Speaker
Description
In recent work we computed 4-loop integrals for self-energy diagrams with 11 massive internal lines. Presently we perform numerical integration and regularization for diagrams with 8 to 11 lines, while considering massive and massless cases. For dimensional regularization, a sequence of integrals is computed depending on a parameter ($\varepsilon$) that is incorporated via the space-time dimension, and approaches zero. We consider diagrams where the leading term in the expansion is in $1/\varepsilon^2$ or in $1/\varepsilon$ or finite. The numerical integration methods include non-adaptive, double exponential integration, and Quasi-Monte Carlo approximations with embedded lattice rules implemented in CUDA C for acceleration on GPU, as well as adaptive integration layered over MPI. The leading term coefficient of $1/\varepsilon^2$ or $1/\varepsilon$ in the integral expansion is obtained via linear or nonlinear extrapolation as epsilon tends to zero.
Significance
We present new numerical approximations for 4-loop integrals, which are compared with results in the literature including (Baikov and Chetyrkin 2010) and (Smirnov and Tentyukov 2010). This work is part of our project on the numerical evaluation of loop integrals and expansions presented in, e.g., (de Doncker et al. 2018, 2019, 2020) and (de Doncker and Yuasa 2021). It stands out that our computations are fully numerical, based on automatic integration and numerical extrapolation for convergence acceleration. For automatic integration, the user is not required to specify characteristics of the integrand function - except for the function definition itself. The packages pySecDec (Borowka et al. 2018) and Forcer (Ruijl, Ueda and Vermaseren 2020) incorporate symbolic computations.
References
[1] Baikov, B.A., Chetyrkin, K.G.: Four loop massless propagators: An algebraic evaluation of all master integrals. Nuclear Physics B 837, 186-220 (2010)
[2] Borowka, S., Heinrich, G., Jahn, S., Jones, S.P., Kerner, M., Schlenk, J., Zirke, T.: pySecDec: A toolbox for the numerical evaluation of multi-scale integrals. Computer Physics Communications 222, 313-326 (2018)
[3] de Doncker, E., Yuasa, F., Kato, K., Ishikawa, T., Kapenga, J., Olagbemi, O.: Regularization with numerical extrapolation for finite and UV-divergent multi-loop integrals. Computer Physics Communications 224, 164-185 (2018), https://doi.org/10.1016/j.cpc.2017.11.001
[4] de Doncker, E., Yuasa, F., Almulihi, A., Nakasato, N., Daisaka, H., Ishikawa, T.: Numerical Multi-Loop Integration on Heterogeneous Many-Core Processors. Journal of Physics: Conf. Ser. (JPCS) 1525, 012002 IOP Series (2019), https://iopscience.iop.org/article/10.1088/1742-6596/1525/1/012002
[5] de Doncker, E., Yuasa, F., Olagbemi, O., Ishikawa, T.: Large scale automatic computations for Feynman diagrams with up to five loops. Springer Lecture Notes in Computer science (LNCS) 12253, 145-162 (2020), https://link.springer.com/chapter/10.1007%2F978-3-030-58814-4_11
[6] de Doncker, E., Yuasa, F.: Self-Energy Feynman Diagrams with Four Loops and 11 Internal Lines. To appear (2021).
[7] Ruijl, B., Ueda, T., Vermaseren, J.A.M.: Forcer, a FORM program for the parametric reduction of four-loop massless propagator diagrams. Computer Physics Communications 253 (107198) (2020)
[8] Smirnov, A.V., Tentyukov, M.: Four-loop massless propagators: A numerical evaluation of all master integrals. Nuclear Physics B 837, 40-49 (2010)
| Speaker time zone | Compatible with America |
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