Renato Fonseca

I received my PhD (2009–2013) at CFTP, Instituto Superior Técnico (University of Lisbon), in Lisbon.

Research areas:

• Effective field theory methods
• Computational automation for EFTs and group-theory
• Neutrino masses, lepton-number violation
• Grand unification
• Flavor symmetries and lepton mixing

Selected publications

1. Renormalization of general Effective Field Theories: Formalism and renormalization of bosonic operators
   Renato M. Fonseca, Pablo Olgoso, José Santiago
   JHEP 07 (2025) 135
2. GroupMath: A Mathematica package for group theory calculations software
   Renato M. Fonseca
   Comput. Phys. Commun. 267 (2021) 108085
3. Enumerating the operators of an effective field theory
   Renato M. Fonseca
   Phys. Rev. D 101 (2020) 035040
4. Systematic classification of three-loop realizations of the Weinberg operator
   Ricardo Cepedello, Renato M. Fonseca, Martin Hirsch
   JHEP 10 (2018) 197 ; Erratum: JHEP 06 (2019) 034
5. The Sym2Int program: going from symmetries to interactions software
   Renato M. Fonseca
   J. Phys. Conf. Ser. 873 (2017) 012045
6. Consistency of the triplet seesaw model revisited
   Cesar Bonilla, Renato M. Fonseca, José W. F. Valle
   Phys. Rev. D 92 (2015) 075028
7. Classification of lepton mixing matrices from finite residual symmetries
   Renato M. Fonseca, Walter Grimus
   JHEP 09 (2014) 033
8. Running soft parameters in SUSY models with multiple U(1) gauge factors
   Renato M. Fonseca, Michal Malinský, Werner Porod, Florian Staub
   Nucl. Phys. B 854 (2012) 28–53

                                       

Software

1. GroupMath
   Functions for Lie-algebra and permutation-group calculations in Mathematica. [paper] [tutorial]
2. Sym2Int
   Generates gauge- and Lorentz-invariant interactions for a given field content. [paper] [tutorial]
3. Susyno
   Computes two-loop renormalization group equations for supersymmetric models with general gauge groups and field content. [paper]
4. SimTeEx
   Simplifies polynomial expressions with tensors (index contractions, expansions, and identities). [paper]

Selected talks and seminars

1. HEFT 2025 (CERN, Geneva, Jun 2025) — Automating the computation of (generalized) functional supertraces beyond one loop [event]
2. SMEFT-Tools 2025 (MITP, Mainz, Jan 2025) — Simplifying complicated tensor expressions arising in the study of EFTs [event]
3. Planck 2024 (University of Lisbon, Jun 2024) — Renormalization group equations of a general effective field theory [event]
4. TTK seminar (RWTH Aachen, Jan 2024) — Automating group theory calculations in high energy physics [event]
5. Hirschfest (IFIC, Valencia, Jan 2024) — A tale of two models of lepton number violation [event]
6. SUSY 2023 (University of Southampton, Jul 2023) — A triplet gauge boson with hypercharge one [event]

Teaching & peer review

• Teaching: Mathematical Physics (Física Matemática), undergraduate course at the University of Granada (2023–2025).
• Graduate-level: Lecturer, “Symmetries in Physics”, 12th International IDPASC School (PhD level). [event]
• Mentoring: Co-supervised a Master’s thesis (University of Valencia) and mentored graduate students on research projects.
• Peer review: Referee for Physical Review Letters, Physical Review D, JHEP, EPJC, and Computer Physics Communications.

Supplementary research data

Data, long lists, and auxiliary material linked to specific papers (click to expand)

• “$\Delta L \ge 4$ processes” — arXiv:1804.10545
  Full list of operators which violate lepton number in four units: operator list
• “High-dimensional neutrino masses” — arXiv:1806.07264
  Full list of tree diagrams implementing the d = 9, 11, 13 neutrino mass operators: diagram list
• “Systematic classification of three-loop realizations of the Weinberg operator” — arXiv:1807.00629
  Topologies and diagrams relevant for the 3-loop realization of the Weinberg operator: list

Notes & side projects

• The Mandelbrot set A small interactive demo with a short discussion of basic features.
• Observing Pluto from home Is the dwarf planet Pluto observable from a city apartment? (Spoiler: yes.)
• Observing an exoplanet from home A home experiment to catch a distant planet’s shadow.

Contact

Address:	Departamento de Física Teórica y del Cosmos Facultad de Ciencias (Edificio Mecenas), Universidad de Granada Campus de Fuentenueva, E-18071 Granada, Spain
Email:	renatofonseca@ugr.es