Tree-level unitarity in Higgs inflation in the metric and the Palatini formulation
Asuka Ito, W. Khater, Syksy Räsänen
Abstract
A bstract We calculate the tree-level amplitudes for electrically neutral 2 → 2 scattering for the Standard Model Higgs doublet non-minimally coupled to the Ricci scalar. We consider both the metric and the Palatini formulation of gravity. We find the partial wave unitarity limit for a general background field value. Our results are in agreement with previous work. In the electroweak vacuum, tree-level unitarity is violated at ∼ M Pl / ξ in the metric formulation, and at $$ \sim {M}_{\mathrm{P}1}/\sqrt{\xi } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>∼</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:msqrt><mml:mi>ξ</mml:mi></mml:msqrt></mml:math> in the Palatini formulation. In the inflationary large field background, the unitarity limit is at $$ \sim {M}_{\mathrm{P}1}/\sqrt{\xi } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>∼</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:msqrt><mml:mi>ξ</mml:mi></mml:msqrt></mml:math> in both formulations. We compare the unitarity violation energy to scales relevant during inflation. We also calculate a direct collider limit on ξ in the Palatini formulation, ξ < 2 . 5 × 10 31 .