Abstract
When facing the computation of more realistic processes, the calculations can become lengthy very fast as the number of Feynman diagrams grows. Before starting the calculation process the problem should be reduced to its minimal form. Here we will present an example of how to reduce the number of calculated diagrams for a given process (which in this case will be a Higgs-like scalar decay to two photons through a charged scalar loop) using gauge symmetry.
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Notes
- 1.
For a nice review of the SM read A. Pich, The Standard Model of Electroweak Interactions, http://arxiv.org/pdf/1201.0537.pdf. Also, for a nice review of the 2HDM read G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher and J.P. Silva, Theory and phenomenology of two-Higgs-doublet models, Phys. Rept. 516 (2012) 1, http://arxiv.org/pdf/1106.0034v3.pdf.
- 2.
Read Chap. 5 for more details.
- 3.
One could equally choose to keep only the \( g^{\mu \nu } \; k'\cdot q\) structure, however, with this choice, one has to compute a greater number of terms and Feynman diagrams as we will shortly see.
- 4.
An useful trick for deriving the Feynman rules corresponding to interaction terms that contain derivatives of fields is given in Appendix C.
Further Reading
V. Ilisie, A. Pich, Low-mass fermiophobic charged Higgs phenomenology in two-Higgs-doublet models. JHEP 1409, 089 (2014). http://arxiv.org/pdf/1405.6639v3.pdf
V. Ilisie, New Barr-Zee contributions to \(\mathbf{(g-2)}_{\mu }\) in two-Higgs-doublet models. JHEP 04, 077 (2015) http://arxiv.org/pdf/1502.04199v3.pdf
A. Pich, The Standard Model of Electroweak Interactions, http://arxiv.org/pdf/1201.0537.pdf
G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher, J.P. Silva, Theory and phenomenology of two-Higgs-doublet models. Phys. Rep. 516, 1 (2012) http://arxiv.org/pdf/1106.0034v3.pdf
C. Itzykson, J. Zuber, Quantum Field Theory
M.E. Peskin and D.V. Schroeder, An Introduction to Quantum Field Theory
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Ilisie, V. (2016). Symmetries and Effective Vertices. In: Concepts in Quantum Field Theory. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-22966-9_10
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DOI: https://doi.org/10.1007/978-3-319-22966-9_10
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