2014/05/31 by Carlos Contreras, Gorazd Cvetic, Gorazd Cvetič +5
Physics and Astronomy · #Black Holes and Theoretical Physics #Coupling (piping) #Gravitational singularity #Holomorphic function #Lepton #Mathematical physics #Order (exchange) #Particle physics #Particle physics theoretical and experimental studies #Perturbation theory (quantum mechanics) #Perturbative QCD #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Series (stratigraphy) #Vacuum expectation value #hep-ph #hep-th
paper · pdf · doi:10.1142/s0217751x15500827
v3: 27 pages; 12 figures; includes new Sec.V - sum rule analysis for semihadronic decays of tau lepton in a proposed QCD scheme; new Refs.: [114,115,118-132]; to appear in Int.J.Mod.Phys.A
arxiv created 2015/03/26 · openalex publication_date 2015/05/21 · arxiv updated 2015/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Perturbative QCD in mass independent schemes leads in general to running coupling a(Q 2 ) which is nonanalytic (nonholomorphic) in the regime of low spacelike momenta |Q 2 |≲1 GeV 2 . Such (Landau) singularities are inconvenient in the following sense: evaluations of spacelike physical quantities 𝒟(Q 2 ) with such a running coupling a(κQ 2 )(κ~1) give us expressions with the same kind of singularities, while the general principles of local quantum field theory require that the mentioned physical quantities have no such singularities. In a previous work, certain classes of perturbative mass independent beta functions were found such that the resulting coupling was holomorphic. However, the resulting perturbation series showed explosive increase of coefficients already at N 4 LO order, as a consequence of the requirement that the theory reproduce the correct value of the τ lepton semihadronic strangeless decay ratio r τ . In this paper, we successfully extend the construction to specific classes of perturbative beta functions such that the perturbation series do not show explosive increase of coefficients, the perturbative coupling is holomorphic, and the correct value of r τ is reproduced. In addition, we extract, with Borel sum rule analysis of the V+A channel of the semihadronic strangeless decays of τ lepton, reasonable values of the corresponding D = 4 and D = 6 condensates.