Pion mass difference from vacuum polarization

Abstract

We calculate the electromagnetic contribution to the pion mass difference, $\Delta m_{\pi }^2=m_{{\pi }^{+}}^2-m_{{\pi }^0}^2$, in the chiral limit through the $VV-AA$ type vacuum polarization using Das-Guralnik-Mathur-Low-Young (DGMLY) sum rule. The calculation is made with two-flavors of dynamical overlap fermions on a $16^3\times 32$ lattice at $a\sim$0.12 fm. The exact chiral symmetry of the overlap fermion is essential to control the systematic error in the difference $VV-AA$. We obtain $\Delta m_{\pi }^2=1024(100)\mathrm{Me}{\mathrm{V}}^2$ combining the lattice data with the perturbative contribution in the high momentum region evaluated by the operator product expansion. By analyzing the momentum dependence of the vacuum polarization, we also obtain pion decay constant $f_{\pi }$ and the low-energy constants $L_{10}^r$ in the chiral limit.

7 pages, 2 figures, talk (Hadron spectroscopy) presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4, 2007, Regensburg, Germany

References in corpus (4)

• Finite volume QCD at fixed topological charge
• Determination of light quark masses from the electromagnetic splitting of pseudoscalar meson masses computed with two flavors of domain wall fermions
• Lattice gauge action suppressing near-zero modes of H_W
• Two-flavor lattice QCD in the epsilon-regime and chiral Random Matrix Theory

Cited by in corpus (4)

• QED in finite volume and finite size scaling effect on electromagnetic properties of hadrons
• Two-flavor QCD simulation with exact chiral symmetry
• Electromagnetic low-energy constants in ChPT
• Towards the large volume limit - A method for lattice QCD + QED simulations