On scalaron decay via the trace of energy-momentum tensor

Abstract

In some inflation scenarios such as R 2 inflation, a gravitational scalar degrees of freedom called scalaron is identified as inflaton. Scalaron linearly couples to matter via the trace of energy-momentum tensor. We study scenarios with a sequestered matter sector, where the trace of energy-momentum tensor predominantly determines the scalaron coupling to matter. In a sequestered setup, heavy degrees of freedom are expected to decouple from low-energy dynamics. On the other hand, it is non-trivial to see the decoupling since scalaron couples to a mass term of heavy degrees of freedom. Actually, when heavy degrees of freedom carry some gauge charge, the amplitude of scalaron decay to two gauge bosons does not vanish in the heavy mass limit. Here a quantum contribution to the trace of energy-momentum tensor plays an essential role. This quantum contribution is known as trace anomaly or Weyl anomaly. The trace anomaly contribution from heavy degrees of freedom cancels with the contribution from the classical scalaron coupling to a mass term of heavy degrees of freedom. We see how trace anomaly appears both in the Fujikawa method and in dimensional renormalization. In dimensional renormalization, one can evaluate the scalaron decay amplitude in principle at all orders, while it is unclear how to process it beyond the one-loop level in the Fujikawa method. We consider scalaron decay to two gauge bosons via the trace of energy-momentum tensor in quantum electrodynamics with scalars and fermions. We evaluate the decay amplitude at the leading order to demonstrate the decoupling of heavy degrees of freedom.

Dynamic scale anomalous transport in QCD with electromagnetic background

“…(2.18) (See, e.g., Refs. [64][65][66][67][68] for Weyl anomaly and discussion on the frame equivalence applied to particle physics). Thus, including this EM scale anomaly, the dilaton effective theory without the dynamics is Weyl equivalent to the Maxwell theory in a curved spacetime.…”

Inflaton Decay in No-Scale Supergravity and Starobinsky-like Models

“…If the matter sector is (classically) conformal, and assuming the absence of direct coupling between the gauge sector and gravity beyond the minimal one in the original frame, T µ µ is predominantly sourced by the trace anomaly. The origin of the trace anomaly depends on the regularization scheme (although the final result itself does not) [79][80][81]. For instance, in dimensional regularization, the inflaton couples to the gauge bosons as ϵϕF µν F µν , with spacetime dimension d = 4 − 2ϵ, after the conformal transformation.…”

Reheating process in the R 2 inflationary model with the baryogenesis scenario

“…There are also quantum contributions to the trace part of the energy-momentum tensor (2.10), which come from the fact that there are no regularization schemes that hold conformal invariance simultaneously. Using the dimensional regularization, the quantum contribution, or anomaly is calculated as [33,[37][38][39]:…”

“…This decay still becomes possible due to the term proportional to the square of the Weyl tensor in the conformal trace anomaly (2.11) [45], but it can be neglected since its rate is typically suppressed by the ratio M 4 /M 4 G compared to (2.12). There are also loop contributions to the Γ ϕ→g , but they can be neglected, too, because the mass of the Higgs boson is very small [39]. 7 There are also contributions from the running of the non-minimal coupling ξ.…”