin Schweitzer
2021 arXiv   pre-print
The master integrals that appear in the amplitude are evaluated by means of generalized power series expansions, which allows for fast and high-precision numerical evaluation of the amplitude in the physical  ...  We report on the two-loop amplitude computation for the mixed QCD-electroweak corrections to the process gg → Hg, with exact dependence on the electroweak boson masses.  ...  Hidding, DiffExp, a Mathematica package for computing Feynman integrals in terms of one-dimensional series expansions, Comput. Phys. Commun. 269 (2021) 108125, [2006.05510]. [50] J.  ... 
arXiv:2112.07578v1 fatcat:bjevuvwurjg25hpjcelakc4vza

Pentagon functions for scattering of five massless particles

D. Chicherin, V. Sotnikov
2020 Journal of High Energy Physics  
We complete the analytic calculation of the full set of two-loop Feynman integrals required for computation of massless five-particle scattering amplitudes.  ...  five-point two-loop Feynman integrals in the whole physical phase space.  ...  Acknowledgments We thank Simon Badger, Gudrun Heinrich, Johannes Henn, Thomas Gehrmann, Simone Zoia for insightful discussions. We are grateful to Johannes Henn for comments on the manuscript.  ... 
doi:10.1007/jhep12(2020)167 fatcat:6rgt7tvyundl5cafvm4mccfv4q

Pentagon Functions for Scattering of Five Massless Particles [article]

Dmitry Chicherin, Vasily Sotnikov
2020 arXiv   pre-print
We complete the analytic calculation of the full set of two-loop Feynman integrals required for computation of massless five-particle scattering amplitudes.  ...  five-point two-loop Feynman integrals in the whole physical phase space.  ...  Acknowledgments We thank Simon Badger, Gudrun Heinrich, Johannes Henn, Thomas Gehrmann, Simone Zoia for insightful discussions. We are grateful to Johannes Henn for comments on the manuscript.  ... 
arXiv:2009.07803v1 fatcat:e5ephloxrnefhcztr2pgskyjwy

Two-loop leading-colour QCD helicity amplitudes for Higgs boson production in association with a bottom-quark pair at the LHC [article]

Simon Badger, Heribertus Bayu Hartanto, Jakub Kryś, Simone Zoia
2021 arXiv   pre-print
We compute the two-loop QCD helicity amplitudes for the production of a Higgs boson in association with a bottom-quark pair at a hadron collider.  ...  We extract analytic expressions from multiple numerical evaluations over finite fields and present the results in terms of an independent set of special functions that can be reliably evaluated over the  ...  Acknowledgments SZ wishes to thank Dmitry Chicherin and Vasily Sotnikov for useful discussions. This project received funding from the European Union's Horizon 2020 research and innovation  ... 
arXiv:2107.14733v1 fatcat:3otiesxmhfgrlnmx5whaqhgh44

Collider Physics at the Precision Frontier [article]

Gudrun Heinrich
2021 arXiv   pre-print
While the first part focuses on phenomenological results, the second part reviews some of the techniques which allowed the rapid progress in the field of precision calculations.  ...  The aim of this review is to give an overview of recent developments in precision calculations within the Standard Model of particle physics, in particular in the Higgs sector.  ...  Acknowledgements First of all I would like to thank all my collaborators for many fruitful discussions and collaborations over the last years. I am also grateful to Ansgar Denner,  ... 
arXiv:2009.00516v2 fatcat:4sibumdd2jdi3cmd7cm26s3ghu

Pentagon Functions for One-Mass Planar Scattering Amplitudes [article]

Dmitry Chicherin, Vasily Sotnikov, Simone Zoia
2022 arXiv   pre-print
We express the integrals in terms of a basis of algebraically-independent transcendental functions, which we call one-mass pentagon functions.  ...  We present analytic results for all planar two-loop Feynman integrals contributing to five-particle scattering amplitudes with one external massive leg.  ...  Henn, Leila Maestri and Tiziano Peraro for useful suggestions at the initial stages of this work. We thank Samuel Abreu, Simon Badger and Johannes M. Henn for comments on the manuscript.  ... 
arXiv:2110.10111v2 fatcat:qmwwti6vhnggbh2xvs4qrox66u

Two-loop leading colour helicity amplitudes for W^±γ+j production at the LHC [article]

Simon Badger, Heribertus Bayu Hartanto, Jakub Kryś, Simone Zoia
2022 arXiv   pre-print
We implement a complete reduction of the amplitudes, including the leptonic decay of the W-boson, using finite field arithmetic, and extract the analytic finite remainders using a recently identified basis  ...  We demonstrate efficient numerical evaluation of the two-loop colour and helicity summed finite remainders for physical kinematics, and hence the suitability for phenomenological applications.  ...  We would also like to thank Tiziano Peraro for useful discussions and comments on the manuscript.  ... 
arXiv:2201.04075v1 fatcat:djw7ijrztnd4zmpvqpyo53av3e

One-loop QCD helicity amplitudes for $pp\to t\bar{t} j$ to $O(ε^2)$ [article]

Simon Badger, Matteo Becchetti, Ekta Chaubey, Robin Marzucca, Francesco Sarandrea
2022
We compute helicity amplitudes for the one-loop QCD corrections to top-quark pair production analytically in terms of a set of uniformly transcendental master integrals.  ...  Analytic forms of the boundary values are obtained in all cases except one where we find a one-dimensional integral representation.  ...  The computation of the boundary terms is described and the numerical evaluation using generalised series expansions with DiffExp is presented.  ... 
doi:10.48550/arxiv.2201.12188 fatcat:tw2kpah26ngirgwagjtfvjcrxm

Deciphering the Maximal Transcendentality Principle via Bootstrap [article]

Yuanhong Guo, Qingjun Jin, Lei Wang, Gang Yang
2022 arXiv   pre-print
Our proof is based on a recently developed bootstrap method using the representation of master integral expansions, together with some unitarity cuts that are universal in general gauge theories.  ...  Thus, the maximal transcendentality principle still holds for the form factor results in 𝒩=4 SYM and QCD, after a proper identification of the fundamental quarks and adjoint gluinos as n_f → 4N_c.  ...  We also thank the support of the HPC Cluster of ITP-CAS. A UT master integrals In this appendix, we list all uniform-transcendentality (UT) integrals we have used in the paper.  ... 
arXiv:2205.12969v1 fatcat:e23mybcnk5fcjg3s4uc4f3bqv4