Unstable loop particle treatment of threshold singularities in Higgs boson production and decay
Abstract
The problem of threshold singularities in Higgs boson production and decay was first realized in connection with the calculation of leading order radiative correction to Higgs boson decay to W boson pair in the on-shell scheme of renormalization. The leading order radiative correction depends, among others, on the Higgs wavefunction renormalization Re[∂sΠHH(s=mH2)], which is proportional to [(2mZ/mH)2 − 1]−1/2 for mH2 close to 4mZ2, where ΠHH(s) is the Higgs boson self-energy and mH and mZ refer to the masses of the Higgs and neutral Z bosons, respectively. The correction and hence the decay width clearly diverges at threshold, mH2 = 4mZ2. This is illustrated here, where the one-loop corrected partial width of the Higgs boson to a pair of W bosons is plotted against the on-shell Higgs boson mass. This threshold singularity is a by-product of treating an unstable particle like the Higgs boson as an asymptotic state of the S-matrix. It is universal in the sense that the problem occurs in all other partial decay modes as long as the kinematically allowed Higgs mass range include values equal to twice the mass of either W and Z bosons.
In this paper, we pin down the source causing the one-loop Higgs boson decay width to diverge at threshold. We then illustrate how the problem is treated by considering the massive vector boson circulating in the loop to be unstable as well. The treatment does not induce spurious gauge dependence. We apply the treatment to the Higgs boson decay to W boson pair.
