Less space for a new family of fermions

TL;DR

This work quantitatively constrains a Standard Model with a fourth fermion generation (SM4) by combining tree-level CKM inputs, FCNC observables, and electroweak oblique parameters S, T, U, along with γ and B_s → μ^+ μ^−, using improved QCD treatment. An exact 4×4 CKM parameterization plus heavy masses is employed, and a large-scale scan reveals that moderately small mixing with the fourth generation is favored, with a minimal V_tb around 0.93; large CP-violating effects in B_s mixing remain unlikely once EW constraints are included. Importantly, the full CKM dependence of S and T allows, in principle, a degenerate fourth generation of quarks, highlighting a delicate interplay between electroweak and flavor observables that resists treating the sectors separately. The study suggests next steps toward a combined EW–CKM fit, inclusion of lepton mixing, and incorporation of additional precision observables to further delimit or reveal fourth-generation physics.

Abstract

We investigate the experimentally allowed parameter space of an extension of the standard model (SM3) by one additional family of fermions. Therefore we extend our previous study of the CKM like mixing constraints of a fourth generation of quarks. In addition to the bounds from tree-level determinations of the 3$\times$3 CKM elements and FCNC processes ($K$-, $D$-, $B_d$-, $B_s$-mixing and the decay $b \to s γ$) we also investigate the electroweak $S$, $T$, $U$ parameters, the angle $γ$ of the unitarity triangle and the rare decay $B_s \to μ^+ μ^-$. Moreover we improve our treatment of the QCD corrections compared to our previous analysis. We also take leptonic contributions into account, but we neglect the mixing among leptons. As a result we find that typically small mixing with the fourth family is favored, but still some sizeable deviations from the SM3 results are not yet excluded. The minimal possible value of $V_{tb}$ is 0.93. Also very large CP-violating effects in $B_s$ mixing seem to be impossible within an extension of the SM3 that consists of an additional fermion family alone. We find a delicate interplay of electroweak and flavor observables, which strongly suggests that a separate treatment of the two sectors is not feasible. In particular we show that the inclusion of the full CKM dependence of the $S$ and $T$ parameters in principle allows the existence of a degenerate fourth generation of quarks.

Figures (6)

• Figure 1: Fit of the electroweak oblique parameters $S$ and $T$. The plot is taken from Gfitterhomepage.
• Figure 2: Schematic diagrams for the necessary ingredients of the golden plated channel $B_d \to J/\Psi K_s$: B-mixing, Kaon mixing and the decay process itself. The left panel shows the tree-level and the right panel the penguin mediated decay. The dashed line represents any current capable of creating a $J/\Psi$, e.g. two gluons.
• Figure 3: Some correlations of the angles and phases.
• Figure 4: Possible modifications of the SM3 CKM matrix elements $V_{cd}$, $V_{cs}$, $V_{cb}$$V_{td}$, $V_{ts}$ and $V_{tb}$ in the SM4 scenario. Depicted is the real part versus the imaginary part of the CKM element (in the standard representation). The crossed lines show the SM3 value; $V_{cb}$ is real by construction in the SM3.
• Figure 5: Complex $\Delta$ plane for $B_s$ mixing. The green shaded area corresponds roughly to the experiment at the 1$\sigma$ level HFAG. The left panel shows the possible phase if one omits the $T$ parameter, the right panel shows the impact of $T$ on the allowed phase $\Phi_s$.