Hidden U(1)_Y Ward-Takahashi identities in the spontaneously brokenAbelian Higgs model and the decoupling of certain heavy particles in its simple extensions

2015/09/22 by Bryan W. Lynn, Glenn D. Starkman, Lynn, Bryan W. +1 · 1 citation
Physics and Astronomy · #Cosmology and Gravitation Theories #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph

paper · pdf · doi:10.48550/arxiv.1509.06471

improved details of text, especially appendix. arXiv admin note: text overlap with arXiv:1509.06199, arXiv:1509.06198

arxiv created 2016/08/14 · arxiv updated 2018/01/08

Abstract

This work is dedicated to the memory of R. Stora. The spontaneously broken (SSB) U(1)_Y Abelian Higgs model (AHM) (the gauge theory of a scalar ϕ∝ (H+iπ)= He^i π/<H> and a transverse vector A) has a massless pseudo-scalar π in Lorenz gauge. Physical states have a conserved global current and Goldstone theorem (GT). π becomes a Nambu-Goldstone boson (NGB). Slavnov-Taylor identities keep on-shell T-matrix elements of physical states independent of anomaly-free gauge, and global, transformations, yielding towers of ϕ-sector Ward-Takahashi Identities (WTI), and constraining external ϕ dynamics. Ultraviolet quadratic divergences (UVQD) contribute only to m_π², forced by the GT to 0, so all UVQD vanish. Weak-scale renormalized gauge-independent Higgs pole-mass and VEV are therefore not fine-tuned. The NGB is "eaten" and decouples, hiding the U(1)_Y WTI from observable particle physics. Our regularization-scheme-independent results are unchanged by the addition of certain heavy fields as the extended WTI and GT cause all relevant operators to vanish. We prove 5 SSB decoupling theorems, illustrating them with two examples: a heavy >>m_Weak Z₂-symmetric singlet real scalar field with 0 VEV; and a heavy singlet right-handed type 1 see-saw Majorana neutrino. Including all loops we prove that certain heavy degrees of freedom decouple from the low-energy effective Lagrangian, contributing only irrelevant operators after renormalization. The ν_R^M cannot completely decouple, but becomes invisible in practice. The NGB decouples, but our hidden SSB U(1)_Y WTI, and a π shift symmetry, protect the low-energy SSB AHM physics from loop contributions of heavy particles! Gauge-independent observable weak-scale m_H;Pole and <H> are Goldstone Exceptionally Natural, not fine-tuned.

Citations

• Global SU(3)_C× SU(2)_L× U(1)_Y linear sigma model: axial-vector Ward Takahashi identities, and decoupling of certain heavy BSM particles due to the Goldstone theorem
• Global U(1)_YxBRST symmetry and the LSS theorem: Ward-Takahashi identities governing Green's functions, on-shell T-Matrix elements, and the effective potential, in the spontaneously broken extended Abelian Higgs model

Cited by

• Global SU(2)_L ⊗BRST symmetry and its LSS theorem: Ward-Takahashi identities governing Green's functions, on-shell T-Matrix elements, and V_eff, in the scalar-sector of certain spontaneously broken non-Abelian gauge theories

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