A Lattice Test of Alternative Interpretations of "Triviality" in (λΦ<sup>4</sup>)<sub>4</sub> Theory

Agodi, Antonella; Andronico, Giuseppe; Cea, Paolo; Consoli, M.; Cosmai, Leonardo; Fiore, R.; Stevenson, P. M.

doi:10.1142/s0217732397001035

Cited by 15 publications

(28 citation statements)

References 24 publications

(50 reference statements)

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“…[8,9,10] focuses on the class of approximations to V eff that are consistent with the non-interacting nature of the shifted field h(x) ≡ Φ(x) − Φ . The resulting predictions, unlike the RGIPT predictions, yield an excellent fit to the lattice data for V eff [12,13].…”

Section: Introductionmentioning

confidence: 87%

First Lattice Evidence for a Nontrivial Renormalization of the Higgs Condensate

1998

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General arguments related to "triviality" predict that, in the broken phase of (λΦ 4 ) 4 theory, the condensate Φ re-scales by a factor Z ϕ different from the conventional wavefunctionrenormalization factor, Z prop . Using a lattice simulation in the Ising limit we measure Z ϕ = m 2 χ from the physical mass and susceptibility and Z prop from the residue of the shifted-field propagator. We find that the two Z's differ, with the difference increasing rapidly as the continuum limit is approached. Since Z ϕ affects the relation of Φ to the Fermi constant it can sizeably affect the present bounds on the Higgs mass.

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Section: Introductionmentioning

confidence: 87%

First Lattice Evidence for a Nontrivial Renormalization of the Higgs Condensate

1998

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“…Since the numerical lattice results, used as supportive evidence, were obtained in the weak-coupling region, they cannot provide any information about triviality. The analyses presented in [131,132] were performed to resolve the difficulties arising in the Higgs sector of the Standard Model in view of the triviality of ϕ 4 theory. No difficulties of this kind arise when the theory is internally-consistent.…”

Section: ])mentioning

confidence: 99%

Divergent perturbation series

Suslov

2005

J. Exp. Theor. Phys.

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-Various perturbation series are factorially divergent. The behavior of their high-order terms can be found by Lipatov's method, according to which they are determined by instanton configurations of appropriate functional integrals. When the Lipatov asymptotics is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight into the behavior of the remaining terms of the series. Summing it, one can solve (in a certain approximation) various strong-coupling problems. This approach is demonstrated by determining the Gell-Mann-Low functions in ϕ 4 theory, QED, and QCD for arbitrary coupling constants. An overview of the mathematical theory of divergent series is presented, and interpretation of perturbation series is discussed. Explicit derivations of the Lipatov asymptotics are presented for some basic problems in theoretical physics. A solution is proposed to the problem of renormalon contributions, which hampered progress in this field in the late 1970s. Practical perturbation-series summation schemes are described for a coupling constant of order unity and in the strong-coupling limit. An interpretation of the Borel integral is given for "non-Borel-summable" series. High-order corrections to the Lipatov asymptotics are discussed.

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“…It provides the key ingredient to get a non trivial effective potential in a "trivial" theory [8][9][10]. It turns out that [11,12] in the continuum limit (Λ → ∞)…”

Section: Introductionmentioning

confidence: 99%