Implications of the Muon g-2 result on the flavour structure of the lepton mass matrix

<jats:title>Abstract</jats:title><jats:p>The confirmation of the discrepancy with the Standard Model predictions in the anomalous magnetic moment by the Muon g-2 experiment at Fermilab points to a low scale of new physics. Flavour symmetries broken at low energies can account for this discrepancy but these models are much more restricted, as they would also generate off-diagonal entries in the dipole moment matrix. Therefore, if we assume that the observed discrepancy in the muon <jats:inline-formula><jats:alternatives><jats:tex-math>$$g-2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> is explained by the contributions of a low-energy flavor symmetry, lepton flavour violating processes can constrain the structure of the lepton mass matrices and therefore the flavour symmetries themselves predicting these structures. We apply these ideas to several discrete flavour symmetries popular in the leptonic sector, such as <jats:inline-formula><jats:alternatives><jats:tex-math>$$\Delta (27)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mo>(</mml:mo> <mml:mn>27</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>, <jats:inline-formula><jats:alternatives><jats:tex-math>$$A_4$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>, and <jats:inline-formula><jats:alternatives><jats:tex-math>$$A_5 < imes \mathrm{CP}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>5</mml:mn> </mml:msub> <mml:mo>⋉</mml:mo> <mml:mi>CP</mml:mi> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>.</jats:p>