[Paper Review] Quantifying the sensitivity of Big Bang Nucleosynthesis to isospin breaking with input from lattice QCD

M. Heffernan, Projjwal Banerjee+1 more|arXiv (Cornell University)|Jun 15, 2017

Particle physics theoretical and experimental studies82 references3 citations

TL;DR

This study quantifies the sensitivity of Big Bang Nucleosynthesis (BBN) to isospin-breaking effects using precise lattice QCD inputs for the neutron-proton mass splitting. It finds that simultaneous variations in the up-down quark mass splitting (δ) and fine-structure constant (α_fs) are constrained to less than 1.25% at 3σ to match observed D and ⁴He abundances, providing tight constraints on beyond-Standard-Model physics.

ABSTRACT

We perform the first quantitative study of the sensitivity of Big Bang Nucleosynthesis to variations in isospin breaking with precise input from lattice QCD calculations. The predicted light nuclear abundances are most sensitive to the neutron-proton mass splitting as both the initial relative abundance of neutrons to protons and the $n ightleftharpoons p$ weak reaction rates are very sensitive to this quantity. Lattice QCD has been used to determine this mass splitting to greater than 5-sigma, including contributions from both the down-quark up-quark mass splitting, $2δ= m_d-m_u$ and from electromagnetic coupling of the quarks to the photons with a strength governed by the fine structure constant, $α_{fs}$. At leading order in isospin breaking, the contribution of $δ$ and $α_{fs}$ to $M_n-M_p$ and the nuclear reaction rates can be varied independently. We use this knowledge and input from lattice QCD to quantitatively study variations of the predicted light nuclear abundances as $δ$ and $α_{fs}$ are varied. The change in the D and ${}^4$He abundances individually allow for potentially large simultaneous variations in $δ$ and $α_{fs}$ while maintaining consistency with the observed abundances, however the combined comparison restricts variations in these sources of isospin breaking to less than $\lesssim1.25\%$ at the 3-sigma confidence level. This sensitivity can be used to place tight constraints on prospective beyond the Standard Model theories that would modify these isospin breaking effects in the primordial Universe.

Motivation & Objective

• To quantitatively assess how variations in fundamental Standard Model parameters—specifically the up-down quark mass splitting (δ) and electromagnetic coupling (α_fs)—affect primordial light element abundances via Big Bang Nucleosynthesis (BBN).
• To integrate state-of-the-art lattice QCD calculations of the neutron-proton mass splitting into BBN simulations for the first time, enabling rigorous, model-independent constraints.
• To test whether variations in δ and α_fs could resolve the longstanding ⁷Li puzzle in BBN, where observed ⁷Li abundances are lower than predicted.
• To establish tight observational constraints on new physics scenarios that would alter isospin-breaking effects in the early universe, such as asymmetric dark matter models.

Proposed method

• Utilized lattice QCD calculations to determine the neutron-proton mass splitting (ΔMₙ₋ₚ) with high precision, isolating contributions from δ = ½(m_d − m_u) and α_fs.
• Modified BBN reaction network codes to independently vary δ and α_fs while tracking their effects on deuterium (D), ⁴He, and ⁷Li yields.
• Applied nuclear statistical equilibrium and weak interaction rates (n ↔ p) dependent on ΔMₙ₋ₚ = (m_n − m_p) to compute light element abundances as functions of δ and α_fs.
• Performed a joint likelihood analysis using observed primordial D and ⁴He abundances to constrain allowed variations in δ and α_fs simultaneously.
• Used 3σ confidence intervals to derive upper bounds on the combined variation of δ and α_fs, ensuring consistency with observational data.
• Validated that variations in δ and α_fs within the constrained region do not resolve the ⁷Li abundance discrepancy.

Experimental results

Research questions

• RQ1 How sensitive are the predicted primordial abundances of deuterium and ⁴He to independent variations in the up-down quark mass splitting (δ) and the fine-structure constant (α_fs)?
• RQ2 To what extent can variations in δ and α_fs simultaneously alter BBN outcomes while remaining consistent with observed light element abundances?
• RQ3 Can the ⁷Li abundance discrepancy be resolved by variations in δ and α_fs within the constraints derived from D and ⁴He observations?
• RQ4 What are the tightest observational bounds on the combined variation of δ and α_fs that preserve consistency with BBN observations at the 3σ level?
• RQ5 How do lattice QCD inputs on the neutron-proton mass splitting inform the sensitivity of BBN to fundamental parameters of the Standard Model?

Key findings

• The predicted ⁴He mass fraction tracks almost perfectly with the neutron-proton mass splitting (ΔMₙ₋ₚ), making it highly sensitive to variations in δ and α_fs.
• Simultaneous variations in δ and α_fs that preserve the physical value of ΔMₙ₋ₚ result in unobservably small changes to the ⁴He abundance.
• The deuterium abundance is sensitive to changes in fusion rates, which depend on α_fs but are weakly sensitive to δ, enabling differential constraints.
• Combined analysis of D and ⁴He abundances restricts the allowed variation of δ and α_fs to less than 1.25% at the 3σ confidence level when variations are correlated.
• Even within the constrained region, variations in δ and α_fs do not resolve the ⁷Li puzzle, as predicted ⁷Li/H remains inconsistent with observations.
• Lattice QCD provides a rigorous, first-principles input for isospin-breaking effects, enabling quantitative constraints on new physics models involving asymmetric couplings to protons and neutrons.