Improved big bang nucleosynthesis constraints on heavy neutral leptons

We constrain the lifetime of thermally produced heavy neutral leptons (HNLs) from big bang nucleosynthesis. We show that even a small fraction of mesons present in the primeval plasma leads to the overproduction of primordial helium-4. This constrains the lifetime of HNLs to be ${\tau }_N<0.02\mathrm{s}$ for masses above the mass of the pion (as compared to 0.1 s reported previously). In combination with accelerator searches, this allows us to put a new lower bound on the HNL masses and define the “bottom line” for HNL searches at the future Intensity Frontier experiments.

Figure 1

Left panel: temperature evolution of the neutron abundance $X_n=n_n/(n_n+n_p)$ in the presence of pions from decays of an HNL with mass $m_N=400\mathrm{MeV}$ and lifetime ${\tau }_N=0.03\mathrm{s}$. Below $T\simeq 100\mathrm{MeV}$, pions drive the neutron abundance to $X_n\approx 0.5$. At temperatures $T_0\simeq 1.3\mathrm{MeV}$ (the blue vertical dashed line) pions disappear, and $X_n$ starts to relax towards its SBBN value but does not reach it. After the neutron decoupling (the gray vertical line) $X_n$ evolves mainly due to the neutron decays. Right panel: a relation between the temperature $T_0$ [defined by Eq. (7)] and corrections to the ${}^4\mathrm{He}$ abundance, as compared to the SBBN central value ${\overline{Y}}_p\approx 0.247$. It corresponds to the case of when only charged pions are present in plasma. The gray horizontal line corresponds to the maximally allowed correction $\mathrm{\Delta }{Y}_p/{\overline{Y}}_p=4.35\%$ that we adopt in this work (see Appendix pp1). The intersection of the gray and colored lines defines the temperature $T_0^{\min }$. Its actual value in the presence of all mesons always lies close to $T_0^{\min }\approx 1.5\mathrm{MeV}$ independently of the HNL mass (see Appendix pp4-s2).

Figure 2

Left panel: BBN bounds on the HNL lifetime for different mixing patterns. The gray region is excluded as a result of this work (for masses below the pion threshold we use the results of Ref. [49]). The magenta shaded region corresponds to the domain excluded in Ref. [31]. We consider HNLs that are produced thermally and sufficiently short lived, such that they do not survive until the onset of nuclear reactions (Appendix pp5). Right panel: comparison of the results of this work (thick blue line) with the results of the previous works [22, 25, 32] (purple lines) assuming mixing with electron flavor only. Notice that other works adopted different values for the maximally admissible ${}^4\mathrm{He}$ abundance when deriving their bounds: $Y_{p,\max }=0.2696$ in Refs. [22, 25] and $Y_{p,\max }=0.253$ in Ref. [32], as compared to $Y_{p,\max }=0.2573$ in this work (see text for details).

Figure 3

Bounds for HNLs mixed with a particular flavor. The blue area is excluded by our present analysis combined with Ref. [49] (for HNL masses below the charged pion production threshold). The dark gray area denotes the excluded HNL parameter space from previous searches [1], including the latest NA62 search [50]. The red and greed dashed lines show the sensitivity of several future Intensity Frontier experiments with the highest sensitivity in the regions of interest: SHiP [51, 52] and DUNE [53, 54, 55] (see Ref. [8]). Finally, the black dashed line denotes the seesaw bound applicable if two degenerate-in-mass HNLs are responsible for neutrino oscillations (as in the $\nu \mathrm{MSM}$) [1, 56]. The lower bound of the blue region shows the limit of the applicability of our approach: we only consider HNLs that are produced thermally and are sufficiently short lived such that they do not change the nuclear reaction framework by their meson decay products.

Figure 4

Measurements of $Y_p$ from recent works [10, 11, 12, 13, 14]. The green shaded region is the PDG recommended value [43] (with $\pm 1\sigma$). The gray dashed line denotes the SBBN prediction ${\overline{Y}}_p=0.247$ from Ref. [15]. The red dash-dotted line is the maximal admissible value $Y_{p,\max }$ on which we base our analysis.

Figure 5

Left panel: dilution factor (b6) for short-lived HNLs mixing with ${\nu }_e$. Right panel: HNL abundance times dilution factor as a function of mass for particular values of the lifetime. Details of the calculation of the abundances and $\zeta$ are given in Ref. [49]. The dilution factor is calculated when most of the HNLs have decayed and do not contribute to the entropy density. Note that we define the abundance at the moment of decoupling, and hence it does not change with decays.

Figure 6

Branching ratios of HNL decays into mesons $h={\pi }^{-}$, $K^{-}$, $K_L^0$. Secondary decays are also included (see text for details).

Figure 7

Left panel: behavior of the $p\to n$ (solid lines) and $n\to p$ (dashed lines) conversion rates in the case of pion- and kaon-driven conversions and SBBN. We consider HNLs mixing with $e$ flavor, mass $m_N=1\mathrm{GeV}$, and lifetime ${\tau }_N=0.02\mathrm{s}$ as an example. Middle panel: temperature dependence of the neutron abundance $X_n$ assuming that its evolution is completely dominated by the meson-driven $p\leftrightarrow n$ conversions. We consider HNLs mixing with $e$ flavor and different masses: $m_N=200\mathrm{MeV}$ (only pions are present), $m_N=700\mathrm{MeV}$ (pions and charged kaons are present), and $m_N=1.5\mathrm{GeV}$ (pions, and charged and neutral kaons are present). The dashed gray line denotes the value of the neutron abundance at equilibrium in SBBN. Right panel: HNL mass dependence of the temperature $T_0^{\min }$.