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Nuclear-Level Effective Theory of μ→e Conversion.
Evan Rule1, W C Haxton1,2, Kenneth McElvain1
1Department of Physics, University of California, Berkeley, California 94720, USA.
Physical Review Letters
|April 17, 2023
Summary
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.
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.
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