Improved Big Bang Nucleosynthesis constraints on decaying massive relics

This paper presents updated and improved Big Bang Nucleosynthesis constraints on heavy, long-lived beyond-the-Standard-Model relics decaying into Standard Model particles by incorporating refined nuclear reaction rates, modern abundance measurements, advanced simulation tools like PYTHIA 8, and a more sophisticated treatment of hadronic and electromagnetic injection effects.

The Gist

Imagine the early universe as a giant, bustling construction site. Just a few minutes after the Big Bang, this site was busy building the very first "bricks" of matter: light elements like hydrogen, helium, and a tiny bit of lithium. This process is called Big Bang Nucleosynthesis (BBN).

For decades, scientists have used the amount of these ancient bricks left over today to check if their blueprints for the universe are correct. If the blueprint says there should be 25% helium, and we measure 25% helium, the blueprint is good. If we measure something different, it means something unexpected happened at the construction site.

This paper is a major renovation of those blueprints. The authors, a team of physicists, have built a much more sophisticated "construction simulator" to see how heavy, mysterious particles (which they call relics) might have crashed the party and changed the outcome.

Here is a breakdown of their work using simple analogies:

1. The Uninvited Guests (The Relics)

Imagine that hidden in the construction site are some heavy, slow-moving guests (the relics) that were produced right at the start. They are invisible and harmless at first, but eventually, they decay (break apart) and release a burst of energy.

• The Problem: If these guests break down too early or too late, or if they release too much energy, they can mess up the construction. They might knock over half-finished walls (disintegrate existing atoms) or change the ratio of workers (turning protons into neutrons), leading to the wrong amount of helium or hydrogen being built.
• The Goal: The paper calculates exactly how much of these "guests" can exist before they ruin the final count of elements we see in the universe today.

2. The Three Ways They Mess Things Up

The authors identified three specific ways these decaying particles disrupt the construction site, depending on when they crash the party:

• The "Worker Swap" (Interconversions):

  • The Analogy: Imagine the construction crew is made of two types of workers: Protons (Red Shirts) and Neutrons (Blue Shirts). To build the best bricks (Helium), you need a specific mix of Red and Blue.
  • The Disruption: When the heavy guest decays, it shoots out particles that act like a chaotic manager, forcing Red Shirts to swap places with Blue Shirts. If this happens too early, you end up with too many Blue Shirts, and the final building has way too much Helium. The paper updates the rules on how fast these swaps happen, including new types of "managers" (like Kaons) that previous blueprints ignored.

• The "Demolition Crew" (Hadrodisintegration):

  • The Analogy: Imagine the construction site is already finished, and the bricks are set. Suddenly, a heavy guest decays and shoots out a high-speed bullet (a fast-moving proton or neutron).
  • The Disruption: This bullet smashes into the finished bricks, breaking them apart. A solid Helium brick might get smashed into smaller pieces (Deuterium or Tritium). This happens when the guests decay a bit later, after the main construction is done but before the site cools down completely.

• The "Laser Show" (Photodisintegration):

  • The Analogy: If the guests decay even later, they release a flood of high-energy light (photons). Think of this as a giant, invisible laser show.
  • The Disruption: These lasers are so energetic they can vaporize the bricks from a distance. They turn Helium back into Hydrogen or Deuterium. This happens very late in the process, long after the main construction crew has gone home.

3. The New Tools and Improvements

The authors didn't just re-run the old numbers; they upgraded their entire toolkit:

• Better Blueprints: They used the most recent measurements of how much Helium and Deuterium actually exist in the universe today. One new measurement of Helium is much more precise than before, which tightened the rules significantly.
• The "Pythia" Simulator: To figure out exactly what happens when a heavy guest decays, they used a powerful computer program called Pythia. Think of this as a high-definition physics engine (like in a video game) that simulates the explosion in detail. It shows exactly how many pions, kaons, and other particles are created, rather than guessing.
• The "Dynamical Equilibrium" Trick: Calculating every single particle interaction in real-time is too slow for a computer. The authors found a clever shortcut. They realized that the chaotic swapping of particles happens so fast that they reach a "steady state" almost instantly. Instead of tracking every second, they calculated this steady state, which made the simulation much faster and more accurate.
• Two Simulators Working Together: They combined two different software programs. One handles the construction phase (when atoms are being built), and the other handles the demolition phase (when atoms are being smashed later). They made sure the handoff between the two was seamless so no data was lost or double-counted.

4. The Results: Tighter Rules

By using these improved tools, the authors drew new "exclusion zones" on a map.

• The Map: The map plots the mass of the heavy guest against its lifetime (how long it lives before decaying) and its abundance (how many of them there are).
• The Finding: The new map shows that the universe is much more sensitive to these guests than we thought.
  • For some types of guests, even a tiny, almost invisible amount is enough to ruin the helium count.
  • In some cases, the rules are so strict that even the minimum amount of these particles that must exist (due to unavoidable physics processes called "freeze-in") is actually too high. This means those specific types of heavy guests simply cannot exist in the universe without contradicting what we see today.

Summary

In short, this paper is a massive upgrade to the "instruction manual" for the early universe. By using better data, more powerful simulations, and smarter math, the authors have proven that the universe is a very delicate construction site. If heavy, long-lived particles exist, they must be incredibly rare or decay at very specific times, or else the recipe for the light elements we see today would be completely wrong. They have effectively closed the door on many theoretical possibilities for what these mysterious particles could be.

Technical Summary

Technical Summary: Improved Big Bang Nucleosynthesis Constraints on Decaying Massive Relics

Problem Statement
Big Bang Nucleosynthesis (BBN) serves as a stringent probe of the thermal history of the early Universe and physics beyond the Standard Model (BSM). Specifically, heavy, long-lived relics ($\phi$) produced in the early Universe can decay into Standard Model (SM) particles during or after the BBN epoch (temperatures $T \lesssim$ few MeV). These decays inject energy into the primordial plasma, altering the abundances of light elements ($^1$H, D, $^3$He, $^4$He, $^7$Li) through distinct mechanisms: modifying the neutron-to-proton ($n/p$) ratio via hadronic interconversions, hadrodisintegrating light nuclei, and photodisintegrating nuclei via electromagnetic cascades. Previous analyses have provided constraints on such relics, but they often relied on outdated abundance measurements, simplified nuclear reaction rates, or approximations in the treatment of final-state radiation and hadronisation. Furthermore, the interplay between early-time interconversions and late-time disintegration processes required a more unified theoretical framework.

Methodology
The authors present a comprehensive update to BBN constraints for heavy relics ($m_\phi \gtrsim \text{few GeV}$) decaying into various two-body SM channels (excluding neutrinos, which are reserved for future work). The analysis relies on a significantly refined computational pipeline:

1. Code Development (AlterAlterBBN & ACROPOLIS): The authors adapted the BBN code AlterBBN into an extended version, AlterAlterBBN, capable of handling arbitrary background cosmologies and injecting hadronic material. This code tracks $p \leftrightarrow n$ interconversions and hadrodisintegration during the active BBN epoch. For late-time evolution ($t \gtrsim 10^4$ s), where photodisintegration becomes dominant, the code interfaces with ACROPOLIS. A critical technical achievement is the seamless matching of these two regimes at $T \approx 5$ keV, ensuring a consistent treatment of nuclear fusion and disintegration without double-counting.
2. Hadronic Injection Spectra (PYTHIA 8): To accurately model the composition of decay products, the authors utilize PYTHIA 8 to simulate final-state radiation (FSR) and hadronisation. This provides precise inputs for the number of injected mesons (pions, kaons) and nucleons, their average kinetic energies, and the fraction of energy deposited into the electromagnetic sector ($\zeta_{EM}$). This approach replaces older, less accurate "universal" spectra approximations.
3. Dynamical Equilibrium Approximation: The authors implement a refined treatment of hadronic abundances using a dynamical equilibrium approximation. Given that hadronic interaction rates (scattering, annihilation) are orders of magnitude faster than the Hubble expansion rate during BBN, the abundances of injected mesons and anti-nucleons are solved algebraically as a function of the source terms and depletion rates. This allows for the efficient tracking of complex interconversion chains involving pions, kaons ($K^\pm, K_L^0$), and nucleon-antinucleon pairs.
4. Updated Physics Inputs:
   • Observational Data: The analysis incorporates the latest primordial abundance measurements, notably the updated $^4$He mass fraction from Ref. [31] and revised deuterium-to-hydrogen ratios.
   • Nuclear Rates: Updated nuclear reaction rates for standard BBN and new, temperature-dependent cross-sections for hadronic interconversions (specifically $p \leftrightarrow n$ via kaons and pions) from Ref. [57] are implemented.
   • Error Treatment: Theoretical uncertainties in nuclear rates, interconversion cross-sections, and hadrodisintegration efficiencies ($\xi$ parameters) are propagated using a Monte-Carlo-like approach (running high, mean, and low rate scenarios) combined with observational errors.
5. Background Cosmology: The code accounts for modifications to the Hubble rate and neutrino decoupling temperature caused by the relic's energy density. It also addresses the irreducible "freeze-in" abundance of relics produced via inverse decays, establishing a physical lower bound on the relic abundance $Y_\phi$.

Key Contributions

• Unified Framework: The paper unifies the treatment of hadronic interconversions (early times), hadrodisintegration (intermediate times), and photodisintegration (late times) into a single, self-consistent pipeline, correcting previous limitations where these regimes were treated separately or with inconsistent boundaries.
• Refined Hadronic Treatment: The inclusion of kaon-induced interconversions and the use of PYTHIA 8 for FSR and hadronisation provide a more accurate description of the injection spectra, particularly for electromagnetic decay channels (e.g., $\phi \to e^+e^-$) which were previously under-constrained regarding hadronic effects.
• Correction of Systematic Errors: The authors correct an error in the electromagnetic energy-loss curve identified in previous work, which had artificially enhanced hadrodisintegration rates by energetic protons. This correction softens constraints in specific parameter regions.
• Comprehensive Channel Coverage: The study covers a wide array of two-body decay channels ($e^+e^-, u\bar{u}, \gamma\gamma, \mu^+\mu^-, \tau^+\tau^-, b\bar{b}, t\bar{t}, gg, WW, ZZ, hh$), providing exclusion contours for each.

Results
The authors present updated exclusion contours in the $(m_\phi Y_\phi, \tau_\phi)$ plane for various decay channels.

• Decay Channels:
  • Electromagnetic ($e^+e^-, \gamma\gamma$): Constraints are driven by $^4$He overproduction at short lifetimes (via interconversions) and D/$^3$He overproduction at longer lifetimes (via disintegration). The inclusion of FSR-induced hadrons significantly tightens bounds for $e^+e^-$ decays compared to previous literature.
  • Hadronic ($u\bar{u}, gg$): These channels yield the strongest constraints due to unsuppressed hadronic energy injection. For $m_\phi = 10$ GeV, the constraints are so severe that they exclude even the irreducible freeze-in abundance for lifetimes $0.1 \text{ s} \lesssim \tau_\phi \lesssim 10^5 \text{ s}$.
  • Leptons ($\mu^+\mu^-, \tau^+\tau^-$): The $\tau^+\tau^-$ channel shows unique features due to the large branching ratio into pions, leading to strong interconversion bounds at low masses.
• Mass Dependence: For heavy relics ($m_\phi \gtrsim 1$ TeV), the constraints tend to become mass-independent at long lifetimes due to the universality of the electromagnetic cascade spectrum. However, in the hadron-dominated regime, constraints can weaken slightly for very high masses due to sub-linear growth in the number of injected hadrons.
• Comparison with Literature: The results generally agree qualitatively with previous studies (e.g., Kawasaki et al.) but show significant quantitative differences. At short lifetimes, the new bounds are much stronger, primarily due to the updated interconversion rates and the proper inclusion of FSR-induced hadrons. At long lifetimes, differences arise from the refined treatment of photodisintegration and the updated $^4$He abundance.

Significance
The paper claims to provide a state-of-the-art treatment of BBN constraints on decaying heavy relics. By integrating updated observational data, precise nuclear cross-sections, and a sophisticated simulation of particle showers, the authors establish robust and improved exclusion limits. These results are particularly significant for constraining BSM models involving heavy, long-lived states, as the updated constraints can rule out parameter space that was previously considered viable, including regions where the relic abundance is as low as the irreducible freeze-in production. The work serves as a critical reference for interpreting BBN data in the context of new physics, while explicitly noting that the treatment of neutrino channels and lighter (MeV-scale) relics remains a subject for future investigation.