Two-loop high-energy electroweak logarithmic corrections in a spontaneously broken $SU(2)$ gauge model

We present the complete analytical result for the two-loop logarithmically enhanced contributions to the high-energy asymptotic behavior of the vector form factor and the four-fermion cross section in a spontaneously broken $SU(2)$ gauge model. On the basis of this result we derive the dominant two-loop electroweak corrections to the neutral current four-fermion processes at high energies.

Figure 1

The LL (short-dashed line), NLL (long-dashed line), NNLL (dot-dashed line) and ${\mathrm{N}}^3\mathrm{LL}$ (solid line) two-loop electroweak corrections to ${\mathcal{R}}_{lq}$ in percent.

Figure 2

The total electroweak logarithmic two-loop corrections to ${\mathcal{R}}_{lQ}$ (dashed line), ${\mathcal{R}}_{lq}$ (dot-dashed line) and ${\mathcal{R}}_{l{l}^{\prime }}$ (solid line) in percent.