Dirac masses and mixings in the (geo)SM(EFT) and beyond

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Talbert, Jim 
Trott, Michael 

jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pWe report a set of exact formulae for computing Dirac masses, mixings, and CP-violation parameter(s) from 3×3 Yukawa matrices jats:italicY</jats:italic> valid when jats:italicYY</jats:italic>jats:sup†</jats:sup> → jats:italicU</jats:italic>jats:sup†</jats:sup>jats:italicYY</jats:italic>jats:sup†</jats:sup>jats:italicU</jats:italic> under global jats:inline-formulajats:alternativesjats:tex-math$$ \mathrm{U}{(3)}_{Q_L} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:miU</mml:mi> mml:msub mml:mfenced mml:mn3</mml:mn> </mml:mfenced> mml:msub mml:miQ</mml:mi> mml:miL</mml:mi> </mml:msub> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> flavour symmetry transformations jats:italicU</jats:italic>. The results apply to the Standard Model Effective Field Theory (SMEFT) and its ‘geometric’ realization (geoSMEFT). We thereby complete, in the Dirac flavour sector, the catalogue of geoSMEFT parameters derived at all orders in the jats:inline-formulajats:alternativesjats:tex-math$$ \sqrt{2\left\langle {H}^{\dagger }H\right\rangle } $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msqrt mml:mrow mml:mn2</mml:mn> mml:mfenced mml:mrow mml:msup mml:miH</mml:mi> mml:mo†</mml:mo> </mml:msup> mml:miH</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:msqrt> </mml:math></jats:alternatives></jats:inline-formula>jats:italic/</jats:italic>Λ expansion. The formalism is basis-independent, and can be applied to models with decoupled ultraviolet flavour dynamics, as well as to models whose infrared dynamics are not minimally flavour violating. We highlight these points with explicit examples and, as a further demonstration of the formalism’s utility, we derive expressions for the renormalization group flow of quark masses, mixings, and CP-violation at all mass dimension and perturbative loop orders in the (geo)SM(EFT) and beyond.</jats:p>

Regular Article - Theoretical Physics, Quark Masses and SM Parameters, Beyond Standard Model, Effective Field Theories
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Journal of High Energy Physics
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Springer Science and Business Media LLC