Bounds on cubic Lorentz-violating terms in the fermionic dispersion relation
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We study the recently proposed Lorentz-violating dispersion relation for fermions and show that it leads to two distinct cubic operators in the momentum. We compute the leading order terms that modify the nonrelativistic equations of motion and use experimental results for the hyperfine transition in the ground state of the $^{9}\mathrm{B}{e}^{+}$ ion to bound the values of the Lorentz-violating parameters ${\ensuremath{\eta}}_{1}$ and ${\ensuremath{\eta}}_{2}$ for neutrons. The resulting bounds depend on the value of the Lorenz-violating background four-vector in the laboratory frame.
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A constraint on the dimension-five neutron operators of Equation (40) was derived using limits on the spatial variation of the Be+ hyperfine nuclear spin transition as a function of the angle between the spin axis and an external magnetic field.
“A constraint of the dimension five operators of Equation (40) for neutrons was recently derived in [52] using limits on the spatial variation of the hyperfine nuclear spin transition in Be+ as a function of the angle between the spin axis and an external magnetic field [64].”
From Modern Tests of Lorentz Invariance (2005) · cites this paper as [52]
If uα is timelike and coincides with the rest frame of the CMBR, the neutron limits are roughly |η1| < 6 × 10−3 and |η2| < 3.
“The limits are roughly |η1| < 6 × 10−3 and |η2| < 3 if uα is timelike and coincides with the rest frame of the CMBR.”
From Modern Tests of Lorentz Invariance (2005) · cites this paper as [52]
If uα is lightlike, both neutron coefficients are bounded at the 10−8 level.
“If uα is lightlike both coefficients are bounded at the 10−8 level.”
From Modern Tests of Lorentz Invariance (2005) · cites this paper as [52]
If uα is spacelike, the neutron limits are |η1| < 2 × 10−8 and |η2| < 10−8.
“If uα is spacelike one has |η1| < 2 × 10−8 and |η2| < 10−8.”
From Modern Tests of Lorentz Invariance (2005) · cites this paper as [52]
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References 25 · Cited by 22
Research works printed but not linked: 1
- [1]V.A. Kosteleck´ y, Phys. Rev. D69 (2004) 105009; O. Bertolami, Gen. Relativity and Gravitation 34 (2002) 707; hep-ph/0301191; R. Lehnert, hep-ph/0312093. · arXiv
- Authors
- Bertolami, O., & Rosa, J. G.
- Affiliations
- Instituto Superior Técnico (PT)
- ORCID
- Rosa, J. G.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2005-05-16
- Volume
- 71
- Issue
- 9
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W1968008193
- Cited by
- 22
- References
- 25
- Citations by year
- 2026: 1 · 2024: 2 · 2021: 1 · 2018: 1 · 2014: 3 · 2013: 2
- FWCI
- 2.50
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
- Keywords
- Lorentz violation, hyperfine transitions, experimental limits
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