Cosmological Phase Transitions and their Properties in the NMSSM

TL;DR

This work investigates cosmological electroweak phase transitions in the scale-invariant NMSSM using an effective-field-theory approach to control large logarithms from heavy stops and to compute a finite-temperature potential. By matching to a 2HD+S EFT at the stop scale and evolving to the electroweak scale, the authors map a phenomenologically viable region (125 GeV Higgs, TeV-scale stops, viable neutralino DM) onto a rich set of phase-transition patterns, including one- and two-step transitions driven by SU(2) and singlet directions. They compute bubble-wall properties (wall widths $L_w$, $L_s$, and $igtriangleup\beta$) and estimate the wall velocity from microphysical friction, finding predominantly subsonic walls suitable for electroweak baryogenesis, though some benchmarks exhibit runaway behavior. While some transitions feature substantial supercooling, the predicted gravitational-wave signals from bubble collisions are too faint for near-future detectors in the studied scenarios. Overall, the NMSSM remains a compelling framework to simultaneously address the Higgs mass, dark matter, and baryogenesis, with the EFT+CosmoTransitions methodology enabling precise, testable predictions for early-universe phase transitions.

Abstract

We study cosmological phase transitions in the Next-to-Minimal Supersymmetric Standard Model (NMSSM) in light of the Higgs discovery. We use an effective field theory approach to calculate the finite temperature effective potential, focusing on regions with significant tree-level contributions to the Higgs mass, a viable neutralino dark matter candidate, 1-2 TeV stops, and with the remaining particle spectrum compatible with current LHC searches and results. The phase transition structure in viable regions of parameter space exhibits a rich phenomenology, potentially giving rise to one- or two-step first-order phase transitions in the singlet and/or $SU(2)$ directions. We compute several parameters pertaining to the bubble wall profile, including the bubble wall width and $Δβ$ (the variation of the ratio in Higgs vacuum expectation values across the wall). These quantities can vary significantly across small regions of parameter space and can be promising for successful electroweak baryogenesis. We estimate the wall velocity microphysically, taking into account the various sources of friction acting on the expanding bubble wall. Ultra-relativistic solutions to the bubble wall equations of motion typically exist when the electroweak phase transition features substantial supercooling. For somewhat weaker transitions, the bubble wall instead tends to be sub-luminal and, in fact, likely sub-sonic, suggesting that successful electroweak baryogenesis may indeed occur in regions of the NMSSM compatible with the Higgs discovery.

Figures (6)

• Figure 1: Signal strengths for the various Higgs prodution and decay channels for our benchmark points (labeled 1--5), compared with the global fit in Ref. Belanger:2013xza obtained using current ATLAS, CMS, and Tevatron data. On the left we consider the diphoton rate arising from vector boson fusion (VBF) + associated production with a gauge boson (VH), and from gluon gluon fusion (ggF) + associated production with a top quark pair (ttH). On the right we plot the corresponding results for vector boson final states. The white star indicates the current best-fit point from Ref. Belanger:2013xza, while the shaded areas correspond to 68%, 95%, and 99.7% C.L. regions from darkest to lightest, respectively. All the benchmark points lie within the 68% CL regions for the observed signal strengths. The $b\bar{b}/\tau\tau$ ellipses are not shown, since all the benchmarks lie very close to the best fit point in this plane. All of our benchmark points feature a very Standard Model-like Higgs in good agreement with observation.
• Figure 2: Late time bubble wall profiles (left) and $\tan \beta$ (right) for the strongly first order electroweak phase transition of BM 1.
• Figure 3: $V$ plotted against $s$ and $\sqrt{h_d^2+h_u^2}$ with $\tan\beta$ fixed. On the left, $\tan \beta = 4.01$, which is its value just outside the bubble wall, i.e. where $\phi = \phi_\mathrm{low} + 0.95\Delta\phi$. On the right $\tan \beta = 1.59$, its value just inside the bubble wall (where $\phi = \phi_\mathrm{low} + 0.05\Delta\phi$), where indeed the potential minimum is at a nonzero value of $s$ and $\sqrt{h_d^2+h_u^2}$. The black lines are the late time tunneling paths.
• Figure 4: Results for strongly first order one-step electroweak phase transitions at different values of $m_{h_s}$ for Sets I (circles), II (diamonds), and III (squares). Shown are the EWPT order parameter, $SU(2)$ wall width, singlet wall width, and $\Delta \beta$, which are quantities relevant for investigations of electroweak baryogenesis. The singlet-like Higgs mass is varied by varying $A_{\kappa}$ as described in the text with all other parameters fixed. The rest of the spectrum varies very little across the scanned points, with the phenomenology as presented in Table \ref{['tab:bm']}. Black points have bubble walls that are guaranteed to be sub-luminal, while the cyan points admit a runaway solution. Note that the late-time bubble wall profile parameBters are only calculated for walls moving with constant velocity and friction, and so are not shown for points with runaway solutions.
• Figure 5: Full (solid) and mean field (dashed) finite temperature 1-loop effective potential for all benchmarks at their respective nucleation temperatures. Benchmarks 1, 3, and 4 have bubble walls which are guaranteed to remain sub-luminal, while the walls of BM 2 and 5 can have $v_w\rightarrow 1$.