Constraining Beyond The Standard Model Physics With Big Bang Nucleosynthesis

Background: Big Bang Nucleosynthesis

One of the most impressive cosmology theories in existence is Big Bang Nucleosynthesis. It is a theory that assumes a starting point, not long after the Big Bang, at which the universe is at a high average temperature (i.e. particles are moving with high average levels of kinetic energy) and all atomic nuclei are initially simple protons and neutrons.

The theory then uses statistics to consider all possible collisions of those protons and neutrons that give rise to nuclear fusion or fission in all possible pathways, and assume that at the end of the nucleosynthesis period that nuclear fusion to create light elements becomes dramatically less common as the temperature of the universe falls as kinetic energy is captured and converted into nuclear binding energy, an indirect form of the strong nuclear force, and as collisions become less common as the size of the universe that is in the Big Bang light cone relative to the number of particles in it increases.

For the most part, the predictions of Big Bang Nucleosynthesis are confirmed by experiment. The relative abundance of light element isotypes in the universe is a reasonably close match to what we would expect if Big Bang Nucleosynthesis is an accurate description of what actually happened. The biggest discrepancy is in abundance of Lithium-7, which differs significantly from the predicted value even though it still has a right order of magnitude.

Using Big Bang Nucleosynthesis To Constrain Beyond The Standard Model Physics

Many predictions of Big Bang Nucleosynthesis are sensitive to the existence of relatively long lived particles (e.g. those with mean lifetimes on the order of seconds or more) beyond those of the Standard Model. Collisions of ordinary protons and neutrons with this particles would cause the relative abundance of light element isotypes to be greater or smaller, although the relationship isn't straightforward because one decays of such particles will tend to increase element abundances, while other decays of the same particles will tend to decrease abundances of some of the same elements.

But, plugging a hypothetical new long lived decaying particle into the Big Bang Nucleosynthesis model involves straightforward, well understood physics. If a long lived decaying particle with certain properties exists, it will decay in a very predictable way and it will have a very precisely discernible impact on light element isotype frequencies.

Thus, beyond the Standard Model physics long lived decaying particles of a very general type that is not very strongly model dependent can be ruled out if they give rise to deviations from the Big Bang Nucleosynthesis predictions by significantly more than existing margins of error in the theoretical calculation and astronomy measurements of these predictions.

The Results

A new pre-print does just that, and reaches the following conclusion:

We have revisited and updated the BBN constraints on long-lived particles. . . .

We have obtained the constraints on the abundance and lifetime of long-lived particles with various decay modes. They are shown in Figs. 11 and 12. The constraints become weaker when we include the p ↔ n conversion effects in inelastic scatterings because energetic neutrons change into protons and stop without causing hadrodissociations. On the other hand, inclusion of the energetic anti-nucleons makes the constraints more stringent. In addition, the recent precise measurement of the D abundance leads to stronger constrains. Thus, in total, the resultant constraints become more stringent than those obtained in the previous studies.  

We have also applied our analysis to unstable gravitino. We have adopted several patterns of mass spectra of superparticles and derived constraints on the reheating temperature after inflation as shown in Fig. 15. The upper bound on the reheating temperature is ∼ 10^5 − 10^6 GeV for gravitino mass m3/2 less than a several TeV and ∼ 10^9 GeV for m3/2 ∼ O(10) TeV. This implies that the gravitino mass should be ∼ O(10) TeV for successful thermal leptogenesis.  

In obtaining the constraints, we have adopted the observed 4He abundance given by Eq. (2.4) which is consistent with SBBN. On the other hand, if we adopt the other estimation (2.3), 4He abundance is inconsistent with SBBN. However, when long-lived particles with large hadronic branch have lifetime τX ∼ 0.1 − 100 sec and abundance mXYX ∼ 10^−9 , Eq. (2.3) becomes consistent with BBN. 

In this work, we did not use 7Li in deriving the constraints since the plateau value in 7Li abundances observed in metal-poor stars (which had been considered as a primordial value) is smaller than the SBBN prediction by a factor 2–3 (lithium problem) and furthermore the recent discovery of much smaller 7Li abundances in very metal-poor stars cannot be explained by any known mechanism. However, the effects of the decaying particles on the 7Li and 6Li abundances are estimated in our numerical calculation. Interestingly, if we assume that the plateau value represents the primordial abundance, the decaying particles which mainly decays into e +e − can solve the lithium problem for τX ∼ 10^2 − 10^3 sec and mXYX ∼ 10^−7.

Figures 11 and 12 basically rule out any decaying particles with a lifetime of more than a fraction of a second in the mass range of 30 GeV to 1000 TeV for hadronically decaying particles (Figure 11), and imposes similar constraints for radiatively decaying particles (Figure 12). This is a nice complement to results from the LHC and other colliders with exclude beyond the Standard Model particles that are lighter than hundreds of GeV with lifetimes up to roughly a fraction of a second. Big Bang Nucleosynthesis constraints, generally speaking, are more sensitive to masses much heavier than the LHC can reach and mean lifetimes longer than the LHC is designed to measure. This also strengthens and makes more robust exclusions based upon an entirely different methodology involving the cosmic microwave background radiation of the universe explored by astronomy experiments such as Planck 2015. This basically rules out any relatively long lived remotely "natural" supersymmetric particle unless supersymmetric particles have extremely weak interactions with ordinary matter.

A thermal relic gravitino in a supersymmetry (SUSY) model with a mass on the order of 10 TeV suggests a very high energy characteristic supersymmetry scale which while not directly ruling out some other SUSY particle as a dark matter candidate, makes a SUSY theory that could supply both a dark matter candidate and explain leptogenesis extremely "unnatural."

The potential Lithium problem solution, a particle with a mean lifetime of 100 to 1000 seconds (on the same order of magnitude as a free neutron), favors a quite light, predominantly radiatively decaying (i.e. decaying via photons, electrons and positrons) particle. The main problem with this is that such a particle ought to have shown up in collider experiments if it existed. Yet, there are no known fundamental particles or hadrons that have the right length mean lifetime but decay primarily radiatively. The muon and pion are both tens of millions of times too short lived (or more), the neutron has primarily hadronic decays (to a proton, an electron and an anti-neutrino), and all other hadrons and fundamental particles are much shorter lived. Ergo, a beyond the Standard Model particle is unlikely to be the solution to the Lithium problem of Big Bang Nucleosynthesis.

Bottom Line

Big Bang Nucleosynthesis indirectly constrains the parameter space of beyond the Standard Model physics in a manner that strongly compliments other methods while not overlapping the exclusion of other methods at all. 

This makes the case against supersymmetry models, one of the most popular kinds of beyond the Standard Model theories, significantly stronger than it already was based on other lines of reasoning from experimental evidence such as the strong evidence disfavoring a SUSY dark matter candidate.

The Paper

The pre-print and its abstract are as follows:

We study effects of long-lived massive particles, which decay during the big-bang nucleosynthesis (BBN) epoch, on the primordial abundances of light elements. Compared to the previous studies, (i) the reaction rates of the standard BBN reactions are updated, (ii) the most recent observational data of light element abundances and cosmological parameters are used, (iii) the effects of the interconversion of energetic nucleons at the time of inelastic scatterings with background nuclei are considered, and (iv) the effects of the hadronic shower induced by energetic high energy anti-nucleons are included. We compare the theoretical predictions on the primordial abundances of light elements with latest observational constraints, and derive upper bounds on relic abundance of the decaying particle as a function of its lifetime. We also apply our analysis to unstable gravitino, the superpartner of the graviton in supersymmetric theories, and obtain constraints on the reheating temperature after inflation.

Masahiro Kawasaki, et al., "Revisiting Big-Bang Nucleosynthesis Constraints on Long-Lived Decaying Particles" (September 5, 2017).