Vectorlike lepton imprints at lepton <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>g</mml:mi> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:math> measurements and <mml:math xmlns:mml="http://www.w3.org/1998/Math/Mat

A fermion can be chiral or vectorlike with respect to a given symmetry, depending on its coupling to the corresponding gauge boson. Vectorlike fermions have a distinct property that their left- and right-handed components behave in the same way under the gauge symmetry. In this paper, we investigate an extension of the standard model with an <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>S</a:mi> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>2</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> doublet of vectorlike leptons and two complex scalars. The new physics effects on the lepton anomalous magnetic moment, as well as the electron and muon pair production processes at <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mi>e</e:mi> <e:mo>+</e:mo> </e:msup> <e:msup> <e:mi>e</e:mi> <e:mo>−</e:mo> </e:msup> </e:math> colliders are analyzed. Taking into account the updated measurement results of the electron and muon <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>g</g:mi> <g:mo>−</g:mo> <g:mn>2</g:mn> </g:math> , as well as the Large Electron-Positron Collider and the LHC data, the viable parameter space of the model is identified. We also examine the prospect of testing the model using <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msup> <i:mi>μ</i:mi> <i:mo>+</i:mo> </i:msup> <i:msup> <i:mi>μ</i:mi> <i:mo>−</i:mo> </i:msup> </i:math> signals from electron-position annihilation at the Future Circular Collider (FCC-ee). The analysis shows that the FCC-ee will be able to exclude a significant part of the parameter space, pinpointing exiguous viable regions to be tested in the future due to its high precision.