[Paper Review] $\mathbf{\beta}$-delayed proton emission from $\mathbf{^{11}}$Be in effective field theory

Wael Elkamhawy, Zichao Yang+2 more|arXiv (Cornell University)|Sep 26, 2019

Nuclear physics research studiesPhysics and Astronomy41 references15 citations

TL;DR

This paper calculates the β-delayed proton emission branching ratio in $^{11}$Be using Halo Effective Field Theory (Halo EFT), incorporating a shallow $1/2^+$ resonance in the $^{10}$Be–p system. It finds $b_p = 4.9^{+5.6}_{-2.9}\text{(exp)}{}^{+4.0}_{-0.8}\text{(theo)} \times 10^{-6}$ and a resonance width $\Gamma_R = (9.0^{+4.8}_{-3.3}\text{(exp)}{}^{+5.3}_{-2.2}\text{(theo)})$ keV, confirming consistency with recent experimental data and showing no need for exotic physics to explain the decay rate.

ABSTRACT

We calculate the rate of the rare decay $^{11} ext{Be}$ into $^{10} ext{Be} + p +e^- + \bar{ u}_e$ using Halo effective field theory, thereby describing the process of beta-delayed proton emission. We assume a shallow $1/2^+$ resonance in the $^{10} ext{Be}-p$ system with an energy consistent with a recent experiment by Ayyad et al. and obtain $b_p = 4.9_{-2.9}^{+5.6} ext{(exp.)}_{-0.8}^{+4.0} ext{(theo.)} imes 10^{-6}$ for the branching ratio of this decay, predicting a resonance width of $\Gamma_R = (9.0^{+4.8}_{-3.3} ext{(exp.)}^{+5.3}_{-2.2} ext{(theo.)})~ ext{keV}$. Our calculation shows that the experimental branching ratio and resonance parameters of Ayyad et al. are consistent with each other. Moreover, we analyze the general impact of a resonance on the branching ratio and demonstrate that a wide range of combinations of resonance energies and widths can reproduce branching ratios of the correct order. Thus, no exotic mechanism (such as beyond the standard model physics) is needed to explain the experimental decay rate.

Motivation & Objective

• To calculate the β-delayed proton emission branching ratio in $^{11}$Be using Halo Effective Field Theory (Halo EFT).
• To assess whether a low-lying $1/2^+$ resonance in the $^{10}$Be–p system can explain the anomalously large experimental branching ratio.
• To evaluate the consistency between the measured branching ratio and resonance parameters (energy and width) from the Ayyad et al. experiment.
• To determine whether exotic physics (e.g., dark matter decay modes) is required to explain the decay rate.
• To quantify theoretical uncertainties in the EFT framework and assess sensitivity to resonance parameters.

Proposed method

• Employing Halo EFT with effective degrees of freedom: $^{10}$Be core, neutron, and proton, including dimer fields for $^{11}$Be and the $^{11}$B resonance.
• Using the two-body T-matrix formalism with the effective range expansion to describe $^{10}$Be–n and $^{10}$Be–p interactions.
• Including weak decays via both Gamow-Teller and Fermi operators in the axial current, with the weak Hamiltonian coupled to the dimer fields.
• Resumming self-energy diagrams to all orders in the non-perturbative regime, with the residue at the bound state pole used to compute physical observables.
• Applying a power-counting scheme in $R_{\text{core}}/R_{\text{halo}} \approx 0.4$ to systematically include higher-order corrections.
• Estimating theoretical uncertainties from higher-order EFT contributions, particularly from the axial current counterterm scaling as $R_{\text{core}}/R_{\text{halo}}$.

Experimental results

Research questions

• RQ1 Can Halo EFT reproduce the experimentally observed branching ratio for β-delayed proton emission in $^{11}$Be?
• RQ2 Is the existence of a low-lying $1/2^+$ resonance in $^{11}$B consistent with the measured branching ratio and resonance parameters?
• RQ3 What is the sensitivity of the partial decay rate to variations in resonance energy and width?
• RQ4 Does the observed decay rate require physics beyond the Standard Model, such as dark matter decay modes?
• RQ5 How do uncertainties from the EFT expansion and input parameters affect the final branching ratio prediction?

Key findings

• The calculated branching ratio is $b_p = 4.9^{+5.6}_{-2.9}\text{(exp)}{}^{+4.0}_{-0.8}\text{(theo)} \times 10^{-6}$, in good agreement with the experimental value of $1.3(3) \times 10^{-5}$ from Ayyad et al.
• The predicted resonance width is $\Gamma_R = (9.0^{+4.8}_{-3.3}\text{(exp)}{}^{+5.3}_{-2.2}\text{(theo)})$ keV, consistent with the experimental estimate of $12(5)$ keV.
• The experimental branching ratio and resonance parameters are mutually consistent within uncertainties, validating the resonance hypothesis.
• The decay rate is highly sensitive to the resonance energy and width, indicating a fine-tuned interplay between these parameters to reproduce the observed rate.
• A pure Gamow-Teller decay scenario can also reproduce the partial decay rate with slightly smaller resonance parameters, reinforcing the need for a resonance but not requiring exotic physics.
• No evidence is found for new physics beyond the Standard Model; the observed decay rate is fully explained by a low-lying resonance within the standard EFT framework.