2003/04/15 by U. Aglietti, Roberto Bonciani, R. Bonciani · 2 citations
Mathematics · Physics and Astronomy · #Annihilation #Boson #Cosmology and Gravitation Theories #Degenerate energy levels #Dimension (graph theory) #Electroweak interaction #Fermion #Form factor (electronics) #Harmonic oscillator #High-Energy Particle Collisions Research #Massless particle #Mathematical physics #Mathematics #Momentum (technical analysis) #Particle physics #Particle physics theoretical and experimental studies #Physics #Propagator #Pure mathematics #Quantum mechanics #hep-ph
paper · pdf · doi:10.1016/j.nuclphysb.2003.07.004
published as Nucl.Phys. B668 (2003) 3-76 · 73 pages, 9 figures, uses feynmf.sty and axodraw.sty, references added
arxiv created 2003/04/15 · openalex publication_date 2003/08/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We compute the master integrals containing one massive propagator entering the two-loop electroweak form factor, i.e., the process ff̄→X, where ff̄ is an on-shell massless fermion pair and X is a singlet particle under SU(2)L×U(1)Y, such as a virtual gluon or an hypothetical Z′. The method used is that of the differential equation in the evolution variable x=−s/m2, where s is the c.m. energy squared and m is the mass of the W or Z bosons (assumed to be degenerate). The 1/ϵ poles and the finite parts are computed exactly in terms of one-dimensional harmonic polylogarithms of the variable x, H(w→;x), with ϵ=2−D/2 and D the space–time dimension. We present large-momentum expansions of the master integrals, i.e., expansions for |s|⪢m2, which are relevant for the study of infrared properties of the Standard Model. We also derive small-momentum expansions of the master integrals, i.e., expansions in the region |s|⪡m2, related to the threshold behaviour of the form factor (soft probe). Comparison with previous results in the literature is performed finding complete agreement.