# Lorentz and CPT Tests Using Penning Traps

## Abstract

**:**

## 1. Introduction

## 2. Theory

_{ψ}confined in an external electromagnetic field specified by potential ${A}_{\mu}$, the conventional gauge-invariant Lagrange density ${\mathcal{L}}_{0}$ takes the form

## 3. Experiment

#### 3.1. Harvard Experiment

#### 3.2. BASE Experiments at Mainz and CERN

## 4. Sensitivity

## 5. Summary

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Coefficient | Previous Constraint in [31] | Recent Result in [2] | This Work |
---|---|---|---|

$|{\tilde{b}}_{e}^{X}|$ | $<6\times {10}^{-25}\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}$ | $<1\times {10}^{-25}\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}$ | |

$|{\tilde{b}}_{e}^{Y}|$ | $<6\times {10}^{-25}\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}$ | $<1\times {10}^{-25}\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}$ | |

$|{\tilde{b}}_{e}^{Z}|$ | $<7\times {10}^{-24}\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}$ | ||

$|{\tilde{b}}_{e}^{*Z}|$ | $<7\times {10}^{-24}\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}$ | ||

$|{\tilde{b}}_{F,e}^{XX}+{\tilde{b}}_{F,e}^{YY}|$ | $<2\times {10}^{-8}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ | ||

$|{\tilde{b}}_{F,e}^{ZZ}|$ | $<8\times {10}^{-9}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ | ||

$|{\tilde{b}}_{F,e}^{\left(XY\right)}|$ | $<2\times {10}^{-10}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ | ||

$|{\tilde{b}}_{F,e}^{\left(XZ\right)}|$ | $<4\times {10}^{-10}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ | $<1\times {10}^{-10}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ | |

$|{\tilde{b}}_{F,e}^{\left(YZ\right)}|$ | $<4\times {10}^{-10}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ | $<1\times {10}^{-10}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ | |

$|{\tilde{b}}_{F,e}^{*XX}+{\tilde{b}}_{F,e}^{*YY}|$ | $<2\times {10}^{-8}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ | ||

$|{\tilde{b}}_{F,e}^{*XX}-{\tilde{b}}_{F,e}^{*YY}|$ | $<4\times {10}^{-10}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ | ||

$|{\tilde{b}}_{F,e}^{*ZZ}|$ | $<8\times {10}^{-9}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ | ||

$|{\tilde{b}}_{p}^{Z}|$ | $<2\times {10}^{-21}\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}$ | $<1.8\times {10}^{-24}\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}$ | $<8\times {10}^{-25}\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}$ |

$|{\tilde{b}}_{p}^{*Z}|$ | $<6\times {10}^{-21}\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}$ | $<3.5\times {10}^{-24}\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}$ | $<1\times {10}^{-24}\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}$ |

$|{\tilde{b}}_{F,p}^{XX}+{\tilde{b}}_{F,p}^{YY}|$ | $<1\times {10}^{-5}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ | $<1.1\times {10}^{-8}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ | $<4\times {10}^{-9}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ |

$|{\tilde{b}}_{F,p}^{ZZ}|$ | $<1\times {10}^{-5}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ | $<7.8\times {10}^{-9}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ | $<3\times {10}^{-9}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ |

$|{\tilde{b}}_{F,p}^{*XX}+{\tilde{b}}_{F,p}^{*YY}|$ | $<2\times {10}^{-5}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ | $<7.4\times {10}^{-9}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ | $<3\times {10}^{-9}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ |

$|{\tilde{b}}_{F,p}^{*ZZ}|$ | $<8\times {10}^{-6}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ | $<2.7\times {10}^{-8}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ | $<1\times {10}^{-8}{\phantom{\rule{3.33333pt}{0ex}}\mathrm{GeV}}^{-1}$ |

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**MDPI and ACS Style**

Ding, Y.
Lorentz and CPT Tests Using Penning Traps. *Symmetry* **2019**, *11*, 1220.
https://doi.org/10.3390/sym11101220

**AMA Style**

Ding Y.
Lorentz and CPT Tests Using Penning Traps. *Symmetry*. 2019; 11(10):1220.
https://doi.org/10.3390/sym11101220

**Chicago/Turabian Style**

Ding, Yunhua.
2019. "Lorentz and CPT Tests Using Penning Traps" *Symmetry* 11, no. 10: 1220.
https://doi.org/10.3390/sym11101220