[Paper Review] The K+K+ Scattering Length from Lattice QCD

Silas R. Beane, Thomas Luu+5 more|RECERCAT (Consorci de Serveis Universitaris de Catalunya)|Sep 7, 2007

Quantum Chromodynamics and Particle Interactions4 citations

TL;DR

This paper presents the first lattice QCD calculation of the $K^+K^+$ scattering length using domain-wall valence quarks on asqtad-improved MILC ensembles with 2+1 dynamical staggered quarks. Using three-flavor mixed-action chiral perturbation theory, it extrapolates results to the physical point, finding $m_{K^+} a_{K^+K^+} = -0.352 \pm 0.016$, consistent with tree-level chiral perturbation theory and providing a benchmark for strange hadron interactions in dense matter.

ABSTRACT

The K+K+ scattering length is calculated in fully-dynamical lattice QCD with domain-wall valence quarks on the MILC asqtad-improved gauge configurations with rooted staggered sea quarks. Three-flavor mixed-action chiral perturbation theory at next-to-leading order, which includes the leading effects of the finite lattice spacing, is used to extrapolate the results of the lattice calculation to the physical value of m_{K+}/f_{K+}. We find m_{K+} a_{K+K+} = -0.352 +- 0.016, where the statistical and systematic errors have been combined in quadrature.

Motivation & Objective

• To calculate the $K^+K^+$ scattering length from first principles in lattice QCD, addressing the lack of direct theoretical constraints on strange meson interactions.
• To perform a chiral and continuum extrapolation using three-flavor mixed-action chiral perturbation theory, including leading-order lattice-spacing effects.
• To test the convergence of $SU(3)$ chiral perturbation theory by comparing lattice results with theoretical predictions for $I=1$ $KK$ scattering.
• To provide a benchmark for kaon condensate formation and strange hadron interactions in neutron stars and heavy-ion collisions.

Proposed method

• Lattice QCD simulations are performed on coarse and fine MILC ensembles with $b \sim 0.125$ fm and $b \sim 0.09$ fm, respectively, using domain-wall valence quarks on asqtad-improved gauge configurations with 2+1 dynamical staggered quarks.
• The scattering length is extracted from the energy shift of two-particle states in a finite volume using L"uscher's method, which relates energy levels to the scattering amplitude.
• Three-flavor mixed-action chiral perturbation theory at next-to-leading order is employed to extrapolate the lattice results to the physical pion and kaon masses and to the continuum limit.
• Systematic errors from the fourth-root trick, finite volume, and discretization effects are estimated and combined with statistical errors in quadrature.
• The physical value of $m_{K^+} a_{K^+K^+}$ is extracted by fitting the lattice data to the chiral perturbation theory framework, including scale dependence of low-energy constants.
• The result is compared with tree-level chiral perturbation theory and with previous lattice results for $\pi^+\pi^+$ scattering to probe flavor-$SU(3)$ breaking effects.

Experimental results

Research questions

• RQ1 What is the $K^+K^+$ scattering length in the physical limit, as computed from lattice QCD with full QCD dynamics?
• RQ2 How do the lattice results compare with predictions from tree-level $SU(3)$ chiral perturbation theory?
• RQ3 To what extent do finite-volume and finite-lattice-spacing effects influence the scattering length, and how are they corrected?
• RQ4 How does the $K^+K^+$ scattering length compare with that of $\pi^+\pi^+$ scattering, and what does this imply for higher-order chiral corrections?

Key findings

• The $K^+K^+$ scattering length is calculated as $m_{K^+} a_{K^+K^+} = -0.352 \pm 0.016$, with statistical and systematic errors combined in quadrature.
• The result is consistent with tree-level chiral perturbation theory predictions, indicating surprisingly small deviations from leading-order behavior.
• The scattering length is found to be stable under chiral and continuum extrapolation, with the mixed-action chiral perturbation theory framework successfully accounting for lattice artifacts.
• The value of the low-energy constant $32(4\pi)^2 L_{KK}^{I=1}(f_K) = 7.1 \pm 0.7$ is extracted, providing a quantitative constraint on $SU(3)$ chiral dynamics.
• The lattice result for $K^+K^+$ scattering is consistent with the $\pi^+\pi^+$ scattering length at similar pion masses, suggesting similar convergence properties in the chiral expansion.
• The calculation demonstrates the feasibility of computing $I=1$ $KK$ scattering in lattice QCD and provides a foundation for future precision studies of strange hadron interactions.