Abstract
We calculate the s-wave pion–pion scattering length in the isospin I=2 channel in lattice QCD for pion masses ranging from 270 MeV to 485 MeV using two flavors of maximally twisted mass fermions at a lattice spacing of 0.086 fm. Additionally, we check for lattice artifacts with one calculation at a finer lattice spacing of 0.067 fm. We use chiral perturbation theory at next-to-leading order to extrapolate our results. At the physical pion mass, we find mπaππI=2=−0.04385(28)(38) for the scattering length, where the first error is statistical and the second is our estimate of several systematic effects.
Highlights
In the limit of massless up and down quarks, the resulting chiral symmetry of QCD is spontaneously broken and the meson spectrum contains three massless Goldstone bosons, π ± and π 0
Due to the unique role played by the pions, their interactions are strongly determined by the underlying chiral symmetry, and the s-wave pion–pion scattering lengths even vanish in the chiral limit
The pion masses ranged from 270 MeV to 485 MeV and the lattice spacing was a = 0.086 fm
Summary
In the limit of massless up and down quarks, the resulting chiral symmetry of QCD is spontaneously broken and the meson spectrum contains three massless Goldstone bosons, π ± and π 0. Due to the unique role played by the pions, their interactions are strongly determined by the underlying chiral symmetry, and the s-wave pion–pion scattering lengths even vanish in the chiral limit. The scattering lengths are sensitive to the chiral dynamics of the strong interactions, and the non-perturbative calculation thereof, the subject of this Letter, is an integral part of understanding the low energy properties of QCD. The masses of the quarks are not zero but small and induce an explicit but weak breaking of chiral symmetry. The pions are not massless but light. This breaking of chiral symmetry is systematically treated in chiral perturbation theory (χ PT) by considering the quark masses as perturbations
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
