We study the renormalization flow of the Higgs potential as a function of both field amplitude and energy scale. This overcomes limitations of conventional techniques that rely, e.g., on an identification of field amplitude and RG scale, or on local field expansions. Using a Higgs-Yukawa model with discrete chiral symmetry as an example, our global flows in field space clarify the origin of possible metastabilities, the fate of the pseudo-stable phase, and provide new information as regards the renormalization of the tunnel barrier. Our results confirm the relaxation of the lower bound for the Higgs mass in the presence of more general microscopic interactions (higher-dimensional operators) to a high quantitative accuracy.

We apply pseudo-spectral methods to integrate functional flow equations with high accuracy, extending earlier work on functional fixed point equations [1]. The advantages of our method are illustrated with the help of two classes of models: first, to make contact with literature, we investigate flows of the O(N )-model in 3 dimensions, for N = 1, 4 and in the large N limit. For the case of a fractal dimension, d = 2.4, and N = 1, we follow the flow along a separatrix from a multicritical fixed point to the Wilson-Fisher fixed point over almost 13 orders of magnitude. As a second example, we consider flows of bounded quantum-mechanical potentials, which can be considered as a toy model for Higgs inflation. Such flows pose substantial numerical difficulties, and represent a perfect test bed to exemplify the power of pseudo-spectral methods.

We noticed a typo in our code in one of the equations for the critical exponents for the O(1) model (Sec. V). The actual values of the critical exponents are as follows: (i) Wilson-Fisher fixed point (Fig. 3): The values are in agreement with recent studies [1].

We apply pseudo-spectral methods to construct global solutions of functional renormalisation group equations in field space to high accuracy. For this, we introduce a basis to resolve both finite as well as asymptotic regions of effective potentials. Our approach is benchmarked using the critical behaviour of the scalar O(1) model, providing results for the global fixed point potential as well as leading critical exponents and their respective global eigenfunctions. We provide new results for (1) multi-critical O(1) models in fractional dimensions, (2) the three-dimensional Gross-Neveu model at both small and large N , and (3) the scalar-tensor model, also in three dimensions.

We measure the polarization state of each guided transversal mode propagating in step-index large-mode-area fibers (V≈4) using a correlation-filter based measurement technique in combination with a Stokes parameter measurement. The entire emerging beam, expressed in terms of a phase-dependent superposition of linearly polarized modes, demonstrates spatially varying polarization properties. By knowing the information about modal amplitudes and phase differences, full information about the optical field is available.