Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops
- PDF / 1,333,963 Bytes
- 37 Pages / 595.276 x 841.89 pts (A4) Page_size
- 103 Downloads / 208 Views
Springer
Received: August 22, Revised: December 24, Accepted: January 9, Published: January 23,
2019 2019 2020 2020
F. Moriello ETH Zurich, Institut fur theoretische Physik, Wolfgang-Paulistr. 27, 8093, Zurich, Switzerland
E-mail: [email protected] Abstract: We obtain generalised power series expansions for a family of planar two-loop master integrals relevant for the QCD corrections to Higgs + jet production, with physical heavy-quark mass. This is achieved by defining differential equations along contours connecting two fixed points, and by solving them in terms of one-dimensional generalised power series. The procedure is efficient, and can be repeated in order to reach any point of the kinematic regions. The analytic continuation of the series is straightforward, and we present new results below and above the physical thresholds. The method we use allows to compute the integrals in all kinematic regions with high precision. For example, performing a series expansion on a typical contour above the heavy-quark threshold takes on average O(1 second) per integral with worst relative error of O(10−32 ), on a single CPU core. After the series is found, the numerical evaluation of the integrals in any point of the contour is virtually instant. Our approach is general, and can be applied to Feynman integrals provided that a set of differential equations is available. Keywords: Higgs Physics, Perturbative QCD ArXiv ePrint: 1907.13234
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP01(2020)150
JHEP01(2020)150
Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops
Contents 1
2 Differential equations for dimensionally regulated Feynman integrals
3
3 Series expansion along a contour 3.1 Canonical differential equations 3.2 Coupled sectors 3.3 Matching
4 6 6 8
4 A planar elliptic family for Higgs+jet production 4.1 Series solution of the differential equations 4.2 Analytic continuation 4.3 Mapping the physical region to a finite region 4.4 Numerical results and timings
10 12 13 17 17
5 Conclusion
19
A General formulation of the Frobenius method
20
B One-loop example
22
C Plots
28
1
Introduction
The computation of Feynman integrals is a central ingredient for the prediction of collider experiments. In the past decades, we have seen an enormous progress in our capabilities to efficiently compute Feynman integrals in closed analytic form or in a purely numerical way. From the analytic side, several techniques are available. Some of the most effective techniques are the differential equations method [1–5] and the direct integration methods [6, 7]. In dimensional regularisation, one is able to reduce a given (generally large) set of scalar Feynman integrals to a minimal set of linearly independent integrals, called master integrals (MIs), by using integration-by-parts identities (IBP) [8–11]. Once a basis is identified, it is possible to define a closed system of first order linear differential equations, that ca
Data Loading...
