Next-to-leading order scalar contributions to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>μ</mml:mi><mml:mo>→</mml:mo><mml:mi>e</mml:mi></mml:mrow></mml:math> conversion
Vincenzo Cirigliano, Kaori Fuyuto, Michael J. Ramsey-Musolf, Evan Rule
Abstract
Within a class of models in which lepton flavor violation is induced dominantly by scalar particle exchanges, we estimate the $\ensuremath{\mu}\ensuremath{\rightarrow}e$ conversion rate in several nuclei. We include next-to-leading order (NLO) terms in the one- and two-nucleon interactions in chiral effective theory, rectifying some incorrect results in the previous literature. We provide an uncertainty budget for the conversion rates and we find that NLO contributions affect the amplitudes at the level of $10%$, which could be larger than the uncertainty on the leading order couplings, dominated by the strange and nonstrange nucleon sigma terms. We study the implications of our results for testing Higgs-mediated charged lepton flavor violation (CLFV) in the future by combining results from various experimental searches, such as $\ensuremath{\mu}\ensuremath{\rightarrow}e$ conversion in multiple target nuclei and $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$.