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

Published version
Peer-reviewed

Change log

Authors

Talbert, Jim 
Trott, Michael 

Abstract

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>

Description

Keywords

Regular Article - Theoretical Physics, Quark Masses and SM Parameters, Beyond Standard Model, Effective Field Theories

Journal Title

Journal of High Energy Physics

Conference Name

Journal ISSN

1126-6708
1029-8479

Volume Title

2021

Publisher

Springer Science and Business Media LLC