Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1995-07-25
Phys.Rev.D53:6226-6240,1996
Physics
High Energy Physics
High Energy Physics - Phenomenology
30 pages, Revtex using epsf, uuencoded, packed Postscript figures. The analysis has been updated to include the 3-loop running
Scientific paper
10.1103/PhysRevD.53.6226
The amplitudes for $2\rightarrow 2$ scattering processes involving longitudinally polarized gauge bosons $( W_L^\pm, Z_L )$ and the Higgs boson are analyzed up to two loops. Assuming $M_H >> M_W$, the trilinear Higgs coupling, $\lambda v$, is dominant for energies of $\sqrt{s}$ < 1.5 -- 2 $M_H$. For larger values of $\sqrt{s}$, the quartic coupling, $\lambda$, becomes dominant, allowing for a simpler calculation of higher-order corrections. The high-energy amplitudes display a large logarithmic dependence on $\sqrt{s}$ which can be resummed using renormalization group techniques. The resummation of leading-log terms is sufficient for Higgs masses of less than 350 GeV. For 350 < $M_H$ < 450 GeV, a next-to-leading-log resummation is necessary. For even larger values of $M_H$, the perturbative approach fails completely since two-loop terms become in magnitude larger than one-loop terms. Choosing the $\overline{{\rm MS}}$ renormalization scheme instead of the OMS scheme, the coefficients of the perturbative series increase in magnitude, making the breakdown of perturbation theory even more apparent. In conclusion, the Standard Model cross sections presented here have very large uncertainties if $M_H\gtrsim 450$ GeV and $\sqrt{s} \gtrsim 2 M_H$, reducing the sensitivity to contributions from new physics significantly.
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