Over the next decade new μ→e 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. By considering the consequence of P and CP on elastic μ→e conversion and the structure of possible charge and current densities, we show that rates are governed by six nuclear responses and a single scale, q/mN, where q≈mμ 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=(qb2)2>|v→N|>|v→μ|>|v→T|, where b is the nuclear size, v→N and v→μ are the nucleon and muon intrinsic velocities, and 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 μ→e 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 qeff 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 μ→e conversion rate, failing to generate three of the six allowed nuclear response functions. The inclusion of the nucleon velocity 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 μ→e conversion. Finally, we expand the NRET operator basis to account for the effects of v→μ, 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 μ→e 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 "knob"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 μ→e 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 μ→e conversion to μ→e+γ and μ→3e, showing how MEG II and Mu3e results will complement those of Mu2e and COMET. Finally we describe a accompanying script - in Mathematica and Python versions - that can be used to compute μ→e conversion rates in various nuclear targets for the full set of NRET operators.

Within a class of models in which lepton flavor violation is induced dominantly by scalar particle exchanges, we estimate the μ→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 μ→e conversion in multiple target nuclei and μ→eγ.

This White Paper was prepared for the Nuclear Science Town Meeting on "Neutrinos, Neutrons and Fundamental Symmetries, held in Chicago on Jan. 17-19, 2007.

Particles beyond the Standard Model (SM) can generically have lifetimes that are long compared to SM particles at the weak scale. When produced at experiments such as the Large Hadron Collider (LHC) at CERN, these long-lived particles (LLPs) can decay far from the interaction vertex of the primary proton-proton collision. Such LLP signatures are distinct from those of promptly decaying particles that are targeted by the majority of searches for new physics at the LHC, often requiring customized techniques to identify, for example, significantly displaced decay vertices, tracks with atypical properties, and short track segments. Given their non-standard nature, a comprehensive overview of LLP signatures at the LHC is beneficial to ensure that possible avenues of the discovery of new physics are not overlooked. Here we report on the joint work of a community of theorists and experimentalists with the ATLAS, CMS, and LHCb experiments-as well as those working on dedicated experiments such as MoEDAL, milliQan, MATHUSLA, CODEX-b, and FASER-to survey the current state of LLP searches at the LHC, and to chart a path for the development of LLP searches into the future, both in the upcoming Run 3 and at the high-luminosity LHC. The work is organized around the current and future potential capabilities of LHC experiments to generally discover new LLPs, and takes a signature-based approach to surveying classes of models that give rise to LLPs rather than emphasizing any particular theory motivation. We develop a set of simplified models; assess the coverage of current searches; document known, often unexpected backgrounds; explore the capabilities of proposed detector upgrades; provide recommendations for the presentation of search results; and look towards the newest frontiers, namely high-multiplicity 'dark showers', highlighting opportunities for expanding the LHC reach for these signals.