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New experiments like Mu2e and COMET probe charged lepton flavor violation. This study introduces a nucleon-level nonrelativistic effective theory to analyze six response functions, offering a more comprehensive understanding of muon-to-electron conversion.

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Area of Science:

  • Particle Physics
  • Nuclear Physics
  • Beyond Standard Model Physics

Background:

  • Muon-to-electron (μ→e) conversion experiments, such as Mu2e and COMET, aim to discover new sources of charged lepton flavor violation.
  • Existing theoretical frameworks primarily focus on two operators, potentially overlooking other contributions to μ→e conversion.

Purpose of the Study:

  • To develop a comprehensive theoretical framework, a nucleon-level nonrelativistic effective theory (NRET), to analyze the full spectrum of six response functions governing μ→e conversion.
  • To clarify the microscopic origins of these response functions and establish relationships between conversion rates observed in targets with different nuclear properties.
  • To identify and address inconsistencies in the treatment of parameters within the NRET framework.

Main Methods:

  • Construction of a nucleon-level nonrelativistic effective theory (NRET) encompassing 16 operators.
  • Accurate treatment of electron Coulomb effects using a novel method to simplify nuclear physics calculations.
  • Analytical evaluation of one-body matrix elements for transition densities.
  • Derivation of bounds on operator coefficients using existing and planned μ→e conversion experiments.

Main Results:

  • Identification of three key operators and their associated small parameters controlling the NRET expansion.
  • Resolution of inconsistencies in the treatment of these parameters in previous studies.
  • Development of a computationally tractable NRET that incorporates complex elements like distorted electron partial waves and bound muon components.

Conclusions:

  • The developed NRET provides a more complete picture of μ→e conversion by analyzing six response functions, advancing the interpretation of experimental results.
  • The methodology, drawing parallels with dark matter phenomenology, offers adaptable tools for future charged lepton flavor violation studies.
  • This work sets improved bounds on operator coefficients, enhancing the sensitivity of future experiments.