Bound States From Regge Trajectories in a Scalar Model

Weber, Axel; Vieyra, J. C. López; Stephens, Christopher R.; Dilcher, S.; Hess, Peter O.

doi:10.1142/s0217751x01005596

Cited by 6 publications

(11 citation statements)

References 19 publications

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“…Work by Mexican researchers has shown how RG techniques can be adapted to deal with such kinematic dimensional reductions [23,24,25]. I will briefly illustrate the phenomenon within the context of a cubic scalar field theory.…”

Section: More Than One Singularity Per Greens Functionmentioning

confidence: 99%

“…The above methodology is generalizable to much more complicated cases. Interestingly, even the simple case of an interaction φ † φ ψ leads to quite complicated renormalization scenario where a matrix renormalization is necessary [24,25] which leads to an extremely rich set of Regge trajectories. As Regge trajectories also give important information about the bound states of a theory the results of this section show that it is possible to use an environmentally friendly renormalization to access some aspects of the crossover between boundstates and unbound states.…”

Section: More Than One Singularity Per Greens Functionmentioning

confidence: 99%

“…By developing an RG methodology for calculating Regge trajectories then, given the relationship between such trajectories and the existence of bound states in a field theory, it has been possible to use the RG in this extreme asymmetric limit to calculate properties of bound states [28,29]. In [28] different charge sectors of a scalar theory with interaction φ † φ ψ were considered and found to have a surprisingly rich bound state spectrum. The results were compared and contrasted with known results of the Bethe-Salpeter equation in the ladder approximation and, in the non-relativistic limit, with the corresponding Schrödinger equation.…”

Section: Bound Statesmentioning

confidence: 99%

“…As of yet such an RG has not been developed. For a reparametrization RG some progress can and has been made by exploiting the information on bound states contained in the Regge limit [28]. A direct access, however, remains very much an open problem.…”

Section: Conclusion and Future Prospectsmentioning

confidence: 99%

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Renormalization Group Theory

Stephens¹

2006

AIP Conference Proceedings

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In this article I give a brief account of the development of research in the Renormalization Group in Mexico, paying particular attention to novel conceptual and technical developments associated with the tool itself, rather than applications of standard Renormalization Group techniques. Some highlights include the development of new methods for understanding and analysing two extreme regimes of great interest in quantum field theory-the "high temperature" regime and the Regge regime.

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Section: More Than One Singularity Per Greens Functionmentioning

confidence: 99%

Section: More Than One Singularity Per Greens Functionmentioning

confidence: 99%

Section: Bound Statesmentioning

confidence: 99%

Section: Conclusion and Future Prospectsmentioning

confidence: 99%

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Stephens¹

2006

AIP Conference Proceedings

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“…4. [20], the leading Regge trajectory [21], the Bethe-Salpeter equation in covariant light-front dynamics [22], and the Haag expansion [23].…”

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confidence: 99%

Relativistic Bound States

Weber¹

2003

AIP Conference Proceedings

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In this contribution, I will give a brief survey of present techniques to treat the bound state problem in relativistic quantum field theories. In particular, I will discuss the Bethe-Salpeter equation, various quasi-potential equations, the Feynman-Schwinger representation, and similarity transformation methods for Hamiltonian approaches in light-front quantization. Finally, I will comment on a related similarity transformation in the usual equal-time quantized theory.Comment: 9 pages, LaTeX, 3 pspicture diagrams, 3 postscript figures, uses aipxfm.sty. Talk delivered at the X Mexican School of Particles and Fields, Playa del Carmen, Mexico, 200

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Exploring Higgs boson Yukawa interactions with a scalar singlet using Dyson-Schwinger equations

Mufti¹

2018

Preprint

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Higgs, being the first discovery of a fundamental scalar field in the standard model (SM), opens the possibility of existence of other scalar or pseudo scalar particles in nature. Though it does not conclusively fulfill the role of inflaton, it does provide motivation for experimental searches involving interactions of scalar (or pseudo scalar) particles as well as implications of such particles' existence from the perspective of theoretical understanding. Yukawa interactions are among the possible interactions. The considered model addresses Yukawa interaction among the Higgs (and Higgs bar) 1 and a real singlet scalar field using Dyson Schwinger equations (DSEs) over a range of bare coupling values relevant to inflation-related physics for several scalar bare masses and cutoff values. The Higgs mass is kept fixed at two values for two different scenarios. It is found that Higgs propagators are tree level dominated while scalar propagators, despite their dependence on parameter region, do not degenerate over the whole parameter space. The interaction vertices show significant deviations from tree level expression for a number of parameters and exhibit two distinct behaviors. Furthermore, the theory does not show any conclusive sign of triviality over the explored parameter space, despite suppressed vertices for some parameters, particularly for small coupling values in a certain region of parameter space.

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Bound States From Regge Trajectories in a Scalar Model

Cited by 6 publications

References 19 publications

Renormalization Group Theory

Renormalization Group Theory

Relativistic Bound States

Exploring Higgs boson Yukawa interactions with a scalar singlet using Dyson-Schwinger equations

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