Axions and saxions from the primordial supersymmetric plasma and extra radiation signatures

TL;DR

This work computes the leading-order thermal production rates of axions and saxions in a primordial SUSY QCD plasma using HTL resummation, deriving their thermally produced yields and decoupling temperature. It shows that saxion decays predominantly into axions can contribute significant ΔN_eff before BBN and into the CMB/LSS epoch, and translates these constraints into bounds on f_PQ, m_σ, and T_R. The analysis connects to BBN and precision cosmology, suggesting that the Planck mission could reveal or constrain SUSY axion scenarios by detecting extra radiation signatures and by probing the regions where thermal saxions feed non-thermally produced axions. The results indicate that late-decaying saxions offer a viable mechanism to explain hints of extra radiation while remaining consistent with cosmological bounds, and they outline two exemplar SUSY settings compatible with high reheating temperatures and Planck-level sensitivity.

Abstract

We calculate the rate for thermal production of axions and saxions via scattering of quarks, gluons, squarks, and gluinos in the primordial supersymmetric plasma. Systematic field theoretical methods such as hard thermal loop resummation are applied to obtain a finite result in a gauge-invariant way that is consistent to leading order in the strong gauge coupling. We calculate the thermally produced yield and the decoupling temperature for both axions and saxions. For the generic case in which saxion decays into axions are possible, the emitted axions can constitute extra radiation already prior to big bang nucleosynthesis and well thereafter. We update associated limits imposed by recent studies of the primordial helium-4 abundance and by precision cosmology of the cosmic microwave background and large scale structure. We show that the trend towards extra radiation seen in those studies can be explained by late decays of thermal saxions into axions and that upcoming Planck results will probe supersymmetric axion models with unprecedented sensitivity.

Figures (7)

• Figure 1: The $2\to2$ processes for saxion production in a SUSY QCD plasma. Additional processes are included in terms of multiplicities in our calculation of the thermal production rate: Process C with antiquarks $\bar{q}_{i,j}$ replacing $q_{i,j}$, process G with antisquarks $\bar{\tilde{q}}_{i,j}$ replacing $\tilde{q}_{i,j}$, process H with antisquarks/quarks $\bar{\tilde{q}}_{i}$/$q_{j}$ replacing $\tilde{q}_{i}$/$\bar{q}_{j}$, and processes I and J with $\bar{q}_{i}$ and $\bar{\tilde{q}}_j$ replacing $q_{i}$ and $\tilde{q}_j$, respectively.
• Figure 2: The saxion self energy used to compute the leading contribution to the thermal production rate of hard saxions. The blob indicates the HTL-resummed gluon propagator.
• Figure 3: The relic saxion yield prior to decay originating from thermal processes in the primordial plasma for cosmological scenarios characterized by different $T_{\mathrm{R}}$ values covering the range from $10^6$ to $10^{10}\,\mathrm{GeV}$. The dash-dotted, dashed, and solid lines are obtained for $f_{\mathrm{PQ}}=10^{10}$, $10^{11}$, and $10^{12}\,\mathrm{GeV}$. The relic axion yield $Y_{a}^{\mathrm{eq/TP}}$ from thermal processes agrees with $Y_{\sigma\xspace}^{\mathrm{eq/TP}}\!\!$ and can thus be read from this figure as well.
• Figure 4: Contours of $\Delta N_\text{eff}$ at $T\sim 1~\mathrm{MeV}$ provided by non-thermally produced axions from decays of thermal saxions for $x=1$, $T_\sigma\xspace>1~\mathrm{MeV}$, and $T_{\mathrm{R}}=10^8\,\mathrm{GeV}$ (black) and $10^{10}\,\mathrm{GeV}$ (gray). The BBN results given in Table \ref{['Tab:Neffconstrains']} are illustrated by the solid (dashed) curves, which indicate the posterior maximum $(\Delta N_\text{eff})_\text{Av(IT)}^\text{p.m.}=0.77$$(0.76)$ and the upper $3\sigma$ limit $(\Delta N_\text{eff})_\text{Av(IT)}^{3\sigma}=3.53$$(1.97)$ that disfavors the region to its left. The dotted lines show $T_\sigma\xspace=1$ and $10~\mathrm{MeV}$.
• Figure 5: Contours of $\Delta N_\text{eff}$ at $T\ll 1~\mathrm{MeV}$ provided by non-thermally produced axions from decays of thermal saxions for $x=1$ and $T_{\mathrm{R}}=10^8\,\mathrm{GeV}$ (black) and $10^{10}\,\mathrm{GeV}$ (gray). The solid curve shows the $2\sigma$ limit $\Delta N_\text{eff}=3.59$ and the dashed curve the mean $\Delta N_\text{eff}=1.73$ based on the CMB + HPS + HST result Hamann:2010pw quoted in Table \ref{['Tab:Neffconstrains']}. The dash-dotted curve indicates $\Delta N_\text{eff} = 0.26$ which is the expected 68% CL sensitivity of the Planck satellite mission Perotto:2006rjHamann:2007sb. On the dotted lines, $T_\sigma\xspace=1$ and $10~\mathrm{MeV}$, as in Fig. \ref{['Fig:extraradBBN']}.