Measuring Electron Energy in Muon-to-Electron Conversion using Holographic Synchrotron Radiation Emission Spectroscopy

The coherent conversion of a muon to an electron in a nuclear field has been one of the most powerful methods to search for Charged Lepton Flavor Violation (CLFV). Recent advancements have significantly enhanced the sensitivity of $\mu \rightarrow e$ searches, primarily driven by advancements in muon beamline design and low-mass tracking detectors, which afford exceptional momentum resolution. Nevertheless, the performance of these detectors is inherently limited by electron scattering and energy loss within detector materials. To overcome these inevitable limitations, we propose a novel holographic track reconstruction leveraging synchrotron radiation emitted by electrons. Similar to cyclotron radiation emission spectroscopy (CRES) which has demonstrated outstanding energy resolutions for low-energy electrons, our technique relies on a precision measurement of cyclotron frequency, but in a regime where photons are emitted stochastically and are projected onto a 2-dimensional inner surface of a solenoidal magnet. We outline the concept of such a massless holographic tracker and feasibility of employing this innovative detection strategy for $\mu \rightarrow e$ conversion. We also address pertinent limitations and challenges inherent to the method.