Higgs Fluctuation Solver in Four Dimensions: Part I-A Matrix-Free Global-Scalar Bounce and Determinant-Renormalization Audit
Abstract
We report a matrix-free numerical pipeline for semiclassical false-vacuum decay in a four-component global-O(4) scalar theory in four Euclidean dimensions. The calculation combines continuum bounce shooting, action relaxation, channel-resolved fluctuation spectra, deflated stochastic Lanczos quadrature (SLQ), and a continuum partial-wave determinant with Gel'fand-Yaglom radial ratios and large-angular-momentum subtraction. For the benchmark potential, the bounce action is B = 145.203947 and the tail residual is 0.281955%. On an L = 26, h = 0.8 lattice, the relaxed field achieves an RMS EOM residual of 4.43 x 10^-12; its low spectrum contains one negative radial mode, four lattice translations, and three near-zero internal modes. The 16-probe bare SLQ trace-log is -2079.9042 +/- 6.4504. Under the subtraction prescription, the scalar partial-wave calculation returns a primed trace-log of 40.9324 at mu = mF = sqrt(0.4), giving a determinant factor of 1.2931 x 10^-9. We show the leading rho^8 potential is not closed under its scalar one-loop divergence: local rho^10 and rho^12 counterterms are required, leaving finite coefficients unmatched; hence this is a prescription-level result, not a complete EFT prediction. The translation-normalized scalar expression is 5.9974 x 10^-70 in lattice energy units to the fourth power, omitting the internal-orientation Jacobian. We summarize tested SU(2) operator and pole-algebra infrastructure, identifying finite full-gauge matching and controlled limits as open work.
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BibTeX
@misc{cook2026higgs,
title = {{Higgs Fluctuation Solver in Four Dimensions: Part I-A Matrix-Free Global-Scalar Bounce and Determinant-Renormalization Audit}},
author = {Merritt s. Cook},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30341},
eprint = {2610.30341},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30341},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Higgs Fluctuation Solver in Four Dimensions: Part I-A Matrix-Free Global-Scalar Bounce and Determinant-Renormalization Audit
AU - Merritt s. Cook
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30341
UR - https://arxiv.org/abs/2610.30341
AB - We report a matrix-free numerical pipeline for semiclassical false-vacuum decay in a four-component global-O(4) scalar theory in four Euclidean dimensions. The calculation combines continuum bounce shooting, action relaxation, channel-resolved fluctuation spectra, deflated stochastic Lanczos quadrature (SLQ), and a continuum partial-wave determinant with Gel'fand-Yaglom radial ratios and large-angular-momentum subtraction. For the benchmark potential, the bounce action is B = 145.203947 and the tail residual is 0.281955%. On an L = 26, h = 0.8 lattice, the relaxed field achieves an RMS EOM residual of 4.43 x 10^-12; its low spectrum contains one negative radial mode, four lattice translations, and three near-zero internal modes. The 16-probe bare SLQ trace-log is -2079.9042 +/- 6.4504. Under the subtraction prescription, the scalar partial-wave calculation returns a primed trace-log of 40.9324 at mu = mF = sqrt(0.4), giving a determinant factor of 1.2931 x 10^-9. We show the leading rho^8 potential is not closed under its scalar one-loop divergence: local rho^10 and rho^12 counterterms are required, leaving finite coefficients unmatched; hence this is a prescription-level result, not a complete EFT prediction. The translation-normalized scalar expression is 5.9974 x 10^-70 in lattice energy units to the fourth power, omitting the internal-orientation Jacobian. We summarize tested SU(2) operator and pole-algebra infrastructure, identifying finite full-gauge matching and controlled limits as open work.
ER -