<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>μ</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>e</mml:mi><mml:mi>γ</mml:mi></mml:math> selecting scalar leptoquark solutions for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo stretchy="false">(</mml:mo><mml:mi>g</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mi>e</mml:mi><mml:mo>,</mml:mo><mml:mi>μ</mml:mi></mml:mrow></mml:msub></mml:math> puzzles
Ilja Doršner, Svjetlana Fajfer, Shaikh Saad
Abstract
We investigate all potentially viable scenarios that can produce the chiral enhancement required to simultaneously explain the $(g\ensuremath{-}2{)}_{e}$ and $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$ data with either a single scalar leptoquark or a pair of scalar leptoquarks. We provide a classification of these scenarios in terms of their ability to satisfy the existing limits on the branching ratio for the $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ process. The simultaneous explanation of the $(g\ensuremath{-}2{)}_{e,\ensuremath{\mu}}$ discrepancies, coupled with the current experimental data, implies that the $(g\ensuremath{-}2{)}_{e}$ loops are exclusively due to the charm-quark propagation, whereas the $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$ loops are due to the top-quark propagation. The scenarios where the $(g\ensuremath{-}2{)}_{e}$ loops are due to the top (bottom) quark propagation are, at best, approximately 9 (3) orders of magnitude away from the experimental limit on the $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ branching ratio. All in all, there are only three particular scenarios that can pass the $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ test and simultaneously create a large enough impact on the $(g\ensuremath{-}2{)}_{e,\ensuremath{\mu}}$ discrepancies when the new physics is based on the Standard Model fermion content. These are the ${S}_{1}$, ${R}_{2}$, and ${S}_{1}&{S}_{3}$ scenarios, where the first two are already known to be phenomenologically viable candidates with respect to all other flavor and collider data constraints. We show that the third scenario---where the right-chiral couplings to charged leptons are due to ${S}_{1}$, the left-chiral couplings to charged leptons are due to ${S}_{3}$, and the two leptoquarks mix through the Standard Model Higgs field---cannot address the $(g\ensuremath{-}2{)}_{e}$ and $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$ discrepancies at the $1\ensuremath{\sigma}$ level due to an interplay between ${K}_{L}^{0}\ensuremath{\rightarrow}{e}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\mu}}^{\ensuremath{\mp}}$, $Z\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}$, and $Z\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ data despite the ability of that scenario to avoid the $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ limit.