Effective description of general extensions of the Standard Model: the complete tree-level dictionary

We thank Nuria Rius and Arcadi Santamaria for an interesting discussion that motivated this work. We also thank Paco del Águila and Toni Pich for useful comments.We compute all the tree-level contributions to the Wilson coefficients of the dimension-six Standard-Model effective theory in ultraviolet completions with general scalar, spinor and vector feld content and arbitrary interactions. No assumption about the renormalizability of the high-energy theory is made. This provides a complete ultraviolet/ infrared dictionary at the classical level, which can be used to study the low-energy implications of any model of interest, and also to look for explicit completions consistent with low-energy dataThe work of J.C.C., M.P.V. and J.S. has been supported by the Spanish MICINN project FPA2013- 47836-C3-2-P, the MINECO project FPA2016-78220-C3-1-P (Fondos FEDER) and the Junta de Andalucía grant FQM101. The work of J.C.C. has also been supported by the Spanish MECD grant FPU14. The work of M.P.V. and J.S. has also been supported by the European Commission through the contract PITN-GA-2012-316704 (HIGGSTOOLS). J.C.C. is grateful for the hospitality of the Dipartimento di Fisica e Astronomia \Galileo Galilei" of the University of Padova during part of this work. J.S. would like to thank the Mainz Institute for Theoretical Physics (MITP) for its hospitality and partial support during the completion of this work