Nuclear Theory·nucl-th

Friday·June 16, 2017

8 papers—3 primary·5 cross-listed

01
The reactions $π π \to π π$ and $γ γ \to π π$ in $χ$ PT with an isosinglet scalar resonance
Arbin Thapaliya🇺🇸 · Daniel R. Phillips🇺🇸
The lowest-lying resonance in the QCD spectrum is the $0^{++}$ isoscalar $σ$ meson, also known as the $f_{0} (500)$ . We augment SU(2) chiral perturbation theory ( $χ$ PT) by including the $σ$ meson as an additional explicit degree of freedom, as proposed by Soto, Talavera, and Tarrús and others. In this effective field theory, denoted $χ$ PT $_{S}$ , the $σ$ meson's well-established mass and decay width are not sufficient to properly renormalize its self energy. At $O (p^{4})$ another low-energy constant appears in the dressed $σ$ -meson propagator; we adjust it so that the isoscalar pion-pion scattering length is also reproduced. We compare the resulting amplitudes for the $π π \to π π$ and $γ γ \to π π$ reactions to data from threshold through the energies at which the $σ$ -meson resonance affects observables. The leading-order (LO) $π π$ amplitude reproduces the $σ$ -meson pole position, the isoscalar $π π$ scattering lengths and $π π$ scattering and $γ γ \to π π$ data up to $s \approx 0.5$ GeV. It also yields a $γ γ \to π π$ amplitude that obeys the Ward identity. The value obtained for the $π^{0}$ polarizability is, however, only slightly larger than that obtained in standard $χ$ PT.
nucl-thhep-phEPJA(2017)·2 citations
02
Isospin breaking from diquark clustering
W. R. Gibbs🇺🇸 · Jean-Pierre Dedonder🇫🇷
Although SU(2) isospin symmetry is generally assumed in the basic theory of the strong interaction, a number of significant violations have been observed in scattering and bound states of nucleons. Many of these violations can be attributed to the electromagnetic interaction but the question of how much of the violation is due to it remains open. A schematic model based on clustering of quarks in the interior of the confinement region of the two-nucleon system is introduced and evaluated. In this model the Coulomb interaction is the source of all isospin breaking. It draws on a picture of the quark density based on the diquark-quark model of hadron structure which has been investigated by a number of groups. The model produces three isospin breaking potentials connecting This illustrative model suggests that the breaking seen in the low-energy NN interaction may be understood in terms of the Coulomb force between members of diquark clusters. It allows the prediction of the charge symmetry breaking interaction and the $nn$ scattering length from the well measured $n p$ singlet scattering length. Values of the $nn$ scattering length around $- 18$ fm are favored. Since the model is based on the quark picture, it can be easily extended, in the SU(3) limit, to calculate isospin breaking in the strange sector in the corresponding channels. A natural consequence of isospin breaking from diquark clustering is that the breaking in the strange sector, as measured by the separation energy difference between $_{Λ}^{4}$ H and $_{Λ}^{4}$ He, is several times larger than that seen in the comparison of three-nucleon mirror nuclei as observed experimentally.
nucl-thPRC(2017)·1 citation
03
Quantifying the sensitivity of Big Bang Nucleosynthesis to isospin breaking with input from lattice QCD
Matthew Heffernan🇨🇦 · Projjwal Banerjee🇨🇳 · Andre Walker-Loud🇺🇸
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 $n ⇌ p$ 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, $2 δ = m_{d} - m_{u}$ and from electromagnetic coupling of the quarks to the photons with a strength governed by the fine structure constant, $α_{f s}$ . At leading order in isospin breaking, the contribution of $δ$ and $α_{f s}$ 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 $α_{f s}$ are varied. The change in the D and $^{4}$ He abundances individually allow for potentially large simultaneous variations in $δ$ and $α_{f s}$ while maintaining consistency with the observed abundances, however the combined comparison restricts variations in these sources of isospin breaking to less than $≲ 1.25%$ 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.
nucl-thastro-ph.COhep-lat5 citations

Affiliations

first authorsco-authorsvia INSPIRE

The reactions ππ→ππ and γγ→ππ in χPT with an isosinglet scalar resonance

Isospin breaking from diquark clustering

Quantifying the sensitivity of Big Bang Nucleosynthesis to isospin breaking with input from lattice QCD

Affiliations

The reactions $π π \to π π$ and $γ γ \to π π$ in $χ$ PT with an isosinglet scalar resonance