Loop Corrections to Standard Model Fields in Inflation

TL;DR

This work analyzes 1-loop corrections to in-in propagators of SM-like fields (spin-0, 1/2, 1) during inflation, focusing on late-time IR divergences in a de Sitter background and their resummation via the dynamical renormalization group. Using Schwinger-Keldysh formalism with renormalizable interactions (including $rac{ extlambda}{24}\phi^4$ and Yukawa couplings, plus gauge interactions), it finds that scalar loops drive leading IR divergences while fermion and gauge loops contribute differently, with UV divergences handled by counterterms. Dynamical RG resummation yields an IR-stable picture: the scalar sector acquires an effective mass $m^2_{ ext{eff}} = rac{ ext{sqrt{3 extvarlambda}}}{4 extpi} H^2$, and the photon sector gains an effective mass $M^2 o rac{ ext{sqrt{3}} e^2}{ extpi extvarlambda^{1/2}} H^2$, while fermions remain massless in this resummation. These results establish a concrete framework to connect inflationary observables to SM parameters, enabling a calibrated cosmological collider analysis of SM and potential new physics in the primordial universe.

Abstract

We calculate 1-loop corrections to the Schwinger-Keldysh propagators of Standard-Model-like fields of spin-0, 1/2, and 1, with all renormalizable interactions during inflation. We pay special attention to the late-time divergences of loop corrections, and show that the divergences can be resummed into finite results in the late-time limit using dynamical renormalization group method. This is our first step toward studying both the standard model and new physics in the primordial universe.

Figures (8)

• Figure 1: Two examples of 3-point function of inflaton field with SM contribution via 1-loop diagrams. The dashed black lines represent inflaton field, the solid blue lines represent SM fields, and $c_{1,2}$ denotes couplings between inflaton and SM fields.
• Figure 2: 1-loop correction to scalar 2-point function from scalar loop via $\phi^4$ interaction in Schwinger-Keldysh formalism.
• Figure 3: 1-loop correction to scalar 2-point function from fermion loop via Yukawa interaction in Schwinger-Keldysh formalism.
• Figure 4: 1-loop correction to scalar 2-point function from photon loop via 4-point gauge interaction in Schwinger-Keldysh formalism.
• Figure 5: 1-loop correction to scalar 2-point function from photon loop via 3-point gauge interaction in Schwinger-Keldysh formalism.