The geometric νSMEFT: operators and connections
Jim Talbert
Abstract
A bstract We write down a geometric realization of the Standard Model Effective Field Theory (SMEFT) extended by n f flavours of light sterile neutrinos, a so-called geo ν SMEFT. As with the geoSMEFT introduced by Helset, Martin and Trott, we show that a refactorization of the ν SMEFT’s operator product expansion is possible, such that two- and three-point composite operator forms are dressed with field-space connections composed of towers of Higgs dressings and symmetry generators, valid at all-orders in the $$ {\overline{v}}_T/\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>v</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>T</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:mi>Λ</mml:mi> </mml:math> expansion parameter of the EFT $$ \left({\overline{v}}_T\equiv \sqrt{2\left\langle {H}^{\dagger }H\right\rangle}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mrow> <mml:msub> <mml:mover> <mml:mi>v</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>T</mml:mi> </mml:msub> <mml:mo>≡</mml:mo> <mml:msqrt> <mml:mrow> <mml:mn>2</mml:mn> <mml:mfenced> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mo>†</mml:mo> </mml:msup> <mml:mi>H</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:msqrt> </mml:mrow> </mml:mfenced> </mml:math> . These connections are parameterized by real Higgs coordinates and contribute to the field-space geometry of the ( ν )SMEFT, with structure linked to the strength of Beyond-the-( ν )Standard Model physics encoded in $$ {\overline{v}}_T/\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>v</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>T</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:mi>Λ</mml:mi> </mml:math> . In addition to enumerating the relevant composite operators and associated connections, we briefly outline the route to calculating all- $$ {\overline{v}}_T/\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>v</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>T</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:mi>Λ</mml:mi> </mml:math> -orders amplitudes, including the flavor-invariant theory required to understand the neutrino mass-eigenstate basis geometrically.