Evidence increased to 3 sigma, published in Nature
Swampland: McNavara and Vafa argue that in \(d\geq 4\) quantum gravity, because of the swampland thinking and the lack of adjustable parameters, baby universes are possible but only if their wave function is unique i.e. a Hartle-Hawking wave function.
The six quarks \((u,c,t;d,s,b)\) have six masses which are eigenvalues. But the up-type quarks, mass eigenstates, aren't exactly \(SU(2)\) partners of the down-type quarks, mass eigenstates. Instead, they are related by the
CKM matrix\[
\begin{bmatrix} d^\prime \\ s^\prime \\ b^\prime \end{bmatrix} = \begin{bmatrix} V_{ud} & V_{us} & V_{ub} \\ V_{cd} & V_{cs} & V_{cb} \\ V_{td} & V_{ts} & V_{tb} \end{bmatrix} \begin{bmatrix} d \\ s \\ b \end{bmatrix}.
\] The \(3\times 3\) matrix is a \(U(3)\) matrix which would have 9 independent parameters but 5 may be eliminated by changing the phases of the 6 eigenstates (one overall change of all these phases doesn't change the \(U(3)\) matrix). The remaining 4 parameters are equivalent to 3 parameters of an \(SO(3)\) rotation matrix decorated with an extra complex CP-violating phase \(\delta_{13}\) which is about \(1.2\pm 0.1\) radians.
The \(SO(3)\) part of the CKM matrix is approximately\[
\begin{bmatrix}
0.9743 \pm 0.0002 & 0.2253 \pm 0.0007 & 0.0035^{+0.0002}_{-0.0001} \\
0.2252 \pm 0.0007 & 0.9734 \pm 0.0002 & 0.041^{+0.001}_{-0.001} \\
0.0087^{+0.0003}_{-0.0003} & 0.040^{+0.001}_{-0.001} & 0.99915^{+0.00002}_{-0.00005}
\end{bmatrix}.
\] Now, just like there are 3+3 species of quarks, there are 3+3 leptons – three charged leptons and their corresponding neutrinos \((e^-,\mu^-,\tau^-;\nu_e, \nu_\mu, \nu_\tau)\).
