3- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> and 4- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> systems within a short-range effective field theory–inspired a

$^{12}\mathrm{C}$ and $^{16}\mathrm{O}$ nuclei represent essential elements for life on Earth. The study of their formation plays a key role in understanding heavy element nucleosynthesis and stellar evolution. In this paper we present the study of $^{12}\mathrm{C}$ and $^{16}\mathrm{O}$ nuclei as systems composed of $\ensuremath{\alpha}$-particle clusters using a short-range effective field theory--inspired approach. The fundamental and excited states of the studied nuclei are calculated within an ab initio approach using the hyperspherical harmonics method. Thanks to the two-body potential and fine-tuning of the three-body force, we have found the $^{12}\mathrm{C}$ system nicely reproduced by theory. However, for the $^{16}\mathrm{O}$ case, it is necessary to include a four-body force in order to achieve agreement with the experimental data.