2017/11/16 by Özenç Güngör, Güngör, Özenç, Bryan W. Lynn +3
Physics and Astronomy · #Atomic and Subatomic Physics Research #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Quantum Chromodynamics and Particle Interactions #hep-ph #hep-th
paper · pdf · doi:10.48550/arxiv.1711.07349
39 pages, 2 figures. arXiv admin note: text overlap with arXiv:1509.06471
openalex publication_date 2017/11/16 · arxiv created 2018/04/17 · arxiv updated 2018/04/20 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28
This work is dedicated to the memory of Raymond Stora (1930-2015). SU(2)L is the simplest spontaneous symmetry breaking (SSB) non-Abelian gauge theory: a complex scalar doublet ϕ=(1)/(√(2))\beginbmatrixH+iπ3-π2 +iπ1\endbmatrix≡(1)/(√(2))He^2it⋅π/<H>\beginbmatrix10\endbmatrix and a vector Wμ. In Landau gauge, Wμ is transverse, π are massless derivatively coupled Nambu-Goldstone bosons (NGB). A global shift symmetry enforces m2π=0. We observe that on-shell T-matrix elements of physical states Wμ,ϕ are independent of global SU(2)L transformations, and the associated global current is exactly conserved for amplitudes of physical states. We identify two towers of "1-soft-pion" global Ward-Takahashi Identities (WTI), which govern the ϕ-sector, and represent a new global symmetry, SU(2)L⊗BRST, a symmetry not of the Lagrangian but of the physical states. The first gives relations among 1-ϕ-I (but one Wμ,Bμ reducible) off-shell Green's functions, the second governs on-shell T-matrix elements, replacing the Adler self-consistency conditions. These WTI constrain the all-loop-orders scalar-sector effective Lagrangian and guarantee IR finiteness of the theory. These on-shell WTI include a Lee-Stora-Symanzik (LSS) theorem, which enforces the condition mπ2=0 (far stronger than mπ2=0) and causes all relevant-operator contributions to the effective Lagrangian to vanish exactly. The global SU(2)L and the BRST transformations commute in Rξ gauges. With the on-shell T-matrix constraints, the physics therefore has more symmetry than does its BRST invariant Lagrangian. We also show that the statements made above hold for the electroweak sector of the Standard Model bosons.