CPT-Odd effects on the electromagnetic properties of charged leptons in the standard model extension

Abstract The impact of the CPT-Odd electroweak gauge sector of the Standard Model Extension on the electromagnetic properties of charged leptons is studied. This gauge sector is characterized by the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mi>μ</mml:mi> </mml:mrow> </mml:msub> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mi>μ</mml:mi> </mml:mrow> </mml:msub> </mml:math> Lorentz violation (LV) coefficients, which have positive mass dimension because they are associated with a U Y (1)-invariant and with an SU L (2)-invariant dimension-three operators, respectively. They belong to the category of relevant interactions, which can have strong effects on low-energy observables. We present a comprehensive study on the impact of this sector on the magnetic dipole moment (MDM) and the electric dipole moment (EDM) of charged leptons, up to second order in these LV coefficients, both at the tree and one-loop levels. We find that the O ( k i ) contributions at the tree and one-loop levels depend on energy, while <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">)</mml:mo> </mml:math> ones at the tree-level do not. As for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">)</mml:mo> </mml:math> one-loop effects, there are both energy-dependent and energy-independent contributions, but we have focused only on those of the latter type. We find that the EDM only is generated at O ( k i ) up to one-loop level, whereas the MDM receives contributions from both O ( k i ) and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">)</mml:mo> </mml:math> at both tree and one-loop levels. The contributions of O ( k i ) to the MDM are found to be suppressed relative to the corresponding contributions to the EDM by approximately three orders of magnitude. Using a recent experimental limit on the electron EDM the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">∣</mml:mo> <mml:msub> <mml:mfenced close=")" open="("> <mml:msub> <mml:mi>k</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mfenced> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>−</mml:mo> <mml:mo stretchy="false">∣</mml:mo> <mml:msub> <mml:mi mathvariant="bold">k</mml:mi> <mml:mn mathvariant="bold">2</mml:mn> </mml:msub> <mml:mo stretchy="false">∣</mml:mo> <mml:mi>cos</mml:mi> <mml:msub> <mml:mi>θ</mml:mi> <mml:mi>γ</mml:mi> </mml:msub> <mml:mo stretchy="false">∣</mml:mo> <mml:mo>&lt;</mml:mo> <mml:mn>0.86</mml:mn> <mml:mspace width="0.25em"/> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:math> bound was obtained. As far as the contributions of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">)</mml:mo> </mml:math> are concerned, we find that the tree-level contributions are suppressed with respect to the one-loop ones by at least a factor of <jats:tex-mat