Estimate of the three-loop MS contribution to σ(WL+WL−→ZLZL)

The three-loop contribution to the MS single-Higgs-doublet standard-model cross-section σ(WL+WL−→ZLZL) at s=(5MH)2 is estimated via least-squares matching of the asymptotic Padé-approximant prediction of the next order term, a procedure that has been previously applied to QCD corrections to correlation functions and decay amplitudes. In contrast to these prior applications, the expansion parameter for the WL+WL−→ZLZL process is the non-asymptotically-free quartic scalar-field coupling of the standard model, suggesting that the least-squares matching be performed over the “infrared” μ2⩽s region of the scale parameter. All three coefficients of logarithms within the three-loop term obtained by such matching are found to be within 6.6% relative error of their true values, as determined via renormalization-group methods. Surprisingly, almost identical results are obtained by performing the least squares matching over the μ2⩾s region.