Some aspects of $L_v^q({\mathbb{R}}^d)\cap W^{p,w}_k({\mathbb{R}}^d)$

Güngör, Ni̇han; Sağır, Birsen

doi:10.18514/mmn.2015.766

Cited by 1 publication

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“…Such heavy-particle decoupling may be the reason why the Standard Model [42,43], viewed as an effective lowenergy weak-scale theory, is the most experimentally and observationally successful and accurate theory of Nature known to humans (when augmented by classical General Relativity and neutrino mixing). That "Core Theory" [58] has no known experimental or observational counterexamples.…”

Section: W Eakmentioning

confidence: 99%

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Global U(1)Y⊗BRST symmetry and the LSS theorem: Ward-Takahashi identities governing Green’s functions, on-shell
Lynn¹,
Starkman²
2017
Phys. Rev. D
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The weak-scale U (1)Y Abelian Higgs Model (AHM) is the simplest spontaneous symmetry breaking (SSB) gauge theory: a scalar φ = 1 √ 2 (H + iπ) ≡ 1 √ 2H e iπ/ H and a vector A µ . The extended AHM (E-AHM) adds certain heavy (M 2 Φ , M 2 ψ ∼ M 2 Heavy H 2 ∼ m 2 W eak ) spin S = 0 scalars Φ and S = 1 2 fermions ψ. In Lorenz gauge, ∂µA µ = 0, the SSB AHM (and E-AHM) has a global U (1)Y conserved physical current, but no conserved charge. As shown by T.W.B. Kibble, the Goldstone theorem applies, soπ is a massless derivatively coupled Nambu-Goldstone boson (NGB).Proof of all-loop-orders renormalizability and unitarity for the SSB case is tricky because the BRST-invariant Lagrangian is not U (1)Y symmetric. Nevertheless, Slavnov-Taylor identities guarantee that on-shell T-matrix elements of physical states A µ ,φ, Φ, ψ (but not ghosts ω,η) are independent of anomaly-free local U (1)Y gauge transformations. We observe here that they are therefore also independent of the usual anomaly-free U (1)Y global/rigid transformations. It follows that the associated global current, which is classically conserved only up to gauge-fixing terms, is exactly conserved for amplitudes of physical states in the AHM and E-AHM. We identify corresponding "un-deformed" (i.e. with full global U (1)Y symmetry) Ward-Takahashi identities (WTI). The proof of renormalizability and unitarity, which relies on BRST invariance, is undisturbed.In Lorenz gauge, two towers of "1-soft-pion" SSB global WTI govern the φ-sector, and represent a new global U (1)Y ⊗BRST symmetry not of the Lagrangian but of the physics. The first gives relations among off-shell Green's functions, yielding powerful constraints on the all-loop-orders φsector SSB E-AHM low-energy effective Lagrangian and an additional global shift symmetry for the NGB:π →π + H θ. A second tower, governing on-shell T-matrix elements, replaces the old Adler self-consistency conditions with those for gauge theories, further severely constrains the effective potential, and guarantees infra-red finiteness for zero NGB (π) mass. The on-shell WTI include a Lee-Stora-Symanzik (LSS) theorem, also for gauge theories. This enforces the strong condition m 2 π = 0 on the pseudoscalar π (not just the much weaker condition m 2 π = 0 on the NGBπ), and causes all relevant-operator contributions to the effective Lagrangian to vanish exactly.In consequence, certain heavy CP -conserving Φ, ψ matter decouple completely in the M 2 Heavy /m 2 W eak → ∞ limit: we prove 4 new low-energy heavy-particle decoupling theorems which, more powerful than the usual Appelquist-Carazzone decoupling theorem, including all virtual Φ, ψ loop-contributions to relevant operators, which vanish exactly due to the exact U (1)Y symmetry of 1-soft-π Adler-self-consistency relations governing on-shell T-Matrix elements.Underlying our results is that global U (1)Y transformations δ U (1) Y , and nilpotent s 2 = 0 BRST transformations, commute: we prove δ U (1) Y , s in G. 't Hooft's R ξ gauges. With its on-shell T-Matrix constraints, SSB E-AHM ph...

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Section: W Eakmentioning

confidence: 99%

“…CP -conserving standard electroweak model with two generations of quarks, charged leptons, and ν L , ν R , with neutrino Dirac masses, but zero Majorana masses. (Ref [42]. analyses local SU (2) ⊗ U (1) Y with one such generation and non-zero Majorana ν R mass.)…”

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confidence: 99%

Global U(1)Y⊗BRST symmetry and the LSS theorem: Ward-Takahashi identities governing Green’s functions, on-shell
Lynn¹,
Starkman²
2017
Phys. Rev. D
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Some aspects of $L_v^q({\mathbb{R}}^d)\cap W^{p,w}_k({\mathbb{R}}^d)$

Abstract: Let 1 Ä q; p < 1 and v; w be Beurling's weight functions on R d. In this article we deal with harmonic properties of intersection space A

Cited by 1 publication

References 6 publications

Global U(1)Y⊗BRST symmetry and the LSS theorem: Ward-Takahashi identities governing Green’s functions, on-shell
Lynn¹,
Starkman²
2017
Phys. Rev. D
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0
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Global U(1)Y⊗BRST symmetry and the LSS theorem: Ward-Takahashi identities governing Green’s functions, on-shell
Lynn¹,
Starkman²
2017
Phys. Rev. D
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Some aspects of $L_v^q({\mathbb{R}}^d)\cap W^{p,w}_k({\mathbb{R}}^d)$

Abstract: Let 1 Ä q; p < 1 and v; w be Beurling's weight functions on R d. In this article we deal with harmonic properties of intersection space A

Cited by 1 publication

References 6 publications

Global U(1)Y⊗BRST symmetry and the LSS theorem: Ward-Takahashi identities governing Green’s functions, on-shell Lynn1, Starkman2 2017Phys. Rev. D0000View full textAdd to dashboardCite

Global U(1)Y⊗BRST symmetry and the LSS theorem: Ward-Takahashi identities governing Green’s functions, on-shell Lynn1, Starkman2 2017Phys. Rev. D0000View full textAdd to dashboardCite

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Global U(1)Y⊗BRST symmetry and the LSS theorem: Ward-Takahashi identities governing Green’s functions, on-shell
Lynn¹,
Starkman²
2017
Phys. Rev. D
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0
0
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Global U(1)Y⊗BRST symmetry and the LSS theorem: Ward-Takahashi identities governing Green’s functions, on-shell
Lynn¹,
Starkman²
2017
Phys. Rev. D
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0
0
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