Addressing the CKM unitarity problem with a vector-like up quark

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>We point out that hints of deviations from unitarity in the first row of the CKM matrix may be explained by the presence of a single vector-like top. We study how the stringent experimental constraints arising from CP Violation in the kaon sector and from meson mixing such as <jats:inline-formula><jats:alternatives><jats:tex-math>$$ {D}^0\hbox{-} {\overline{D}}^0,{K}^0\hbox{-} {\overline{K}}^0 $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:mo>‐</mml:mo> <mml:msup> <mml:mover> <mml:mi>D</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mn>0</mml:mn> </mml:msup> <mml:mo>,</mml:mo> <mml:msup> <mml:mi>K</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:mo>‐</mml:mo> <mml:msup> <mml:mover> <mml:mi>K</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mn>0</mml:mn> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$ {B}_{d,s}^0\hbox{-} {\overline{B}}_{d,s}^0 $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>,</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> <mml:mn>0</mml:mn> </mml:msubsup> <mml:mo>‐</mml:mo> <mml:msubsup> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>,</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> <mml:mn>0</mml:mn> </mml:msubsup> </mml:math></jats:alternatives></jats:inline-formula> can be satisfied in the proposed framework. In order for the deviations from unitarity to be of the required size while keeping the theory perturbative, the new top quark should have a mass <jats:italic>m</jats:italic><jats:sub><jats:italic>T</jats:italic></jats:sub> ≲ 7 TeV which could be probed in upcoming experiments at the energy frontier.</jats:p>