Interplay between the muon $g-2$ anomaly and the PTA nHZ gravitational waves from domain walls in next-to minimal supersymmetric standard model

TL;DR

This paper explores how domain wall collapse in the NMSSM can produce gravitational waves detectable by PTA experiments and examines the potential connection to the muon g-2 anomaly, highlighting the interplay between particle physics and cosmological signals.

Contribution

It demonstrates that gravitational waves from domain wall collapse in the NMSSM can explain PTA observations and potentially account for the muon g-2 anomaly within certain parameter ranges.

Findings

GW signals from domain wall collapse match NANOGrav data with tiny parameter values.

Some parameter points can simultaneously explain PTA signals and muon g-2 within 1σ.

The model links supersymmetry breaking, gravitational waves, and muon anomaly explanations.

Abstract

With some explicitly $Z_3$ breaking terms in the NMSSM effective superpotential and scalar potential, domain walls (DWs) from spontaneously breaking of the discrete symmetry in approximate $Z_3$-invariant NMSSM can collapse and lead to observable stochastic gravitational wave (GW) background signals. In the presence of a hidden sector, such terms may originate from the geometric superconformal breaking with holomorphic quadratic correction to frame function when the global scale-invariant superpotential is naturally embedded into the canonical superconformal supergravity models. The smallness of such mass parameters in the NMSSM may be traced back to the original superconformal invariance. Naive estimations indicate that a SUSY explanation to muon $g-2$ anomaly can have tension with the constraints on SUSY by PTA data, because large SUSY contributions to $\Delta a_\mu$ in general needs relatively light superpartners while present $\Omega_{gw}^0$ can set the lower bounds for $m_{soft}$. We calculate numerically the signatures of GW produced from the collapse of DWs and find that the observed nHZ stochastic GW background by NANOGrav, etc., can indeed be explained with proper tiny values of $\chi m_{3/2}\sim 10^{-14}{\rm eV}$ for $\chi S^2$ case (and $\chi m_{3/2}\sim 10^{-10}{\rm eV}$ for $\chi H_u H_d$ case), respectively. Besides, there are still some parameter points, whose GW spectra intersect with the NANOGrav signal region, that can explain the muon $g-2$ anomaly to $1\sigma$ range.