How much space is left for a new family?

TL;DR

This study explores the parameter space for a potential fourth quark family, analyzing experimental constraints to determine allowed mixing ranges, and finds that both small and surprisingly large mixings remain possible.

Contribution

It provides an exploratory analysis of the permissible CKM-like mixing parameters for a hypothetical fourth quark family using current experimental constraints.

Findings

Small mixing with the fourth family is generally favored.

Large mixing with the fourth family is still compatible with existing data.

The allowed parameter space for the fourth family mixing is broader than previously expected.

Abstract

We perform an exploratory study of the allowed parameter range for the CKM-like mixing of hypothetical quarks of a fourth generation. As experimental constraints we use the tree-level determinations of the 3 $\times$ 3 CKM elements and FCNC processes ($K$-, $D$-, $B_d$-, $B_s$-mixing and the decay $b \to s \gamma$) under the assumption that the 4 $\times$ 4 CKM matrix is unitary. For the FCNCs we use some simplifying assumptions concerning the QCD corrections. Typically small mixing with the fourth family is favoured, but contrary to expectation we find that also a quite large mixing with the 4th family is not yet excluded.