Bare effective potential and Goldstone boson anti-resummation
Abstract
I discuss the evaluation of the effective potential and related quantities starting from bare perturbation theory followed by MS̅ renormalization. The advantages of this method include a simple new way of avoiding infrared problems associated with Goldstone bosons, by treating their bare squared masses as two-point interaction vertices instead of incorporating them into the propagators. Thus, only positive integer powers of the Goldstone-boson squared masses appear at every stage of calculation, avoiding the imaginary parts and singularities encountered in intermediate steps of previous resummation methods for the minimization conditions. This Goldstone boson anti-resummation approach is implemented using simple rules provided through three-loop order in terms of the master vacuum integrals. Explicit results are given for the Standard Model at three-loop order. The method is shown to give effective potential minimization conditions that are consistent with previous resummation methods, but in a form more directly useful for related future multi-loop calculations of observables in the tadpole-free scheme.
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BibTeX
@misc{martin2026bare,
title = {{Bare effective potential and Goldstone boson anti-resummation}},
author = {Stephen P. Martin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.04182},
eprint = {2608.04182},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.04182},
}
RIS
TY - UNPB
TI - Bare effective potential and Goldstone boson anti-resummation
AU - Stephen P. Martin
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2608.04182
UR - https://arxiv.org/abs/2608.04182
AB - I discuss the evaluation of the effective potential and related quantities starting from bare perturbation theory followed by MS̅ renormalization. The advantages of this method include a simple new way of avoiding infrared problems associated with Goldstone bosons, by treating their bare squared masses as two-point interaction vertices instead of incorporating them into the propagators. Thus, only positive integer powers of the Goldstone-boson squared masses appear at every stage of calculation, avoiding the imaginary parts and singularities encountered in intermediate steps of previous resummation methods for the minimization conditions. This Goldstone boson anti-resummation approach is implemented using simple rules provided through three-loop order in terms of the master vacuum integrals. Explicit results are given for the Standard Model at three-loop order. The method is shown to give effective potential minimization conditions that are consistent with previous resummation methods, but in a form more directly useful for related future multi-loop calculations of observables in the tadpole-free scheme.
ER -