Nuclear-Level Effective Theory of μ→e\mu\rightarrow e Conversion

The Mu2e and COMET $\mu \rightarrow e$ conversion experiments are expected to significantly advance limits on new sources of charged lepton flavor violation (CLFV). Almost all theoretical work in the field has focused on just two operators. However, general symmetry arguments lead to a $\mu \rightarrow e$ 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 $\mu \rightarrow e$ 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 CLFV studies.Comment: 5 pages, 2 figures, to be submitted to PR

Nuclear-level Effective Theory of Muon-to-Electron Conversion: Formalism and Applications

New mu-to-e conversion searches aim to advance limits on charged lepton flavor violation (CLFV) by four orders of magnitude. By considering P and CP selection rules and the structure of possible charge and current densities, we show that rates are governed by six nuclear responses. To generate a microscopic formulation of these responses, we construct in non-relativistic effective theory (NRET) the CLFV nucleon-level interaction, then embed it in a nucleus. We discuss previous work, noting the lack of a systematic treatment of the various small parameters. Because the momentum transfer is comparable to the inverse nuclear size, a full multipole expansion of the response functions is necessary, a daunting task with Coulomb-distorted electron partial waves. We perform such an expansion to high precision by introducing a simplifying local electron momentum, treating the full set of 16 NRET operators. Previous work has been limited to the simplest charge/spin operators, ignored Coulomb distortion (or alternatively truncated the partial wave expansion) and the nucleon velocity operator, which is responsible for three of the response functions. This generates inconsistencies in the treatment of small parameters. We obtain a "master formula" for mu-to-e conversion that properly treats all such effects and those of the muon velocity. We compute muon-to-electron conversion rates for a series of experimental targets, deriving bounds on the coefficients of the CLFV operators. We discuss the nuclear physics: two types of coherence enhance certain CLFV operators and selection rules blind elastic mu-to-e conversion to others. We discuss the matching of the NRET onto higher level EFTs, and the relation to mu-to-e conversion to other CLFV tests. Finally we describe a publicly available script that can be used to compute mu-to-e conversion rates in nuclear targets.Comment: 50 pages, 10 figures; a few typos fixed in v

Simulating the weak death of the neutron in a femtoscale universe with near-Exascale computing

The fundamental particle theory called Quantum Chromodynamics (QCD) dictates everything about protons and neutrons, from their intrinsic properties to interactions that bind them into atomic nuclei. Quantities that cannot be fully resolved through experiment, such as the neutron lifetime (whose precise value is important for the existence of light-atomic elements that make the sun shine and life possible), may be understood through numerical solutions to QCD. We directly solve QCD using Lattice Gauge Theory and calculate nuclear observables such as neutron lifetime. We have developed an improved algorithm that exponentially decreases the time-to solution and applied it on the new CORAL supercomputers, Sierra and Summit. We use run-time autotuning to distribute GPU resources, achieving 20% performance at low node count. We also developed optimal application mapping through a job manager, which allows CPU and GPU jobs to be interleaved, yielding 15% of peak performance when deployed across large fractions of CORAL.Comment: 2018 Gordon Bell Finalist: 9 pages, 9 figures; v2: fixed 2 typos and appended acknowledgement

Simulating the weak death of the neutron in a femtoscale universe with near-Exascale computing

The fundamental particle theory called Quantum Chromodynamics (QCD) dictates everything about protons and neutrons, from their intrinsic properties to interactions that bind them into atomic nuclei. Quantities that cannot be fully resolved through experiment, such as the neutron lifetime (whose precise value is important for the existence of light-atomic elements that make the sun shine and life possible), may be understood through numerical solutions to QCD. We directly solve QCD using Lattice Gauge Theory and calculate nuclear observables such as neutron lifetime. We have developed an improved algorithm that exponentially decreases the time-to solution and applied it on the new CORAL supercomputers, Sierra and Summit. We use run-time autotuning to distribute GPU resources, achieving 20% performance at low node count. We also developed optimal application mapping through a job manager, which allows CPU and GPU jobs to be interleaved, yielding 15% of peak performance when deployed across large fractions of CORAL