Auxiliary Functions in Mapping Effective Operators to Observables

In our paper "How to use the Standard Model effective field theory" by Brian Henning, Xiaochuan Lu, and Hitoshi Murayama, we discuss how to derive the effective theory from an arbitrary UV theory using the covariant-derivative expansion, and also how to map the resultant effective opertors onto experimental observables. The latter part requires numerical integrals.

In this short notebook, we provide the numerical results of the auxiliary functions fa(s), fb(s), and fc(s) we defined in the WW fusion production mode of Higgs boson. The physical origin of these auxiliary functions is explained in Appendix B.3 of the paper. The notations of this notebook also follows that in the appendix of our paper.

This notebook consists of two parts. In the first part, one can obtain the plots quickly by reading the data files

  • tablefa.dat
  • tablefb.dat
  • tablefc.dat
    • already produced before. In the second part, one can evaluate the integrals numerically and reproduce the data files. It take about 10min for the code to reproduce the table data.