Multiloop spectra in general scalar EFTs and CFTs
Johan Henriksson (Theoretical Physics Department, CERN, Geneva, 1211, Switzerland)
; Franz Herzog (School of Physics and Astronomy, Higgs Centre for Theoretical Physics, The University of Edinburgh, Edinburgh, EH9 3FD, Scotland, UK); Stefanos R. Kousvos (Department of Physics, section of Pisa, University of Pisa, INFN, Largo Pontecorvo 3, Pisa, I-56127, Italy, Department of Physics, University of Torino, INFN, section of Torino, Via P. Giuria 1, Torino, 10125, Italy); Jasper Roosmale Nepveu (Leung Center for Cosmology and Particle Astrophysics, Taipei, 10617, Taiwan, Department of Physics and Center for Theoretical Physics, National Taiwan University, Taipei, 10617, Taiwan)
We consider the most general effective field theory (EFT) Lagrangian with scalar fields and derivatives, and renormalise it to substantially higher loop order than existing results in the literature. EFT Lagrangians have phenomenological applications, for example by encoding corrections to the Standard Model from unknown new physics. At the same time, scalar EFTs capture the spectrum of Wilson–Fisher conformal field theories (CFTs) in dimensions. Our results are enabled by a more efficient version of the R* method for renormalisation, in which the IR divergences are subtracted via a small-momentum asymptotic expansion. In particular, we renormalise the most general set of composite operators up to engineering dimension six and Lorentz rank two. We exhibit direct applications of our results to Ising ( Z 2), O( n), and hypercubic ( Sn⋉( Z 2) n) CFTs, relevant for a plethora of real-world critical phenomena. The computed scaling dimensions agree well with known non-perturbative results, and they lead to new predictions where such results do not yet exist. We thereby expand the understanding of generic EFTs and open new possibilities in diverse fields, such as the numerical conformal bootstrap.
