Calculation of the SM beta functions at four-loop accuracy
Final Report Abstract
During the funding period mentioned above, we computed the four-loop anomalous dimensions for the Yukawa and the Higgs-quartic couplings in the gaugeless limit. This calculation enabled us to make very precise predictions for the critical exponents of Gross-Neveu-Yukawa models and study their renormalization group (RG) flows. These models are currently hot topics both in condensed-matter physics for describing continuous phase transitions and in high-energy physics as possible candidates for asymptotic safe extensions of the Standard Model. Although other theoretical and numerical methods like conformal bootstrap, functional renormalization and Monte Carlo lattice simulations are well established tools for condensed matter theory, our perturbative calculation is already considered within the community as a benchmark result. As stated in the project proposal one of our main motivation was also to test the consistency of our set-up for higher order calculations, especially the treatment of γ5 within dimensional regularization. Therefore, we have explicitly checked through four loops that, for Gross-Neveu-Yukawa models with equal numbers of fermionic and bosonic degrees of freedom compatible with an emergent supersymetry (SUSY), all superscaling relations between the critical exponents derived within conformal field theory are preserved also in the perturbative approach. This test allowed us to check directly the treatment of γ5 through four loops and also to get a closer insight into the intriguing link between space-time SUSY and topological phases, both of them being fundamental subjects of the modern theoretical physics. A first continuation of the project is already ongoing together with the theoretical condensed matter groups at the University of Cologne and Dresden. It is based on the inclusion of an U (1) gauge boson into the Gross-Neveu model. Our calculation might give an answer to a number of experimental puzzles in correlated electron systems and enable us to perform further explicit checks of results and conjectures derived within conformal field theory. A second line of research derived from it is the collaboration with the theoretical particle physics group at SISSA Trieste, on building asymptotically safe extensions of the standard model. The guiding principle is to find models with a small number of additional new particles for which all couplings go to a fixed point that can be matched at low scale to the standard model values. The four-loop calculation provides a powerful constraint for the allowed new interactions, whose fixed points must be stable upon inclusion of higher order corrections. A second result obtained during the funding period is the two-loop computation of the threshold coefficients for the top-Yukawa coupling and top-quark mass in SUSY theories. These provide the most precise predictions for the input parameters required for the evaluation of the lightest Higgs mass in SUSY theories. The results are already implemented in the code H3m and provide the first building block for the calculation of the resummed Higgs mass through three loops. This project is currently ongoing in collaboration with the theoretical particle physics group at KIT.
Publications
- “Fourloop critical exponents for the Gross-Neveu-Yukawa models”. In: Phys. Rev. D96.9 (2017), p. 096010
Nikolai Zerf, Luminita N. Mihaila, Peter Marquard, Igor F. Herbut, and Michael M. Scherer
(See online at https://doi.org/10.1103/PhysRevD.96.096010) - “Gross-Neveu-Yukawa model at three loops and Ising critical behavior of Dirac systems”. In: Phys. Rev. B96.16 (2017), p. 165133
Luminita N. Mihaila, Nikolai Zerf, Bernhard Ihrig, Igor F. Herbut, and Michael M. Scherer
(See online at https://doi.org/10.1103/PhysRevB.96.165133) - “O(αs αt) (non)decoupling effects within the top-sector of the MSSM”. In: JHEP 05 (2017), p. 019
L. Mihaila and N. Zerf
(See online at https://doi.org/10.1007/JHEP05(2017)019) - “RG analysis at higher orders in perturbative QFTs in CMP”. In: 13th International Symposium on Radiative Corrections: Application of Quantum Field Theory to Phenomenology (RAD-COR 2017) St. Gilgen, Austria, September 24-29, 2017
Nikolai Zerf
