Model-independent representation of electroweak data

Stuart, Robin G.

doi:10.1103/physrevd.56.1515

Cited by 10 publications

(11 citation statements)

References 19 publications

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“…After one noticed the problems with gauge invariance of the on-the-mass-shell definition [22,23], one became aware of the arbitrariness in the definition of the Z-boson mass and width, and concluded that there was no fundamental criterion to define the mass and width separately [29]. Similar problems were also pointed out for the nucleon [30,31] and meson [32] resonances.…”

Section: Introductionmentioning

confidence: 93%

Relativistic resonances: Their masses, widths, lifetimes, superposition, and causal evolution

Böhm

Sato

2005

Phys. Rev. D

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Whether one starts from the analytic S-matrix definition or the requirement of gauge-parameter independence in renormalization theory, a relativistic resonance is given by a pole at a complex value sR of the energy squared s. The complex number sR does not define the mass and the width separately, and the pole definition alone is also not sufficient to describe the interference of two or more Breit-Wigner resonances as observed in experiments. To achieve this and obtain a unified theory of relativistic resonances and decay, we invoke the decaying particle aspect of a resonance and associate to each pole a space of relativistic Gamow kets. The Gamow kets transform irreducibly under causal Poincaré transformations and have an exponential time evolution. Therefore one can choose of the many possible width parameters, the width ΓR of the relativistic resonance such that the lifetime τ = /ΓR. This leads to the parameterization sR = (MR − iΓR/2) 2 and uniquely defines these (MR, ΓR) as the mass and width parameters for a resonance. Further it leads to the following new results: Two poles in the same partial wave are given by the sum of two Breit-Wigner amplitudes and by a superposition of two Gamow vectors with each Gamow vector corresponding to one BreitWigner amplitude. In addition to the sum of Breit-Wigner amplitudes the scattering amplitude contains a background amplitude representing direct production of the final state (contact terms). This contact amplitude is associated to a background vector representing the non-exponential energy continuum, omitting it gives the two interfering exponentials of the Weisskopf-Wigner methods. To accomplish all this required a minor modification in the foundation of quantum theory, which led to a quantum theory that contains the time asymmetry of causality.

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Section: Introductionmentioning

confidence: 93%

Relativistic resonances: Their masses, widths, lifetimes, superposition, and causal evolution

Böhm

Sato

2005

Phys. Rev. D

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“…This choice has the advantage of making the denition of s 0 unambiguous, and is more suitable for interpreting the measurements in terms of theoretical parameters. For example, the S-matrix ansatz used to t the data, described in section 4.1, is unsuitable when the non-resonant part of the interference between initial-and nal-state radiation contributes [26].…”

Section: Initial-nal State Photon Interferencementioning

confidence: 99%

Tests of the standard model and constraints on new physics from measurements of fermion-pair production at 130–172 GeV at LEP

al.

1998

Eur. Phys. J. C

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Production of events with hadronic and leptonic nal states has been measured in e + e collisions at centre-of-mass energies of 130{172 GeV, using the OPAL detector at LEP. Cross-sections and leptonic forward-backward asymmetries are presented, both including and excluding the dominant production of radiative Z events, and compared to Standard Model expectations. The ratio R b of the cross-section for bb production to the hadronic cross-section has been measured. In a model-independent t to the Z lineshape, the data have been used to obtain an improved precision on the measurement o f -Z interference. The energy dependence of em has been investigated. The measurements have also been used to obtain limits on extensions of the Standard Model described by eective four-fermion contact interactions, to search for t-channel contributions from new massive particles and to place limits on chargino pair production with subsequent decay of the chargino into a light gluino and a quark pair.

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“…The global fit is good (χ 2 ≈ 12 for 12 degrees of freedom), confirming to the present level of accuracy the experimental data and also the Standard Model as a theory, including electroweak radiative corrections. The exact definition of the Z-boson mass (and other resonance masses) is not a central issue of the Standard Model, and the prevailing opinion is that there are many ways to parameterize the experimental data of electroweak physics [6,9] and m 1 may be as good a value for the Z-boson mass asM Z and M R . However, though not presently needed for the Standard Model fits, the extraordinary accuracy of the Z-lineshape data, obtained with great expense of time and effort, allowed for the first time to discuss the problem of the definition of mass and width for an unstable relativistic particle and go beyond the level of precision given by the Weisskopf-Wigner approximation and one-loop effects.…”

Section: Introductionmentioning

confidence: 99%

The Definition of Mass and Width of Relativistic Resonances

Böhm¹,

Mithaiwala²

2003

AIP Conference Proceedings

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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 Φ− and 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, s] ± as functionals on the spaces Φ∓, one obtains Gamow kets |[j, sR] − with complex centre-of-mass energy value 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) GeV from the Z-boson lineshape data.

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Model-independent representation of electroweak data

Cited by 10 publications

References 19 publications

Relativistic resonances: Their masses, widths, lifetimes, superposition, and causal evolution

Relativistic resonances: Their masses, widths, lifetimes, superposition, and causal evolution

Tests of the standard model and constraints on new physics from measurements of fermion-pair production at 130–172 GeV at LEP

The Definition of Mass and Width of Relativistic Resonances

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