Electroweak Constraints on the Fourth Generation at Two Loop Order

TL;DR

This paper investigates the electroweak corrections at two-loop order in four-generation models of the Standard Model, revealing significant effects of hypercharge corrections on the rho parameter and estimating the validity range of perturbation theory.

Contribution

It introduces the first detailed analysis of two-loop hypercharge corrections in 4G models, highlighting their impact on electroweak fits and perturbation theory validity.

Findings

Two-loop hypercharge correction significantly affects the rho parameter.

Perturbation theory remains valid up to quark masses of about 600 GeV.

Large negative two-loop correction challenges previous one-loop assumptions.

Abstract

If the Higgs-like particle at 126 GeV is the standard model Higgs boson, then SM4, the simplest four generation extension of the SM, is inconsistent with the most recent LHC data. However, 4G variations (BSM4) are possible if the new particle is not the SM Higgs boson and/or if other new quanta modify its production and decay rates. Since LHC searches have pushed 4G quarks to high mass and strong coupling where perturbation theory eventually fails, we examine the leading nondecoupling EW (electroweak) corrections at two loop order to estimate the domain of validity for perturbation theory. We find that the two loop hypercharge correction, which has not been included in previous EW fits of 4G models, makes the largest quark sector contribution to the rho parameter, much larger even than the nominally leading one loop term. Because it is large and negative, it has a big effect on the EW fits. It does not invalidate perturbation theory since it only first appears at two loop order and is large because it does not vanish for equal quark doublet masses, unlike the one loop term. We estimate that perturbation theory is useful for $m_Q\simeq 600$ GeV but begins to become marginal for $m_Q\, \gtap\, 900$ GeV. The results apply directly to BSM4 models that retain the SM Higgs sector but must be re-evaluated for non-SM Higgs sectors.