In the Standard Model of particle physics, the mass of the Higgs particle can be linked to the scale at which the Standard Model breaks down due to a Landau pole/triviality problem: for a Higgs mass somewhat higher than the measured value, the Standard Model breaks down before the Planck scale. We take a first step towards investigating this relation in the context of causal set quantum gravity. We use a scalar-field propagator that carries the imprints of spacetime discreteness in a modified ultraviolet behavior that depends on a nonlocality scale. We investigate whether the modification can shift the scale of the Landau pole in a scalar field theory with quartic interaction. We discover that the modifications speed up the onset of the Landau pole considerably, so that the scale of new physics occurs roughly at the nonlocality scale. Our results call into question, whether a separation between the nonlocality scale and the discreteness scale, which is postulated within causal set quantum gravity, and which has been argued to give rise to phenomenological consequences, is in fact achievable. Methodologically, our paper is the first to apply continuum functional Renormalization Group techniques in the context of a causal-set inspired setting.

在粒子物理学的标准模型中，希格斯粒子的质量可以与标准模型因朗道极点/平凡问题而崩溃的尺度联系起来：对于略高于测量值的希格斯质量，标准模型在普朗克尺度之前崩溃。我们在因果集量子引力的背景下迈出了研究这种关系的第一步。我们使用标量场传播器，它在取决于非定域尺度的修改后的紫外线行为中携带时空离散性的印记。我们研究了这种修改是否可以改变具有四次相互作用的标量场理论中朗道极的尺度。我们发现这些修改大大加速了朗道极点的出现，因此新物理学的尺度大致发生在非定域尺度上。我们的结果提出了问题：非局域性尺度和离散性尺度之间的分离实际上是否可以实现，这种分离是在因果集量子引力内假设的，并且被认为会引起现象学后果。从方法论上来说，我们的论文是第一个在因果集启发的背景下应用连续函数重整化群技术的论文。