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Four-Boson Continuous Scale Symmetry Breaking

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Abstract

We show that the homogeneous Faddeev–Yakubovski formalism for the bound state of four identical bosons with zero-range interaction in the unitary limit (infinite two-body scattering length) presents scale invariance in the ultraviolet (UV) region. By resorting to an approximate form of the integral equations in the UV limit (considering exclusively an attractive pairwise zero-range interaction), we demonstrate that a pair of log-periodic solutions, with a cycle distinct from the three-boson one, exists with a four-body scale required to define the phase between them.

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Acknowledgements

The authors thank the following agencies for partial support: Conselho Nacional de Desenvolvimento Científico e Tecnológico [Procs. 313236/2018-6 and 438562/2018-6 (WP), 310205/2017-4(AD), 308486/2015-3(TF), 306191/2014-8(LT), 302075/2016-0(MTY) and INCT-FNA Proc.464898/2014-5], Fundação de Amparo à Pesquisa do Estado de São Paulo [Projs. 2017/05660-0(LT and TF), 2016/01816-2 (MTY)], and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Grant 88881.030363/2013-01 (MTY) and 88881.309870/2018-01 (WP and LT). This study was financed in part by CAPES - Finance Code 001.

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Authors and Affiliations

  1. DCTA, Instituto Tecnológico de Aeronáutica, São José dos Campos, 12228-900, Brazil

    T. Frederico & W. de Paula

  2. Instituto de Física, Universidade Federal Fluminense, Niterói, 24210-900, Brazil

    A. Delfino

  3. Instituto de Física Teórica, Universidade Estadual Paulista, São Paulo, 01405-900, Brazil

    M. T. Yamashita & Lauro Tomio

Authors
  1. T. Frederico
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  2. W. de Paula
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  3. A. Delfino
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  4. M. T. Yamashita
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  5. Lauro Tomio
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Correspondence to T. Frederico.

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Frederico, T., de Paula, W., Delfino, A. et al. Four-Boson Continuous Scale Symmetry Breaking. Few-Body Syst 60, 46 (2019). https://doi.org/10.1007/s00601-019-1514-z

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