Time Asymmetric Boundary Conditions and the Definition of Mass and Width for Relativistic Resonances

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dc.creatorBohm, A. R.
dc.creatorde la Madrid, R.
dc.creatorTay, B. A.
dc.creatorKielanowski, P.
dc.date2001-01-18
dc.date.accessioned2026-07-07T04:11:15Z
dc.date.available2026-07-07T04:11:15Z
dc.descriptionThe 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 $|[j,{\mathsf s}]^{\pm}>$ as functionals on the spaces ${\mathbf Φ}_{\mp}$, one obtains Gamow kets $|[j,{\mathsf s}_R]^- >$ with complex centre-of-mass energy value ${\mathsf s}_R=(M_R-iΓ_R/2)^2$. The Gamow kets have an exponential time evolution given by $\exp{(-iM_Rt-Γ_Rt/2)}$ which suggests that $(M_R,Γ_R)$ 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 $M_R=(91.1626\pm 0.0031) {\rm GeV}$ from the $Z$-boson lineshape data.
dc.description21 pages revtex file
dc.identifierhttps://arxiv.org/abs/hep-th/0101121
dc.identifierhttp://arxiv.org/abs/hep-th/0101121
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/50510
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.titleTime Asymmetric Boundary Conditions and the Definition of Mass and Width for Relativistic Resonances
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