高阶导数Hořava-Lifshitz费米子：从超导到原子光谱
Higher derivative Hořava-Lifshitz fermions: from superconductivity to atomic spectroscopy
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中文总结 AI 辅助
研究各向同性Hořava-Lifshitz费米子理论中六阶空间导数项的影响，通过BCS/NJL平均场、Born散射和氢原子能级移动分析，揭示了超导相、散射截面及光谱约束，为短距离物理提供新探针。
中文摘要 AI 辅助
我们研究了一个各向同性的Hořava-Lifshitz费米子理论，该理论补充了一个维度为六的空间导数算子，在保持一阶时间演化的同时修改了紫外色散关系。在导数展开的有效范围内，我们发展了$z=2$扇区的三个互补结果。首先，对费米子配对进行Bardeen-Cooper-Schrieffer/Nambu-Jona-Lasinio（BCS/NJL）平均场处理，得到了粒子和反粒子准粒子谱、有限温度隙方程以及稳定超导相的规范不变判据。修正的色散关系改变了控制配对尺度的态密度和进入迈斯纳响应的电磁顶点。其次，使用标量极点分母作为最小自旋无关交换核，我们推导出一个指数衰减且振荡的有质量势，并获得了相应的Born散射振幅。四次动量依赖性使得前向和总截面有限，并产生了一种不同于卢瑟福散射的大转移行为。最后，我们以闭合形式评估了氢原子$1S$、$2S$和$2P$能级的诱导移动，保留了相互作用范围的完整依赖性。换句话说，这些结果直接给出了核子与轻子耦合乘积的光谱约束，其中介子原子显示了各自对短距离Hořava-Lifshitz扇区的敏感性。
英文摘要
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.
发表机构
- Universidade Federal da Paraíba（帕拉伊巴联邦大学）
- Universidade Federal de Campina Grande（坎皮纳格兰德联邦大学）
- Khazar University（哈扎尔大学）
- Centre of Excellence ENSEMBLE3 Sp. z o. o.（ENSEMBLE3卓越中心有限公司）
- Damghan University（达姆甘大学）
- Instituto Federal de Educação, Ciência e Tecnologia do Estado do Rio Grande do Norte（北里奥格兰德州联邦教育、科学与技术学院）
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