2001/01/18 by Arno Böhm, A. R. Bohm, Rafael de la Madrid +8
Mathematics · Physics and Astronomy · #Experimental and Theoretical Physics Studies #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Quantum and Classical Electrodynamics #Relativity and Gravitational Theory #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.hep-th/0101121
21 pages revtex file
arxiv created 2001/01/18 · openalex publication_date 2001/01/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The definition of mass and width of relativistic resonances and in particular of the Z-boson is discussed. For this we use the theory based on time asymmetric boundary conditions given by Hardy class spaces \mathbf Φ- and \mathbf Φ+ for prepared in-states and detected out-states respectively, rather than time symmetric Hilbert space theory. This Hardy class boundary condition is a mathematically rigorous form of the singular Lippmann-Schwinger equation. In addition to the rigorous definition of the Lippmann-Schwinger kets |[j,\mathsf s]±> as functionals on the spaces \mathbf Φ∓, one obtains Gamow kets |[j,\mathsf sR]- > with complex centre-of-mass energy value \mathsf sR=(MR-iΓR/2)2. The Gamow kets have an exponential time evolution given by exp(-iMRt-ΓRt/2) which suggests that (MR,ΓR) is the right definition of the mass and width of a resonance. This is different from the two definitions of the Z-boson mass and width used in the Particle Data Table and leads to a numerical value of MR=(91.1626± 0.0031) \rm GeV from the Z-boson lineshape data.