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Yukawa hierarchies from spontaneous breaking of the SU(3) L × SU(3) R flavour symmetry?

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Abstract

The tree level potential for a scalar multiplet of ‘Yukawa fields’ Y for one type of quarks admits the promising vacuum configuration 〈Y〉 ∝ diag(0, 0, 1) that breaks spontaneously SU(3) L × SU(3) R flavour symmetry. We investigate whether the vanishing entries could be lifted to nonvanishing values by slightly perturbing the potential, thus providing a mechanism to generate the Yukawa hierarchies. For theories where at the lowest order the only massless states are Nambu-Goldstone bosons we find, as a general result, that the structure of the tree-level vacuum is perturbatively stable against corrections from scalar loops or higher dimensional operators. We discuss the reasons for this stability, and give an explicit illustration in the case of loop corrections by direct computation of the one-loop effective potential of Yukawa fields. Nevertheless, a hierarchical configuration 〈Y 〉 ∝ diag(ϵ′, ϵ, 1) (with ϵ′, ϵ ≪ 1) can be generated by enlarging the scalar Yukawa sector. We present a simple model in which spontaneous breaking of the flavour symmetry can give rise to the fermion mass hierarchies.

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Authors and Affiliations

  1. IFAE, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Spain

    José R. Espinosa

  2. ICREA, Instituciò Catalana de Recerca i Estudis Avançats, Barcelona, Spain

    José R. Espinosa

  3. INFN, Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044, Frascati, Italy

    Chee Sheng Fong & Enrico Nardi

Authors
  1. José R. Espinosa
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  2. Chee Sheng Fong
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  3. Enrico Nardi
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Correspondence to Enrico Nardi.

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ArXiv ePrint: 1211.6428

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Espinosa, J.R., Fong, C.S. & Nardi, E. Yukawa hierarchies from spontaneous breaking of the SU(3) L × SU(3) R flavour symmetry?. J. High Energ. Phys. 2013, 137 (2013). https://doi.org/10.1007/JHEP02(2013)137

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