Abstract
Using a full resummation of the Adler function in the large-${\ensuremath{\beta}}_{0}$ approximation of QCD and a mathematical framework of resurgence suitable for the specific properties of the Borel transform in this particular case, we derive a compact resurgent representation of the QCD Adler function, valid in the whole complex momentum plane. The representation is expressed in terms of the inverse Mellin transform of the Borel function and is analytic in the complex momentum plane, except for cuts along the timelike axis and the Landau region of the spacelike axis. It contains a purely nonperturbative term singular at the origin of the coupling plane, depending on a single real arbitrary constant. We compare the resurgent Adler function derived in this work with a previous determination in a similar framework and use its values in the complex plane for a calculation of the hadronic width of the $\ensuremath{\tau}$ lepton in the Standard Model.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
