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Rule, Evan

Publications and source records attributed to Rule, Evan.

4 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Effective theory tower for ΞΌ β†’ e conversion

We present theoretical predictions for ΞΌ β†’ e conversion rates using a tower of effective field theories connecting the UV to nuclear physics scales. The interactions in nuclei are described using a recently developed nonrelativistic effective theory (NRET) that organizes contributions according to bound nucleon and muon velocities, ${\overrightarrow{v}}_N$ and ${\overrightarrow{v}}_ΞΌ$, with |${\overrightarrow{v}}_N$| > |${\overrightarrow{v}}_ΞΌ$|. To facilitate the top-down matching, we enlarge the set of Lorentz covariant nucleon-level interactions mapped onto the NRET operators to include those mediated by tensor interactions, in addition to the scalar and vector interactions already considered previously, and then match NRET nonperturbatively onto the Weak Effective Theory (WET). At the scale ΞΌ β‰ˆ 2 GeV WET is formulated in terms of u, d, s quarks, gluons and photons as the light degrees of freedom, along with the flavor-violating leptonic current. We retain contributions from WET operators up to dimension 7, which requires the full set of 26 NRET operators. The results are encoded in the open-source Python- and Mathematica-based software suite MuonBridge, which we make available to the theoretical and experimental communities interested in ΞΌ β†’ e conversion.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Nuclear-level effective theory of πœ‡β†’π‘’ conversion: Formalism and applications

Over the next decade new πœ‡β†’π‘’ conversion searches at Fermilab (Mu2e) and J-PARC (COMET, DeeMe) are expected to advance limits on charged lepton flavor violation (CLFV) by more than four orders of magnitude. Here, by considering the consequence of 𝑃 and 𝐢⁒𝑃 on elastic πœ‡β†’π‘’ conversion and the structure of possible charge and current densities, we show that rates are governed by six nuclear responses and a single scale, π‘ž/π‘š 𝑁 , where π‘ž β‰ˆ π‘š πœ‡ is the momentum transferred from the leptons to the nucleus. To relate this result to microscopic formulations of CLFV, we construct in nonrelativistic effective theory (NRET) the CLFV nucleon-level interaction, pointing out the relevance of the dimensionless scales 𝑦=($^{π‘žβ’π‘}_2$) 2 ⁒ > |$\overrightarrow{𝑣}_N$⁒|>|$\overrightarrow{𝑣}_ΞΌ$⁒|>|$\overrightarrow{𝑣}_T$| , where 𝑏 is the nuclear size, $\overrightarrow{𝑣}_N$ and $\overrightarrow{𝑣}_ΞΌ$ are the nucleon and muon intrinsic velocities, and $\overrightarrow{𝑣}_T$ is the target recoil velocity. We discuss previous work, noting the lack of a systematic treatment of the various small parameters. Because the parameter 𝑦 is not small, a proper calculation of πœ‡β†’π‘’ conversion requires a full multipole expansion of the nuclear response functions, an apparently daunting task with Coulomb-distorted electron partial waves. We demonstrate that the multipole expansion can be carried out to high precision by introducing a simplifying local momentum π‘ž eff for the electron. Previous work has been limited to simple charge or spin interactions, thereby treating the nucleus effectively as a point particle. We show that such formulations are not compatible with the general form of the πœ‡β†’π‘’ conversion rate, failing to generate three of the six allowed nuclear response functions. The inclusion of the nucleon velocity $\overrightarrow{𝑣}_N$ yields an NRET with 16 operators and a rate of the general form. Consequently, in the current discovery era for CLFV, it provides the most sensible starting point for experimental analysis, defining what can and cannot be determined about CLFV from the highly exclusive process of πœ‡β†’π‘’ conversion. Finally, we expand the NRET operator basis to account for the effects of $\overrightarrow{𝑣}_ΞΌ$, associated with the muon's lower component, generating corrections to the CLFV coefficients of the point-nucleus response functions. Using advanced shell-model methods, we compute πœ‡β†’π‘’ conversion rates for a series of experimental targets, deriving bounds on the coefficients of the CLFV operators. These calculations are the first to include a general basis of CLFV operators, full evaluation of the associated nuclear response functions, and an accurate treatment of electron and muon Coulomb effects. We discuss target selection as an experimental β€œknob” that can be turned to probe the microscopic origins of CLFV. We describe two types of coherence that enhance certain CLFV operators and selection rules that blind elastic πœ‡β†’π‘’ conversion to others. We discuss the matching of the NRET onto higher level effective field theories, such as those constructed at the light quark level, noting opportunities to build on existing work in direct detection of dark matter. We discuss the relation of πœ‡β†’π‘’ conversion to πœ‡β†’π‘’+𝛾 and πœ‡β†’3⁒𝑒, showing how MEG II and Mu3e results will complement those of Mu2e and COMET. Finally we describe a accompanying scriptβ€”in Mathematica and Python versionsβ€”that can be used to compute πœ‡β†’π‘’ conversion rates in various nuclear targets for the full set of NRET operators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Nuclear-Level Effective Theory of πœ‡ β†’ 𝑒 Conversion

The Mu2e and COMET πœ‡ β†’ 𝑒 conversion experiments are expected to significantly advance limits on new sources of charged lepton flavor violation. Almost all theoretical work in the field has focused on just two operators. However, general symmetry arguments lead to a πœ‡ β†’ 𝑒 conversion rate with six response functions, each of which, in principle, is observable by varying nuclear properties of targets. We construct a nucleon-level nonrelativistic effective theory (NRET) to clarify the microscopic origin of these response functions and to relate rate measurements in different targets. This exercise identifies three operators and their small parameters that control the NRET operator expansion. We note inconsistencies in past treatments of these parameters. The NRET is technically challenging, involving 16 operators, several distorted electron partial waves, bound muon upper and lower components, and an exclusive nuclear matrix element. We introduce a trick for treating the electron Coulomb effects accurately, which enables us to include all of these effects while producing transition densities whose one-body matrix elements can be evaluated analytically, greatly simplifying the nuclear physics. We derive bounds on operator coefficients from existing and anticipated πœ‡ β†’ 𝑒 conversion experiments. We discuss how similar NRET formulations have impacted dark matter phenomenology, noting that the tools this community has developed could be adapted for charged lepton flavor violation studies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Next-to-leading order scalar contributions to πœ‡β†’π‘’ conversion

Within a class of models in which lepton flavor violation is induced dominantly by scalar particle exchanges, we estimate the πœ‡β†’π‘’ 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 πœ‡β†’π‘’ conversion in multiple target nuclei and πœ‡β†’π‘’β’π›Ύ.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗