Some remarks about the asymptotic behaviour of the partial-wave amplitude for large angular momenta in potential scattering

1966 ◽  
Vol 45 (3) ◽  
pp. 740-746 ◽  
Author(s):  
M. Bertero
Keyword(s):  
Asymptotic Behaviour ◽  
Partial Wave ◽  
Wave Amplitude ◽  
Potential Scattering ◽  
Partial Wave Amplitude ◽  
Angular Momenta

UNITARITY BOUNDS ON WW SCATTERING AND ELECTROWEAK TESTS AT LEP

1993 ◽  
Vol 08 (07) ◽  
pp. 647-660
Author(s):  
G. GOUNARIS ◽  
F.M. RENARD ◽  
D. SCHILDKNECHT
Keyword(s):  
Integral Representation ◽  
Partial Wave ◽  
Upper Bound ◽  
Top Quark ◽  
Wave Amplitude ◽  
Vector Boson ◽  
High Energy ◽  
Partial Wave Amplitude ◽  
Vector Boson Scattering ◽  
Higgs Scalar

Replacing elementary Higgs exchange in vector-boson scattering by an angular-momentum-zero unitarity-saturating partial wave amplitude described by a dispersion relation which incorporates low-energy gauge theory and high-energy partial-wave unitarity constraints, we find an upper bound of Λ≲Λmax≅0.8 TeV for the scale, Λ, at which saturation of partial wave unitarity is to occur. Upon inserting the partial wave amplitude into a novel integral representation for the bosonic vacuum polarization contribution to the electroweak ρ parameter, Δρb, we establish an upper bound on −Δρb(≲0.033), while for the case of the elementary Higgs scalar, the integral representation reproduces the well known ln mH/mW formula for Δρb. The upper bound on −Δρb implies that the value of the mass of the top quark extracted from LEP1 measurements becomes justified even in the case when the Higgs scalar is replaced by a strong-interaction-like J=0 partial wave.

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