Higher derivative Hořava-Lifshitz fermions: from superconductivity to atomic spectroscopy
Abstract
We investigate an isotropic Hořava-Lifshitz fermion theory supplemented by a dimension-six spatial derivative operator, preserving first order time evolution while modifying the ultraviolet dispersion relation. Within the regime of validity of the derivative expansion, we develop three complementary consequences of the z=2 sector. First, a Bardeen-Cooper-Schrieffer/Nambu-Jona-Lasinio (BCS/NJL) mean field treatment of fermion pairing yields the particle and antiparticle quasiparticle spectra, the finite temperature gap equation, and the gauge invariant criterion for a stable superconducting phase. The modified dispersion alters both the density of states governing the pairing scale and the electromagnetic vertices entering the Meissner response. Second, using the scalar pole denominator as a minimal spin independent exchange kernel, we derive an exponentially damped and oscillatory massive potential and obtain the corresponding Born scattering amplitudes. The quartic momentum dependence renders both the forward and total cross sections finite and produces a large transfer behavior distinct from Rutherford scattering. Finally, we evaluate the induced shifts of the hydrogenic 1S, 2S, and 2P levels in closed form, retaining the full dependence on the interaction range. In other words, these latter results gives direct spectroscopic constraints on the product of nuclear and leptonic couplings, with muonic atoms, showing the respective sensitivity to the short distance Hořava-Lifshitz sector.
Related
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BibTeX
@misc{filho2026higher,
title = {{Higher derivative Hořava-Lifshitz fermions: from superconductivity to atomic spectroscopy}},
author = {A. A. Araújo Filho and K. E. L. de Farias and N. Heidari and M. Paganelly and A. F. Santos},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25236},
eprint = {2609.25236},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25236},
}
RIS
TY - UNPB
TI - Higher derivative Hořava-Lifshitz fermions: from superconductivity to atomic spectroscopy
AU - A. A. Araújo Filho
AU - K. E. L. de Farias
AU - N. Heidari
AU - M. Paganelly
AU - A. F. Santos
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25236
UR - https://arxiv.org/abs/2609.25236
AB - We investigate an isotropic Hořava-Lifshitz fermion theory supplemented by a dimension-six spatial derivative operator, preserving first order time evolution while modifying the ultraviolet dispersion relation. Within the regime of validity of the derivative expansion, we develop three complementary consequences of the z=2 sector. First, a Bardeen-Cooper-Schrieffer/Nambu-Jona-Lasinio (BCS/NJL) mean field treatment of fermion pairing yields the particle and antiparticle quasiparticle spectra, the finite temperature gap equation, and the gauge invariant criterion for a stable superconducting phase. The modified dispersion alters both the density of states governing the pairing scale and the electromagnetic vertices entering the Meissner response. Second, using the scalar pole denominator as a minimal spin independent exchange kernel, we derive an exponentially damped and oscillatory massive potential and obtain the corresponding Born scattering amplitudes. The quartic momentum dependence renders both the forward and total cross sections finite and produces a large transfer behavior distinct from Rutherford scattering. Finally, we evaluate the induced shifts of the hydrogenic 1S, 2S, and 2P levels in closed form, retaining the full dependence on the interaction range. In other words, these latter results gives direct spectroscopic constraints on the product of nuclear and leptonic couplings, with muonic atoms, showing the respective sensitivity to the short distance Hořava-Lifshitz sector.
ER -