Verifying the Resonance Schemes of Unstable Particles at Lepton Colliders

Abstract

We propose practical ways of differentiating the various (Breit-Wigner, theoretical, and energy-dependent) resonance schemes of unstable particles at lepton colliders. First, the energy-dependent scheme can be distinguished from the other two by fitting the $Z$ lineshape scan and forward-backward asymmetries at LEP and future lepton colliders with the $Z$ mass $m_Z$, decay width ${\Gamma }_Z$, and coupling strength as fitting parameters. Although the Breit-Wigner and theoretical schemes work equally well, the scheme conversion requires the decay width ${\Gamma }_Z$ to scale inversely with $m_Z$ rather than the usual linear dependence from theoretical calculation. These contradicting behaviors can be used to distinguish the Breit-Wigner and theoretical schemes by the precision $Z$ measurements with single parameter ($m_Z$) fit at future lepton colliders. For the $WW$ threshold scan, its combination with the precise Fermi constant provides another way of distinguishing the Breit-Wigner and theoretical schemes.

arXiv comment6 pages, 1 table. v2: match the published version in PLB

References in corpus (12)

• Precision Electroweak Measurements on the Z Resonance
• Electroweak Measurements in Electron-Positron Collisions at W-Boson-Pair Energies at LEP
• ZFITTER v.6.21 - A Semi-Analytical Program for Fermion Pair Production in e+e- Annihilation
• Gauge Invariance and Unstable Particles
• A Gauge-Independent Approach to Resonant Transition Amplitudes
• Gauge-Invariant Resummation Formalism for Two-Point Correlation Functions
• Measurements of Cross Sections and Forward-Backward Asymmetries at the Z Resonance and Determination of Electroweak Parameters
• Precise Determination of the Z Resonance Parameters at LEP : Zedometry
• Relativistic resonances: Their masses, widths, lifetimes, superposition, and causal evolution
• Measurement of the W-boson mass and width with the ATLAS detector using proton-proton collisions at $\sqrt{s}$ = 7 TeV
• A simple alternative to the Breit-Wigner distribution
• Measurement of Heavy Quark Forward-Backward Asymmetries and Average B Mixing Using Leptons in Hadronic Z Decays