Matching scalar leptoquarks to the SMEFT at one loop
Valerio Gherardi, David Marzocca, Elena Venturini
Abstract
A bstract In this paper we present the complete one-loop matching conditions, up to dimension-six operators of the Standard Model effective field theory, resulting by integrating out the two scalar leptoquarks $$ {S}_1\sim {\left(\mathbf{3},\mathbf{1}\right)}_{\frac{1}{3}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>∼</mml:mo> <mml:msub> <mml:mfenced> <mml:mn>3</mml:mn> <mml:mn>1</mml:mn> </mml:mfenced> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>3</mml:mn> </mml:mfrac> </mml:msub> </mml:math> and $$ {S}_3\sim {\left(\mathbf{3},\mathbf{3}\right)}_{\frac{1}{3}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mo>∼</mml:mo> <mml:msub> <mml:mfenced> <mml:mn>3</mml:mn> <mml:mn>3</mml:mn> </mml:mfenced> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>3</mml:mn> </mml:mfrac> </mml:msub> </mml:math> . This allows a phenomenological study of low-energy constraints on this model at one-loop accuracy, which will be the focus of a subsequent work. Furthermore, it provides a rich comparison for functional and computational methods for one-loop matching, that are being developed. As a corollary result, we derive a complete set of dimension-six operators independent under integration by parts, but not under equations of motions, called Green’s basis , as well as the complete reduction formulae from this set to the Warsaw basis.