Higgs Inflation as Nonlinear Sigma Model and Scalaron as its $sigma$-meson. (arXiv:2002.11739v1 [hep-ph])
<a href="http://arxiv.org/find/hep-ph/1/au:+Ema_Y/0/1/0/all/0/1">Yohei Ema</a>, <a href="http://arxiv.org/find/hep-ph/1/au:+Mukaida_K/0/1/0/all/0/1">Kyohei Mukaida</a>, <a href="http://arxiv.org/find/hep-ph/1/au:+Vis_J/0/1/0/all/0/1">Jorinde van de Vis</a>
We point out that a model with scalar fields with a large nonminimal coupling
to the Ricci scalar, such as Higgs inflation, can be regarded as a nonlinear
sigma model (NLSM). The $sigma$-meson, which is induced by quantum
corrections, is identified as the scalaron in this model. Our understanding
provides a novel alternative picture for the emergence of the scalaron, which
was previously studied in the Jordan frame by computing the running of the term
quadratic in the Ricci scalar. We demonstrate that quantum corrections
inevitably induce other operators on top of this NLSM, which give rise to the
$sigma$-meson. We confirm that the $sigma$-meson indeed corresponds to the
scalaron. With the help of the $sigma$-meson, the NLSM is UV-completed to be a
linear sigma model (LSM). We show that the LSM only involves renormalizable
interactions and hence its perturbative unitarity holds up to the Planck scale
unless it hits a Landau pole, which is in agreement with the renormalizability
of quadratic gravity.
We point out that a model with scalar fields with a large nonminimal coupling
to the Ricci scalar, such as Higgs inflation, can be regarded as a nonlinear
sigma model (NLSM). The $sigma$-meson, which is induced by quantum
corrections, is identified as the scalaron in this model. Our understanding
provides a novel alternative picture for the emergence of the scalaron, which
was previously studied in the Jordan frame by computing the running of the term
quadratic in the Ricci scalar. We demonstrate that quantum corrections
inevitably induce other operators on top of this NLSM, which give rise to the
$sigma$-meson. We confirm that the $sigma$-meson indeed corresponds to the
scalaron. With the help of the $sigma$-meson, the NLSM is UV-completed to be a
linear sigma model (LSM). We show that the LSM only involves renormalizable
interactions and hence its perturbative unitarity holds up to the Planck scale
unless it hits a Landau pole, which is in agreement with the renormalizability
of quadratic gravity.
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