I=2 pi-pi Scattering from Fully-Dynamical Mixed-Action Lattice QCD

TL;DR

The paper addresses the problem of determining the I=2 ππ scattering length from first-principles QCD calculations. It employs a fully-dynamical mixed-action lattice QCD framework (domain-wall valence quarks on asqtad MILC configurations) and Lüscher's finite-volume method to extract the s-wave scattering amplitude, complemented by a one-loop chiral perturbation theory extrapolation to the physical point. The main result is a physical scattering length of $m_\pi a_2 = -0.0426 \pm 0.0006 \pm 0.0003 \pm 0.0018$, in good agreement with experimental determinations, along with a phase-shift estimate at a heavier pion mass, $\delta(p) = -43 \pm 10 \pm 5$ degrees. Overall, the work validates mixed-action lattice techniques for low-energy hadron scattering and provides a data-driven determination of a chiral low-energy constant $l_{\pi\pi}$, informing the chiral Lagrangian beyond leading order.

Abstract

We compute the I=2 pi-pi scattering length at pion masses of m_pi ~ 294, 348 and 484 MeV in fully-dynamical lattice QCD using Luscher's finite-volume method. The calculation is performed with domain-wall valence-quark propagators on asqtad-improved MILC configurations with staggered sea quarks at a single lattice spacing, b ~ 0.125 fm. Chiral perturbation theory is used to perform the extrapolation of the scattering length from lattice quark masses down to the physical value, and we find m_pi a_2 = -0.0426 +- 0.0006 +- 0.0003 +- 0.0018, in good agreement with experiment. The I=2 pi-pi scattering phase shift is calculated to be delta = -43 +- 10 +- 5 degrees at |p| ~ 544 MeV for m_pi ~ 484 MeV.

Figures (4)

• Figure 1: Log plots of the ratio of correlation functions, $G_{\pi\pi}$, defined in eq. (\ref{['ratio_correlator']}). The left panel shows the correlation function $G_{\pi\pi}(0, t)$ for the three sets of MILC configurations, each of which is dominated by the $\pi\pi$ ground-state. The right panel shows the logarithm of the absolute value of $G_{\pi\pi}({2\pi/L}, t)$ for the heaviest quark-mass with and without subtraction of the (small) ground-state component.
• Figure 2: The results of this lattice QCD calculation of $m_\pi a_2$ as a function of $m_\pi/f_\pi$ (ovals) with statistical (dark bars) and systematic (light bars) uncertainties. Also shown are the experimental value from Ref. Pislak:2003sv (diamond) and the lowest quark mass result of the dynamical calculation of CP-PACS Yamazaki:2004qb (square). The gray band corresponds to a weighted fit to our three data points using the one-loop $\chi$-PT formula in eq. (\ref{['eq:ascattGLwithchexp2']}) which gives $l_{\pi\pi}=3.3 \pm 0.6 \pm 0.3$ (the shaded region corresponds only to the statistical error). The dashed line is the tree-level $\chi$-PT result.
• Figure 3: $\mathcal{C}(m_\pi/f_\pi,l_{\pi\pi})$ as a function of $m_\pi/f_\pi$ for our three lattice data points (ovals) with statistical (dark bars) and systematic (light bars) uncertainties, plotted with the experimental value from Ref. Pislak:2003sv (diamond) and the lowest-mass dynamical CP-PACS Yamazaki:2004qb point (square). The gray band corresponds to a fit to our three data points (weighted by statistical errors) using the one-loop $\chi$-PT formula in eq. (\ref{['eq:curvefun']}).
• Figure :