Low-energy implications of cosmological data in $U(1{)}_X$ Higgs inflation

A scalar field having the Coleman-Weinberg type effective potential arises in various contexts of particle physics and serves as a useful framework for discussing cosmic inflation. According to recent studies based on the Markov chain Monte Carlo analysis, the coefficients of such an effective potential are severely constrained by the cosmological data. We investigate the impact of this observation on the physics beyond the Standard Model, focusing on an inflationary model based on the $U(1{)}_X$-extended Standard Model as a well-motivated example. We examine the parameter region that is not excluded by the Large Hadron Collider (LHC) run-2 at $139{\mathrm{fb}}^{-1}$ integrated luminosity, and show that the model parameters can be further constrained by the high-luminosity LHC experiments in the near future. We also comment on the possible reheating mechanism and the dark matter candidates of this scenario.

Figure 1

The RG flows of the $U(1{)}_X$ gauge coupling $g_X$ (left panel) and the $U(1{)}_X$ Higgs self-coupling $\lambda ={\lambda }_{\mathrm{\Phi }}$ (right panel). The value of the Majorana Yukawa coupling at $\mu =M_{\mathrm{P}}$ is varied as $y_M(M_{\mathrm{P}})=0.01$ (pink, dotted), 0.10 (green, dashed), 0.15 (orange, dot-dashed), 0.20 (cyan, long-dashed), and 0.30 (blue, solid). The parameter $x_H$ is fixed at 10. Negative $\lambda$ indicates that the $U(1{)}_X$ symmetry is broken by the Coleman-Weinberg mechanism.

Figure 2

The RG flows of the $U(1{)}_X$ gauge coupling $g_X$ (left panel) and the $U(1{)}_X$ Higgs self-coupling $\lambda ={\lambda }_{\mathrm{\Phi }}$ (right panel). The values of $x_H$ is varied as $x_H=0$ (pink, dotted), 10 (green, dashed), and 20 (blue, solid). The Majorana Yukawa coupling at the Planck scale is fixed at $y_M(M_{\mathrm{P}})=0.1$.

Figure 3

The contour plot of the $Z^{\prime }$ boson mass $M_{z^{\prime }}$ on the $x_H-y_M(M_{\mathrm{P}})$ plane. The left (right) panel uses the $1\text{−}\sigma$ upper (lower) bound (9) on the coefficient $b$ of the effective potential obtained from the cosmological MCMC analysis [11]. The red curve is the threshold above which the $U(1{)}_X$ symmetry breaking by the Coleman-Weinberg mechanism does not occur.

Figure 4

Constraints on the $Z^{\prime }$ boson mass and the $U(1{)}_X$ gauge coupling by the LHC run-2 (blue), and the region which will be searched by the HL-LHC (green). The left panel uses the $1\text{−}\sigma$ lower bound, and the right panel uses the $1\text{−}\sigma$ upper bound value set by the cosmological data fitting (9). The red lines are the prediction of the inflationary model, with the Yukawa coupling at $\mu =M_{\mathrm{P}}$ chosen to be $y_M(M_{\mathrm{P}})=0.04$. $M_{Z^{\prime }}=6.0\mathrm{TeV}$ is the upper bound of the $Z^{\prime }$ boson mass searched by the LHC run-2 with $139{\mathrm{fb}}^{-1}$ integrated luminosity.

Figure 5

Constraints on the $M_{Z^{\prime }}-y_M(M_{\mathrm{P}})$ parameter space. The left (right) panel uses the lower (upper) $1\text{−}\sigma$ bound of the cosmological data (9). The blue region has been excluded by the LHC run-2. The green region is the expected coverage by the HL-LHC.