Abstract
We investigate the possibility of an ultraviolet (UV) zero in the $n$-loop beta function of a $\lambda (\vec{\phi}^2)^2$ field theory with an $N$-component scalar field, $\vec{\phi}$, in four spacetime dimensions, up to the level of $n=5$ loops. Although the two-loop beta function has a UV zero, we find that the $n$-loop beta function for $n=3, \ 4, \ 5$ either does not have a UV zero or does not have one at a value of $\lambda$ in approximate agreement with the two-loop calculation. Similar results are obtained after application of scheme transformations to the beta function and via calculation of Pad\'e approximants. We thus conclude that in the range of $\lambda$ where the perturbative calculation of the $n$-loop beta function is reliable, the theory does not exhibit robust evidence of a UV zero up to the level of $n=5$ loops.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.